Research ArticlePacket Scheduling for Multiple-Switch Software-DefinedNetworking in Edge Computing Environment

Hai Xue Kyung Tae Kim and Hee Yong Youn

College of Information and Communication Engineering Sungkyunkwan University Suwon Republic of Korea

Correspondence should be addressed to Hee Yong Youn youn7147skkuedu

Received 23 August 2018 Revised 10 October 2018 Accepted 31 October 2018 Published 18 November 2018

Guest Editor Jorge Navarro-Ortiz

Copyright copy 2018 Hai Xue et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Software-defined networking (SDN) decouples the control plane and data forwarding plane to overcome the limitations oftraditional networking infrastructureAmong several communication protocols employed for SDN OpenFlow is most widely usedfor the communication between the controller and switch In this paper two packet scheduling schemes FCFS-Pushout (FCFS-PO)and FCFS-Pushout-Priority (FCFS-PO-P) are proposed to effectively handle the overload issue of multiple-switch SDN targetingthe edge computing environment Analyticalmodels on their operations are developed and extensive experiment based on a testbedis carried out to evaluate the schemesThey reveal that both of them are better than the typical FCFS-Block (FCFS-BL) schedulingalgorithm in terms of packet wait time Furthermore FCFS-PO-P is found to bemore effective than FCFS-PO in the edge computingenvironment

1 Introduction

Nowadays the traditional IP network can hardly deal withthe huge volume of traffic generated in the rapidly growingInternet ofThings (IoT) As an efficient solution to this issuea new type of networking paradigm called software-definednetworking (SDN) had been proposed [1] In SDN the controlplane and data plane of the network are decoupled unlikethe traditional network The role of the switches in SDN isdelivering the data packets while the controller is installedseparately for controlling the whole network OpenFlow [2]is one of the most popular protocols developed for thecommunication between the controller and switch in SDNand it is only an open protocol [3]

The proliferation of IoT and the success of rich cloudservice induced the horizon of a new computing paradigmcalled edge computing [4] Here how to efficiently deliverthe data from the IoT nodes to the relevant switches is akey issue While there exist numerous nodes in the edgecomputing environment some of them are deployed to detectcritical events such as fire or earthquakes For such peculiaredge nodes the data must be delivered with the highestpriority due to its importance Therefore effective priority-based scheduling and a robust queueing mechanism are

imperative to maximize the performance of the networkwhere the data processing occurs at the edge of the networkA variety of network traffics are also needed to be consideredfor accurately estimating the performance [5] allowing earlyidentification of a potential traffic hotspot or bottleneck Thisis a fundamental issue in the deployment of SDN for edgecomputing

Recently numerous studies have been conducted tomaximize the performance of the controller and OpenFlowswitch of SDN However to the best of our knowledgelittle explorations exist for the performance of SDN switcheswith priority scheduling This is an undoubtedly importantissue for edge computing since the edge nodes deal with thereceived data based on the priority Furthermore priorityscheduling is necessary with multiple switches In this paperthus the priority scheduling scheme for multiple-switchSDN is proposed Here packet-in messages might be sentto the controller from each of the switches On the basisof the MG1 queueing model for the OpenFlow switch theFirst Come First Served-Pushout (FCFS-PO) and First ComeFirst Served-Pushout-Priority (FCFS-PO-P) mechanism areproposed for efficiently handling the overload issue WithFCFS-PO the packets are served based on the order of arrivalwhile the oldest one is pushed out when the buffer is full

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 7659085 11 pageshttpsdoiorg10115520187659085

2 Wireless Communications and Mobile Computing

OpenFlow Switch

OpenFlow Switch

OpenFlow Switch

OpenFlow Switch

OpenFlow Switch

Network Services

Business Applications

SDNControl Soware

API API API

ControlData Plane OpenFlow Protocol

Application Layer

Control Layer

Infrastructure Layer

Figure 1 The three-layer structure of SDN

With FCFS-PO-P the packets are serviced by the order ofthe priority on top of the FCFS-PO Extensive experiment ona testbed reveals that FCFS-PO-P scheduling allows betterperformance than FCFS-PO in terms of sojourn and waittime for various traffic conditions Furthermore both of themdisplay much smaller wait time than the typical FCFS-Block(FCFS-BL) scheduling The main contributions of the paperare summarized as follows

(i) The packet scheduling issue is identified with theSDN controller in edge computing environment TheFCFS-PO and FCFS-PO-P scheduling scheme areproposed for coping with this issue

(ii) Analytical model of the proposed scheduling schemeis developed using queueing theory which can beapplied to the evaluation of priority-based schedulingscheme

(iii) The scheduling for solving the packet schedulingproblem of SDN controller in edge computing envi-ronment is revealed by comparing the proposedmethod with existing methods

The rest of the paper is structured as follows Section 2provides an overview of SDN and edge computing InSection 3 the priority-based scheduling schemes formultiple-switch SDN are proposed along with their analytical mod-eling Section 4 evaluates the performance of the proposedschemes At last Section 5 concludes the paper and outlinesthe future research direction

2 Related Work

SDN decouples the control logic from the underlying routersand switches It promotes the logical centralization of net-work control and introduces the capability of programmingthe network [6ndash8] As a result flexible dynamic and pro-grammable functionality of network operations could beoffered However the merits are achieved with the sacrificeon essential network performance such as packet processingspeed and throughput [9] which is attributed to the involve-ment of a remote controller for the administration of allforwarding devices

21 SDN SDN was originated from a project of UC Berkeleyand Stanford University [10] In SDN the network controlplane making decisions on traffic routing and load balancingis decoupled from the data plane forwarding the traffic tothe destination The network is directly programmable andthe infrastructure is allowed to be abstracted for flexiblysupporting various applications and servicesThe experts andvendors claim that this greatly simplifies the networking task[11] There exist three layers in SDN unlike the traditionalnetwork of two layers and a typical structure of SDN basedon the OpenFlow protocol is depicted in Figure 1

The separation of control plane and data plane can berealized by means of a well-defined programming interfacebetween the controller and switches The controller exercisesdirect control covering the state of the data plane elementsvia a well-defined application programming interface (API)as shown in Figure 1Themost notable example of suchAPI is

Wireless Communications and Mobile Computing 3

Table 1 The fields of an entry of a flow table

Field Description

Match Port packet header and metadata forwardedfrom the previous flow table

Priority Matching precedence of the entryCounter Statistics for matching the packetsInstruction Action or pipeline processing

Timeout Maximum effective time or free time before theentry is overdue

Cookie Opaque data sent by the OpenFlow controller

OpenFlow interface

Forwarding table

Forwarding path

OpenFlow switch

IncomingPacket

OutgoingPacket

OpenFlow API (via secure channel)

OpenFlow controller

Figure 2 The structure of the OpenFlow protocol

OpenFlowThere exists one ormore tables of packet-handlingrules (flow table) in an OpenFlow switch Each entry of a flowtable consists of mainly six fields as listed in Table 1 The ruleismatchedwith a subset of the traffic and proper actions suchas dropping forwarding and modifying are applied to thetrafficThe flow tables are used to determine how to deal withthe incoming packets

The communication protocol between the controller andswitches is particularly important due to the decoupling of thetwo planes The OpenFlow protocol is widely used for SDNwhich defines the API for the communication between themas Figure 2 illustrates

In SDN the controller manipulates the flow tables of theswitch by adding updating and deleting the flow entriesThe operation occurs either reactively as the controllerreceives a packet from the switch or proactively accordingto the implementation of the OpenFlow controller A securechannel is supported for the communication between thecontroller and switch The OpenFlow switch supports theflow-based forwarding by keeping one or more flow tables[12 13]

In Xiong et al [14] a queueing model was proposed forestimating the performance of the SDN controller with theinput of a hybrid Poisson stream of packet-in messages Theyalso modeled the packet forwarding of OpenFlow switchesin terms of packet sojourn time [15] In Sood et al [16] an

analytical model for an SDN switch was developed whichincludes the key factors such as flow-table size packet arrivalrate number of rules and position of rules Ma et al [17]focused on delay estimation with real traffic and end-to-enddelay control A model was proposed in Mahmood et al [18]which approximates multiple nodes of the data plane as anopen Jackson network with the controller A hybrid routingforwarding scheme as well as a congestion control algorithmwas proposed in Shen et al [19] to solve the traffic schedulingand load balancing problem in software-defined mobilewireless networks In Miao et al [20] the performance ofSDN was investigated using the Markov Modulated PoissonProcess (MMPP) in the presence of bursty and correlatedarrivals

22 Edge Computing With the new era of computing par-adigm called edge computing data are transferred to thenetwork edge for the service including analytics As a resultcomputing occurs close to the data sources [21] The numberof sensor nodes deployed on the surroundings is rapidlyincreasing due to the prevalence of IoT in recent years Edgecomputing is an emerging ecosystem which aims at converg-ing telecommunication and IT services providing a cloudcomputing platformat the edge of thewhole network It offersstorage and computational resources at the edge reducingthe latency and increasing resource utilization A simplifiedstructure of edge computing is depicted in Figure 3

As the futuristic vision of IoT the latest development ofSDN could be integrated with edge computing to providemore efficient service Here how to make the edge nodesmore efficient in processing the data is a matter of greatconcern Besides it is essential to accurately estimate theperformance of the OpenFlow switch for better usage Whilemore than thousands of edge nodes may exist in the realenvironment some of them are deployed in the critical areawhose data must be processed with high priority Thereforepriority-based scheduling is inevitable to dynamically controlthe operation of the network considering the property of thetraffics

3 The Proposed Scheme

In this section the proposed scheduling schemes for SDNhaving multiple switches and the analytical models of theperformance are presented First the priority schedulingschemewith a single switch and controller is presentedThenthe FCFS-PO and FCFS-PO-P scheme based on multipleswitches are introduced which can effectively handle theswitch overload issue

