research article application scheduling in mobile cloud...

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013 Article ID 409539 13 pageshttpdxdoiorg1011552013409539

Research ArticleApplication Scheduling in Mobile CloudComputing with Load Balancing

Xianglin Wei1 Jianhua Fan1 Ziyi Lu1 and Ke Ding2

1 Nanjing Telecommunication Technology Research Institute Nanjing 21007 China2 College of Command Information Systems PLA University of Science and Technology Nanjing 21007 China

Correspondence should be addressed to Xianglin Wei wei xianglin163com

Received 19 April 2013 Revised 15 September 2013 Accepted 27 September 2013

Academic Editor Chih-Hao Lin

Copyright copy 2013 Xianglin Wei et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Mobile cloud computing (MCC) enables the mobile devices to offload their applications to the cloud and thus greatly enrichesthe types of applications on mobile devices and enhances the quality of service of the applications Under various circumstancesresearchers have put forward several MCC architectures However how to reduce the response latency while efficiently utilizing theidle service capacities of the mobile devices still remains a challenge In this paper we firstly give a definition of MCC and dividethe recently proposed architectures into four categories Secondly we present a Hybrid Local Mobile Cloud Model (HLMCM)by extending the Cloudlet architecture Then after formulating the application scheduling problems in HLMCM and bringingforward the Hybrid Ant Colony algorithm based Application Scheduling (HACAS) algorithm we finally validate the efficiency ofthe HACAS algorithm by simulation experiments

1 Introduction

Recent years have witnessed the rapid development of mobiledevices such as PDAs and smartphones The tremendousimprovement of hardware and software enables them tomake calls and send short messages and emails but it alsogives them the ability to sense the environment and makesocial contacts health care and mobile learning Moreoverthe inherent mobility of the mobile devices enables theusers to interact with the devices environment and socialcommunity without time and space restriction Thus themobile devices are able to integrate the capabilities of com-munication work medical treatment and mobile learningand they become important components of peoplersquos dailylife According to the International Data Corporation (IDC)Worldwide Quarterly Mobile Phone Tracker it is estimatedthat 982 million smartphones will be shipped worldwide in2015 [1] However mobile devices also have some inherentdefects such as their limited battery energy low CPU speedinsufficient storage space and inadequate sensing capacities[2] These limitations have brought for mobile applicationsmany challenges in mobility management quality of service(QoS) insurance energy management and security issues

On the other hand the lack of resources also motivatesthe researchers in mobile computing area to search for theinfrastructure which can provide the needed resources forthe mobile devices [3] Consequently cloud computing wasintroduced to fulfill this gap since it can theoretically providenearly inexhaustible resources for mobile computing Thecombination of cloud computing and mobile computinghas stimulated the emergence of mobile cloud computing(MCC)

MCC brings rich resources of the cloud computing formobile devices and applications as well as inheriting thecloudrsquos advantages such as low cost high scalability androbustness Therefore it greatly improves the potential ofmobile computing InMCC environmentmobile devices canoffload full or part of their mobile applications to the datacenters of the cloud in order to relieve their own burdenin CPU load and energy consumption This enables themto support more sophisticated and richer applications andservices such as mobile game [4] mobile locating [5] voicekey words and picture searching [6ndash8] and mobile sensing[9] In order to support these applications researchers haveproposed various architectures forMCC such asMobiCloudMAUI CloneCloud Cloudlet and Hyrax These proposals

2 Journal of Applied Mathematics

attempt to utilize the cloud infrastructure as well as themobile devicesrsquo idle CPUs or sensing capacities to achievehighQoSHowever offloading to remote cloud infrastructurewill introduce long response latency Hence to reduce theresponse latency the offloaded applications should be han-dled by local cloud infrastructure which usually has fewerresources than those of the remote ones Therefore how toefficiently schedule the limited resources while fulfilling therequirements of a large number of offloaded applications is acritical problem for MCC to address

In this paper we first give the definition of MCC anddivide the recently proposed architectures into four ca-tegories Secondly Hybrid Local Mobile Cloud Model(HLMCM) is put forward after combining the advantages ofcurrent proposals such as Cloudlet and Hyrax Thirdly weformulate the application scheduling problems in HLMCMand bring forward the Hybrid Ant Colony algorithm basedApplication Scheduling (HACAS) algorithm Finally theeffectiveness of HACAS algorithm is validated by simulationexperiments

The rest of the paper is organized as follows Section 2summarizes related work Section 3 gives the definition ofMCC and introduces the HLMCM Section 4 formulatesthe application scheduling problem and proposes HACASalgorithm Simulation experiments and results are shown inSection 5 Finally we conclude our main work and presentfurther research directions in Section 6

2 Related Work

Application scheduling in cloud infrastructure has attractedmuch attention in recent years In fact the applicationscheduling and load balancing inMCC are burgeoning areasLiu et al have established a macroscopic scheduling modelwith cognition and decision components for the cloud com-puting which considers both the requirements of differentjobs and the circumstances of computing infrastructureTheyhave also put forward a job scheduling algorithm basedon Multiobjective Genetic Algorithm (MO-GA) taking intoaccount the energy consumption and the profits of the serviceproviders [10] In order to reduce the operator cost and toincrease the reliability of the cloud service provider Felleret al have modeled the workload placement problem asan instance of the multidimensional bin-packing (MDBP)problem and have designed a novel nature-inspired algo-rithm based on the Ant Colony Optimization (ACO) meta-heuristics to compute the placement dynamically accordingto the current load [11] Goudarzi and Pedram have consid-ered a multitier cloud computing environment in which theclients have Service Level Agreements (SLAs) and the totalprofit in the system depends on how the system can meetthese SLAsThey have proposed an algorithm based on force-directed search to allocate the resources such as processingmemory requirement and communication resources [12]

In the shared data center environment Nagendram et alhave depicted the resource scheduling problem to a boundedmultidimensional knapsack problem taking into account therequirement dependency amongmultidimensional resources

including memory storage CPU and network bandwidthThen they have presented a Multidimensional resourceintegrated scheduling (MRIS) an inquisitive algorithm toobtain the approximate optimal solution [13] To schedulethe tasks and achieve load balance Tayal has put forward anoptimized algorithm based on the Fuzzy-GA optimizationwhich makes a scheduling decision by evaluating the entiregroup of tasks in the job queue [14] In the private cloudenvironment constructed for e-learning Morariu et al havepresented a workload scheduling algorithm based on geneticalgorithm [15] For the load balancing problem of the VMscheduling in the cloud computing Gu et al have proposeda scheduling strategy on load balancing of VM resourcesbased on genetic algorithm [16] Yamauchi et al proposeda distributed parallel scheduling methodology for MCC anddeveloped a simulator to analyze the bottleneck of MCC [17]

Ant Colony Optimization (ACO) has also been used tobalance the load in cloud environment In [18] Mishra et alhave proposed amethod to utilize theACO for load balancingin cloud environment The routing packets in this environ-ment are treated as the ants in the network Moreover theyreplaced the routing tables in the network nodes by tables ofprobabilities These tables are also called ldquopheromone tablesrdquosince the pheromone strengths used in ACO are representedby these probabilities Every node has a pheromone table forevery possible destination in the network and each table hasan entry for every neighbor The entries in the tables are theprobabilities which influence the antsrsquo selection of the nextnode on the way to their destination node Consequently ateach node the ant should choose the next node toward itsfinal destination node according to the probabilities Afterarriving at a node the ants update the probabilities of thatnodersquos pheromone table entries corresponding to their sourcenode that is ants lay the kind of pheromone associatedwith the node they were launched from They alter the tableto increase the probability pointing to their previous nodeBesides in order to distribute the load among many pathsfrom the source node to the destination node the ants fromone colony will consult the routing tables of other coloniesso as to avoid routing packets to those paths that are highlypreferred by the other groupsThrough thismethod the loadsare separated among many possible paths in the network

Zhu et al considered the task scheduling in cloudenvironment from the perspectives of QoS fulfillment andshortest path [19] Nishant et al have proposed an algorithmfor load distribution of workloads among nodes of a cloud bythe use of ACO Moreover they have presented another loadbalancing algorithm which ensures that there is no conflictof interests based on relocating the tasks among nodes [20]In these works they do not take each taskrsquos profit intoconsideration and cannot maximize the profit of the systemwhich is an import target of the scheduling algorithm for thecommercial mobile cloud environment In grid computingan ACO algorithm is proposed by Suryadevera et al forload balancing which will determine the best resource to beallocated to the jobs based on resource capacity and at thesame time balance the load of entire resources on grid Themain objective of this algorithm is to achieve high throughputand thus increases the performance in grid environment

Journal of Applied Mathematics 3

[21] A review on the load balancing studies for the cloudenvironment is presented in [22]

Different from the scheduling algorithm in cloud envi-ronment the scheduling algorithms forMCC should take theenergy consumption into consideration To make the systemlast longer the scheduling algorithms should balance the loadof the mobile devices to avoid some heavy-loaded nodesleaving the system too early Therefore these schedulingalgorithms for cloud computing cannot be applied to theMCC environment directly In order to bridge this gapwe propose an architecture for MCC and then present ascheduling algorithm for MCC which can maximize theprofit and balance the load of the mobile devices

