research article minimized delay with reliability...

Research ArticleMinimized Delay with Reliability Guaranteed by Using VariableWidth Tiered Structure Routing in WSNs

Jinhuan Zhang Jun Long Guihu Zhao and Hao Zhang

School of Information Science and Engineering Central South University Changsha 410083 China

Correspondence should be addressed to Jun Long jlongcsueducn

Received 8 May 2015 Accepted 9 September 2015

Academic Editor Tom H Luan

Copyright copy 2015 Jinhuan Zhang et alThis 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

Data collection should take reliability and delay into consideration To address these problems a novel variable width tieredstructure routing scheme named variable width tiered structure routing (VWTSR) is proposed The proposed VWTSR schemeintegrates two core phases namely circular tiers and cells partition anddistributed in-network aggregationThekey idea ofVWTSRis to partition the network into circular tiers with different widths and each tier is further partitioned into cells Those cells thatdo not interfere with each other could simultaneously finish data aggregation by broadcast and retransmission within each cellMoreover the tier width could meet the goal that when collecting nodes in outer layer finish transmission to parent collectingnodes in inner layer the collecting nodes in inner layer just finish data aggregation thus minimizing the latency while maintainingreliability for data collection The problem is formulated as to minimize the delay under reliability constraint by controlling thesystem parameters To demonstrate the effectiveness of the proposed scheme extensive theoretical analysis and simulations areconducted to evaluate the performance of VWTSRThe analysis and simulations show that VWTSR leads to lower delay subject toreliability constraint than the existing scheme

1 Introduction

Wireless sensor networks (WSNs) have been widely recog-nized as a ubiquitous and general approach for extensiveapplications in unattended environment such as habitatmonitoring surveillance and tracking for military It con-sists of a large number of low-cost and low-power sensornodes which collaborate with each other to collect data anddisseminate them to sink through an established routingpath Multihop communication is often used to relay theinformation from the source node to the sink Distributedin-network aggregation can improve the communicationefficiency of the system It can result in significant per-formance improvements in energy consumption memoryusage bandwidth and delay [1]

Reliable communications are essential for most appli-cations in wireless sensor networks (WSNs) [2ndash7] Manyapplications require that each data packet is successfullydelivered to sink with statistical probability 120575 lt 1 suchas 60ndash95 [6 8] which is sufficient for these applicationssuch as environment (temperature humidity) and agriculture

(water tank irrigation) [8] In such cases 100 reliablecommunications are costly and not necessary [5] But someof the reports reveal that wireless link packet error rate maybe as high as 30 in real WSNs which are far from beingsatisfactory [9]

In addition delay is also an important metric inWSNs Itplays a vital role in the application to transport the detectedinformation quickly to sink in order tomake a rapid responseto the event Therefore the delay is generally defined as thetime required for sensor nodes to send the sensed data to sinknamed transport delay [10] In many safety-critical applica-tions the missing of urgent information may cause severeproperty loss and casualties which are often not acceptable

To address these issues a novel routing scheme based ontiered structure routing is proposed in this paper It integratesthe consideration of data reliability and transport delay andis called VWTSR (variable width tiered structure routing)Compared with the previous study we make the followingcontributions

(1) A novel VWTSR scheme is proposed to achievedelay performance subject to reliability constraint Since

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 689504 12 pageshttpdxdoiorg1011552015689504

2 International Journal of Distributed Sensor Networks

many applications have both reliability and delay constraintsthe new network architecture is developed for in-networkaggregation to improve the reliability and delay performanceThe proposed scheme named VWTSR is targeting bothoptimization of reliability and network delay The key ideaof VWTSR is to partition the network into circular tierswith different widths and each tier is further partitioned intocells Those cells that do not interfere with each other couldsimultaneously finish data aggregation by broadcast andretransmission within each cell In each cell noncollectingnodes transmit data packet to collecting nodes When thepacket is lost in the transmission it will be retransmitteduntil the maximum number of retransmission Moreover thetier width could meet the goal that when collecting nodes inouter layer finish transmission to parent collecting nodes ininner layer the collecting nodes in inner layer just finish dataaggregation thus minimizing the latency while maintainingreliability for data collection

Compared with the existing data aggregation schemesthe proposed approach couldmaintain the network transmis-sion success rate by broadcast and retransmission Further-more it could reduce the delay of all nodes data aggregatedto sink through distributed in-network data aggregation(2) It can effectively minimize aggregation latency in

WSNs It is very challenging to reduce delay in the pre-condition of ensuring reliability In this paper a routingapproach named variable width tiered structure routing isproposed to obtain optimized network delay In the approachthe careful design of tiers and cells partition of WSN isexploited to reduce network delay by using distributed in-network aggregation In this way the network delay could beoptimized in the precondition of reliability guaranteed(3) The theoretical analysis on latency is offered The

theoretical analysis on transport delay is presented The-oretical analysis is conducted by comparing the proposedVWTSR scheme with the existing tiered structure routingwith identical width to show that VWTSR could effectivelyreduce network delay In addition comprehensive simulationexperiments are conducted to verify the effectiveness of theVWTSR schemeThe results show that the proposedVWTSRcould obtain the goal of optimization of transport delaysubject to transmission reliability The optimized parameterscan be obtained to ensure the reduction of transport delaywithout reduction of the data reliability In the simulation themaximum transport delay could be decreased by 1948 com-pared with identical width tiered structure routing approachwhich presents the superiority of the strategy

The rest of this paper is organized as follows In Section 2the relatedworks are reviewedThe systemmodel is describedin Section 3 The novel VWTSR scheme is presented inSection 4 including performance analysis Performance eval-uations through simulations are presented in Section 5 Weconclude in Section 6

2 Related Work

Data collection is a key function for wireless sensor networksProcessing the gathered information efficiently is a key issuefor wireless sensor networks A great deal of work has been

devoted to this field [11ndash14] Reference [15] studies the timecomplexity message complexity and energy cost complexityof some data collection data aggregation and queries for amultihop wireless sensor network of 119899 nodes Network delayand reliable communication are important performancemet-rics and need to be considered in many WSNs studies

Network delay has an important influence on WSNsapplications So there is a great deal of research in this fieldHan and Lee conduct analysis on WSNs transport delay ofNAK-based SR-ARQ [16] There is also much research onSW E2E and SW H2H for example [17ndash21] However it isworth attention that most of the existing studies do researchon simple linear network and analysis on network delay of theflat network which is widely applied in real environments isstill relatively rare And in most of the studies network life ishardly considered

Moreover recently for flat network Shanti and Sahoo[22] presented a new contention-free TDMA-based inte-grated MAC and routing protocol named DGRAM Consid-ering the unique phenomenon of data aggregation in WSNsHuang et al [23] proposed a centralized scheduling algorithmwith the delay bound of 23119877 + Δ + 18 time slots where 119877 isthe network radius and Δ is the maximum node degree Yu etal [24] proposed a distributed schedulingmethod generatingcollision-free schedules with delay at most 24119863 + 6Δ + 16time slots where 119863 is the network diameter Xu et al [25]theoretically prove that the delay of the aggregation schedulegenerated by their algorithm is at most 16119877 + Δ minus 14 timeslots Joo and Shroff develop a new network architecture forin-network computation for a class of generalized maximumfunctions [1] It focuses on the delay performance of thefunction computation subject to reliability constraint inlossy wireless environments It shows that aggregation withwireless broadcast can substantially reduce the delay whilesatisfying the reliability constraint