31 Priority Scheduling with Single Switch

311 Basic Structure SDN allows easy implementation of anew scheme on the existing network infrastructure by decou-pling the control plane from the data plane and connectingthem via an open interface The SDN of a single switch andcontroller is depicted in Figure 4

Both the controller and switch support the OpenFlowprotocol for the communication between them When a

4 Wireless Communications and Mobile Computing

Figure 3 A simplified structure of edge computing

Controller

OpenFlow Switch

124 35

1

2

3

4

Packet-in message

Incoming packets

MG1 queue

MM1 queue

Figure 4 The structure with a single switch and controller

packet arrives at the OpenFlow switch the switch performslookup with its flow tables If a table entry matches the switchforwards the packet in the conventional way Otherwisethe switch requests the controller for the instruction bysending a packet-in message which encapsulates the packetinformation The controller then determines the rule for it

which is installed in other switches After that all the packetsbelonging to the flow are forwarded to the destination with-out requesting the controller again [15]The process of packetmatching operation is illustrated in Figure 5 Notice from thefigure that both the incoming packets and packet-in mes-sages are queued Here the incoming packets and packet-in

Wireless Communications and Mobile Computing 5

Table 0

Table k

Table n

Execute Action

Set

Packet-InIngress Port + Null Action Set

Controller

Send Packet to Controller

Drop Packet

Controller

Packet+Ingress Port+Metadata+Action Set

Send Packet to Controller

Drop Packet

Packet+Ingress Port+Metadata+Action Set

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet + Action Set

ControllerDrop Packet

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet Out

Send Packet to Controller

OpenFlow Switch

Figure 5 The process of packet matching

messages are handled with the MG1 model and MM1model respectively as in the existing researches [14 16]

312 Priority-Based Scheduling Refer to Figure 5 Theincoming packets to the OpenFlow switch are queued andthey are scheduled by either the FCFS or FCFS with priority(FCFS-P) scheduling policy FCFS is applied for regulartraffic while FCFS-P is applied for urgent packets

In the FCFSMG1 queueing system the average sojourntime of a packet consists of two components The firstcomponent is the time required for the processing of thepackets which are waiting in the queue at the time of thepacket arrival and the second one is the time due to thepacket which is in service The second component is nonzeroif the system is busy while it is zero if the system is emptyConsidering the two components the average sojourn timeof a packet with FCFS scheduling is obtained as follows Withthe MG1 queue 120582 is the arrival rate of the Poisson processand 119909 is average service time The models in this subsectioncan be referred to in [22]

119878 = 119873119902119909 + 12058811990922119909 (1)

Here 119873119902 is the number of packets in the queue 120588 is theprobability that the queue is busy and x2(2119909) is the average

residual lifetime of the service By adopting Littlersquos equationand the P-K (Pollaczek and Khinchin) equation (1) can beexpressed as follows

119878 = 119909 + 12058211990922 (1 minus 120588) (2)

The model for FCFS-P is different from the FCFSMG1queue due to the out-of-order operation There exist severalclasses of packets having different Poisson arrival rates andservice times Assuming that there arem classes 119909119894 and 120582119894 areaverage service time and arrival rate of class-i respectivelyThe time fraction of the systemworking on class-i is then 120588119894 =120582119894 119909119894Thepackets are processed according to the prioritywithpreemptive node while the class of a smaller number is givenhigher priority

In the MG1 queueing system of FCFS-P the averagesojourn time of an incoming packet consists of three compo-nents The first component is the time taken for the packetcurrently in service to be finished S0 The second one isthe time taken for the service of the packets waiting in thequeue whose priority is higher than or equal to it The thirdcomponent is for the service of the packets arriving after itselfbut having higher priority The number of packets of class-m is 120582119898119878119898 according to Littlersquos result theorem [23] Hence

6 Wireless Communications and Mobile Computing

Topology discovery Path Computation

Routing protocols

Routing Information Base

Forwarding Information Base

Controller

Internal Structure

OpenFlow Switch

Figure 6 The processing of packet-in messages in the SDN controller

the sojourn time of the FCFS-PMG1 queueing system is asfollows

119878119898 = 1198780 +119898

sum119894=1

119909119894 (120582119894119878119894) +119898minus1

sum119894=1

119909119894 (120582119894119878119894) (3)

Equation (3) can be solved by recursively applying theequation as follows

120590119898 =119898

sum119894=1

120588119894 (4)

119878119898 = 1198780(1 minus 120590119898) (1 minus 120590119898minus1) (5)

With preemptive scheduling S0 is due to the packets ofhigher priority Therefore it can be expressed as follows

1198780 =119898

sum119894=1

120588119894 1199092119894

2119909119894 (6)

313 Packet-InMessages Aspreviously stated theOpenFlowswitch sends a packet-in message to the relevant controlleras a flow setup request when a packet fails to match theflow table The diagram of the processing of the packet-inmessage is illustrated in Figure 6 Notice that the process ofpacket-in message has a one-to-one correspondence with theprocess of flow arrival regardless of the number of switchesconnected to the controller Each flow arrival is assumedto follow the Poisson distribution Therefore the packet-in

messages coming from several switches constitute a Poissonstream by the superposition theorem [15]

32 Priority Scheduling with Multiple Switches

321 Basic Structure Since SDN decouples the control planeand data forwarding plane the data transmission consists oftwo types One is from the edge nodes to the switches andthe other one is from a switch to the remote controller for thepacket-in message They are illustrated in Figure 7

There is at least one flow table in an OpenFlow switchand the incoming packets are matched from the first flowtable Upon a match with a flow entry the instruction setof the flow entry is executed On table miss there are threeoptions dropping forwarding to the subsequent flow tablesand transmitting to the controller as a packet-inmessageOneoption is selected by the programmerwhen the flow tables aresent to the OpenFlow switches

322 FCFS-PO Scheduling With FCFS-PO if the buffer isfull when a packet enters it is put at the tail of the queuewhile the packet at the head is pushed out All the packetsmove forward one position when a packet is served Here theposition of a packet in the buffer is decided by the number ofwaiting packets

The FCFS-PO mechanism is modeled assuming that thepackets arriving at the switch follow the Poisson arrival withthe rate of 120582(120582 gt 0) This means that the interarrival timesare independent and follow exponential distribution Thepacket service times are also independent and follow general

Wireless Communications and Mobile Computing 7

SDN Controller

OpenFlow Switch OpenFlow Switch OpenFlow Switch

Packet-in M

essage

Packet-in Message

Packet-in Message

Controller Plane

Data Forwarding Plane

Host Host Host Host Host Host

Figure 7The structure of multiple-switch SDN

distribution (1120583) Also assume that the system can containNpackets atmost and the buffer size is (119873minus1) At last the arrivalprocess and service process are assumed to be independent

Assume that 119876119894(1 le 119894 le(119873 minus 1)) is the steady stateprobability of theMG1N queue while 119875119894(1 le 119894 le (119873 minus 1))represents the steady state probability of theMG1 queue Q119894is obtained as follows using the approach employed in [24]

119876119894 = 119875119894sum119873minus1119894=0 119875119894 1 le 119894 le (119873 minus 1) (7)

119876119886(1 le 119886 le 119873) is the steady state probability of a packetsalready in the system when a new packet arrives

Then according to the Poisson Arrivals See Time Aver-ages (PASTA) character [24] the following equation can beobtained

119876119886 = 1198761198861198760 + 120588 119886 = 0 1 2 (119873 minus 1)

119876119873 = 1 minus 11198760 + 120588 119886 = 119873

(8)

Here 120588 = (120582120583) And two performance indicators of thequeue in the steady state are dealt with as follows

(i) The probability of the packets to get the service 119875119909119875119909 = 1

(1198760 + 120588) (9)

(ii) The packet loss rate of the system 119875119897119875119897 = 1 minus 119875119909 = 1 minus 1

1198760 + 120588 (10)

With the FCFS-PO mechanism when the buffer is fullof packets the incoming packet will be put at the end andthe buffer management policy will push out the head-of-line(HOL) packet for the newly incoming packet Let us denoteby 119875119904(119886 119887) the steady state probability for the packet in state(119886 119887) and it finally gets the service when a packet leaves thesystemWhen119886 = 1 the packet is in serviceWhen 2 le 119886 le 119873and 0 le 119887 le (119873 minus 119886) 119901119904(119886 119887) needs to wait for the serviceAssume that there are119898 incoming packets while a packet is inserviceThen119898 le (119873minus119887minus2) for 119901119904(119886 119887) to get the service If119898 le (119873minus119886minus119887) there is no packet to be pushed outThen theposition of the packet is changed from (119886 119887) to (119886 minus 1 119887 +119898)The buffer is full while (119873 minus 119886 minus 119887) + 1 le 119898 le (119873 minus 119887 minus 2)and the incoming packet pushes out the packet at position 2Then the position of the packet is changed from (119886 119887) to(119873 minus 119898 minus 119887 minus 1 119887 + 119898) Finally the state-transition equationof 119875119904(119886 119887) is obtained as follows [25]

119875119904 (119886 119887)= prod120572119898 ∙ (119898 | (119886 119887))

+119873minus119887minus2

sum119898=119873minus119886minus119887+1

120572119898 ∙ 119875119904 (119873 minus 119898 minus 119887 minus 1 119887 + 119898) (11)

Here 120572119898 can be obtained from the result of imbeddedMarkov points in [26] Then the average waiting time isanalyzed The following Boolean function is used to show ifthe packet was served or not

119871 =

0 119878119890119903V1198901198891 119873119900119905 119904119890119903V119890119889 (12)