3 Definition and Architecture

31 The Definition of MCC and Current Proposed Architec-tures The Mobile Cloud Computing Forum defines MCCas follows [23] ldquoMobile cloud computing at its simplestrefers to an infrastructure where both the data storage andthe data processing happen outside of the mobile deviceMobile cloud applications move the computing power anddata storage away from mobile phones and into the cloudbringing applications and mobile computing to not justsmartphone users but a much broader range of mobilesubscribersrdquo Aepona describes MCC as a new paradigmfor mobile applications whereby the data processing andstorage are moved from the mobile device to powerful andcentralized computing platforms located in clouds [24]Thesecentralized applications are then accessed over the wirelessconnection based on a thin native client or web browseron the mobile devices In [25 26] MCC is described as acombination of mobile web and cloud computing which isthe most popular tool for mobile users to access applicationsand services on the Internet Dinh et al defined MCC as anentity that providesmobile users with the data processing andstorage services in clouds [27]

These definitions are mostly descriptive This paper givesthe following definition MCC is a mobile application-oriented computing paradigm in mobile and dynamic envi-ronment which makes use of the resources provided byclouds mobile devices and network facilities to fulfill usersrsquorequirements on QoS quality of experience (QoE) securityand privacy with some particular cost energy and program-ming model and context information

In order to efficiently utilize the available resourcesresearchers have brought forward severalMCC architecturesIn this paper we divide them into four categories In theproposals of the first category mobile devices first offloadapplications to the remote large data centers of the cloudsfrom which the results will be returned the typical proposalsinclude MAUI [28] and CloneCloud [29] In the secondcategory Satyanarayanan et al introduced the Cloudlet entityto the system which is a local service infrastructure logicallyimplemented at the access point of mobile devices andthe mobile devices only have to offload applications to theCloudlet rather than remote data centers [27 30] It shouldbe noted that Cloudlet can reduce the server response latency

since the offloading happens locally most of the time In theproposals of the third category mobile devices collaboratewith each other to run applications without the need to relyon any cloud infrastructureThis sounds like themobile Peer-to-Peer systemandmobile grid computing but different fromthese computing paradigms the typical schemes (such asHyrax [31] Misco [32] and the virtual cloud [33]) of thiscategory adopt the unique characteristics of MCC such asfault tolerant and application partition The typical schemesof the fourth category move the cloud infrastructure closeto the users to improve the timeliness of the service such asMobiCloud [34ndash36]

Figure 1 illustrates the traditional architecture which usesremote cloud infrastructure via the backbone network Asshown in Figure 1 the latency of this architecture consistsof the time spent on the access network the backbonenetwork and the time spent inside the cloud infrastructureIn the Cloudlet architecture as shown in Figure 2 mostof the time the application will not deliver to the remotecloud infrastructure and thus the latency is composed ofthe one-hop time spent on the access network which ismuch lower than those using architecture of Figure 1 [30 37]Under some special conditions Cloudlet cannot handle theoffloaded applications locally and it needs the remote cloudinfrastructurersquos help for processing them The latency underthese conditions approximates the traditional architecturewhich directly uses the remote cloud infrastructure

32 Hybrid Local Mobile Cloud Model In order to providehigh QoS for mobile applications the MCC architectureshould have low response latency Moreover the mobiledevicesrsquo participation for providing their idle computing andsensing capabilities is also very critical for the promotionof the usersrsquo QoE (quality of experience) This is due to thefact that one single mobile devicersquos sensing result can beeasily influenced by its local environment and hence is error-prone while aggregating a fewmobile devicesrsquo sensing resultsabout the area can provide more correct context informationTherefore we have modified the Cloudlet architecture tomake the mobile devices contribute their computing andsensing capabilities like they do in Hyrax [31] and Miscomodels [32] This new mobile cloud computing model iscalled the Hybrid Local Mobile CloudModel (HLMCM) andis illustrated in Figure 3

From Figure 3 we can see that HLMCM consists of aCloudlet and a set of mobile devices The mobile devices areconnected to the Cloudlet via wireless links such asWiFi andWiMAX Similar to the original Cloudlet architecture theCloudlet in HLMCM is logically attached to the access pointof themobile devices to achieve low response latency and themobile devices can offload their mobile applications to theCloudlet However different from Satyanarayananrsquos scheme[30] in HLMCM the mobile devices collaborate with theCloudlet to provide service This designation is based on thefollowing considerations

(1) Mobile devicesrsquo computing storage and sensing ca-pabilities are increasingly becoming powerful How-ever the utilization ratio of these resources is low


Mobile devices

middotmiddotmiddot

Backbonenetwork

Cloudinfrastructure

Figure 1 The architecture that uses the remote cloud infrastructure

Cloudlet

Mobile devices

Backbonenetwork

Cloudinfrastructure

middotmiddotmiddot

Figure 2 The Cloudlet architecture

Cloudlet

Mobile devices

Figure 3 The architecture of the hybrid local mobile cloud model

at most times which means that the mobile devicesusually have idle resources for sharing

(2) The Cloudlet usually only contains a few serversand is much less powerful than the data center ofthe typical large-scale cloud Therefore the mobiledevicesrsquo participation can promote the scalability ofHLMCM

Cloudlet

Mobile devices

(1) (2)

(2)(2)

(4)

(3)(3)

(3)Client

(1)

(1)

(4)

(4)

Client

Client

middotmiddotmiddot

Figure 4 The general working process of HLMCM

(3) The involvement of the mobile devices can helpimprove theQoS provided byHLMCM especially thesensing capabilities

The general working process of HLMCM is shown inFigure 4 and it mainly contains the following four steps

(1) The clients offload part or full of their applications tothe Cloudlet Note that the clients are mobile devices


as well and they can provide service for other devicesrsquomobile applications

(2) The Cloudlet executes the application schedulingalgorithm to offload the applications to a few mobiledevices that are willing to provide resources

(3) The mobile devices handle the applications receivedand send their results to the Cloudlet

(4) The Cloudlet sends the results of the applicationsfrom the mobile devices to the clients

Note that there may be a large number of mobile devicesrequesting for offloading applications to the HLMCMwhosesensibility computing and storage capabilities are usuallymuch less than those of the large cloud infrastructureThere-fore efficient application scheduling algorithm is critical forHLMCM to provide high QoS Moreover the applicationscheduling algorithm should consider the profits of theHLMCM as well as balancing the load of the mobile devicesto make the whole system last longer

4 Model and Algorithm

41Model andProblemStatement InHLMCMenvironmentthe scheduling algorithm is in charge of allocating theoffloaded applications from the mobile devices to the serviceproviders including the Cloudlet and119898minus1 mobile devices inthe system For ease of description the service provider willbe referred to as provider in the following analysis

Assume the dimension of the resources is 119889 and eachproviderrsquos resources can be expressed as a vector 119888

119894=

(1198881

119894 119888

119889

119894) in which 119888

119896

119894is the 119896th dimensional resource that

the provider 119894 has Assume that the set of applications thatarrives at some particular time slot is 119868 = 1 2 119899 andthe value of the application 119895 is 119901

119895 119895 = 1 2 119899

The resources consumed by application 119895 when executedon provider 119894 are a vector 119903

119894119895= (1199031

119894119895 119903119889

119894119895) 119894 = 1 2 119898

Assume that each application can only be executed on oneprovider and cannot be further partitioned Once an appli-cation is executed successfully on some provider HLMCMwill receive the value of this application as its profit Herethe scheduling target is to maximize the total profits ofHLMCM with the constraint of resource capacity of eachservice provider Therefore the scheduling problem can beformulated as follows

Maximize119899

sum

119895=1

119901119895

119898

sum

119894=1

119909119894119895

subject to119899

sum

119895=1

119903119894119895119909119894119895le 119888119894 119894 = 1 2 119898

119898

sum

119894=1

119909119894119895le 1 119895 = 1 2 119899

119909119894119895isin 0 1 119895 = 1 2 119899

(1)

From (1) we can see that this can be seen as a multidi-mensional 0-1 knapsack problem and is NP-hard

Besides in order to make HLMCM last longer theapplications should be uniformly executed on the mobiledevices This will make the devices consume their energyevenly to avoid the phenomenon that some mobile deviceswith heavy load consume their energy too early and have toleave the system

For some particular provider 119894 the load of its 119896thdimensional resource is defined as

119871119894119896=

sum119899

119895=1119903119896

119894119895119909119894119895

119888119896

119894

(2)

1198941015840s load119871

119894is defined as themean value of all its 119889-dimensional

resourcesrsquo loads that is

119871119894=

sum119889

119896=1119871119894119896

119889

(3)

42 HACAS Algorithm In order to solve this problemthis paper proposes a scheduling algorithm based on thehybrid ant colony algorithm which has been widely usedto solve complex combinatorial optimization problems [38]The following part of this section presentsHACAS algorithmwhich contains the pheromone value and its update modellocal heuristic value application scheduling probability tabulist and the bulletin board and provider selection scheme