A great deal of research efforts have been devoted inthis field to providing a reliable transmission service inWSNs because of the unreliable links Reference [4] pointsout that the existing works mainly fall into two categoriespacket-loss avoidance and packet-loss recovery Packet-lossavoidance (eg [8 9]) attempted to reduce the occurrenceof packet loss and packet-loss recovery (eg [26]) tried torecover the packet losswhen it happened Because packet-lossavoidancemethods need to pay a high price and from the costconsideration themechanismwidely used in network is basedon packet-loss recovery While the reliable protocol based onpacket-loss recovery can be divided into two categories Oneway is the retransmission after packets loss scheme whoserepresentative protocol is Automatic Repeat reQuest (ARQ)Another way is the packets reproduction strategy

Network lifetime is an important performancemetric andneeds to be considered in all WSNs studies There is also agreat deal of research in the field [27] However as far as weknow there is most of the research only on one performancemetric of WSNs because of the network complexity andresearch difficulty for example reliability [6 8] and networkdelay [20ndash25] Some research integrates network delay andreliability for example [1 4] or integrates network lifetimeand delay for example [28]Themain focus of the paper is to

International Journal of Distributed Sensor Networks 3

consider delay performance of in-network aggregation underthe reliability constraint

3 The System Model and Problem Statement

31 The System Model Consider a wireless sensor networkconsisting of sensor nodes that are uniformly and randomlyscattered in a flat network with the radius of 119877 the areaof 119882 and the node density of 120588 And nodes do not moveafter being deployed On detecting an event a sensor nodewill generate a message and forward to a special nodecalled the sink The information generated at each sensornode is exact without error The sensor nodes are dividedinto two types of collecting and noncollecting nodes Eachcollecting sensor node not only generates its own data butalso aggregates and relays othersrsquo data to the sink viamultihopwireless communications And each noncollecting node onlygenerates its own data and forwards it to the correspondingcollecting nodes Routing is fixed and time is slotted Allsensor nodes are assumed to be synchronized Each nodehas an identical transmission range of 119903 andmultiple wirelesschannels The wireless channel is assumed to be lossy withnonzero packet loss reliability119901 A packet loss can be restoredby retransmitting the lost packet which however results inadditional delay

32 The Data Aggregation Model For data aggregation thelossless step-by-step multihop aggregation model is adoptedIn such aggregation model the aggregation of 120581 multipleinputs with node 119894 is performed sequentially that is incom-ing data is aggregated with existing data in order of arrival weierp

119894

denotes the origin data packet of node 119894 and 120593(119894 119895) denotesthe intermediate aggregation result of node 119894 and node 119895 orsimply use 120593

119894to denote the current intermediate aggregation

result of node 119894 120601119894denotes the final aggregation result of node

119894 to all incoming nodesrsquo data and its own dataWhen node 119894 receives data 120601

119895from node 119895 node 119894

aggregates 120601119895with its own data (may be the origin data weierp

119894

or the intermediate data 120593119894) If current data packet of node

119894 is weierp119894 and data from 119895 is 120601

119895= weierp119895 namely the data to be

aggregated is both origin data then the aggregation formulais the following

120593 (119894 119895) = 119888max (weierp119894 weierp119895) + (1 minus 119888)min (weierp

119894 weierp119895) (1)

In formula (1) 119888 is the correlation coefficient and it isbetween 0 and 1 If any part of data to be aggregated is notsource data when being aggregated the aggregation formulais the following

120593 (120593119894 120601119895) = 120589max (120593

119894 120601119895) + (1 minus 120589)min (120593

119894 120601119895) (2)

In formula (2) 120589 is called an impact factor which is adecimal less than 1 for example 120589 = 08 120593

119894and 120601

119895 respec-

tively refer to intermediate aggregation result and final resultof child nodes there is at least one nonorigin data packet in120593119894and 120593

119895

33 Problem Statement In this part some definitions aregiven firstly to ensure clear statement They are as follows

Definition 1 (transport delay) One defines the transportdelay as the time from a packetrsquos first transmission until itsfinal transmission to the sink [10] Let Γ

119894denote the transport

delay from node 119894 to sink

Definition 2 (network reliability) It represents the probabil-ity of packets successfully forwarded to sink from one nodeLet 120575119894denote the network reliability of packets transmitted

from node 119894 to sink

Definition 3 (network delay) One defines the network delayas the time required for each node in the network to finishits single transmission to the sink Let 119863 denote the networkdelay

The information obtained by an individual sensor nodecalled noncollecting node is collected by some special nodescalled colleting nodes and these collecting nodes are respon-sible for data aggregation and information delivery to thesink Each collecting node at depth 119889 or tier 119889 has at least 119909(119899)collecting parents at depth or tier 119889minus1 and transmits a packetthrough the wireless broadcast channel to all parents (1 + 120583

119905)

times where 120583119905denotes the retransmission timesWe say that

a node successfully transmits a packet if the broadcast packetis successfully received by one of the 119909(119899) parents And in themeantime we try to minimize network delay

Following the network model in [17] assume that thetransmission reliability of node 119894 is 119901

119894and assume that

there are ℎ hops from the source node 119894 to the sink Let119875119894denote the routing path from node 119894 to the sink where

119875119894= V1198940 V1198941 V119894

ℎ and V119894

ℎdenotes the node whose distance

to the sink is ℎ hops in the routing path of node 119894 Thetransmission reliability and the delay at each hop are denotedby 119901119879119894= [1199010 1199011 119901

ℎ] and 120591119879

119894= [1205910 1205911 120591

ℎ] respectively

Therefore the network reliability and transport delay ofpacket transmitted to sink from node 119894 are respectively 120575

119894=

[prodℎ1

119896=0[1 minus (1 minus 119901

119896+1)119909(119899)(1+120583

119905)] sdot [1 minus (1 minus 119901

119896)(1+120583119905)]] and

Γ119894= sumℎ

119896=0120591119896 And for the distributed in-network aggregation

we have the equation 119863 = maxΓ119894 (119894 = 1 2 3 ) The

focus of the paper is to improve the delay performance whileachieving the same level of reliability That is 120575

119894ge 120575 where 120575

represents the network transmission success rate constraintTo sum up the above the network optimization goal can beexpressed as the following that is as for any node 119894 in thenetwork it meets the following formula

min (119863) = minmax0lt119894le119899

(Γ119894)

st Γ119894=

ℎ

sum

119896=0

120591119896

120575119894ge 120575

(3)

Hence the optimization goal is minimizing the maxi-mum transport delay under the guarantee of transport servicequality for example 120575

119894ge 120575


Sink

Level 1

R

Level 2 Level 3 Level 4(a)

Sink

Level 1

R

Level 2 Level 3 Level 4(b)

Figure 1 The overall approach the black nodes are collecting nodes and white nodes are noncollecting nodes (a) Phase I (b) Phase II

4 Design of the VWTSR Scheme

The proposed VWTSR scheme consists of two phases (1)circular tiers and cells partition and (2) in-network aggrega-tion and multiroute simultaneously As an illustration of themethods these phases will be presented in the following twosections At the end of the section a theoretical analysis ondelay performance will be demonstrated

41 The Overall Approach In this section the overall ap-proach is described An example is illustrated in Figure 1 Itconsists of two phases (1) each noncollecting node transmitsits packet to its parent collecting node in the same cell and(2) each collecting node receives the packet and does aggre-gation And it transmits the aggregated packet to its parentcollecting nodes in inner tier The procedure is repeated tierby tier from the outermost tier

42 VWTSR Scheme In the scheme the network is par-titioned into circular tiers with different widths and eachtier is further partitioned into cells Those cells that donot interfere with each other could simultaneously finishdata aggregation by broadcast and retransmission withineach cell In each cell noncollecting nodes transmit datapacket to collecting nodes When the packet is lost in thetransmission it will be retransmitted until the maximumnumber of retransmissions Moreover the tier width couldmeet the goal that when collecting nodes in outer layer finishtransmission to parent collecting nodes in inner layer thecollecting nodes in inner layer just finish data aggregationthus minimizing the latency while maintaining reliability fordata collection All the data will be gradually aggregated tosink by the distributed in-network aggregation