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

Wireless Communications and Mobile Computing 3

Table 1 The fields of an entry of a flow table

Field Description

Match Port packet header and metadata forwardedfrom the previous flow table

Priority Matching precedence of the entryCounter Statistics for matching the packetsInstruction Action or pipeline processing

Timeout Maximum effective time or free time before theentry is overdue

Cookie Opaque data sent by the OpenFlow controller

OpenFlow interface

Forwarding table

Forwarding path

OpenFlow switch

IncomingPacket

OutgoingPacket

OpenFlow API (via secure channel)

OpenFlow controller

Figure 2 The structure of the OpenFlow protocol

OpenFlowThere exists one ormore tables of packet-handlingrules (flow table) in an OpenFlow switch Each entry of a flowtable consists of mainly six fields as listed in Table 1 The ruleismatchedwith a subset of the traffic and proper actions suchas dropping forwarding and modifying are applied to thetrafficThe flow tables are used to determine how to deal withthe incoming packets

The communication protocol between the controller andswitches is particularly important due to the decoupling of thetwo planes The OpenFlow protocol is widely used for SDNwhich defines the API for the communication between themas Figure 2 illustrates

In SDN the controller manipulates the flow tables of theswitch by adding updating and deleting the flow entriesThe operation occurs either reactively as the controllerreceives a packet from the switch or proactively accordingto the implementation of the OpenFlow controller A securechannel is supported for the communication between thecontroller and switch The OpenFlow switch supports theflow-based forwarding by keeping one or more flow tables[12 13]

In Xiong et al [14] a queueing model was proposed forestimating the performance of the SDN controller with theinput of a hybrid Poisson stream of packet-in messages Theyalso modeled the packet forwarding of OpenFlow switchesin terms of packet sojourn time [15] In Sood et al [16] an

analytical model for an SDN switch was developed whichincludes the key factors such as flow-table size packet arrivalrate number of rules and position of rules Ma et al [17]focused on delay estimation with real traffic and end-to-enddelay control A model was proposed in Mahmood et al [18]which approximates multiple nodes of the data plane as anopen Jackson network with the controller A hybrid routingforwarding scheme as well as a congestion control algorithmwas proposed in Shen et al [19] to solve the traffic schedulingand load balancing problem in software-defined mobilewireless networks In Miao et al [20] the performance ofSDN was investigated using the Markov Modulated PoissonProcess (MMPP) in the presence of bursty and correlatedarrivals

22 Edge Computing With the new era of computing par-adigm called edge computing data are transferred to thenetwork edge for the service including analytics As a resultcomputing occurs close to the data sources [21] The numberof sensor nodes deployed on the surroundings is rapidlyincreasing due to the prevalence of IoT in recent years Edgecomputing is an emerging ecosystem which aims at converg-ing telecommunication and IT services providing a cloudcomputing platformat the edge of thewhole network It offersstorage and computational resources at the edge reducingthe latency and increasing resource utilization A simplifiedstructure of edge computing is depicted in Figure 3

As the futuristic vision of IoT the latest development ofSDN could be integrated with edge computing to providemore efficient service Here how to make the edge nodesmore efficient in processing the data is a matter of greatconcern Besides it is essential to accurately estimate theperformance of the OpenFlow switch for better usage Whilemore than thousands of edge nodes may exist in the realenvironment some of them are deployed in the critical areawhose data must be processed with high priority Thereforepriority-based scheduling is inevitable to dynamically controlthe operation of the network considering the property of thetraffics

3 The Proposed Scheme

In this section the proposed scheduling schemes for SDNhaving multiple switches and the analytical models of theperformance are presented First the priority schedulingschemewith a single switch and controller is presentedThenthe FCFS-PO and FCFS-PO-P scheme based on multipleswitches are introduced which can effectively handle theswitch overload issue

31 Priority Scheduling with Single Switch

311 Basic Structure SDN allows easy implementation of anew scheme on the existing network infrastructure by decou-pling the control plane from the data plane and connectingthem via an open interface The SDN of a single switch andcontroller is depicted in Figure 4

Both the controller and switch support the OpenFlowprotocol for the communication between them When a

4 Wireless Communications and Mobile Computing

Figure 3 A simplified structure of edge computing

Controller

OpenFlow Switch

124 35

1

2

3

4

Packet-in message

Incoming packets

MG1 queue

MM1 queue

Figure 4 The structure with a single switch and controller

packet arrives at the OpenFlow switch the switch performslookup with its flow tables If a table entry matches the switchforwards the packet in the conventional way Otherwisethe switch requests the controller for the instruction bysending a packet-in message which encapsulates the packetinformation The controller then determines the rule for it

which is installed in other switches After that all the packetsbelonging to the flow are forwarded to the destination with-out requesting the controller again [15]The process of packetmatching operation is illustrated in Figure 5 Notice from thefigure that both the incoming packets and packet-in mes-sages are queued Here the incoming packets and packet-in

Wireless Communications and Mobile Computing 5

Table 0

Table k

Table n

Execute Action

Set

Packet-InIngress Port + Null Action Set

Controller

Send Packet to Controller

Drop Packet

Controller

Packet+Ingress Port+Metadata+Action Set

Send Packet to Controller

Drop Packet

Packet+Ingress Port+Metadata+Action Set

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet + Action Set

ControllerDrop Packet

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet Out

Send Packet to Controller

OpenFlow Switch

Figure 5 The process of packet matching

messages are handled with the MG1 model and MM1model respectively as in the existing researches [14 16]

312 Priority-Based Scheduling Refer to Figure 5 Theincoming packets to the OpenFlow switch are queued andthey are scheduled by either the FCFS or FCFS with priority(FCFS-P) scheduling policy FCFS is applied for regulartraffic while FCFS-P is applied for urgent packets

In the FCFSMG1 queueing system the average sojourntime of a packet consists of two components The firstcomponent is the time required for the processing of thepackets which are waiting in the queue at the time of thepacket arrival and the second one is the time due to thepacket which is in service The second component is nonzeroif the system is busy while it is zero if the system is emptyConsidering the two components the average sojourn timeof a packet with FCFS scheduling is obtained as follows Withthe MG1 queue 120582 is the arrival rate of the Poisson processand 119909 is average service time The models in this subsectioncan be referred to in [22]

119878 = 119873119902119909 + 12058811990922119909 (1)

Here 119873119902 is the number of packets in the queue 120588 is theprobability that the queue is busy and x2(2119909) is the average

residual lifetime of the service By adopting Littlersquos equationand the P-K (Pollaczek and Khinchin) equation (1) can beexpressed as follows

119878 = 119909 + 12058211990922 (1 minus 120588) (2)

The model for FCFS-P is different from the FCFSMG1queue due to the out-of-order operation There exist severalclasses of packets having different Poisson arrival rates andservice times Assuming that there arem classes 119909119894 and 120582119894 areaverage service time and arrival rate of class-i respectivelyThe time fraction of the systemworking on class-i is then 120588119894 =120582119894 119909119894Thepackets are processed according to the prioritywithpreemptive node while the class of a smaller number is givenhigher priority

In the MG1 queueing system of FCFS-P the averagesojourn time of an incoming packet consists of three compo-nents The first component is the time taken for the packetcurrently in service to be finished S0 The second one isthe time taken for the service of the packets waiting in thequeue whose priority is higher than or equal to it The thirdcomponent is for the service of the packets arriving after itselfbut having higher priority The number of packets of class-m is 120582119898119878119898 according to Littlersquos result theorem [23] Hence

6 Wireless Communications and Mobile Computing

Topology discovery Path Computation

Routing protocols

Routing Information Base

Forwarding Information Base

Controller

Internal Structure

OpenFlow Switch

Figure 6 The processing of packet-in messages in the SDN controller

the sojourn time of the FCFS-PMG1 queueing system is asfollows

119878119898 = 1198780 +119898

sum119894=1

119909119894 (120582119894119878119894) +119898minus1

sum119894=1

119909119894 (120582119894119878119894) (3)

Equation (3) can be solved by recursively applying theequation as follows

120590119898 =119898

sum119894=1

120588119894 (4)

119878119898 = 1198780(1 minus 120590119898) (1 minus 120590119898minus1) (5)

With preemptive scheduling S0 is due to the packets ofhigher priority Therefore it can be expressed as follows

1198780 =119898

sum119894=1

120588119894 1199092119894

2119909119894 (6)

313 Packet-InMessages Aspreviously stated theOpenFlowswitch sends a packet-in message to the relevant controlleras a flow setup request when a packet fails to match theflow table The diagram of the processing of the packet-inmessage is illustrated in Figure 6 Notice that the process ofpacket-in message has a one-to-one correspondence with theprocess of flow arrival regardless of the number of switchesconnected to the controller Each flow arrival is assumedto follow the Poisson distribution Therefore the packet-in

messages coming from several switches constitute a Poissonstream by the superposition theorem [15]

32 Priority Scheduling with Multiple Switches

321 Basic Structure Since SDN decouples the control planeand data forwarding plane the data transmission consists oftwo types One is from the edge nodes to the switches andthe other one is from a switch to the remote controller for thepacket-in message They are illustrated in Figure 7

There is at least one flow table in an OpenFlow switchand the incoming packets are matched from the first flowtable Upon a match with a flow entry the instruction setof the flow entry is executed On table miss there are threeoptions dropping forwarding to the subsequent flow tablesand transmitting to the controller as a packet-inmessageOneoption is selected by the programmerwhen the flow tables aresent to the OpenFlow switches

322 FCFS-PO Scheduling With FCFS-PO if the buffer isfull when a packet enters it is put at the tail of the queuewhile the packet at the head is pushed out All the packetsmove forward one position when a packet is served Here theposition of a packet in the buffer is decided by the number ofwaiting packets