421 Pheromone Value and Its Update Model The appli-cation scheduling problem in this paper belongs to thesubset problem [39] that is given a set 119878 which contains119899 applications for scheduling and the evaluation function119891( ) the target is to select the best subset of 119878 to maximizeor minimize 119891( ) There may be more than one evaluationfunctions while this section focuses on the case where thereis only one evaluation function In this situation the order ofthe selected applications is not important and the pheromonevalue is placed on the application rather than the connectionamong the applications which means that applications witha higher pheromone value can better satisfy the requirementsof the evaluation function When the specific condition ismet such as a partial solution with some particular lengthis obtained the pheromone value needs to be updated Theupdate process includes two parts Firstly the pheromonevalue of each application is reduced by a certain percentage toemulate the real-life behavior of evaporation of pheromonecount over time Secondly the pheromone value incrementlaid by the new partial solutions of the ants will be addedAssume that the pheromone value on application 119894 at time 119905 is120591119894(119905) then at the next update time 1199051015840 the value is updated to

120591119894(1199051015840)

120591119894(1199051015840) = (1 minus 120588) 120591

119894 (119905) + Δ120591

119894(119905 1199051015840) (4)

where 0 lt 120588 le 1 is a coefficient which represents pheromoneevaporation Δ120591

119894(119905 1199051015840) is the pheromone value increment

obtained from all the antsrsquo partial solutions that is

Δ120591119894(119905 1199051015840) =

119902

sum

119895=1

Δ120591119895

119894(119905 1199051015840) (5)


where 119902 is the number of the ants and Δ120591119895

119894(119905 1199051015840) is the

pheromone value laid on application 119894 by ant 119895rsquos partialsolution at time 1199051015840 and is defined as

Δ120591119895

119894(119905 1199051015840)

=

119866 (119891 (119878119895(1199051015840))) if 119895th ant incoporates application 119894

0 otherwise(6)

where 119878119895(1199051015840) is the partial solution of ant 119895 at time 119905

1015840 and119891(119878119895(1199051015840)) is the value of the evaluation function of this

solution To maximize the profit the evaluation is defined as

119891 (119878119895(1199051015840)) = sum

119896isin119878119895(1199051015840)

119901119896 (7)

that is the total value of the applications belongs to 119878119895(1199051015840)

The function 119866 in (4) depends on the problem in this paperit is defined as 119866(119891(119878

119895(1199051015840))) = 119876119891(119878

119895(1199051015840)) in which 119876 is a

parameter of the method

422 Local Heuristic Value The positive feedback of the antcolony algorithm is usually combinedwith some local heuris-tic schemes to accelerate the search process In HLMCM thelocal heuristic scheme needs to consider the profits of theapplications as well as the resources they consume

Let 119896(119895 119905) = sum

119897isin119878119895(119905)119903119896119897

be the resources consumedon provider 119896 by the partial solution 119878

119895(119905) constructed by

ant 119895 Then the remaining resources on provider 119896 are120574119896(119895 119905) = 119888

119896minus119896(119895 119905) = (120574

1

119896(119895 119905) 120574

119889

119896(119895 119905)) in which 120574119894

119896(119895 119905)

is the remaining amount of the 119894th dimensional resourceThe tightness of application ℎ on provider 119896 on the 119894thdimensional resource is defined as

100381610038161003816100381610038161003816100381610038161003816

119903119894

119896ℎ

120574119894

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

(8)

that is the ratio between 119903119894

119896ℎ the amount of provider 119896rsquos

resource consumed by application ℎ and 120574119894

119896(119895 119905) Moreover

the tightness of application ℎ on provider 119896 is defined as

120575119896ℎ

(119895 119905) =

100381610038161003816100381610038161003816100381610038161003816

1199031

119896ℎ

1205741

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

+ sdot sdot sdot +

1003816100381610038161003816100381610038161003816100381610038161003816

119903119889

119896ℎ

120574119889

119896(119895 119905)

1003816100381610038161003816100381610038161003816100381610038161003816

(9)

In (9) the tightness of the 119889-dimensional resources isconverted into a single value which comprehensively consid-ers all dimensions of the resources

The average tightness on all providers in case of applica-tion ℎ being chosen to be included in 119878

119895(119905) is

120575ℎ(119895 119905) =

sum119898

119896=1120575119896ℎ

(119895 119905)

119898

(10)

In order to consider the application ℎrsquos profit as well asits resource requirement the local heuristic value 120578

ℎ(119878119895(119905)) is

defined as

120578ℎ(119878119895 (119905)) =

119901ℎ

120575ℎ(119895 119905)

(11)

423 Application Scheduling Probability After obtaining thepheromone value and local heuristic value on each appli-cation the probability that ℎ has to be selected as the nextscheduling application of 119878

119895(119905) is

119875119895

ℎ(t)

=

[120591ℎ (119905)]120572[120578ℎ(119878119895 (119905))]

120573

sum119896isinallowed119895(119905)

[120591119896 (119905)]120572[120578119896(119878119895 (119905))]

120573 if ℎ isin allowed

119895 (119905)

0 otherwise(12)

where allowed119895(119905) sube 119878 minus 119878

119895(119905) is the set of the remaining

schedulable applications From (12) we can see that the morepheromone value and local heuristic value an application hasthe higher the probability will be scheduled

424 Tabu List and the Bulletin Board A data structurecalled a tabu list is associated to each ant in order to avoidthat ant from scheduling an application more than onceThislist tabu

119895(119905) maintains a set of scheduled applications up to

time 119905 by ant 119895 Let the applications that can be executed onat least one of the providers be 119865 then we have allowed

119895(119905) =

119865 cap ℎ | ℎ notin tabu119895(119905)

In addition we set a bulletin board to record the bestsolution up to time 119905 with which each ant can compare itsown solution If its solution is better than the best one it willupdate the best one with its solution

425 Provider Selection Scheme After deciding the sched-uled application there is usually more than one providerwho have sufficient resources to execute the applicationNote that traditional hybrid algorithm only focuses on theapplication scheduling probability In order to balance theload of the providers we take the provider selection schemeinto consideration in this section

For some particular feasible provider 119894 the load of its119896th dimensional resource is 119871

119894119896as defined in (2) After

adding application ℎ the expected load of its 119896th dimensionalresource is

1198711015840

119894119896= 119871119894119896+

119903119896

119894ℎ

119888119896

119894

(13)

The expected load of provider 119894 is defined as

1198711015840

119894=

sum119889

119896=11198711015840

119894119896

119889

(14)

This means that if is ℎ executed on provider 119894 119894rsquos expectedload will be 1198711015840

119894

In order to balance the load of all the providers theprovider with the lowest expected load will be selected toexecute application ℎ

426 Algorithm The HACAS algorithm is illustrated inAlgorithm 1 The parameters needed to be settled include 119862


(1) Initialize 119903119894119895 119888119894 119901119895 1 le 119894 le 119898 1 le 119895 le 119899 119902 = 119899 number

of cycles 119862 120591119895(0) = 1119902 1 le 119895 le 119902 tabu list = []

best solution = 0 application provider 120572 = 120573 = 1 120588 = 03 119876 = 1

(2) for (119905 = 1 119905 lt= 119862 t++)(3) for (119895 = 1 119895 lt 119902 j++)(4) random first = 0(5) while 119886119897119897119900119908119890119889

119895(119905) = 0

(6) if random first == 0(7) Select the first scheduled application randomly(8) random first = 1(9) else(10) Select the scheduled application ℎ according to (12)(11) end if(12) Calculate the expected loads of all feasible providers according to (14)(13) Rank the feasible providers according to their expected loads in an increasing order(14) The provider with the lowest expected load is selected for ℎ(15) Add ℎ to 119878

119895(119905) and the tabu list

(16) end while(17) Calculate 119891(119878

119895(119905)) which is the object function of the generated solution of ant 119895

(18) if 119891(119878119895(119905)) gt best solution

(19) best solution = 119891(119878119895(119905))

(20) Save ant jrsquos solution in application provider(21) end if(22) end for(23) Calculate the incremental pheromone on each application according to (5)(24) Clear the tabu list for each ant(25) end for(26) print best solution(27) print application provider

Algorithm 1 The HACAS algorithm

120572 120573 120588 119902 119876 119903119894119895 119888119894 and 119901

119895 The initial pheromone trail value

on each application is set to be 1119902Step 1 initiates the parameters Step 4 introduces a variable

random first to enable each ant to randomly select its firstscheduling application Steps 5 to 16 present the solution-searching process of an ant Firstly Steps 6 to 11 select the nextscheduled application that is randomly selecting the firstone and then scheduling other applications according to theprobabilities calculated in (12) Secondly Step 12 calculatesthe expected loads of all feasible providers according to(14) Step 13 ranks the feasible providers according to theirexpected loads in an increasing order Step 14 selects theprovider with the lowest expected load for ℎ and finally Step15 adds the newly scheduled application to the partial solutionas well as the tabu list At the end of Step 16 each ant hasfound its solution 119878

119895(119905) Step 17 calculates 119891(119878

119895(119905)) If 119891(119878

119895(119905))

is larger than the best solution in the bulletin board then Step19 will assign119891(119878