As the above description the proposed VWTSR consistsof two phases In the part more details will be given on theimplementation

(1) Circular Tiers and Cells Partition For a flat circle networkas described in Section 31 assume that the sink is located atthe center and nodesrsquo interference radius is 2119903 The circulartiers and cells partition are shown in Figure 2 The width ofeach tier is firstly computed according to the constraint thatthe collecting nodes in inner layer just finish data aggregationwhen collecting nodes in outer layer finish transmission toparent collecting nodes in the inner layer Accordingly thenetwork is divided into circular tiers 119879

119896

Assume that the width of the outmost tier 119879119896is 120575119903 where

0 lt 120575 lt 1 It is partitioned into cells 119862119898119896 and each cell has

a width of 119903 at the boundary of the inner tier as shown inFigure 2 There are numset = 2120587 sdot (119877 minus 120575119903)119903 cells (actually itis an integer no smaller than numset)

For a cell in the outmost tier 119879119896 the circular angle (in

radian) is 120579 = 119903(119877 minus 120575119903) So we can get the area of each cell119904block 119896 = 120579sdot119877sdot1198772minus120579sdot(119877minus120575119903)sdot(119877minus120575119903)2 = (1205792)(2119877120575119903minus120575

21199032)

Finally a simplified formula 119904block 119896 = 1205751199032(2119877minus120575119903)2(119877minus 120575119903)

can be obtainedTherefore the number of nodes in each cell is120585119896= 120588sdot119904block 119896 where120588denotes the node density Accordingly

we can get the time required for collecting nodes in theoutmost tier to finish data aggregation of the tier It is 120591

119896 119899=

3120585119896(1+120583)with the assumption that there is only one collecting

nodewithin each cell and themaximum retransmission timesare 120583 The collecting nodes need to deliver the aggregatedinformation to the collecting nodes in inner layer and thetime for forwarding is 120591

119896 119892= 3(1 + 120583) So the total time

required for all nodes in the outmost tier to finish transmis-sion to inner layer is computed by the following formula

120591119896= 120591119896 119899+ 120591119896 119892= 3120585119896(1 + 120583) + 3 (1 + 120583) (4)

For inner tier 119879119896minus1

the similar calculations can be done Sothe following results can be obtained The number of cellspartitioned in the tier 119879

119896minus1is

num119896minus1=2120587 sdot (119877 minus 120575

119896119903 minus 120575119896minus1119903)

119903 (5)


Tier 1

Tier 2

Tier 3

Tier 4

Width

Cell

Cell

Cell

Cell

120579

120575r

Sink

r

R

Cmk

middot middot middot

Figure 2 Illustration of tiers and cells partition

The area of each cell is calculated by

119904block 119896minus1 =120579 sdot (119877 minus 120575

119896119903) sdot (119877 minus 120575

119896119903)

2

minus120579 sdot (119877 minus 120575

119896119903 minus 120575119896minus1119903) sdot (119877 minus 120575

119896119903 minus 120575119896minus1119903)

2=120579

21198772

+ 1205752

1198961199032minus 2120575119896119903

minus [1198772+ (120575119896119903 + 120575119896minus1119903)2minus 2119877 (120575

119896119903 + 120575119896minus1119903)]

=120579

2minus2120575119896119903

minus [(2120575119896120575119896minus11199032+ 1205752

119896minus11199032) minus 2119877 (120575

119896119903 + 120575119896minus1119903)]

(6)

So we can get that the number of nodes in each cell is 120585119896minus1=

120588 sdot 119904block 119896minus1 and the time required for collecting nodes inthe tier to finish data aggregation is 120591

119896minus1 119899= 3120585119896minus1(1 + 120583)

Considering the constraint that the tier width could meetthe goal that when collecting nodes in outer layer finishtransmission to parent collecting nodes in inner layer and thecollecting nodes in inner layer just finish data aggregationwe have the equation 120591

119896minus1 119899= 120591119896 It is 120585

119896minus1= 120585119896+ 1 after

simplificationTherefore the tierwidth can be obtained If theprocedure is repeated we can obtain the width of each tier

(2) Distributed In-Network Aggregation The informationobtained by an individual sensor node is collected bysome special colleting nodes and these collecting nodes areresponsible for data aggregation and information delivery tothe sink

Let 119867(119896119898) be the subset of nodes in 119879119896that are

scheduled simultaneously and | sdot | denotes the cardinality ofthe set Let 119867(119896119898) include a node from every three cells

that is 119867(119896119898) has a node from cells 119862119898119896 119862119898+3

119896 Since

any two nodes in 119867(119896119898) are separated more than 2119903 theirtransmissions do not interfere with each other Moreoversince all cells have the same number of nodes (possibly exceptone cell which may have a smaller number of nodes) thenumber of nodes in each 119867(119896119898) is identical and would beabout a third of the number of cells Moreover since all cellshave the same number of nodes the number of nodes in each119867(119896119898) is identical andwould be about a third of the numberof 119862119898119896

|119867 (119896119898)| = lfloor1

3lceil2120587 (119877 minus 120575119903)

119903rceilrfloor (7)

Since each node has multiple wireless channels asdescribed in Section 31 the subset of nodes 119867(119896119898) in 119879

119896

could transmit data simultaneously with subsets in othertiers Thus we could ensure node transmission simulta-neously as much as possible When collecting nodes inouter layer finish transmission to parent collecting nodesin inner layer and the collecting nodes in inner layer justfinish data aggregation the colleting nodes in inner layergo on forwarding the aggregated information together totheir parent collecting nodes in more inner layer until thedestination of sink

The VWTSR protocol is implemented as shown inAlgorithm 1 in detail

43 Performance Analysis In this section the delay of thedata aggregation based on the proposed scheme is theoreti-cally proved

Theorem4 Consider that the network depth is119889 let ℏ119889denote

the total number of subsets in tier 119879119889 and assume that the

maximum number of retransmissions is 120583 The time requiredfor all nodes to finish a single transmission is 119863 = ℏ

119889(1 + 120583) +

sum119889minus1

119894=1(1 + 120583)

Proof Consider that the network depth is 119889 which repre-sents the number of tiers From Section 42 we know that119867(119896119898) is the subset of nodes in 119879

119896that can be scheduled

simultaneously Let ℏ119896denote the total number of subsets in

each tier 119879119896such that ⋃ℏ119896

119898=1119867(119896119898) = 119879

119896 Clearly all nodes

in 119879119896can finish a single transmission in ℏ

119896time slots Based

on the assumption that nodes transmission in different tiersdo not interfere with each other the subset of nodes119867(119896119898)in different tiers could transmit data simultaneously That isnodes in 119879

119896can start their transmissions simultaneously with

nodes in119879119896+1

But the number of nodes in119879119896ismore than that

in119879119896+1

Assume that themaximumnumber of retransmissionis 120583 Therefore we can obtain the time required for all nodesto finish a single transmission as follows

119863 = ℏ119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (8)

Theorem 5 Let 119863 and 1198631015840 respectively represent the timerequired for all nodes to finish a single transmission under the


Input A flat network with the radius of 119877 the node density of 120588 transmission range of 119903 and nonzero packet loss reliability 119901retransmission times 120583

119905

OutputData aggregation routeStage 1 Circular tiers and cells partition

(1) According to formula (3) the network is partitioned into tiers 119879119896 (119896 = 1 2 3 119889) with different width