The FCFS-PO mechanism is modeled assuming that thepackets arriving at the switch follow the Poisson arrival withthe rate of 120582(120582 gt 0) This means that the interarrival timesare independent and follow exponential distribution Thepacket service times are also independent and follow general

Wireless Communications and Mobile Computing 7

SDN Controller

OpenFlow Switch OpenFlow Switch OpenFlow Switch

Packet-in M

essage

Packet-in Message

Packet-in Message

Controller Plane

Data Forwarding Plane

Host Host Host Host Host Host

Figure 7The structure of multiple-switch SDN

distribution (1120583) Also assume that the system can containNpackets atmost and the buffer size is (119873minus1) At last the arrivalprocess and service process are assumed to be independent

Assume that 119876119894(1 le 119894 le(119873 minus 1)) is the steady stateprobability of theMG1N queue while 119875119894(1 le 119894 le (119873 minus 1))represents the steady state probability of theMG1 queue Q119894is obtained as follows using the approach employed in [24]

119876119894 = 119875119894sum119873minus1119894=0 119875119894 1 le 119894 le (119873 minus 1) (7)

119876119886(1 le 119886 le 119873) is the steady state probability of a packetsalready in the system when a new packet arrives

Then according to the Poisson Arrivals See Time Aver-ages (PASTA) character [24] the following equation can beobtained

119876119886 = 1198761198861198760 + 120588 119886 = 0 1 2 (119873 minus 1)

119876119873 = 1 minus 11198760 + 120588 119886 = 119873

(8)

Here 120588 = (120582120583) And two performance indicators of thequeue in the steady state are dealt with as follows

(i) The probability of the packets to get the service 119875119909119875119909 = 1

(1198760 + 120588) (9)

(ii) The packet loss rate of the system 119875119897119875119897 = 1 minus 119875119909 = 1 minus 1

1198760 + 120588 (10)

With the FCFS-PO mechanism when the buffer is fullof packets the incoming packet will be put at the end andthe buffer management policy will push out the head-of-line(HOL) packet for the newly incoming packet Let us denoteby 119875119904(119886 119887) the steady state probability for the packet in state(119886 119887) and it finally gets the service when a packet leaves thesystemWhen119886 = 1 the packet is in serviceWhen 2 le 119886 le 119873and 0 le 119887 le (119873 minus 119886) 119901119904(119886 119887) needs to wait for the serviceAssume that there are119898 incoming packets while a packet is inserviceThen119898 le (119873minus119887minus2) for 119901119904(119886 119887) to get the service If119898 le (119873minus119886minus119887) there is no packet to be pushed outThen theposition of the packet is changed from (119886 119887) to (119886 minus 1 119887 +119898)The buffer is full while (119873 minus 119886 minus 119887) + 1 le 119898 le (119873 minus 119887 minus 2)and the incoming packet pushes out the packet at position 2Then the position of the packet is changed from (119886 119887) to(119873 minus 119898 minus 119887 minus 1 119887 + 119898) Finally the state-transition equationof 119875119904(119886 119887) is obtained as follows [25]

119875119904 (119886 119887)= prod120572119898 ∙ (119898 | (119886 119887))

+119873minus119887minus2

sum119898=119873minus119886minus119887+1

120572119898 ∙ 119875119904 (119873 minus 119898 minus 119887 minus 1 119887 + 119898) (11)

Here 120572119898 can be obtained from the result of imbeddedMarkov points in [26] Then the average waiting time isanalyzed The following Boolean function is used to show ifthe packet was served or not

119871 =

0 119878119890119903V1198901198891 119873119900119905 119904119890119903V119890119889 (12)

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

4 Wireless Communications and Mobile Computing

Figure 3 A simplified structure of edge computing

Controller

OpenFlow Switch

124 35

1

2

3

4

Packet-in message

Incoming packets

MG1 queue

MM1 queue

Figure 4 The structure with a single switch and controller

packet arrives at the OpenFlow switch the switch performslookup with its flow tables If a table entry matches the switchforwards the packet in the conventional way Otherwisethe switch requests the controller for the instruction bysending a packet-in message which encapsulates the packetinformation The controller then determines the rule for it

which is installed in other switches After that all the packetsbelonging to the flow are forwarded to the destination with-out requesting the controller again [15]The process of packetmatching operation is illustrated in Figure 5 Notice from thefigure that both the incoming packets and packet-in mes-sages are queued Here the incoming packets and packet-in

Wireless Communications and Mobile Computing 5

Table 0

Table k

Table n

Execute Action

Set

Packet-InIngress Port + Null Action Set

Controller

Send Packet to Controller

Drop Packet

Controller

Packet+Ingress Port+Metadata+Action Set

Send Packet to Controller

Drop Packet

Packet+Ingress Port+Metadata+Action Set

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet + Action Set

ControllerDrop Packet

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet Out

Send Packet to Controller

OpenFlow Switch

Figure 5 The process of packet matching

messages are handled with the MG1 model and MM1model respectively as in the existing researches [14 16]

312 Priority-Based Scheduling Refer to Figure 5 Theincoming packets to the OpenFlow switch are queued andthey are scheduled by either the FCFS or FCFS with priority(FCFS-P) scheduling policy FCFS is applied for regulartraffic while FCFS-P is applied for urgent packets

In the FCFSMG1 queueing system the average sojourntime of a packet consists of two components The firstcomponent is the time required for the processing of thepackets which are waiting in the queue at the time of thepacket arrival and the second one is the time due to thepacket which is in service The second component is nonzeroif the system is busy while it is zero if the system is emptyConsidering the two components the average sojourn timeof a packet with FCFS scheduling is obtained as follows Withthe MG1 queue 120582 is the arrival rate of the Poisson processand 119909 is average service time The models in this subsectioncan be referred to in [22]

119878 = 119873119902119909 + 12058811990922119909 (1)

Here 119873119902 is the number of packets in the queue 120588 is theprobability that the queue is busy and x2(2119909) is the average

residual lifetime of the service By adopting Littlersquos equationand the P-K (Pollaczek and Khinchin) equation (1) can beexpressed as follows

119878 = 119909 + 12058211990922 (1 minus 120588) (2)

The model for FCFS-P is different from the FCFSMG1queue due to the out-of-order operation There exist severalclasses of packets having different Poisson arrival rates andservice times Assuming that there arem classes 119909119894 and 120582119894 areaverage service time and arrival rate of class-i respectivelyThe time fraction of the systemworking on class-i is then 120588119894 =120582119894 119909119894Thepackets are processed according to the prioritywithpreemptive node while the class of a smaller number is givenhigher priority

In the MG1 queueing system of FCFS-P the averagesojourn time of an incoming packet consists of three compo-nents The first component is the time taken for the packetcurrently in service to be finished S0 The second one isthe time taken for the service of the packets waiting in thequeue whose priority is higher than or equal to it The thirdcomponent is for the service of the packets arriving after itselfbut having higher priority The number of packets of class-m is 120582119898119878119898 according to Littlersquos result theorem [23] Hence

6 Wireless Communications and Mobile Computing

Topology discovery Path Computation

Routing protocols

Routing Information Base

Forwarding Information Base

Controller

Internal Structure

OpenFlow Switch

Figure 6 The processing of packet-in messages in the SDN controller

the sojourn time of the FCFS-PMG1 queueing system is asfollows

119878119898 = 1198780 +119898

sum119894=1

119909119894 (120582119894119878119894) +119898minus1

sum119894=1

119909119894 (120582119894119878119894) (3)

Equation (3) can be solved by recursively applying theequation as follows

120590119898 =119898

sum119894=1

120588119894 (4)

119878119898 = 1198780(1 minus 120590119898) (1 minus 120590119898minus1) (5)

With preemptive scheduling S0 is due to the packets ofhigher priority Therefore it can be expressed as follows

1198780 =119898

sum119894=1

120588119894 1199092119894

2119909119894 (6)

313 Packet-InMessages Aspreviously stated theOpenFlowswitch sends a packet-in message to the relevant controlleras a flow setup request when a packet fails to match theflow table The diagram of the processing of the packet-inmessage is illustrated in Figure 6 Notice that the process ofpacket-in message has a one-to-one correspondence with theprocess of flow arrival regardless of the number of switchesconnected to the controller Each flow arrival is assumedto follow the Poisson distribution Therefore the packet-in

messages coming from several switches constitute a Poissonstream by the superposition theorem [15]

32 Priority Scheduling with Multiple Switches

321 Basic Structure Since SDN decouples the control planeand data forwarding plane the data transmission consists oftwo types One is from the edge nodes to the switches andthe other one is from a switch to the remote controller for thepacket-in message They are illustrated in Figure 7

There is at least one flow table in an OpenFlow switchand the incoming packets are matched from the first flowtable Upon a match with a flow entry the instruction setof the flow entry is executed On table miss there are threeoptions dropping forwarding to the subsequent flow tablesand transmitting to the controller as a packet-inmessageOneoption is selected by the programmerwhen the flow tables aresent to the OpenFlow switches

322 FCFS-PO Scheduling With FCFS-PO if the buffer isfull when a packet enters it is put at the tail of the queuewhile the packet at the head is pushed out All the packetsmove forward one position when a packet is served Here theposition of a packet in the buffer is decided by the number ofwaiting packets

The FCFS-PO mechanism is modeled assuming that thepackets arriving at the switch follow the Poisson arrival withthe rate of 120582(120582 gt 0) This means that the interarrival timesare independent and follow exponential distribution Thepacket service times are also independent and follow general

Wireless Communications and Mobile Computing 7

SDN Controller

OpenFlow Switch OpenFlow Switch OpenFlow Switch

Packet-in M

essage

Packet-in Message

Packet-in Message

Controller Plane

Data Forwarding Plane

Host Host Host Host Host Host

Figure 7The structure of multiple-switch SDN

distribution (1120583) Also assume that the system can containNpackets atmost and the buffer size is (119873minus1) At last the arrivalprocess and service process are assumed to be independent