119895(119905)) to best solution and save the scheduling

results into application provider After Step 22 all the antshave finished searching for the solutions and one cycle isfinished Step 23 calculates the pheromone value incrementaccording to (5) Step 24 clears the tabu lists of the ants Steps26 to 27 print the best solution found at the 119862th cycle and thescheduling results

5 Simulation Results and Discussion

51 Experimental Settings

511 Experimental Environment To evaluate the perfor-mance of the algorithms proposed in this paper we haveconducted many simulation experiments whose parametersare listed in Table 1

In this simulation the dimension of the resources is 2Both the first and the second dimensional resources pos-sessed by each provider obey uniform distribution in theinterval [119886

1 1198862] There are 119898 providers and 119899 applications

in the system At time 119905 these applications arrive simultane-ouslyThe applicationsrsquo resource consumption of the first andthe second dimensional resources on some provider obeysuniform distribution in the intervals [119886

3 1198864] and [119886

5 1198866]

respectively Moreover the applicationsrsquo profits obey uniformdistribution in the interval [119886

7 1198868]The number of cycles (ie

119862) is set to be 10 The default parameters are listed in Table 1Based on these parameters a series of simulation exper-

iments has been conducted The experiments contain 10cycles In each cycle each ant searches for its own schedulingresult based on the method presented in the schedulingalgorithm in the above section At the end of each cycle


Table 1 Simulation parameters

Parameter Default Value119899 1001198861

311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1

the pheromone value on the applications will be updated andthe bulletin board is used to record the best scheduling result

512 Comparison Benchmark and Metrics We evaluateHACAS algorithm from two different angles Firstly in orderto validate the effectiveness of HACAS algorithm we com-pare it with the First-Come-First-Served (FCFS) algorithmIn FCFS the applications are scheduled according to theirarrival order and the providers are selected randomly fromthose who can execute the application The profit of thescheduling algorithm which is defined as the total profits ofall the applications scheduled by the algorithm is chosen asthe metrics to compare them

Secondly in order to evaluate the provider selectionscheme of HACAS algorithm a scheduling algorithm withrandom provider selection is adopted as the comparisonbenchmark in which steps 12ndash14 in Algorithm 1 are replacedwith the following step

(12) Randomly select the service provider for ℎ from thosefeasible providers

The scheduling algorithm with this modification is calledtheHybridAntColony algorithmbasedApplication Schedul-ing with Random Provider Selection (HACASRPS) algo-rithm

For the solution of ant 119895 at the 119896th cycle let provider 119894rsquosload be 119871119895119896

119894 The mean value (120583119895

119896) and the standard deviation

(120590119895119896) of all the 119898 providersrsquo loads at the 119896th cycle of ant 119895rsquos

solution are defined as

120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895

119896reflects the deviation of all the providersrsquo loads of ant 119895rsquos

solution at the 119896th cycle Then at the end of the 119896th cyclethe mean value of the standard deviation of all the providersrsquoloads of all the 119902 antsrsquo solution is defined as

120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)

In order to simplify the expression 120583119896120590will be referred

to as the load variation of the scheduling algorithm at the119896th cycle Then the average load variation of the schedulingalgorithm of all the simulation cycles can be defined as

120583120590=

sum119862

119896=1120583119896

120590

119862

(17)

We define the average load of a scheduling algorithm in119896th cycle by

120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)

Then the average load of a scheduling algorithm is definedby

120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896

120590are selected as the metrics to evaluate the

effectiveness of the provider selection scheme of the HACASalgorithm

52 Experimental Results

521 The Profits With the parameters in Table 1 the profitof FCFS algorithm is 1324 The profits of HACASRPS andHACAS algorithms are shown in Figure 5

From Figure 5 we can see that as cycle increases theprofits of both HACASRPS and HACAS algorithms increaseThis is due to the fact that as cycle increases both theHACASRPS and HACAS algorithms will find more prof-itable scheduling results which will bring more profits Atthe end of the 10th cycle the profits of HACASRPS andHACAS algorithms are 1747 and 1794 respectively whichare more than 30 higher than that of FCFS algorithmThis phenomenon can be attributed to the local heuristicvalue adopted by both algorithms which enables them toschedule those applications which consume less resourceswhile bringing more profits with preference

522 Load Balancing Balancing the load of all the providersto make the system last longer is an important target ofHACAS algorithmrsquos provider selection scheme This sectioninvestigates the effectiveness of this selection scheme andcompares it with random provider selection method adoptedin HACASRPS algorithm

With the parameters in Table 1 the average loads ofHACAS and HACASRPS algorithms are 0800 and 0779


1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS

Figure 5 The profits of HACASRPS and HACAS algorithms Thehorizontal axis represents the simulation cycle the longitudinal axisrepresents the profit of the algorithm

1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583

Figure 6 The average load of HACAS and HACASRPS algorithmsin different simulation cycles 119896 is the simulation cycle and 120583

119896

120583is the

average load of the algorithm in the 119896th cycle

respectively The former is slightly higher than the latterwhich is due to the fact that HACAS schedules more appli-cations than HACASRPS algorithm as shown in Figure 5The average load of HACAS and HACASRPS algorithms indifferent simulation cycles (as defined in (18)) are shown inFigure 6 From Figure 6 we can see that the average load ofboth algorithms stays stable as cycle increases

Figure 6 tells us that the average loads of HACAS andHACASRPS algorithms are 08 and 078 respectively Wefurther investigate the load variations of both algorithms

1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590

Figure 7 The load variations of HACAS and HACASRPS algo-rithms in different simulation cycles 119896 is the simulation cycle and120583119896

120590is the load variation of the algorithm in the 119896th cycle

in different simulation cycles and the results are shown inFigure 7

From Figure 7 we can see that the load variations of thesetwo algorithms maintain stable as simulation cycle increasesMoreover the load variation of HACAS algorithm is muchlower than that of HACASRPS algorithm In some particularcycle HACAS algorithmrsquos load variation is about 13 lowerthan that of the HACASRPS algorithm This is because theprovider selection scheme adopted in HACAS algorithmtakes the providersrsquo load into account when choosing theprovider for the scheduled applications This means thatthe provider selection scheme in HACAS algorithm caneffectively balance the load of the providers more effectively

523 Parametersrsquo Influence In the above experiments thenumber of the applications for scheduling is large and theload of the providers is high This section shows the resultswhen the number of the applications for scheduling isrelatively small Concretely speaking we set 119898 = 20 with119899 = 30 in this experiment

Firstly we investigate the load of all the providers of the10th antrsquos solution at the 5th cycle and the results are shownin Figure 8

From Figure 8 we can see that the load of the providersin HACASRPS algorithm fluctuates in a much wider rangethan that of HACAS algorithm In HACASRPS algorithmthe load of the 7th provider is almost 08 while the loadsof the 16th and the 18th provider are 0 In contrast the loadof the providers in HACAS algorithm is mostly between 03and 06The notable differences of the resource consumptionamong different applications (from 10 to 30) have led to thedifferences among the loads of the providers

Then we show the standard deviation of all the providersrsquoloads of the antrsquos solution in the 5th cycle in Figure 10 Notethat there are 30 ants in the algorithm since 119902 = 119899


0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS

Figure 8 The load of all the providers of the 10th antrsquos solution atthe 5th cycle

0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion

Figure 9 The standard deviation of all the providersrsquo loads of theantrsquos solution in the 5th cycle

Figure 9 reveals that the standard deviations of all theprovidersrsquo loads of the antrsquos solution of HACAS algorithm aremuch lower than those of the HACASRPS algorithm

Similar to Figure 7 Figure 10 further reveals the loadvariations of HACAS andHACASRPS algorithms in differentsimulation cycles when 119899 = 30 from which we canderive similar observations with those drawn from Figure 7Moreover in some particular cycle in Figure 10 HACASalgorithmrsquos load variation is about 60 lower than that of theHACASRPS algorithm Therefore after combining Figures7 and 10 we know that the effectiveness of the provider

1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS



selection scheme of the HACAS algorithm becomes moreprominent when the load of the system is low

53 Discussion and Application Scenario

531 Discussion As shown in Section 52 the performanceof HACAS algorithm is better than that of FCFS andHACASRPS algorithms This phenomenon can be attributedto HACAS algorithmrsquos pheromone value and its updatemodel application scheduling model and provider selec-tion scheme Concretely speaking pheromone value and itsupdatemodel makeHACAS learn from its historical decisionto raise the profit of the system Moreover applicationscheduling model takes the pheromone value as well asapplicationrsquos resource consumption into consideration andcan help HACAS algorithm choose those applications withthe highest profit and the lowest resource consumption Lastbut not the least the provider selection scheme can balancethe load of the mobile devices which is very important tomake the system last longer

In addition the following section shows the reason whywe propose HLMCM and choose simulation parameters