(2) for each tier 119879119896

Tier 119879119896is partitioned into cells 119862119898

119896 according to width 119903 at the boundary of the inner tier

Select a node from cells 119862119898119896 119862119898+3

119896 so on to construct119867(119896119898) that is⋃ℏ119896

119898=1119867(119896119898) = 119879

119896

endStage 2 Distributed in-network aggregation

(3) for 119896 = 119889 to 1for 119898 = 1 to ℏ

119896

each non-collecting node 119894 in119867(119896119898) broadcasts its original or aggregated information (1 + 120583119905) times to

its collecting node 120582 in the same cellif collecting node 120582 receives all the packet from non-collecting nodes in the same cell thennode 120582

119894does aggregation and broadcasts the information (1 + 120583

119905) times to its parent collecting nodes in

inner tierend if

end forend for

(4) Output results

Algorithm 1 A variable width tiered structure routing algorithm for WSNs

cases of network partition with the VWTSR scheme and theidentical width That is1198631015840 minus 119863 gt 0

Proof It is needed to estimate ℏ119889to obtain119863 Obviously the

circular angle of each cell in the outmost layer is 120579 = 119903(119877minus120575119903)and the area is 119904block 119896 = 120579 sdot 119877 sdot 1198772 minus 120579 sdot (119877 minus 120575119903) sdot (119877 minus 120575119903)2 =(1205792)(2119877120575119903 minus 120575

21199032) We can obtain after simplification

119904block 119896 =1205751199032(2119877 minus 120575119903)

2 (119877 minus 120575119903) (9)

So ℏ119889= 3120588sdot119904block 119896 and the time required for collecting nodes

to finish data aggregation within each cell is 3120588sdot119904block 119896(1+120583)The collecting nodes go on forwarding the aggregated datapackets and the required time is 120591

119896 119892= 3(1 + 120583) So we get

119863 = 3120588 sdot 119904block 119896(1 + 120583) +sum119889minus1

119894=1(1 + 120583) 119904block 119896 is substituted by

formula (9) Then the following formula can be obtained

119863 = 3120588 sdot119903 (2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (10)

If the network depth is 119889 and the partitioned tiers have theidentical width of 120574 that is 119877 = 120574119889 so we have 120574 = 119877119889 Let1198631015840 denote the time required for all nodes to finish a single

transmission Similarly 1198631015840 is calculated by the followingformula

1198631015840= ℏ1015840

119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (11)

For the case of identical width circular partition according tothe previous calculation method the area of each cell can becomputed by 1199041015840block 119896 = 120579

1015840sdot 119877 sdot 1198772 minus 120579 sdot (119877 minus 120574) sdot (119877 minus 120574)2 =

(12057910158402)(2119877120574 minus 120574

2) Substitute the circular angle 1205791015840 = 119903(119877 minus 120574)

into 1199041015840block 119896 and 1199041015840

block 119896 = 119903(2119877120574minus1205742)2(119877minus120574) can be obtained

Consequently1198631015840 has

1198631015840= 3120588

119903 (2119877120574 minus 1205742)

2 (119877 minus 120574)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (12)

Since 120574 gt 1205751199031198631015840 is compared with119863 and it has the followingresult

1198631015840minus 119863 = 3120588119903 [

(2119877120574 minus 1205742)

2 (119877 minus 120574)minus(2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)]

=(119877 minus 120575119903) [2119877120574 minus 120574

2] minus (119877 minus 120574) [2119877120575119903 minus 120575

21199032]

2 (119877 minus 120574) (119877 minus 120575119903)

(13)

It can be obtained after further simplification

1198631015840minus 119863 =

(120574 minus 120575119903) [21198772+ 120574120575119903 minus 119877 (120574 + 120575119903)]

2 (119877 minus 120574) (119877 minus 120575119903)

ge(120574 minus 120575119903) [2119877

2+ 120574120575119903 minus 119877

2]

2 (119877 minus 120574) (119877 minus 120575119903)

=(120574 minus 120575119903) [119877

2+ 120574120575119903]

2 (119877 minus 120574) (119877 minus 120575119903)

(14)

Since (120574minus120575119903)[1198772+120574120575119903]2(119877minus120574)(119877minus120575119903) gt 0 we get1198631015840minus119863 gt 0This proves that there is lower delay for circular partitionwithdifferent widths than that with identical width

5 Simulation

In this section the simulation results are presented to evaluatethe VWTSR scheme The simulation environment is firstly


Table 1 The number of packets lost and network delay underdifferent 119901 and 120583 for network with 600 nodes

Number ofpacketslostdelay

119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234

introduced focusing more on the network model appliedin simulation experiments Then we present the evaluationresults for the proposed routing scheme Finally some com-parisons with existing routing mechanism are presented

51 Simulation Parameter Setting The test beds are respec-tively two wireless sensor networks with 600 nodes and900 nodes randomly placed in a disk of radius 119877 = 1The transmission range of each node 119903 is set to 05 Theretransmission number 120583 is changed from 1 to 4 All linksare assumed to fail transmission with the same probability 119901Changing119901 the number of time units required for the sink toreceive the information value is counted and the rate of packetlost is measured Each simulation is run 1000 times and theresults are averaged

52 Evaluation on the Proposed Scheme The proposedscheme is evaluated firstly Here the performance evaluationmainly focuses on two metrics the reliability and networkdelay We investigate the performance of VWTSR throughsimulations When 120575 = 05 according to Algorithm 1 thenetwork is divided into three circular tiers whose widthsare respectively 025 02749 and 04751 from outer tier toinner tier The network circular partitions for network with600 nodes and 900 nodes are as shown in Figures 3 and 4respectively Tables 1 and 2 respectively show the number ofpackets lost and network delay under different 119901 and 120583 fornetworks with 600 nodes and with 900 nodes

Figures 5(a) and 5(b) respectively show the reliabilityand delay under different 119901 and 120583 for the network with 600nodes As shown in Figure 5 there is more number of packetslost when 119901 is smaller and otherwise there are less packetslost Since the packet will be retransmitted if it is lost in thejourney there is higher delay when 120583 is bigger which means

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

minus05 0 05 1minus1

Figure 3 Network circular partition with 600 nodes

minus02

minus06

minus04

minus08

04

06

08

02

minus1

0

1



that the number of packets lost is reduced under the same 119901(as can be seen from Figure 5(a))

Figures 6(a) and 6(b) respectively illustrate the relationsof the reliability and delay with parameters of 119901 and 120583 for thenetwork with 900 nodes As can be seen from Figure 6 thereare more packets lost when 119901 is smaller and there are lesspackets lost when 119901 is bigger Under the same 119901 the packetloss is reduced and the network delay is higher when 120583 isbigger

53 Comparisons with Existing Scheme In this part wecompare the proposed VWTSR routing with existing schemethrough the above-mentioned networks focusing on delayand reliability performance In order to prove the effective-ness of the scheme it is compared with the tiered structurerouting with the identical tier width named IWTSR in [1]and that with general varied width named GVWTSR InGVWTSR the width and network partition are not carefullydesigned and it is a general form based on IWTSR Forthe case of network circular partition with identical widththe circular width is 03333 in order to ensure that there is


0

20

40

60

80

100

120

140

160

180

200

220N

umbe

r of p

acke

ts lo

st

04 045 05 055 06 065 07 075 08 085035Probability of link error (p)

Retransmission times = 4



(a)

180

200

220

240

260

280

300

320

340

Dela

y (ti

me u

nit)





(b)

Figure 5 Comparisons under different 119901 and 120583 for the network with 600 nodes (a) the number of packets lost (b) network delay

0

50

100

150

200

250

300

Num

ber o

f pac

kets

lost





(a)

250

300

350

400

450

Dela

y (ti

me u

nit)