Assume that 119876119894(1 le 119894 le(119873 minus 1)) is the steady stateprobability of theMG1N queue while 119875119894(1 le 119894 le (119873 minus 1))represents the steady state probability of theMG1 queue Q119894is obtained as follows using the approach employed in [24]

119876119894 = 119875119894sum119873minus1119894=0 119875119894 1 le 119894 le (119873 minus 1) (7)

119876119886(1 le 119886 le 119873) is the steady state probability of a packetsalready in the system when a new packet arrives

Then according to the Poisson Arrivals See Time Aver-ages (PASTA) character [24] the following equation can beobtained

119876119886 = 1198761198861198760 + 120588 119886 = 0 1 2 (119873 minus 1)

119876119873 = 1 minus 11198760 + 120588 119886 = 119873

(8)

Here 120588 = (120582120583) And two performance indicators of thequeue in the steady state are dealt with as follows

(i) The probability of the packets to get the service 119875119909119875119909 = 1

(1198760 + 120588) (9)

(ii) The packet loss rate of the system 119875119897119875119897 = 1 minus 119875119909 = 1 minus 1

1198760 + 120588 (10)

With the FCFS-PO mechanism when the buffer is fullof packets the incoming packet will be put at the end andthe buffer management policy will push out the head-of-line(HOL) packet for the newly incoming packet Let us denoteby 119875119904(119886 119887) the steady state probability for the packet in state(119886 119887) and it finally gets the service when a packet leaves thesystemWhen119886 = 1 the packet is in serviceWhen 2 le 119886 le 119873and 0 le 119887 le (119873 minus 119886) 119901119904(119886 119887) needs to wait for the serviceAssume that there are119898 incoming packets while a packet is inserviceThen119898 le (119873minus119887minus2) for 119901119904(119886 119887) to get the service If119898 le (119873minus119886minus119887) there is no packet to be pushed outThen theposition of the packet is changed from (119886 119887) to (119886 minus 1 119887 +119898)The buffer is full while (119873 minus 119886 minus 119887) + 1 le 119898 le (119873 minus 119887 minus 2)and the incoming packet pushes out the packet at position 2Then the position of the packet is changed from (119886 119887) to(119873 minus 119898 minus 119887 minus 1 119887 + 119898) Finally the state-transition equationof 119875119904(119886 119887) is obtained as follows [25]

119875119904 (119886 119887)= prod120572119898 ∙ (119898 | (119886 119887))

+119873minus119887minus2

sum119898=119873minus119886minus119887+1

120572119898 ∙ 119875119904 (119873 minus 119898 minus 119887 minus 1 119887 + 119898) (11)

Here 120572119898 can be obtained from the result of imbeddedMarkov points in [26] Then the average waiting time isanalyzed The following Boolean function is used to show ifthe packet was served or not

119871 =

0 119878119890119903V1198901198891 119873119900119905 119904119890119903V119890119889 (12)

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

Wireless Communications and Mobile Computing 5

Table 0

Table k

Table n

Execute Action

Set

Packet-InIngress Port + Null Action Set

Controller

Send Packet to Controller

Drop Packet

Controller

Packet+Ingress Port+Metadata+Action Set

Send Packet to Controller

Drop Packet

Packet+Ingress Port+Metadata+Action Set

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet + Action Set

ControllerDrop Packet

Send to a Flow Table Group Table Meter Table or Direct to Output Port

Packet Out

Send Packet to Controller

OpenFlow Switch

Figure 5 The process of packet matching

messages are handled with the MG1 model and MM1model respectively as in the existing researches [14 16]

312 Priority-Based Scheduling Refer to Figure 5 Theincoming packets to the OpenFlow switch are queued andthey are scheduled by either the FCFS or FCFS with priority(FCFS-P) scheduling policy FCFS is applied for regulartraffic while FCFS-P is applied for urgent packets

In the FCFSMG1 queueing system the average sojourntime of a packet consists of two components The firstcomponent is the time required for the processing of thepackets which are waiting in the queue at the time of thepacket arrival and the second one is the time due to thepacket which is in service The second component is nonzeroif the system is busy while it is zero if the system is emptyConsidering the two components the average sojourn timeof a packet with FCFS scheduling is obtained as follows Withthe MG1 queue 120582 is the arrival rate of the Poisson processand 119909 is average service time The models in this subsectioncan be referred to in [22]

119878 = 119873119902119909 + 12058811990922119909 (1)

Here 119873119902 is the number of packets in the queue 120588 is theprobability that the queue is busy and x2(2119909) is the average

residual lifetime of the service By adopting Littlersquos equationand the P-K (Pollaczek and Khinchin) equation (1) can beexpressed as follows

119878 = 119909 + 12058211990922 (1 minus 120588) (2)

The model for FCFS-P is different from the FCFSMG1queue due to the out-of-order operation There exist severalclasses of packets having different Poisson arrival rates andservice times Assuming that there arem classes 119909119894 and 120582119894 areaverage service time and arrival rate of class-i respectivelyThe time fraction of the systemworking on class-i is then 120588119894 =120582119894 119909119894Thepackets are processed according to the prioritywithpreemptive node while the class of a smaller number is givenhigher priority

In the MG1 queueing system of FCFS-P the averagesojourn time of an incoming packet consists of three compo-nents The first component is the time taken for the packetcurrently in service to be finished S0 The second one isthe time taken for the service of the packets waiting in thequeue whose priority is higher than or equal to it The thirdcomponent is for the service of the packets arriving after itselfbut having higher priority The number of packets of class-m is 120582119898119878119898 according to Littlersquos result theorem [23] Hence

6 Wireless Communications and Mobile Computing

Topology discovery Path Computation

Routing protocols

Routing Information Base

Forwarding Information Base

Controller

Internal Structure

OpenFlow Switch

Figure 6 The processing of packet-in messages in the SDN controller

the sojourn time of the FCFS-PMG1 queueing system is asfollows

119878119898 = 1198780 +119898

sum119894=1

119909119894 (120582119894119878119894) +119898minus1

sum119894=1

119909119894 (120582119894119878119894) (3)

Equation (3) can be solved by recursively applying theequation as follows

120590119898 =119898

sum119894=1

120588119894 (4)

119878119898 = 1198780(1 minus 120590119898) (1 minus 120590119898minus1) (5)

With preemptive scheduling S0 is due to the packets ofhigher priority Therefore it can be expressed as follows

1198780 =119898

sum119894=1

120588119894 1199092119894

2119909119894 (6)

313 Packet-InMessages Aspreviously stated theOpenFlowswitch sends a packet-in message to the relevant controlleras a flow setup request when a packet fails to match theflow table The diagram of the processing of the packet-inmessage is illustrated in Figure 6 Notice that the process ofpacket-in message has a one-to-one correspondence with theprocess of flow arrival regardless of the number of switchesconnected to the controller Each flow arrival is assumedto follow the Poisson distribution Therefore the packet-in

messages coming from several switches constitute a Poissonstream by the superposition theorem [15]

32 Priority Scheduling with Multiple Switches

321 Basic Structure Since SDN decouples the control planeand data forwarding plane the data transmission consists oftwo types One is from the edge nodes to the switches andthe other one is from a switch to the remote controller for thepacket-in message They are illustrated in Figure 7

There is at least one flow table in an OpenFlow switchand the incoming packets are matched from the first flowtable Upon a match with a flow entry the instruction setof the flow entry is executed On table miss there are threeoptions dropping forwarding to the subsequent flow tablesand transmitting to the controller as a packet-inmessageOneoption is selected by the programmerwhen the flow tables aresent to the OpenFlow switches

322 FCFS-PO Scheduling With FCFS-PO if the buffer isfull when a packet enters it is put at the tail of the queuewhile the packet at the head is pushed out All the packetsmove forward one position when a packet is served Here theposition of a packet in the buffer is decided by the number ofwaiting packets

The FCFS-PO mechanism is modeled assuming that thepackets arriving at the switch follow the Poisson arrival withthe rate of 120582(120582 gt 0) This means that the interarrival timesare independent and follow exponential distribution Thepacket service times are also independent and follow general

Wireless Communications and Mobile Computing 7

SDN Controller

OpenFlow Switch OpenFlow Switch OpenFlow Switch

Packet-in M

essage

Packet-in Message

Packet-in Message

Controller Plane

Data Forwarding Plane

Host Host Host Host Host Host

Figure 7The structure of multiple-switch SDN

distribution (1120583) Also assume that the system can containNpackets atmost and the buffer size is (119873minus1) At last the arrivalprocess and service process are assumed to be independent

Assume that 119876119894(1 le 119894 le(119873 minus 1)) is the steady stateprobability of theMG1N queue while 119875119894(1 le 119894 le (119873 minus 1))represents the steady state probability of theMG1 queue Q119894is obtained as follows using the approach employed in [24]

119876119894 = 119875119894sum119873minus1119894=0 119875119894 1 le 119894 le (119873 minus 1) (7)

119876119886(1 le 119886 le 119873) is the steady state probability of a packetsalready in the system when a new packet arrives

Then according to the Poisson Arrivals See Time Aver-ages (PASTA) character [24] the following equation can beobtained

119876119886 = 1198761198861198760 + 120588 119886 = 0 1 2 (119873 minus 1)

119876119873 = 1 minus 11198760 + 120588 119886 = 119873

(8)

Here 120588 = (120582120583) And two performance indicators of thequeue in the steady state are dealt with as follows

(i) The probability of the packets to get the service 119875119909119875119909 = 1

(1198760 + 120588) (9)