532 The Rationale behind Proposing HLMCM We put for-wardHLMCMsincewe cannot fulfill usersrsquo QoE requirementthrough simply extending the cloud infrastructure or theCloudlet entityrsquos computing or storage capacity For instancein a cooperation sensing environment the accurate sensingresult can only be drawn through jointly using many mobiledevicesrsquo diverse sensing results (such as location orientationand temperature) [3] Besides in some circumstances com-munication using backbone links may not be always presentin some isolated areas during rescue missions uprisingsand disaster scenarios [37 40] Under these circumstance


themobile devices can only search for the local infrastructuresuch as the Cloudlet entity which is easy to implement

533 Rationale for Choosing the Simulation Parameters Pre-sented in Table 1 In the simulation part a mobile device isassumed to have at least enough resources to run an offloadedapplicationThis is also the basic assumption in the knapsackproblem that the maximum volume of the objects (in thispaper 30) is smaller than the minimum capacity of the knap-sacks (in this paper 31) Moreover we notice that in Table 1the resources possessed by each provider obey uniformdistri-bution in the interval [119886

1 1198862] while 119886

1= 31 and 119886

2= 100This

setting is attributed to following observation The resourcesin mobile devices mainly contain CPU storage and sensorsand so forth The process frequency of mainstream smart-phonesrsquo CPU ranges from 800MHz to 2GHz Moreover thestorage capacity of the mainstream smartphones ranges from16GB to 64GB The number of sensors (including proximitysensor Global Positioning System accelerometer compassand gyros) on each smartphones ranges from 2 to 6 If wetreat these devices as general resources then we know thatthe volume difference of the resource possessed by the devicesis about 3 times Therefore in Table 1 the volume differenceof the resource processed by the devices is also set to bearound 3 Based on this consideration the maximum and theminimum resources possessed by each device in Table 1 areset to be in the interval (31 100) The profit and the energyconsumption difference of the applications are based on theobservations and current studies [41] on the mainstreamapplications (such as game web browser etc) in the app store(such as the iPhone App store)The other parameters such as120572 120573 120588 and 119876 are decided by the default parameters used bythe hybrid ant colony algorithm

In this paper the parameters used in Table 1 can validatethat HACAS algorithm is effective under heavy load envi-ronment (ie the applicationsrsquo total resource requirementsexceed the resources possessed by the system) Moreoverin the section ldquoParametersrsquo influencerdquo 119899 is set to be 20to evaluate the effectiveness of HACAS under light loadenvironment Notice that these parameters can be adjustedas the simulation needs and the proposed HACAS algorithmcan adapt to various circumstances

534 Application Scenario The case for mobile cloud com-puting can be argued by considering the unique advantagesof empoweredmobile computing and a wide range of poten-tial mobile cloud applications have been recognized in theliterature These applications fall into different areas such asimage processing natural language processing sharing GPSsharing Internet access sensor data applications queryingcrowd computing and multimedia search A survey of thepossible applications can be referred to [42]

Here we show an application scenario that appliesMCC for disaster rescue In a disaster-stricken environment(such as hurricane tsunamim and earthquake) the com-munication infrastructure can be seriously damaged if notcompletely destroyed Moreover many roads could also getblocked These damages make it difficult for the rescuers to

find the location of wounded people or even to get a globalview of the disaster area Under such circumstances therescuers can deploy some emergency communication facili-ties (such as communication vehicles) with Cloudlet entitiesThen the mobile devices (especially the smartphones) nearthe vehicles can communicate with each other report thelocation of the wounded people and upload the pictures orvideos around themselves for processing to help the rescueprocess Moreover the devices also need the Cloudlet toprovide them with the needed information (such as thelatest map in the area) and to process their images capturedAmong these requests searching for wounded or missingpersons is one of the most critical yet excruciating tasks(applications) Therefore the HLMCM which is composedby the Cloudlet and the mobile devices can run HACASalgorithm to effectively schedule these applications

6 Conclusion and Future Work

Efficiently exploiting the mobile devicesrsquo idle computingstorage and sensing capacity can greatly improve the qualityof service provided by mobile cloud computing (MCC) Toachieve this goal an appropriate architecture of MCC anda dedicated scheduling algorithm are considered importantTo address these issues this paper contributes in severalways by providing suitable definitions of critical aspects andproposing efficient algorithms and approaches

Our simulation results have revealed that when the loadof the system is heavy HACAS algorithm can select thoseapplications with maximum profit and minimum energyconsumption With the parameters setting in the simulationthe profit of HACAS algorithm is about 30 higher thanthat of FCFS algorithm Besides when the load of the systemis light the provider selection scheme adopted in HACAScan effectively balance the load of the devices in the systemConcretely speaking HACAS algorithmrsquos load variation isabout 60 better than that of the random provider selectionscheme Moreover in the discussion part of the paper wehave presented the rationale for devising HLMCM andfor selecting those simulation parameters In simple termsHLMCM can effectively use mobile devicesrsquo diverse sensingresults which cannot be realized by extending the cloudinfrastructure or the Cloudlet entityrsquos service capabilityMoreover the simulation parameters are chosen based onthe observation of mainstream smartphones The discussionsection also gives an application scenario where HACASalgorithm is used for disaster rescue

In the future we will further extend the schedulingalgorithm by considering the dynamic resource requirementof the applications

Acknowledgments

This research was supported in part by the Major State BasicResearch Development Program of China (973 Program)no 2012CB315806 National Natural Science Foundation ofChina under Grant no 61070173 National Natural ScienceFoundation of China under Grant no 61201216 Jiangsu


Province Natural Science Foundation of China under Grantno BK2010133 Jiangsu Province Natural Science Foundationof China under Grant no BK2009058 and China Postdoc-toral Science Foundation funded project under Grant no201150M1512

References

[1] IDC Worldwide smartphone market expected to grow 55in 2011 and approach shipments of one billion in 2015according to IDC httpwwwidccomgetdocjspcontainer-Id=prUS22871611

[2] MConti S Chong S Fdida et al ldquoResearch challenges towardsthe Future Internetrdquo Computer Communications vol 34 no 18pp 2115ndash2134 2011

[3] D Yang G Xue X Fang and J Tang ldquoCrowdsourcing to smart-phones incentivemechanismdesign formobile phone sensingrdquoin Proceedings of the 18th Annual International Conference onMobile Computing and Networking (Mobicom rsquo12) pp 173ndash184ACM 2012

[4] L Duan T Kubo K Sugiyama J Huang T Hasegawa and JWalrand ldquoIncentive mechanisms for smartphone collaborationin data acquisition and distributed computingrdquo in Proceedingsof the Annual IEEE International Conference on ComputerCommunications (INFOCOM rsquo12) pp 1701ndash1709 Orlando FlaUSA March 2012

[5] Y-K Kwok K Hwang and S Song ldquoSelfish grids game-theoreticmodeling andNASPSA benchmark evaluationrdquo IEEETransactions on Parallel and Distributed Systems vol 18 no 5pp 621ndash636 2007

[6] R Subrata A Y Zomaya and B Landfeldt ldquoA cooperative gameframework for QoS guided job allocation schemes in gridsrdquoIEEE Transactions on Computers vol 57 no 10 pp 1413ndash14222008

[7] P Ghosh K Basu and S K Das ldquoA game theory-based pricingstrategy to support singlemulticlass job allocation schemes forbandwidth-constrained distributed computing systemsrdquo IEEETransactions on Parallel and Distributed Systems vol 18 no 3pp 289ndash306 2007

[8] G Danezis S Lewis and R Anderson ldquoHow much is locationprivacy worthrdquo in Proceedings of Workshop on the Economics ofInformation Security Series (WEIS rsquo05) 2005

[9] J-S Lee and B Hoh ldquoSell your experiences a market mecha-nism based incentive for participatory sensingrdquo in Proceedingsof the 8th IEEE International Conference on Pervasive Computingand Communications (PerCom rsquo10) pp 60ndash68 April 2010

[10] J Liu X Luo X Zhang F Zhang and B Li ldquoJob schedulingmodel for cloud computing based on multi-objective geneticalgorithmrdquo IJCSI International Journal of Computer ScienceIssues vol 10 no 1 2013

[11] E Feller L Rilling and C Morin ldquoEnergy-aware ant colonybased workload placement in cloudsrdquo in Proceedings of the 12thIEEEACM International Conference on Grid Computing (Gridrsquo11) pp 26ndash33 September 2011

[12] H Goudarzi and M Pedram ldquoMulti-dimensional SLA-basedresource allocation for multi-tier cloud computing systemsrdquo inProceedings of the IEEE 4th International Conference on CloudComputing (CLOUD rsquo11) pp 324ndash331 July 2011

[13] S Nagendram J Vijaya Lakshmi and D Venkata NarasimhaRao ldquoEfficient resource scheduling in data centers usingMRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 pp 764ndash769 2011

[14] S Tayal ldquoTask scheduling optimization for the cloud computingsystemsrdquo International Journal of Adcanced Engineering Sciencesand Technologies vol 5 no 2 pp 111ndash115 2011

[15] O Morariu C Morariu and T Borangiu ldquoA genetic algorithmfor workload scheduling in cloud based e-Learningrdquo in Pro-ceedings of the 2nd InternationalWorkshop on Cloud ComputingPlatforms (CloudCP rsquo12) ACM April 2012