(b)


the same number of circular rings with VWTSR describedin Section 52 Accordingly for the GVWTSR the circularwidths are randomly set and they are 020 035 and 045 fromouter layer to inner layer The network partitions of IWTSRand GVWTSR are respectively shown in Figures 7(a) and7(b)

The comparisons of the number of packet lost andnetwork delay under different 119901 and 120583 for the network with600 nodes are shown in Table 3 Figures 8 and 9 respectivelyshow the corresponding comparisons on the metrics of thenumber of packets lost and network delay by exploiting the

different schemes of VWTSR IWTSR and GVWTSR Asshown in Figure 8 when 120583 = 2 the proposed VWTSR issuperior both in reliability and in delay In the case when 119901 =08 the network delay is reduced by 1948 and the numberof packets lost is reduced by 5 compared with IWTSR Andwhen 120583 = 4 the proposed VWTSR has significant advantageover IWTSR and GVWTSR in the network delay which canbe seen from Figure 9(a) And the transmission success rateis maintained as shown in Figure 9(b)

Figure 10 illustrates the network partition in the two casesof the identical circular width of 03333 and different circular


minus05 0 05 1minus1minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

(a)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


(b)

Figure 7 Network partition (a) with identical circular width of 03333 and (b) with circular width of 020 035 and 045

Comparisons of delay

0

50

100

150

200

250

300

350

400

450

Dela

y (ti

me u

nit)

05 06 07 08 09 104Link error probability

VWTSRGVWTSRIWTSR

(a)

Comparisons of reliability

03

04

05

06

07

08

09

1

11

12N

etw

ork

relia

bilit

y


VWTSRGVWTSRIWTSR

(b)

Figure 8 Comparisons of VWTSR GVWTSR and IWTSR for network with 600 nodes and 120583 = 2 (a) Network delay (b) success rate

Table 3 Comparisons of the number of packets lost and networkdelay under different 119901 and 120583 for the network with 600 nodesexploiting schemes of VWTSR IWTSR and GVWTSR


120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08

VWTSR 112324 29240 2186 38327 5252 0183IWTSR 116420 39315 7231 32456 9297 3246GVWTSR 112333 39261 4204 40381 7264 3207

width of 020 035 and 045 for the network with 900 nodesThe comparisons of the number of packet lost and network

Table 4 Comparisons of the number of packet lost under different119901 and 120583 for the network with 900 nodes


120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08


delay under different 119901 and 120583 are shown in Table 4 Figures 11and 12 respectively show the corresponding comparisons onthe metrics of the number of packet lost and network delay



0

50

100

150

200

250

300

350

400

450

500D

elay

(tim

e uni

t)


VWTSRGVWTSRIWTSR

(a)


03

04

05

06

07

08

09

1

11

12

Net

wor

k re

liabi

lity


VWTSRGVWTSRIWTSR

(b)



minus08

minus06

minus04

minus02

0

02

04

06

08

1

(a)minus05 0 05 1minus1

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

(b)


by exploiting the different schemes of VWTSR IWTSR andGVWTSR As shown in Figure 11 when 120583 = 2 the proposedVWTSR is superior both in reliability and in delay than theother two schemes For instance when 119901 = 08 the networkdelay is reduced by 1919 comparedwith IWTSRAndwhen120583 = 4 the proposed VWTSR has obvious advantage overIWTSR and GVWTSR in the network delay which can beseen from Figure 12(a) And the transmission success rate issatisfied as shown in Figures 11(b) and 12(b)

6 Conclusion

In this paper the problem of distributed in-network aggre-gation to reduce delay in WSNs is studied Data aggregationshould take reliability as well as delay into consideration

To address these problems a novel routing scheme namedVWTSR is proposed The improved VWTSR consists of twophases The theoretical analysis and simulation results showthat the method outperforms the existing methods Carefullydesigned system parameters grant VWTSR lower transportdelay under given reliability In our simulation it can be seenthat the network delay could be reduced by 1948 under theguarantee of reliability

There are many interesting open questions to considerAlthough we focus on the delay performance other perfor-mance metrics such as time complexity and the communica-tion overhead of the routing protocol are also of importanceIt would be interesting to study the relationship between thesemetrics with data aggregation and network topologies



0

50

100

150

200

250

300

350

400

450

500D

elay

(tim

e uni

t)


VWTSRGVWTSRIWTSR

(a)


03

04

05

06

07

08

09

1

11

12

Net

wor

k re

liabi

lity


VWTSRGVWTSRIWTSR

(b)



0

100

200

300

400

500

600

700

Dela

y (ti

me u

nit)


VWTSRGVWTSRIWTSR

(a)


03

04

05

06

07

08

09

1

11

12

Net

wor

k re

liabi

lity


VWTSRGVWTSRIWTSR

(b)


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (61272150 61379110 and61472450) Science Foundation of Ministry of Education

of China (20130162110079 and MCM20121031) theNational High Technology Research and DevelopmentProgram of China (863 Program) (2012AA010105) and theNational Basic Research Program of China (973 Program)(2014CB046305)

References

[1] C Joo and N B Shroff ldquoOn the delay performance ofin-network aggregation in lossy wireless sensor networksrdquo


IEEEACM Transactions on Networking vol 22 no 2 pp 662ndash673 2014

[2] S C Ergen and P Varaiya TDMA scheduling algorithmsfor sensor networks [PhD thesis] Department of ElectricalEngineering and Computer Sciences University of CaliforniaBerkeley Calif USA 2005

[3] L X Cai Y Liu T H Luan X S Shen J W Mark and H Vin-cent Poor ldquoSustainability analysis and resourcemanagement forwireless mesh networks with renewable energy suppliesrdquo IEEEJournal on Selected Areas in Communications vol 32 no 2 pp345ndash355 2014

[4] T H Luan L X Cai J Chen X S Shen and F Bai ldquoEngi-neering a distributed infrastructure for large-scale cost-effectivecontent dissemination over urban vehicular networksrdquo IEEETransactions on Vehicular Technology vol 63 no 3 pp 1419ndash1435 2014

[5] S Boulfekhar andM Benmohammed ldquoA novel energy efficientand lifetime maximization routing protocol in wireless sensornetworksrdquoWireless Personal Communications vol 72 no 2 pp1333ndash1349 2013

[6] R Saifan and O Al-Jarrah ldquoA novel algorithm for defend-ing path-based denial of service attacks in sensor networksrdquoInternational Journal of Distributed Sensor Networks vol 2010Article ID 793981 9 pages 2010

[7] TH Luan S LiM Asefi andX S Shen ldquoQuality of experienceoriented video streaming in challenged wireless networks anal-ysis protocol design and case studyrdquo IEEE COMSOC MMTCE-Letter vol 7 no 3 2012

[8] W R Claycomb andD Shin ldquoA novel node level security policyframework for wireless sensor networksrdquo Journal of Networkand Computer Applications vol 34 no 1 pp 418ndash428 2011

[9] T Shu M Krunz and S Liu ldquoSecure data collection in wirelesssensor networks using randomized dispersive routesrdquo IEEETransactions on Mobile Computing vol 9 no 7 pp 941ndash9542010

[10] H Yousefi K Mizanian and A H Jahangir ldquoModeling andevaluating the reliability of cluster-based wireless sensor net-worksrdquo in Proceedings of the 24th IEEE International Conferenceon Advanced Information Networking and Applications (AINArsquo10) pp 827ndash834 Perth Australia April 2010

[11] S He X Li J Chen P Cheng Y Sun and D Simplot-RylldquoEMD energy-efficient p2p message dissemination in delay-tolerant wireless sensor and actor networksrdquo IEEE Journal onSelected Areas in Communications vol 31 no 9 pp 75ndash84 2013

[12] S He J Chen D K Y Yau and Y Sun ldquoCross-layer optimiza-tion of correlated data gathering in wireless sensor networksrdquoIEEE Transactions onMobile Computing vol 11 no 11 pp 1678ndash1691 2012