(ii) The packet loss rate of the system 119875119897119875119897 = 1 minus 119875119909 = 1 minus 1

1198760 + 120588 (10)

With the FCFS-PO mechanism when the buffer is fullof packets the incoming packet will be put at the end andthe buffer management policy will push out the head-of-line(HOL) packet for the newly incoming packet Let us denoteby 119875119904(119886 119887) the steady state probability for the packet in state(119886 119887) and it finally gets the service when a packet leaves thesystemWhen119886 = 1 the packet is in serviceWhen 2 le 119886 le 119873and 0 le 119887 le (119873 minus 119886) 119901119904(119886 119887) needs to wait for the serviceAssume that there are119898 incoming packets while a packet is inserviceThen119898 le (119873minus119887minus2) for 119901119904(119886 119887) to get the service If119898 le (119873minus119886minus119887) there is no packet to be pushed outThen theposition of the packet is changed from (119886 119887) to (119886 minus 1 119887 +119898)The buffer is full while (119873 minus 119886 minus 119887) + 1 le 119898 le (119873 minus 119887 minus 2)and the incoming packet pushes out the packet at position 2Then the position of the packet is changed from (119886 119887) to(119873 minus 119898 minus 119887 minus 1 119887 + 119898) Finally the state-transition equationof 119875119904(119886 119887) is obtained as follows [25]

119875119904 (119886 119887)= prod120572119898 ∙ (119898 | (119886 119887))

+119873minus119887minus2

sum119898=119873minus119886minus119887+1

120572119898 ∙ 119875119904 (119873 minus 119898 minus 119887 minus 1 119887 + 119898) (11)

Here 120572119898 can be obtained from the result of imbeddedMarkov points in [26] Then the average waiting time isanalyzed The following Boolean function is used to show ifthe packet was served or not

119871 =

0 119878119890119903V1198901198891 119873119900119905 119904119890119903V119890119889 (12)

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

6 Wireless Communications and Mobile Computing

Topology discovery Path Computation

Routing protocols

Routing Information Base

Forwarding Information Base

Controller

Internal Structure

OpenFlow Switch

Figure 6 The processing of packet-in messages in the SDN controller

the sojourn time of the FCFS-PMG1 queueing system is asfollows

119878119898 = 1198780 +119898

sum119894=1

119909119894 (120582119894119878119894) +119898minus1

sum119894=1

119909119894 (120582119894119878119894) (3)

Equation (3) can be solved by recursively applying theequation as follows

120590119898 =119898

sum119894=1

120588119894 (4)

119878119898 = 1198780(1 minus 120590119898) (1 minus 120590119898minus1) (5)

With preemptive scheduling S0 is due to the packets ofhigher priority Therefore it can be expressed as follows

1198780 =119898

sum119894=1

120588119894 1199092119894

2119909119894 (6)

313 Packet-InMessages Aspreviously stated theOpenFlowswitch sends a packet-in message to the relevant controlleras a flow setup request when a packet fails to match theflow table The diagram of the processing of the packet-inmessage is illustrated in Figure 6 Notice that the process ofpacket-in message has a one-to-one correspondence with theprocess of flow arrival regardless of the number of switchesconnected to the controller Each flow arrival is assumedto follow the Poisson distribution Therefore the packet-in

messages coming from several switches constitute a Poissonstream by the superposition theorem [15]

32 Priority Scheduling with Multiple Switches

321 Basic Structure Since SDN decouples the control planeand data forwarding plane the data transmission consists oftwo types One is from the edge nodes to the switches andthe other one is from a switch to the remote controller for thepacket-in message They are illustrated in Figure 7

There is at least one flow table in an OpenFlow switchand the incoming packets are matched from the first flowtable Upon a match with a flow entry the instruction setof the flow entry is executed On table miss there are threeoptions dropping forwarding to the subsequent flow tablesand transmitting to the controller as a packet-inmessageOneoption is selected by the programmerwhen the flow tables aresent to the OpenFlow switches

322 FCFS-PO Scheduling With FCFS-PO if the buffer isfull when a packet enters it is put at the tail of the queuewhile the packet at the head is pushed out All the packetsmove forward one position when a packet is served Here theposition of a packet in the buffer is decided by the number ofwaiting packets

The FCFS-PO mechanism is modeled assuming that thepackets arriving at the switch follow the Poisson arrival withthe rate of 120582(120582 gt 0) This means that the interarrival timesare independent and follow exponential distribution Thepacket service times are also independent and follow general

Wireless Communications and Mobile Computing 7

SDN Controller

OpenFlow Switch OpenFlow Switch OpenFlow Switch

Packet-in M

essage

Packet-in Message

Packet-in Message

Controller Plane

Data Forwarding Plane

Host Host Host Host Host Host

Figure 7The structure of multiple-switch SDN

distribution (1120583) Also assume that the system can containNpackets atmost and the buffer size is (119873minus1) At last the arrivalprocess and service process are assumed to be independent

Assume that 119876119894(1 le 119894 le(119873 minus 1)) is the steady stateprobability of theMG1N queue while 119875119894(1 le 119894 le (119873 minus 1))represents the steady state probability of theMG1 queue Q119894is obtained as follows using the approach employed in [24]

119876119894 = 119875119894sum119873minus1119894=0 119875119894 1 le 119894 le (119873 minus 1) (7)

119876119886(1 le 119886 le 119873) is the steady state probability of a packetsalready in the system when a new packet arrives

Then according to the Poisson Arrivals See Time Aver-ages (PASTA) character [24] the following equation can beobtained

119876119886 = 1198761198861198760 + 120588 119886 = 0 1 2 (119873 minus 1)

119876119873 = 1 minus 11198760 + 120588 119886 = 119873

(8)

Here 120588 = (120582120583) And two performance indicators of thequeue in the steady state are dealt with as follows

(i) The probability of the packets to get the service 119875119909119875119909 = 1

(1198760 + 120588) (9)

(ii) The packet loss rate of the system 119875119897119875119897 = 1 minus 119875119909 = 1 minus 1

1198760 + 120588 (10)

With the FCFS-PO mechanism when the buffer is fullof packets the incoming packet will be put at the end andthe buffer management policy will push out the head-of-line(HOL) packet for the newly incoming packet Let us denoteby 119875119904(119886 119887) the steady state probability for the packet in state(119886 119887) and it finally gets the service when a packet leaves thesystemWhen119886 = 1 the packet is in serviceWhen 2 le 119886 le 119873and 0 le 119887 le (119873 minus 119886) 119901119904(119886 119887) needs to wait for the serviceAssume that there are119898 incoming packets while a packet is inserviceThen119898 le (119873minus119887minus2) for 119901119904(119886 119887) to get the service If119898 le (119873minus119886minus119887) there is no packet to be pushed outThen theposition of the packet is changed from (119886 119887) to (119886 minus 1 119887 +119898)The buffer is full while (119873 minus 119886 minus 119887) + 1 le 119898 le (119873 minus 119887 minus 2)and the incoming packet pushes out the packet at position 2Then the position of the packet is changed from (119886 119887) to(119873 minus 119898 minus 119887 minus 1 119887 + 119898) Finally the state-transition equationof 119875119904(119886 119887) is obtained as follows [25]

119875119904 (119886 119887)= prod120572119898 ∙ (119898 | (119886 119887))

+119873minus119887minus2

sum119898=119873minus119886minus119887+1

120572119898 ∙ 119875119904 (119873 minus 119898 minus 119887 minus 1 119887 + 119898) (11)

Here 120572119898 can be obtained from the result of imbeddedMarkov points in [26] Then the average waiting time isanalyzed The following Boolean function is used to show ifthe packet was served or not

119871 =

0 119878119890119903V1198901198891 119873119900119905 119904119890119903V119890119889 (12)

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

Wireless Communications and Mobile Computing 7

SDN Controller

OpenFlow Switch OpenFlow Switch OpenFlow Switch

Packet-in M

essage

Packet-in Message

Packet-in Message

Controller Plane

Data Forwarding Plane

Host Host Host Host Host Host

Figure 7The structure of multiple-switch SDN

distribution (1120583) Also assume that the system can containNpackets atmost and the buffer size is (119873minus1) At last the arrivalprocess and service process are assumed to be independent

Assume that 119876119894(1 le 119894 le(119873 minus 1)) is the steady stateprobability of theMG1N queue while 119875119894(1 le 119894 le (119873 minus 1))represents the steady state probability of theMG1 queue Q119894is obtained as follows using the approach employed in [24]

119876119894 = 119875119894sum119873minus1119894=0 119875119894 1 le 119894 le (119873 minus 1) (7)

119876119886(1 le 119886 le 119873) is the steady state probability of a packetsalready in the system when a new packet arrives

Then according to the Poisson Arrivals See Time Aver-ages (PASTA) character [24] the following equation can beobtained

119876119886 = 1198761198861198760 + 120588 119886 = 0 1 2 (119873 minus 1)

119876119873 = 1 minus 11198760 + 120588 119886 = 119873

(8)

Here 120588 = (120582120583) And two performance indicators of thequeue in the steady state are dealt with as follows

(i) The probability of the packets to get the service 119875119909119875119909 = 1

(1198760 + 120588) (9)

(ii) The packet loss rate of the system 119875119897119875119897 = 1 minus 119875119909 = 1 minus 1

1198760 + 120588 (10)