[16] J Gu J Hu T Zhao and G Sun ldquoA new resource schedulingstrategy based on genetic algorithm in cloud computing envi-ronmentrdquo Journal of Computers vol 7 no 1 pp 42ndash52 2012

[17] H Yamauchi K Kurihara T Otomo Y Teranishi T Suzukiand K Yamashita ldquoEffective distributed parallel schedulingmethodology for mobile cloud computingrdquo in Proceedings ofthe 17th Workshop on Synthesis and System Integration of MixedInformation Technologies (SASIMI rsquo12) pp 516ndash521 2012

[18] R Mishra and A Jaiswa ldquoAnt colony optimization a solutionof load balancing in cloudrdquo International Journal of Web ampSemantic Technology vol 3 no 2 2012

[19] L Zhu Q Li and L He ldquoStudy on cloud computing resourcescheduling strategy based on the ant colony optimizationalgorithmrdquo IJCSI International Journal of Computer Science vol9 no 5 2012

[20] K Nishant P Sharma V Krishna et al ldquoLoad balancing ofnodes in cloud using ant colony optimizationrdquo in Proceedingsof the 14th International Conference on Computer Modelling andSimulation (UKSim rsquo12) pp 3ndash8 March 2012

[21] S Suryadevera J Chourasia S Rathore and A JhummarwalaldquoLoad balancing in computational grids using ant colonyoptimization algorithmrdquo International Journal of Computer ampCommunication Technology vol 3 no 3 2012

[22] N J Kansal and I Chana ldquoCloud load balancing techniquesa step towards green computingrdquo IJCSI International Journal ofComputer Science vol 9 no 1 2012

[23] httpwwwmobilecloudcomputingforumcom[24] White Paper Mobile Cloud Computing Solution Brief AE-

PONA November 2010[25] J H Christensen ldquoUsing RESTful web-services and cloud

computing to create next generation mobile applicationsrdquo inProceedings of the 24th Annual ACM Conference on Object-Oriented Programming Systems Languages and Applications(OOPSLA rsquo09) pp 627ndash633 October 2009

[26] L Liu R Moulic and D Shea ldquoCloud service portal for mobiledevice managementrdquo in IEEE International Conference on E-Business Engineering (ICEBE rsquo10) pp 474ndash478 January 2011

[27] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications and Mobile Computing 2012

[28] E Cuervoy A BalasubramanianD-K Cho et al ldquoMAUImak-ing smartphones last longer with code offloadrdquo in Proceedingsof the 8th Annual International Conference on Mobile SystemsApplications and Services (MobiSys rsquo10) pp 49ndash62 June 2010

[29] B-G Chun and P Maniatis ldquoAugmented smartphone applica-tions through clone cloud executionrdquo in Proceedings of the 12thWorkshop on Hot Topics in Operating Systems (HotOS XII rsquo09)Monte Verita Switzerland 2009

[30] M Satyanarayanan P Bahl R Caceres andNDavies ldquoThe casefor VM-based cloudlets in mobile computingrdquo IEEE PervasiveComputing vol 8 no 4 pp 14ndash23 2009

[31] E E Marinelli Hyrax cloud computing on mobile devices usingMapReduce [MS thesis] Carnegie Mellon University 2009


[32] A Dou V Kalogeraki D Gunopulos T Mielikainen and V HTuulos ldquoMisco a MapReduce framework for mobile systemsrdquoin Proceedings of the 3rd International Conference on PErvasiveTechnologies Related to Assistive Environments (PETRA rsquo10)ACM June 2010

[33] G Huerta-Canepa and D Lee ldquoA virtual cloud computing pro-vider for mobile devicesrdquo in Proceedings of the 1st ACM Work-shop on Mobile Cloud Computing amp Services Social Networksand Beyond (MCS rsquo10) New York NY USA June 2010

[34] DHuang X ZhangMKang and J Luo ldquoMobiCloud buildingsecure cloud framework for mobile computing and communi-cationrdquo in Proceedings of the 5th IEEE International Symposiumon Service-Oriented System Engineering (SOSE rsquo10) pp 27ndash34June 2010

[35] T Xing D Huang S Ata and D Medhi ldquoMobiCloud a geo-distributedmobile cloud computing platformrdquo in Proceedings ofthe 8th International Conference on Network and Service Man-agement (CNSM rsquo12) Las Vegas Nev USA October 2012

[36] Q Liu X Jian JHuH Zhao and S Zhang ldquoAnoptimized solu-tion for mobile environment using mobile cloud computingrdquoin Proceedings of the 5th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo09) pp 1ndash5 September 2009

[37] D Fesehaye Y Gao K Nahrstedt and G Wang ldquoImpact ofcloudlets on interactivemobile cloud applicationsrdquo in IEEE 16thInternationa Enterprise Distributed Object Computing Confer-ence (EDOC rsquo12) pp 123ndash132 2012

[38] M Dorigo G Di Caro and LM Gambardella ldquoAnt algorithmsfor discrete optimizationrdquo Artificial Life vol 5 no 2 pp 137ndash172 1999

[39] G Leguizamon and Z Michalewicz ldquoA new version of ant sys-tem for subset problemsrdquo in Proceedings of the Congress onEvolutionary Computation (CEC rsquo99) vol 2 p 1464 1999

[40] H Mehendale A Paranjpe and S Vempala ldquoLifenet a flexiblead hoc networking solution for transient environmentsrdquo ACMSIGCOMMComputer Communication Review vol 41 no 4 pp446ndash447 2011

[41] Y Cui X Ma H Wang I Stojmenovic and J Liu ldquoA survey ofenergy efficientWireless transmission and modeling in mobilecloud computingrdquoMobileNetworks andApplications vol 18 no1 pp 148ndash155 2012

[42] N Fernando S W Loke and W Rahayu ldquoMobile cloud com-puting a surveyrdquo Future Generation Computer Systems vol 29pp 84ndash106 2013

Submit your manuscripts athttpwwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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OptimizationJournal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


attempt to utilize the cloud infrastructure as well as themobile devicesrsquo idle CPUs or sensing capacities to achievehighQoSHowever offloading to remote cloud infrastructurewill introduce long response latency Hence to reduce theresponse latency the offloaded applications should be han-dled by local cloud infrastructure which usually has fewerresources than those of the remote ones Therefore how toefficiently schedule the limited resources while fulfilling therequirements of a large number of offloaded applications is acritical problem for MCC to address

In this paper we first give the definition of MCC anddivide the recently proposed architectures into four ca-tegories Secondly Hybrid Local Mobile Cloud Model(HLMCM) is put forward after combining the advantages ofcurrent proposals such as Cloudlet and Hyrax Thirdly weformulate the application scheduling problems in HLMCMand bring forward the Hybrid Ant Colony algorithm basedApplication Scheduling (HACAS) algorithm Finally theeffectiveness of HACAS algorithm is validated by simulationexperiments

The rest of the paper is organized as follows Section 2summarizes related work Section 3 gives the definition ofMCC and introduces the HLMCM Section 4 formulatesthe application scheduling problem and proposes HACASalgorithm Simulation experiments and results are shown inSection 5 Finally we conclude our main work and presentfurther research directions in Section 6

2 Related Work

Application scheduling in cloud infrastructure has attractedmuch attention in recent years In fact the applicationscheduling and load balancing inMCC are burgeoning areasLiu et al have established a macroscopic scheduling modelwith cognition and decision components for the cloud com-puting which considers both the requirements of differentjobs and the circumstances of computing infrastructureTheyhave also put forward a job scheduling algorithm basedon Multiobjective Genetic Algorithm (MO-GA) taking intoaccount the energy consumption and the profits of the serviceproviders [10] In order to reduce the operator cost and toincrease the reliability of the cloud service provider Felleret al have modeled the workload placement problem asan instance of the multidimensional bin-packing (MDBP)problem and have designed a novel nature-inspired algo-rithm based on the Ant Colony Optimization (ACO) meta-heuristics to compute the placement dynamically accordingto the current load [11] Goudarzi and Pedram have consid-ered a multitier cloud computing environment in which theclients have Service Level Agreements (SLAs) and the totalprofit in the system depends on how the system can meetthese SLAsThey have proposed an algorithm based on force-directed search to allocate the resources such as processingmemory requirement and communication resources [12]

In the shared data center environment Nagendram et alhave depicted the resource scheduling problem to a boundedmultidimensional knapsack problem taking into account therequirement dependency amongmultidimensional resources

including memory storage CPU and network bandwidthThen they have presented a Multidimensional resourceintegrated scheduling (MRIS) an inquisitive algorithm toobtain the approximate optimal solution [13] To schedulethe tasks and achieve load balance Tayal has put forward anoptimized algorithm based on the Fuzzy-GA optimizationwhich makes a scheduling decision by evaluating the entiregroup of tasks in the job queue [14] In the private cloudenvironment constructed for e-learning Morariu et al havepresented a workload scheduling algorithm based on geneticalgorithm [15] For the load balancing problem of the VMscheduling in the cloud computing Gu et al have proposeda scheduling strategy on load balancing of VM resourcesbased on genetic algorithm [16] Yamauchi et al proposeda distributed parallel scheduling methodology for MCC anddeveloped a simulator to analyze the bottleneck of MCC [17]