[13] Y Cao D Qu and T Jiang ldquoThroughput maximization in cog-nitive radio system with transmission probability schedulingand traffic pattern predictionrdquo Mobile Networks and Applica-tions vol 17 no 5 pp 604ndash617 2012

[14] S He J Chen X Li X S Shen and Y Sun ldquoMobility andintruder prior information improving the barrier coverage ofsparse sensor networksrdquo IEEE Transactions on Mobile Comput-ing vol 13 no 6 pp 1268ndash1282 2014

[15] X-Y Li Y Wang and Y Wang ldquoComplexity of data collectionaggregation and selection for wireless sensor networksrdquo IEEETransactions on Computers vol 60 no 3 pp 386ndash399 2011

[16] J Han and J Lee ldquoAnalysis model for the transport delayof NAK-based SR-ARQ with a finite retransmissionrdquo in Pro-ceedings of the 23rd International Technical Conference on

CircuitsSystems Computers and Communications (ITC-CSCCrsquo08) pp 1709ndash1712 Shimonoseki Japan July 2008

[17] L S Jiang A F Liu Y L Hu and Z G Chen ldquoLifetime maxi-mization through dynamic ring-based routing scheme for cor-related data collecting in WSNsrdquo Computers amp Electrical Engi-neering vol 41 no 1 pp 191ndash215 2015

[18] Y Liu A Liu and Z Chen ldquoAnalysis and improvement of send-and-wait automatic repeat-request protocols for wireless sensornetworksrdquoWireless Personal Communications vol 81 no 3 pp923ndash959 2015

[19] A F Liu D Y Zhang P H Zhang G H Cui and Z G ChenldquoOnmitigating hotspots tomaximize network lifetime inmulti-hop wireless sensor network with guaranteed transport delayand reliabilityrdquo Peer-to-Peer Networking and Applications vol 7no 3 pp 255ndash273 2014

[20] J Han and J Lee ldquoAnalysis model for the transport delayof NAK-based SR-ARQ with a finite retransmissionrdquo in Pro-ceedings of the 23rd International Technical Conference on Cir-cuitsSystems Computers andCommunications (ITC-CSCC rsquo08)pp 1709ndash1712 Yamaguchi Japan July 2008

[21] O B Akan and I F Akyildiz ldquoEvent-to-sink reliable transportin wireless sensor networksrdquo IEEEACM Transactions on Net-working vol 13 no 5 pp 1003ndash1016 2005

[22] C Shanti and A Sahoo ldquoDGRAM a delay guaranteed routingand MAC protocol for wireless sensor networksrdquo IEEE Trans-actions on Mobile Computing vol 9 no 10 pp 1407ndash1423 2010

[23] S C-H Huang P-J Wan C T Vu Y Li and F Yao ldquoNearlyconstant approximation for data aggregation scheduling inwireless sensor networksrdquo in Proceedings of the 26th IEEE Inter-national Conference on Computer Communications (INFOCOMrsquo07) pp 366ndash372 Anchorage Alaska USA May 2007

[24] B Yu J Li and Y Li ldquoDistributed data aggregation schedulingin wireless sensor networksrdquo in Proceedings of the 28th IEEEConference on Computer Communications (INFOCOM rsquo09) pp2159ndash2167 IEEE Rio de Janeiro Brazil August 2009

[25] X Xu X-Y Li X Mao S Tang and S Wang ldquoA delay-effi-cient algorithm for data aggregation in multihop wireless sen-sor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 23 no 1 pp 163ndash175 2011

[26] Z Rosberg R P Liu T L Dinh Y F Dong and S Jha ldquoSta-tistical reliability for energy efficient data transport in wirelesssensor networksrdquoWireless Networks vol 16 no 7 pp 1913ndash19272010

[27] A Liu X Jin G Cui and Z Chen ldquoDeployment guidelinesfor achieving maximum lifetime and avoiding energy holes insensor networkrdquo Information Sciences vol 230 pp 197ndash2262013

[28] A E A A Abdulla H Nishiyama J Yang N Ansari and NKato ldquoHYMN A novel hybrid multi-hop routing algorithm toimprove the longevity of WSNsrdquo IEEE Transactions on WirelessCommunications vol 11 no 7 pp 2531ndash2541 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



many applications have both reliability and delay constraintsthe new network architecture is developed for in-networkaggregation to improve the reliability and delay performanceThe proposed scheme named VWTSR is targeting bothoptimization of reliability and network delay The key ideaof VWTSR is to partition the network into circular tierswith different widths and each tier is further partitioned intocells Those cells that do not interfere with each other couldsimultaneously finish data aggregation by broadcast andretransmission within each cell In each cell noncollectingnodes transmit data packet to collecting nodes When thepacket is lost in the transmission it will be retransmitteduntil the maximum number of retransmission Moreover thetier width could meet the goal that when collecting nodes inouter layer finish transmission to parent collecting nodes ininner layer the collecting nodes in inner layer just finish dataaggregation thus minimizing the latency while maintainingreliability for data collection

Compared with the existing data aggregation schemesthe proposed approach couldmaintain the network transmis-sion success rate by broadcast and retransmission Further-more it could reduce the delay of all nodes data aggregatedto sink through distributed in-network data aggregation(2) It can effectively minimize aggregation latency in

WSNs It is very challenging to reduce delay in the pre-condition of ensuring reliability In this paper a routingapproach named variable width tiered structure routing isproposed to obtain optimized network delay In the approachthe careful design of tiers and cells partition of WSN isexploited to reduce network delay by using distributed in-network aggregation In this way the network delay could beoptimized in the precondition of reliability guaranteed(3) The theoretical analysis on latency is offered The

theoretical analysis on transport delay is presented The-oretical analysis is conducted by comparing the proposedVWTSR scheme with the existing tiered structure routingwith identical width to show that VWTSR could effectivelyreduce network delay In addition comprehensive simulationexperiments are conducted to verify the effectiveness of theVWTSR schemeThe results show that the proposedVWTSRcould obtain the goal of optimization of transport delaysubject to transmission reliability The optimized parameterscan be obtained to ensure the reduction of transport delaywithout reduction of the data reliability In the simulation themaximum transport delay could be decreased by 1948 com-pared with identical width tiered structure routing approachwhich presents the superiority of the strategy

The rest of this paper is organized as follows In Section 2the relatedworks are reviewedThe systemmodel is describedin Section 3 The novel VWTSR scheme is presented inSection 4 including performance analysis Performance eval-uations through simulations are presented in Section 5 Weconclude in Section 6

2 Related Work

Data collection is a key function for wireless sensor networksProcessing the gathered information efficiently is a key issuefor wireless sensor networks A great deal of work has been

devoted to this field [11ndash14] Reference [15] studies the timecomplexity message complexity and energy cost complexityof some data collection data aggregation and queries for amultihop wireless sensor network of 119899 nodes Network delayand reliable communication are important performancemet-rics and need to be considered in many WSNs studies

Network delay has an important influence on WSNsapplications So there is a great deal of research in this fieldHan and Lee conduct analysis on WSNs transport delay ofNAK-based SR-ARQ [16] There is also much research onSW E2E and SW H2H for example [17ndash21] However it isworth attention that most of the existing studies do researchon simple linear network and analysis on network delay of theflat network which is widely applied in real environments isstill relatively rare And in most of the studies network life ishardly considered