With the FCFS-PO mechanism when the buffer is fullof packets the incoming packet will be put at the end andthe buffer management policy will push out the head-of-line(HOL) packet for the newly incoming packet Let us denoteby 119875119904(119886 119887) the steady state probability for the packet in state(119886 119887) and it finally gets the service when a packet leaves thesystemWhen119886 = 1 the packet is in serviceWhen 2 le 119886 le 119873and 0 le 119887 le (119873 minus 119886) 119901119904(119886 119887) needs to wait for the serviceAssume that there are119898 incoming packets while a packet is inserviceThen119898 le (119873minus119887minus2) for 119901119904(119886 119887) to get the service If119898 le (119873minus119886minus119887) there is no packet to be pushed outThen theposition of the packet is changed from (119886 119887) to (119886 minus 1 119887 +119898)The buffer is full while (119873 minus 119886 minus 119887) + 1 le 119898 le (119873 minus 119887 minus 2)and the incoming packet pushes out the packet at position 2Then the position of the packet is changed from (119886 119887) to(119873 minus 119898 minus 119887 minus 1 119887 + 119898) Finally the state-transition equationof 119875119904(119886 119887) is obtained as follows [25]

119875119904 (119886 119887)= prod120572119898 ∙ (119898 | (119886 119887))

+119873minus119887minus2

sum119898=119873minus119886minus119887+1

120572119898 ∙ 119875119904 (119873 minus 119898 minus 119887 minus 1 119887 + 119898) (11)

Here 120572119898 can be obtained from the result of imbeddedMarkov points in [26] Then the average waiting time isanalyzed The following Boolean function is used to show ifthe packet was served or not

119871 =

0 119878119890119903V1198901198891 119873119900119905 119904119890119903V119890119889 (12)

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

8 Wireless Communications and Mobile Computing

Using (9) and (10) the probability of 119875(119871 = 0) and 119875(119871 =1) functions can be easily obtained

Let 119861119899 (119899 ge 1) represent the number of incoming packetswhile 119899 packets are being served and 119877(119905) is the remainingtime of the current packet in service The Laplace-StieltjesTransform (LST) of 119887119886 is obtained as follows

119887119886 (120579) = [intinfin0

(120582119888)119886119886 119890minus(120582+120579)119888119889119877 (119905) | 119876119899 + 120588 minus 1

119876119899 + 120588 ]

sdot (119876119899 + 120588 minus 1119876119899 + 120588 )

(13)

Denote by119867(119886 119887) the average waiting time for119875119904(119886 119887) until itfinally gets the service and the waiting time is no longer than119905 Then the probability of 119867(119886 119887 120579) is shown as follows

119867(119886 119887 120579) = intinfin0

119890minus120579119905119889119867 (119886 119887 120579) (14)

So 119867(119886 119887) can be obtained

119867(119886 119887) = minus lim120579997888rarr0

119867 (119886 119887 120579) (15)

The conditional average waiting time for 119901119904(119886 119887) is asfollows

119879 = 120588 ∙119873minus1

sum119886=1

119873minus119886minus1

sum119887=0

119876119886 [119887119886 ∙ 119867 (119886 119887) + 119875119904 (119886 119887)

∙ (119887 + 1)120582 ∙ 119887119887+1] + 120588 ∙

119873minus1

sum119886=1

119873minus2

sum119887=119873minus119886

119876119886 [119887119886∙ 119867 (119873 minus 119887 minus 1 119887) + 119875119904 (119873 minus 119887 minus 1 119887)

∙ (119887 + 1)120582 119887119887+1] + 120588 ∙

119873minus2

sum119887=0

119876119873 [119887119886119867 (119873 minus 119887 minus 1 119887)

+ 119875119904 (119873 minus 119887 minus 1 119887) ∙ (119887 + 1)120582 ∙ 119887119887+1]

(16)

Here 119876119886 and 119887119886(1 le 119886 le 119873) are given by (8) and (13)respectively 119867(119886 119887) is given by (15)

323 FCFS-PO-P Scheduling In the modeling of FCFS-PO-P the arrival process and service process of the incomingpackets are the same as the modeling of FCFS-PO In thispaper assume that the newly incoming packet has the highestpriority among the packets already in the queue Then thenewly incoming packet will be put in the front position toget service first And the buffer management policy pushesout the packet in position N which waited longest in thequeue Let 119875119904(119886) denote the steady state probability of packetin position a and it is finally served With the FCFS-PO-Ppolicy119901119904(119886)(2 le 119886 le 119873) waits in the sequence Assume thatm incoming packets arrived while a packet is in serviceThen119898 le (119873 minus 119886) for the packet to be served and 119901119904(119886) moves to

position (119886+119898minus1)when the service endsThe state-transitionequation of 119875119904(119886) is as follows [25]

119875119904 (119886) = prod 120572119898 ∙ (119898 | (119886 119887))

+119873minus119886

sum119898=0

120572119898 ∙ 119875119904 (119886 + 119898 minus 1) 119886 = 2 3 119873(17)

Similarly 120572119898 can be obtained from [26] Now the averagewaiting time is analyzed The probability of 119901119904(119886) to get theservice and the service time not being larger than 119905 is 119866(119886 119888)Assume that the following equation is the LST of 119866(119886 119888)

ℎ (119886 120579) = intinfin0

119890minus120579119888119889119866 (119886 119888) (18)

Similar to (17) the recursive equation of ℎ(119886 120579) isobtained

ℎ (119886 120579) =119873minus119886

sum119898=0

120572119898 (120579) ∙ ℎ (119886 + 119898 minus 1 120579)

119886 = 2 3 119873(19)

Let 119867(119886) denote average waiting time for 119901119904(119886) until itfinally gets the service Similar to (14) and (15) 119867(119886) can beobtained as follows

119867 (119886) = minus lim120579997888rarr0

ℎ (119886 120579) (20)

At last the average waiting time for 119901119904(119886) is as follows

119879 = 120588 ∙119873minus2

sum119886=0

119887119886119867 (119886 + 1) + 119875119904 (119886 + 1) ∙ (119886 + 1)120582 ∙ 119887119886+1 (21)

4 Performance Evaluation

In this section the performance of the proposed schedulingschemes for the OpenFlow switch is evaluated

41 Experiment Environment A testbed is implemented withthree Raspberry Pi nodes for the experiment The data withthe priority scheduling are collected from the testbed andthey are compared with the analytical models Open vSwitchis installed in the Raspberry Pi node to implement thereal switch with the OpenFlow protocol Open vSwitch isa multilayer open source virtual switch targeting all majorhypervisor platforms It was designed for networking invirtual environment and thus it is quite different from thetraditional software switch architecture [27] The parametersof the Raspberry Pi nodes are listed in Table 2

For the experiment one remote controller and threeOpenFlow switches are implemented Three Raspberry Pinodes operate as the OpenFlow switches and Floodlight wasinstalled in another computer working as a remote controllerFloodlight is a Java-based open source controller and it isone of the most popular SDN controllers supporting physicaland virtual OpenFlow compatible switches It is based on theBacon controller from Stanford University [28] Note that

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

Wireless Communications and Mobile Computing 9

Table 2 The parameters of Raspberry Pi node

Version Raspberry Pi 3 Model BSoC BCM2837CPU Quad Cortex A5312GHZInstruction set ARMv8-AGPU 400MHz VideoCore IVRAM 1GB SDRAMStorage 32GEthernet 10100

0015

0016

0017

0018

0019

002

0021

0022

0023

Sojo

urn

time (

ms)

20 30 40 50 60 70 80 90 10010Number of simulation runs

FCFS-PFCFS

Figure 8 The comparison of sojourn times with FCFS and FCFS-P

four network interfaces are supplied with the Raspberry Pinode Therefore three OpenFlow switches are installed forcollecting data and one interface is used to be connectedto the controller network The network traffics are generatedby the software tool ldquoiPerfrdquo [29] One host is selected asthe server and another as the terminal by iPerf Then thehost sends packets to the server by the UDP protocol in thebandwidth of 200Mbps

42 Simulation Results First the simulation results of theproposed scheduling algorithm with a single switch are pre-sented Figure 8 compares the FCFS and FCFS-P schedulingalgorithm Notice that the FCFS-P algorithm mostly causeslonger sojourn time than the FCFS algorithm The FCFS-Palgorithm occasionally displays similar performance to FCFSwhen the incoming packets have high priority

Figure 9 compares the data from the experiment andanalytical model As aforementioned three variables 120582 119909and 120588 are used in the FCFS scheduling algorithm Similarto the previous research [13] 120582 and 119909 are empirically set tobe 2 and 0016 respectively 120588 is set to be 01 05 and 09 tocheck the performancewith various conditions It reveals that

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 9 The comparison of the data from the experiment andanalytical model with FCFS

Sojo

urn

time (

ms)

0

002

0025

20 30 40 50 60 70 80 90 10010Number of simulation runs

times 10minus3

ExperimentSTDEVP of Experimentp=01

p=05p=09

Figure 10 The comparison of the data from the experiment andanalytical model with FCFS-P

the data stabilizes as the simulation time passes and 120588 of 05allows the closest estimation

Figure 10 is for the case of FCFS-P Here the values of 1205960119909119894 120582119894 and 119878119894 are 002 0018 0016 and 2 respectively In thiscase 120588 of 09 shows the best result

Assume that119873 = 10 and 120583 = 5 Figure 11 compares FCFS-PO and FCFS-PO-P as 120582 varies Observe from the figure thatthe average waiting time with FCFS-PO-P is smaller thanwith the FCFS-PO mechanism

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

10 Wireless Communications and Mobile Computing

0

01

02

03

04

05

06

07

08

Aver

age w

aitin

g tim

e

2 3 4 5 6 7 8 9 101

STDEVP FCFS-POFCFS-PO

STDEVP FCFS-PO-P FCFS-PO-P

Figure 11 The comparison of waiting times with FCFS-PO andFCFS-PO-P

The probability density function of wait time with FCFS-PO in the steady state is as follows [30]

119882(119905) =119873minus1

sum119899=1

119881119899 [119861(119899minus1) (119905) ∙ 119877 (119905)] + 1198810 (22)