Ant Colony Optimization (ACO) has also been used tobalance the load in cloud environment In [18] Mishra et alhave proposed amethod to utilize theACO for load balancingin cloud environment The routing packets in this environ-ment are treated as the ants in the network Moreover theyreplaced the routing tables in the network nodes by tables ofprobabilities These tables are also called ldquopheromone tablesrdquosince the pheromone strengths used in ACO are representedby these probabilities Every node has a pheromone table forevery possible destination in the network and each table hasan entry for every neighbor The entries in the tables are theprobabilities which influence the antsrsquo selection of the nextnode on the way to their destination node Consequently ateach node the ant should choose the next node toward itsfinal destination node according to the probabilities Afterarriving at a node the ants update the probabilities of thatnodersquos pheromone table entries corresponding to their sourcenode that is ants lay the kind of pheromone associatedwith the node they were launched from They alter the tableto increase the probability pointing to their previous nodeBesides in order to distribute the load among many pathsfrom the source node to the destination node the ants fromone colony will consult the routing tables of other coloniesso as to avoid routing packets to those paths that are highlypreferred by the other groupsThrough thismethod the loadsare separated among many possible paths in the network

Zhu et al considered the task scheduling in cloudenvironment from the perspectives of QoS fulfillment andshortest path [19] Nishant et al have proposed an algorithmfor load distribution of workloads among nodes of a cloud bythe use of ACO Moreover they have presented another loadbalancing algorithm which ensures that there is no conflictof interests based on relocating the tasks among nodes [20]In these works they do not take each taskrsquos profit intoconsideration and cannot maximize the profit of the systemwhich is an import target of the scheduling algorithm for thecommercial mobile cloud environment In grid computingan ACO algorithm is proposed by Suryadevera et al forload balancing which will determine the best resource to beallocated to the jobs based on resource capacity and at thesame time balance the load of entire resources on grid Themain objective of this algorithm is to achieve high throughputand thus increases the performance in grid environment














Mobile devices

middotmiddotmiddot

Backbonenetwork

Cloudinfrastructure


Cloudlet

Mobile devices

Backbonenetwork

Cloudinfrastructure

middotmiddotmiddot


Cloudlet

Mobile devices




Cloudlet

Mobile devices

(1) (2)

(2)(2)

(4)

(3)(3)

(3)Client

(1)

(1)

(4)

(4)

Client

Client

middotmiddotmiddot














119894=

(1198881

119894 119888

119889

119894) in which 119888

119896



119895 119895 = 1 2 119899


119894119895= (1199031

119894119895 119903119889

119894119895) 119894 = 1 2 119898


Maximize119899

sum

119895=1

119901119895

119898

sum

119894=1

119909119894119895

subject to119899

sum

119895=1

119903119894119895119909119894119895le 119888119894 119894 = 1 2 119898

119898

sum

119894=1

119909119894119895le 1 119895 = 1 2 119899

119909119894119895isin 0 1 119895 = 1 2 119899

(1)




119871119894119896=

sum119899

119895=1119903119896

119894119895119909119894119895

119888119896

119894

(2)

1198941015840s load119871



119871119894=

sum119889

119896=1119871119894119896

119889

(3)



120591119894(1199051015840)

120591119894(1199051015840) = (1 minus 120588) 120591

119894 (119905) + Δ120591

119894(119905 1199051015840) (4)




Δ120591119894(119905 1199051015840) =

119902

sum

119895=1

Δ120591119895

119894(119905 1199051015840) (5)



119894(119905 1199051015840) is the


Δ120591119895

119894(119905 1199051015840)

=


0 otherwise(6)




119891 (119878119895(1199051015840)) = sum

119896isin119878119895(1199051015840)

119901119896 (7)



119895(1199051015840))) = 119876119891(119878

119895(1199051015840)) in which 119876 is a



Let 119896(119895 119905) = sum

119897isin119878119895(119905)119903119896119897




119896minus119896(119895 119905) = (120574

1

119896(119895 119905) 120574

119889

119896(119895 119905)) in which 120574119894

119896(119895 119905)


100381610038161003816100381610038161003816100381610038161003816

119903119894

119896ℎ

120574119894

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

(8)




119896(119895 119905) Moreover


120575119896ℎ

(119895 119905) =

100381610038161003816100381610038161003816100381610038161003816

1199031

119896ℎ

1205741

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

+ sdot sdot sdot +

1003816100381610038161003816100381610038161003816100381610038161003816

119903119889

119896ℎ

120574119889

119896(119895 119905)

1003816100381610038161003816100381610038161003816100381610038161003816

(9)



119895(119905) is

120575ℎ(119895 119905) =

sum119898

119896=1120575119896ℎ

(119895 119905)

119898

(10)


ℎ(119878119895(119905)) is

defined as

120578ℎ(119878119895 (119905)) =

119901ℎ

120575ℎ(119895 119905)

(11)


119895(119905) is

119875119895

ℎ(t)

=

[120591ℎ (119905)]120572[120578ℎ(119878119895 (119905))]

120573


[120591119896 (119905)]120572[120578119896(119878119895 (119905))]


119895 (119905)

0 otherwise(12)







119895(119905) =

119865 cap ℎ | ℎ notin tabu119895(119905)






1198711015840

119894119896= 119871119894119896+

119903119896

119894ℎ

119888119896

119894

(13)


1198711015840

119894=

sum119889

119896=11198711015840

119894119896

119889

(14)


119894








119895(119905) = 0






(19) best solution = 119891(119878119895(119905))



120572 120573 120588 119902 119876 119903119894119895 119888119894 and 119901




119895(119905) Step 17 calculates 119891(119878

119895(119905)) If 119891(119878

119895(119905))










3 1198864] and [119886

5 1198866]








311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1







119894 The mean value (120583119895




120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895



120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)



120583120590=

sum119862

119896=1120583119896

120590

119862

(17)


120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)


120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896









1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















Mobile devices

middotmiddotmiddot

Backbonenetwork

Cloudinfrastructure


Cloudlet

Mobile devices

Backbonenetwork

Cloudinfrastructure

middotmiddotmiddot


Cloudlet

Mobile devices




Cloudlet

Mobile devices

(1) (2)

(2)(2)

(4)

(3)(3)

(3)Client

(1)

(1)

(4)

(4)

Client

Client

middotmiddotmiddot














119894=

(1198881

119894 119888

119889

119894) in which 119888

119896



119895 119895 = 1 2 119899


119894119895= (1199031

119894119895 119903119889

119894119895) 119894 = 1 2 119898


Maximize119899

sum

119895=1

119901119895

119898

sum

119894=1

119909119894119895

subject to119899

sum

119895=1

119903119894119895119909119894119895le 119888119894 119894 = 1 2 119898

119898

sum

119894=1

119909119894119895le 1 119895 = 1 2 119899

119909119894119895isin 0 1 119895 = 1 2 119899

(1)




119871119894119896=

sum119899

119895=1119903119896

119894119895119909119894119895

119888119896

119894

(2)

1198941015840s load119871



119871119894=

sum119889

119896=1119871119894119896

119889

(3)



120591119894(1199051015840)

120591119894(1199051015840) = (1 minus 120588) 120591

119894 (119905) + Δ120591

119894(119905 1199051015840) (4)




Δ120591119894(119905 1199051015840) =

119902

sum

119895=1

Δ120591119895

119894(119905 1199051015840) (5)



119894(119905 1199051015840) is the


Δ120591119895

119894(119905 1199051015840)

=


0 otherwise(6)




119891 (119878119895(1199051015840)) = sum

119896isin119878119895(1199051015840)

119901119896 (7)



119895(1199051015840))) = 119876119891(119878

119895(1199051015840)) in which 119876 is a



Let 119896(119895 119905) = sum

119897isin119878119895(119905)119903119896119897




119896minus119896(119895 119905) = (120574

1

119896(119895 119905) 120574

119889

119896(119895 119905)) in which 120574119894

119896(119895 119905)


100381610038161003816100381610038161003816100381610038161003816

119903119894

119896ℎ

120574119894

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

(8)




119896(119895 119905) Moreover


120575119896ℎ

(119895 119905) =

100381610038161003816100381610038161003816100381610038161003816

1199031

119896ℎ

1205741

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

+ sdot sdot sdot +

1003816100381610038161003816100381610038161003816100381610038161003816

119903119889

119896ℎ

120574119889

119896(119895 119905)

1003816100381610038161003816100381610038161003816100381610038161003816

(9)



119895(119905) is

120575ℎ(119895 119905) =

sum119898

119896=1120575119896ℎ

(119895 119905)

119898

(10)


ℎ(119878119895(119905)) is

defined as

120578ℎ(119878119895 (119905)) =

119901ℎ

120575ℎ(119895 119905)

(11)


119895(119905) is

119875119895

ℎ(t)

=

[120591ℎ (119905)]120572[120578ℎ(119878119895 (119905))]

120573


[120591119896 (119905)]120572[120578119896(119878119895 (119905))]