Moreover recently for flat network Shanti and Sahoo[22] presented a new contention-free TDMA-based inte-grated MAC and routing protocol named DGRAM Consid-ering the unique phenomenon of data aggregation in WSNsHuang et al [23] proposed a centralized scheduling algorithmwith the delay bound of 23119877 + Δ + 18 time slots where 119877 isthe network radius and Δ is the maximum node degree Yu etal [24] proposed a distributed schedulingmethod generatingcollision-free schedules with delay at most 24119863 + 6Δ + 16time slots where 119863 is the network diameter Xu et al [25]theoretically prove that the delay of the aggregation schedulegenerated by their algorithm is at most 16119877 + Δ minus 14 timeslots Joo and Shroff develop a new network architecture forin-network computation for a class of generalized maximumfunctions [1] It focuses on the delay performance of thefunction computation subject to reliability constraint inlossy wireless environments It shows that aggregation withwireless broadcast can substantially reduce the delay whilesatisfying the reliability constraint

A great deal of research efforts have been devoted inthis field to providing a reliable transmission service inWSNs because of the unreliable links Reference [4] pointsout that the existing works mainly fall into two categoriespacket-loss avoidance and packet-loss recovery Packet-lossavoidance (eg [8 9]) attempted to reduce the occurrenceof packet loss and packet-loss recovery (eg [26]) tried torecover the packet losswhen it happened Because packet-lossavoidancemethods need to pay a high price and from the costconsideration themechanismwidely used in network is basedon packet-loss recovery While the reliable protocol based onpacket-loss recovery can be divided into two categories Oneway is the retransmission after packets loss scheme whoserepresentative protocol is Automatic Repeat reQuest (ARQ)Another way is the packets reproduction strategy

Network lifetime is an important performancemetric andneeds to be considered in all WSNs studies There is also agreat deal of research in the field [27] However as far as weknow there is most of the research only on one performancemetric of WSNs because of the network complexity andresearch difficulty for example reliability [6 8] and networkdelay [20ndash25] Some research integrates network delay andreliability for example [1 4] or integrates network lifetimeand delay for example [28]Themain focus of the paper is to






119894





119895from node 119895 node 119894


119894






119894 weierp119895) (1)


120593 (120593119894 120601119895) = 120589max (120593

119894 120601119895) + (1 minus 120589)min (120593

119894 120601119895) (2)


119894and 120601

119895 respec-


119895









119905)






119875119894= V1198940 V1198941 V119894

ℎ and V119894



ℎ] and 120591119879

119894= [1205910 1205911 120591

ℎ] respectively


119894=

[prodℎ1

119896=0[1 minus (1 minus 119901

119896+1)119909(119899)(1+120583

119905)] sdot [1 minus (1 minus 119901

119896)(1+120583119905)]] and

Γ119894= sumℎ




119894ge 120575 where 120575


min (119863) = minmax0lt119894le119899

(Γ119894)

st Γ119894=

ℎ

sum

119896=0

120591119896

120575119894ge 120575

(3)


119894ge 120575


Sink

Level 1

R


Sink

Level 1

R









119896






21199032)




119896 119899=



119896 119892= 3(1 + 120583) So the total time


120591119896= 120591119896 119899+ 120591119896 119892= 3120585119896(1 + 120583) + 3 (1 + 120583) (4)



119896minus1is


119896119903 minus 120575119896minus1119903)

119903 (5)


Tier 1

Tier 2

Tier 3

Tier 4

Width

Cell

Cell

Cell

Cell

120579

120575r

Sink

r

R

Cmk





119896119903) sdot (119877 minus 120575

119896119903)

2

minus120579 sdot (119877 minus 120575


119896119903 minus 120575119896minus1119903)

2=120579

21198772

+ 1205752

1198961199032minus 2120575119896119903


119896119903 + 120575119896minus1119903)]

=120579

2minus2120575119896119903

minus [(2120575119896120575119896minus11199032+ 1205752

119896minus11199032) minus 2119877 (120575

119896119903 + 120575119896minus1119903)]

(6)



119896minus1 119899= 3120585119896minus1(1 + 120583)


119896minus1 119899= 120591119896 It is 120585

119896minus1= 120585119896+ 1 after






119896 Since


|119867 (119896119898)| = lfloor1

3lceil2120587 (119877 minus 120575119903)



119896







119889(1 + 120583) +

sum119889minus1

119894=1(1 + 120583)





119898=1119867(119896119898) = 119879






nodes in119879119896+1


in119879119896+1


119863 = ℏ119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (8)




119905



(2) for each tier 119879119896





119898=1119867(119896119898) = 119879

119896


(3) for 119896 = 119889 to 1for 119898 = 1 to ℏ

119896





inner tierend if

end forend for

(4) Output results






119904block 119896 =1205751199032(2119877 minus 120575119903)

2 (119877 minus 120575119903) (9)



119896 119892= 3(1 + 120583) So we get




119863 = 3120588 sdot119903 (2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (10)



1198631015840= ℏ1015840

119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (11)



(12057910158402)(2119877120574 minus 120574


into 1199041015840block 119896 and 1199041015840



1198631015840= 3120588

119903 (2119877120574 minus 1205742)

2 (119877 minus 120574)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (12)


1198631015840minus 119863 = 3120588119903 [

(2119877120574 minus 1205742)


21199032)

2 (119877 minus 120575119903)]

=(119877 minus 120575119903) [2119877120574 minus 120574


21199032]

2 (119877 minus 120574) (119877 minus 120575119903)

(13)


1198631015840minus 119863 =

(120574 minus 120575119903) [21198772+ 120574120575119903 minus 119877 (120574 + 120575119903)]

2 (119877 minus 120574) (119877 minus 120575119903)

ge(120574 minus 120575119903) [2119877

2+ 120574120575119903 minus 119877

2]

2 (119877 minus 120574) (119877 minus 120575119903)

=(120574 minus 120575119903) [119877

2+ 120574120575119903]

2 (119877 minus 120574) (119877 minus 120575119903)

(14)


5 Simulation





119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234





minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1



minus02

minus06

minus04

minus08

04

06

08

02

minus1

0

1







0

20

40

60

80

100

120

140

160

180

200

220N

umbe

r of p

acke

ts lo

st





(a)

180

200

220

240

260

280

300

320

340

Dela

y (ti

me u

nit)





(b)


0

50

100

150

200

250

300

Num

ber o

f pac

kets

lost





(a)

250

300

350

400

450

Dela

y (ti

me u

nit)





(b)








minus08

minus06

minus04

minus02

0

02

04

06

08

1

(a)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


(b)



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VWTSRGVWTSRIWTSR

(a)


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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





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6 Conclusion






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(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














119894





119895from node 119895 node 119894


119894






119894 weierp119895) (1)


120593 (120593119894 120601119895) = 120589max (120593

119894 120601119895) + (1 minus 120589)min (120593

119894 120601119895) (2)


119894and 120601

119895 respec-


119895









119905)






119875119894= V1198940 V1198941 V119894

ℎ and V119894



ℎ] and 120591119879

119894= [1205910 1205911 120591

ℎ] respectively


119894=

[prodℎ1

119896=0[1 minus (1 minus 119901

119896+1)119909(119899)(1+120583

119905)] sdot [1 minus (1 minus 119901

119896)(1+120583119905)]] and

Γ119894= sumℎ




119894ge 120575 where 120575


min (119863) = minmax0lt119894le119899

(Γ119894)

st Γ119894=

ℎ

sum

119896=0

120591119896

120575119894ge 120575

(3)


119894ge 120575


Sink

Level 1

R


Sink

Level 1

R









119896






21199032)




119896 119899=



119896 119892= 3(1 + 120583) So the total time


120591119896= 120591119896 119899+ 120591119896 119892= 3120585119896(1 + 120583) + 3 (1 + 120583) (4)



119896minus1is


119896119903 minus 120575119896minus1119903)

119903 (5)