Here119861(119899)(119905) is the n-fold convolution of119861(119905) and119861(119905)sdot119877(119905)is the convolution of 119861(119905) and 119877(119905) The incoming packetwill be processed directly if there is no packet waiting inthe system by which means the waiting time of the packetis 0 1198810 is the probability of the system to be idle and 119881119899 isthe probability that there are n(1 le 119899 le (119873 minus 1)) packetswaiting in the system Then the incoming packet will wait atposition (119899+1)The total wait time consists of the remainingservice time and the service time of the packet in front of itThe average wait time can then be obtained as follows

119879 (119905) = intinfin0

119905119889119882 (119905) (23)

The FCFS-PO-P mechanism is compared with FCFS-BLand FCFS-PO in Figure 12 With FCFS-BL the incomingpacket is lost if the buffer is full Notice from the figurethat the pushout mechanism is more effective than the BLmechanism Particularly the superiority gets higher as 120582increases Generally speaking the FCFS-PO-Pmechanism isthe best among the three mechanisms

5 Conclusion

In this paper the FCFS-PO and FCFS-PO-P schedulingalgorithms for multiple-switch SDN have been proposedtargeting the edge computing environment Since there existsome nodes requiring urgent processing in this environmentthe priority-based scheduling approach was proposed Heresome switches might be overloaded if the packet arrival

0

02

04

06

08

1

12

14

16

18

Aver

age w

aitin

g tim

e

STDEVP FCFS-PO

FCFS-PO STDEVP FCFS-PO-P FCFS-PO-P

2 3 4 5 6 7 8 9 101

FCFS-BLSTDEVP of FCFS-BL

Figure 12 The comparison of the waiting time of the threemechanisms

rate is high and the proposed FCFS-PO and FCFS-PO-Pmechanism are able to effectively deal with the situation TheSDN environment was implemented with three RaspberryPi node switches and one independent computer of remotecontroller and the sojourn time and wait time were analyzedThe measured data from the testbed were compared withthose from the analytical models to validate them Theexperiment results show that the FCFS-PO-P schedulingis better than the FCFS-PO scheduling based on the waittime The comparison with the existing FCFS-BL schedulingalgorithm reveals that FCFS-PO-P scheduling is the bestamong them while FCFS-BL is the worst

Several parameter values have been set empirically forthe network operation In the future the analytical modelswill be developed by which the value of the parameterscan be properly decided Also for a more comprehensiveunderstanding of the scheduling issues in SDN the processof packet-in messages based on the MM1 model will bedeveloped

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was partly supported by the Institute for Infor-mation amp Communications Technology Promotion (IITP)

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

Wireless Communications and Mobile Computing 11

grant funded by the Korea government (MSIT) (No 2016-0-00133 research on edge computing via collective intelligenceof hyperconnection IoT nodes) Korea under the NationalProgram for Excellence in SW supervised by the IITP (Insti-tute for Information amp Communications Technology Pro-motion) (2015-0-00914) the Basic Science Research Programthrough the National Research Foundation of Korea (NRF)funded by theMinistry of Education Science andTechnology(2016R1A6A3A11931385 research of key technologies basedon software-defined wireless sensor network for real-timepublic safety service 2017R1A2B2009095 research on SDN-based WSN supporting real-time stream data processing andmulticonnectivity) the second Brain Korea 21 PLUS projectand Samsung Electronics

References

[1] D Kreutz F M V Ramos P E Verissimo C E RothenbergS Azodolmolky and S Uhlig ldquoSoftware-defined networking acomprehensive surveyrdquo Proceedings of the IEEE vol 103 no 1pp 14ndash76 2015

[2] N McKeown T Anderson H Balakrishnan et al ldquoOpenFlowenabling innovation in campus networksrdquo Computer Commu-nication Review vol 38 no 2 pp 69ndash74 2008

[3] Open Networking Foundationrdquo Available at httpwwwopennetworkingorg access March 2014

[4] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Things Journal vol 3no 5 pp 637ndash646 2016

[5] J Ansell W Seah B Ng and S Marshall ldquoMaking Queue-ing Theory More Palatable to SDNOpenFlow-based NetworkPractitionersrdquo in Proceedings of the 8th Internatioanl Workshopon Management of the Future Internet (ManFI) pp 1119ndash11242016

[6] H Farhady H Lee and A Nakao ldquoSoftware-Defined Network-ing a surveyrdquo Computer Networks vol 81 pp 79ndash95 2015

[7] B A A Nunes M Mendonca X-N Nguyen K Obraczkaand T Turletti ldquoA survey of software-defined networking pastpresent and future of programmable networksrdquo IEEE Commu-nications Surveys amp Tutorials vol 16 no 3 pp 1617ndash1634 2014

[8] M Jammal T Singh A Shami R Asal and Y Li ldquoSoftwaredefined networking state of the art and research challengesrdquoComputer Networks vol 72 pp 74ndash98 2014

[9] A Gelberger N Yemini and R Giladi ldquoPerformance anal-ysis of Software-Defined Networking (SDN)rdquo in Proceedingsof the 2013 IEEE 21st International Symposium on ModelingAnalysis and Simulation of Computer and TelecommunicationMASCOTS 2013 pp 389ndash393 USA August 2013

[10] H Kim and N Feamster ldquoImproving network managementwith software definednetworkingrdquo IEEECommunicationsMag-azine vol 51 no 2 pp 114ndash119 2013

[11] M-K Shin K-H Nam and H-J Kim ldquoSoftware-definednetworking (SDN) A reference architecture and open APIsrdquoin Proceedings of the 2012 International Conference on ICTConvergence ldquoGlobal Open Innovation Summit for Smart ICTConvergencerdquo ICTC 2012 pp 360-361 October 2012

[12] WXia YWen CHeng FohDNiyato andHXie ldquoA survey onsoftware-defined networkingrdquo IEEE Communications Surveysamp Tutorials vol 17 no 1 pp 27ndash51 2015

[13] F R B Cruz and T Van Woensel ldquoFinite queueing modelingand optimization A selected reviewrdquo Journal of Applied Mathe-matics vol 2014 2014

[14] K Choi Y Suh and D Yoo ldquoExtended collaborative filteringtechnique for mitigating the sparsity problemrdquo InternationalJournal of Computers Communications amp Control vol 11 no 5p 631 2016

[15] B Xiong K Yang J Zhao W Li and K Li ldquoPerformance eval-uation of OpenFlow-based software-defined networks basedon queueing modelrdquo Computer Networks vol 102 pp 172ndash1852016

[16] K Sood S Yu and Y Xiang ldquoPerformance Analysis of Soft-ware-Defined Network Switch Using MGeo1 Modelrdquo IEEECommunications Letters pp 114ndash119 2016

[17] H Ma J Yan P Georgopoulos and B Plattner ldquoTowards SDNbased queuing delay estimationrdquo China Communications vol13 no 3 pp 27ndash36 2016

[18] K Mahmood A Chilwan O Oslashsterboslash and M Jarschel ldquoMod-elling of OpenFlow-based software-defined networksThemul-tiple node caserdquo IET Networks vol 4 no 5 pp 278ndash284 2015

[19] D Shen W Yan Y Peng Y Fu and Q Deng ldquoCongestionControl and Traffic Scheduling for Collaborative Crowdsourc-ing in SDN Enabled Mobile Wireless Networksrdquo WirelessCommunications and Mobile Computing vol 2018 2018

[20] W Miao G Min Y Wu H Wang and J Hu ldquoPerformanceModelling and Analysis of Software Defined Networking underBursty Multimedia Trafficrdquo ACM Transactions on MultimediaComputing Communication and Applications vol 12 no 5s pp77-19 2016

[21] M Patel and A Pandya ldquoEdge Computing Design a Frame-work for Monitoring Performance between Datacenters andDevices of Edge Networksrdquo International Journal of Computeramp Mathematical Sciences vol 6 no 6 pp 73ndash77 2017

[22] D Finkel ldquoBook review Fundamentals of Performance Mod-eling by MK Molloy (Macmillan 1989)rdquo ACM SIGMETRICSPerformance Evaluation Review vol 18 no 3 p 23 1990

[23] J D C Little ldquoLittlersquos Law as viewed on its 50th anniversaryrdquoOperations Research vol 59 no 3 pp 536ndash549 2011

[24] J Shortle J Thompson D Gross and C Harris Fundamentalsof Queueing Theory John Wiley Sons New York USA

[25] Y Lee B Choi B Kim and D Sung ldquoDelay Analysis of anMG1K Priority Queueing System with Push-out SchemerdquoMathematical Problems in Engineering 2007

[26] S Kasahara H Takagi Y Takahashi and T Hasegawa ldquoMGLK System with Push-Out Scheme Under Vacation PolicyrdquoJournal of Applied Mathematics and Stochastic Analysis vol 9no 2 pp 143ndash157 1996

[27] B Pfaff J Pettit T Koponen et al ldquoThe design and imple-mentation of open vSwitchrdquo in Proceedings of the 12th USENIXSymposium on Networked Systems Design and ImplementationNSDI 2015 pp 117ndash130 USA May 2015

[28] H Akcay and D Kaplan ldquoWeb-Based User Interface for theFloodlight SDN Controllerrdquo International Journal of AdvancedNetworking andApplications vol 08 no 05 pp 3175ndash3180 2017

[29] H Zheng Y Zhao X Lu and R Cao ldquoA Mobile FogComputing-Assisted DASH QoE Prediction SchemerdquoWirelessCommunications and Mobile Computing vol 2018 2018

[30] M Rawat H Rawat and S Ansari ldquoAnalysis of GIGI1 Queueby Push-Out Simulation Techniquerdquo International Journal ofScientific and Research Publications vol 3 no 6 pp 1ndash4 2013

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