119895 (119905)

0 otherwise(12)







119895(119905) =

119865 cap ℎ | ℎ notin tabu119895(119905)






1198711015840

119894119896= 119871119894119896+

119903119896

119894ℎ

119888119896

119894

(13)


1198711015840

119894=

sum119889

119896=11198711015840

119894119896

119889

(14)


119894








119895(119905) = 0






(19) best solution = 119891(119878119895(119905))



120572 120573 120588 119902 119876 119903119894119895 119888119894 and 119901




119895(119905) Step 17 calculates 119891(119878

119895(119905)) If 119891(119878

119895(119905))










3 1198864] and [119886

5 1198866]








311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1







119894 The mean value (120583119895




120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895



120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)



120583120590=

sum119862

119896=1120583119896

120590

119862

(17)


120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)


120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896









1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















119894=

(1198881

119894 119888

119889

119894) in which 119888

119896



119895 119895 = 1 2 119899


119894119895= (1199031

119894119895 119903119889

119894119895) 119894 = 1 2 119898


Maximize119899

sum

119895=1

119901119895

119898

sum

119894=1

119909119894119895

subject to119899

sum

119895=1

119903119894119895119909119894119895le 119888119894 119894 = 1 2 119898

119898

sum

119894=1

119909119894119895le 1 119895 = 1 2 119899

119909119894119895isin 0 1 119895 = 1 2 119899

(1)




119871119894119896=

sum119899

119895=1119903119896

119894119895119909119894119895

119888119896

119894

(2)

1198941015840s load119871



119871119894=

sum119889

119896=1119871119894119896

119889

(3)



120591119894(1199051015840)

120591119894(1199051015840) = (1 minus 120588) 120591

119894 (119905) + Δ120591

119894(119905 1199051015840) (4)




Δ120591119894(119905 1199051015840) =

119902

sum

119895=1

Δ120591119895

119894(119905 1199051015840) (5)



119894(119905 1199051015840) is the


Δ120591119895

119894(119905 1199051015840)

=


0 otherwise(6)




119891 (119878119895(1199051015840)) = sum

119896isin119878119895(1199051015840)

119901119896 (7)



119895(1199051015840))) = 119876119891(119878

119895(1199051015840)) in which 119876 is a



Let 119896(119895 119905) = sum

119897isin119878119895(119905)119903119896119897




119896minus119896(119895 119905) = (120574

1

119896(119895 119905) 120574

119889

119896(119895 119905)) in which 120574119894

119896(119895 119905)


100381610038161003816100381610038161003816100381610038161003816

119903119894

119896ℎ

120574119894

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

(8)




119896(119895 119905) Moreover


120575119896ℎ

(119895 119905) =

100381610038161003816100381610038161003816100381610038161003816

1199031

119896ℎ

1205741

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

+ sdot sdot sdot +

1003816100381610038161003816100381610038161003816100381610038161003816

119903119889

119896ℎ

120574119889

119896(119895 119905)

1003816100381610038161003816100381610038161003816100381610038161003816

(9)



119895(119905) is

120575ℎ(119895 119905) =

sum119898

119896=1120575119896ℎ

(119895 119905)

119898

(10)


ℎ(119878119895(119905)) is

defined as

120578ℎ(119878119895 (119905)) =

119901ℎ

120575ℎ(119895 119905)

(11)


119895(119905) is

119875119895

ℎ(t)

=

[120591ℎ (119905)]120572[120578ℎ(119878119895 (119905))]

120573


[120591119896 (119905)]120572[120578119896(119878119895 (119905))]


119895 (119905)

0 otherwise(12)







119895(119905) =

119865 cap ℎ | ℎ notin tabu119895(119905)






1198711015840

119894119896= 119871119894119896+

119903119896

119894ℎ

119888119896

119894

(13)


1198711015840

119894=

sum119889

119896=11198711015840

119894119896

119889

(14)


119894








119895(119905) = 0






(19) best solution = 119891(119878119895(119905))



120572 120573 120588 119902 119876 119903119894119895 119888119894 and 119901




119895(119905) Step 17 calculates 119891(119878

119895(119905)) If 119891(119878

119895(119905))










3 1198864] and [119886

5 1198866]








311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1







119894 The mean value (120583119895




120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895



120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)



120583120590=

sum119862

119896=1120583119896

120590

119862

(17)


120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)


120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896









1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119894(119905 1199051015840) is the


Δ120591119895

119894(119905 1199051015840)

=


0 otherwise(6)




119891 (119878119895(1199051015840)) = sum

119896isin119878119895(1199051015840)

119901119896 (7)



119895(1199051015840))) = 119876119891(119878

119895(1199051015840)) in which 119876 is a



Let 119896(119895 119905) = sum

119897isin119878119895(119905)119903119896119897




119896minus119896(119895 119905) = (120574

1

119896(119895 119905) 120574

119889

119896(119895 119905)) in which 120574119894

119896(119895 119905)


100381610038161003816100381610038161003816100381610038161003816

119903119894

119896ℎ

120574119894

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

(8)




119896(119895 119905) Moreover


120575119896ℎ

(119895 119905) =

100381610038161003816100381610038161003816100381610038161003816

1199031

119896ℎ

1205741

119896(119895 119905)

100381610038161003816100381610038161003816100381610038161003816

+ sdot sdot sdot +

1003816100381610038161003816100381610038161003816100381610038161003816

119903119889

119896ℎ

120574119889

119896(119895 119905)

1003816100381610038161003816100381610038161003816100381610038161003816

(9)



119895(119905) is

120575ℎ(119895 119905) =

sum119898

119896=1120575119896ℎ

(119895 119905)

119898

(10)


ℎ(119878119895(119905)) is

defined as

120578ℎ(119878119895 (119905)) =

119901ℎ

120575ℎ(119895 119905)

(11)


119895(119905) is

119875119895

ℎ(t)

=

[120591ℎ (119905)]120572[120578ℎ(119878119895 (119905))]

120573


[120591119896 (119905)]120572[120578119896(119878119895 (119905))]


119895 (119905)

0 otherwise(12)







119895(119905) =

119865 cap ℎ | ℎ notin tabu119895(119905)






1198711015840

119894119896= 119871119894119896+

119903119896

119894ℎ

119888119896

119894

(13)


1198711015840

119894=

sum119889

119896=11198711015840

119894119896

119889

(14)


119894








119895(119905) = 0






(19) best solution = 119891(119878119895(119905))



120572 120573 120588 119902 119876 119903119894119895 119888119894 and 119901




119895(119905) Step 17 calculates 119891(119878

119895(119905)) If 119891(119878

119895(119905))










3 1198864] and [119886

5 1198866]








311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1







119894 The mean value (120583119895




120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895



120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)



120583120590=

sum119862

119896=1120583119896

120590

119862

(17)


120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)


120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896









1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119895(119905) = 0






(19) best solution = 119891(119878119895(119905))



120572 120573 120588 119902 119876 119903119894119895 119888119894 and 119901




119895(119905) Step 17 calculates 119891(119878

119895(119905)) If 119891(119878

119895(119905))










3 1198864] and [119886

5 1198866]








311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1







119894 The mean value (120583119895




120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895



120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)



120583120590=

sum119862

119896=1120583119896

120590

119862

(17)


120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)


120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896









1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












311198862

1001198863

101198864

301198865

10119862 10120573 1119876 1119898 201198866

301198867

51198868

30120572 1120588 03120579 1120582 1







119894 The mean value (120583119895




120583119895

119896=

sum119898

119894=1119871119895119896

119894

119898

120590119895

119896= radic

1

119898

119898

sum

119894=1

(119871119895119896

119894minus 120583119895

119896)

2

(15)

120590119895



120583119896

120590=

sum119902

119895=1120590119895

119896

119902

(16)



120583120590=

sum119862

119896=1120583119896

120590

119862

(17)


120583119896

120583=

sum119902

119895=1120583119895

119896

119902

(18)


120583120583=

sum119862

119896=1120583119896

120583

119862

(19)

120590119895

119896 120583120583 and 120583

119896









1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1 2 3 4 5 6 7 8 9 101550

1600

1650

1700

1750

1800

Cycle

Profi

t

HACASRPSHACAS


1 2 3 4 5 6 7 8 9 10077

078

079

08

081

082

083

HACASRPSHACAS

k

120583k 120583


119896

120583is the




1 2 3 4 5 6 7 8 9 1001

0105

011

0115

012

0125

013

HACASRPSHACAS

k

120583k 120590










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 5 10 15 200

01

02

03

04

05

06

07

08

Provider

The l

oad

of th

e pro

vide

r

HACASRPSHACAS


0 5 10 15 20 25 30005

01

015

02

025

03

035

04

Ant

HACASRPSHACAS

The s

tand

ard

devi

atio

n of

all t

he p

rovi

ders

rsquo lo

ad o

f the

antrsquos

solu

tion




1 2 3 4 5 6 7 8 9 10008

01

012

014

016

018

02

022

024

026

028

k

120583k 120590

HACASRPSHACAS











1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1 1198862] while 119886

1= 31 and 119886

2= 100This










Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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