Tier 1

Tier 2

Tier 3

Tier 4

Width

Cell

Cell

Cell

Cell

120579

120575r

Sink

r

R

Cmk





119896119903) sdot (119877 minus 120575

119896119903)

2

minus120579 sdot (119877 minus 120575


119896119903 minus 120575119896minus1119903)

2=120579

21198772

+ 1205752

1198961199032minus 2120575119896119903


119896119903 + 120575119896minus1119903)]

=120579

2minus2120575119896119903

minus [(2120575119896120575119896minus11199032+ 1205752

119896minus11199032) minus 2119877 (120575

119896119903 + 120575119896minus1119903)]

(6)



119896minus1 119899= 3120585119896minus1(1 + 120583)


119896minus1 119899= 120591119896 It is 120585

119896minus1= 120585119896+ 1 after






119896 Since


|119867 (119896119898)| = lfloor1

3lceil2120587 (119877 minus 120575119903)



119896







119889(1 + 120583) +

sum119889minus1

119894=1(1 + 120583)





119898=1119867(119896119898) = 119879






nodes in119879119896+1


in119879119896+1


119863 = ℏ119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (8)




119905



(2) for each tier 119879119896





119898=1119867(119896119898) = 119879

119896


(3) for 119896 = 119889 to 1for 119898 = 1 to ℏ

119896





inner tierend if

end forend for

(4) Output results






119904block 119896 =1205751199032(2119877 minus 120575119903)

2 (119877 minus 120575119903) (9)



119896 119892= 3(1 + 120583) So we get




119863 = 3120588 sdot119903 (2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (10)



1198631015840= ℏ1015840

119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (11)



(12057910158402)(2119877120574 minus 120574


into 1199041015840block 119896 and 1199041015840



1198631015840= 3120588

119903 (2119877120574 minus 1205742)

2 (119877 minus 120574)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (12)


1198631015840minus 119863 = 3120588119903 [

(2119877120574 minus 1205742)


21199032)

2 (119877 minus 120575119903)]

=(119877 minus 120575119903) [2119877120574 minus 120574


21199032]

2 (119877 minus 120574) (119877 minus 120575119903)

(13)


1198631015840minus 119863 =

(120574 minus 120575119903) [21198772+ 120574120575119903 minus 119877 (120574 + 120575119903)]

2 (119877 minus 120574) (119877 minus 120575119903)

ge(120574 minus 120575119903) [2119877

2+ 120574120575119903 minus 119877

2]

2 (119877 minus 120574) (119877 minus 120575119903)

=(120574 minus 120575119903) [119877

2+ 120574120575119903]

2 (119877 minus 120574) (119877 minus 120575119903)

(14)


5 Simulation





119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234





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VWTSRGVWTSRIWTSR

(a)


03

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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





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VWTSRGVWTSRIWTSR

(b)



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(b)



6 Conclusion






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VWTSRGVWTSRIWTSR

(a)


03

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Net

wor

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VWTSRGVWTSRIWTSR

(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Sink

Level 1

R


Sink

Level 1

R









119896






21199032)




119896 119899=



119896 119892= 3(1 + 120583) So the total time


120591119896= 120591119896 119899+ 120591119896 119892= 3120585119896(1 + 120583) + 3 (1 + 120583) (4)



119896minus1is


119896119903 minus 120575119896minus1119903)

119903 (5)


Tier 1

Tier 2

Tier 3

Tier 4

Width

Cell

Cell

Cell

Cell

120579

120575r

Sink

r

R

Cmk





119896119903) sdot (119877 minus 120575

119896119903)

2

minus120579 sdot (119877 minus 120575


119896119903 minus 120575119896minus1119903)

2=120579

21198772

+ 1205752

1198961199032minus 2120575119896119903


119896119903 + 120575119896minus1119903)]

=120579

2minus2120575119896119903

minus [(2120575119896120575119896minus11199032+ 1205752

119896minus11199032) minus 2119877 (120575

119896119903 + 120575119896minus1119903)]

(6)



119896minus1 119899= 3120585119896minus1(1 + 120583)


119896minus1 119899= 120591119896 It is 120585

119896minus1= 120585119896+ 1 after






119896 Since


|119867 (119896119898)| = lfloor1

3lceil2120587 (119877 minus 120575119903)



119896







119889(1 + 120583) +

sum119889minus1

119894=1(1 + 120583)





119898=1119867(119896119898) = 119879






nodes in119879119896+1


in119879119896+1


119863 = ℏ119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (8)




119905



(2) for each tier 119879119896





119898=1119867(119896119898) = 119879

119896


(3) for 119896 = 119889 to 1for 119898 = 1 to ℏ

119896





inner tierend if

end forend for

(4) Output results






119904block 119896 =1205751199032(2119877 minus 120575119903)

2 (119877 minus 120575119903) (9)



119896 119892= 3(1 + 120583) So we get




119863 = 3120588 sdot119903 (2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (10)



1198631015840= ℏ1015840

119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (11)



(12057910158402)(2119877120574 minus 120574


into 1199041015840block 119896 and 1199041015840



1198631015840= 3120588

119903 (2119877120574 minus 1205742)

2 (119877 minus 120574)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (12)


1198631015840minus 119863 = 3120588119903 [

(2119877120574 minus 1205742)


21199032)

2 (119877 minus 120575119903)]

=(119877 minus 120575119903) [2119877120574 minus 120574


21199032]

2 (119877 minus 120574) (119877 minus 120575119903)

(13)


1198631015840minus 119863 =

(120574 minus 120575119903) [21198772+ 120574120575119903 minus 119877 (120574 + 120575119903)]

2 (119877 minus 120574) (119877 minus 120575119903)

ge(120574 minus 120575119903) [2119877

2+ 120574120575119903 minus 119877

2]

2 (119877 minus 120574) (119877 minus 120575119903)

=(120574 minus 120575119903) [119877

2+ 120574120575119903]

2 (119877 minus 120574) (119877 minus 120575119903)

(14)


5 Simulation





119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234





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VWTSRGVWTSRIWTSR

(a)


03

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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





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VWTSRGVWTSRIWTSR

(b)



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(b)



6 Conclusion






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Dela

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VWTSRGVWTSRIWTSR

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Net

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(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tier 1

Tier 2

Tier 3

Tier 4

Width

Cell

Cell

Cell

Cell

120579

120575r

Sink

r

R

Cmk





119896119903) sdot (119877 minus 120575

119896119903)

2

minus120579 sdot (119877 minus 120575


119896119903 minus 120575119896minus1119903)

2=120579

21198772

+ 1205752

1198961199032minus 2120575119896119903


119896119903 + 120575119896minus1119903)]

=120579

2minus2120575119896119903

minus [(2120575119896120575119896minus11199032+ 1205752

119896minus11199032) minus 2119877 (120575

119896119903 + 120575119896minus1119903)]

(6)



119896minus1 119899= 3120585119896minus1(1 + 120583)


119896minus1 119899= 120591119896 It is 120585

119896minus1= 120585119896+ 1 after






119896 Since


|119867 (119896119898)| = lfloor1

3lceil2120587 (119877 minus 120575119903)



119896







119889(1 + 120583) +

sum119889minus1

119894=1(1 + 120583)





119898=1119867(119896119898) = 119879






nodes in119879119896+1


in119879119896+1


119863 = ℏ119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (8)




119905



(2) for each tier 119879119896





119898=1119867(119896119898) = 119879

119896


(3) for 119896 = 119889 to 1for 119898 = 1 to ℏ

119896





inner tierend if

end forend for

(4) Output results






119904block 119896 =1205751199032(2119877 minus 120575119903)

2 (119877 minus 120575119903) (9)



119896 119892= 3(1 + 120583) So we get




119863 = 3120588 sdot119903 (2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (10)



1198631015840= ℏ1015840

119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (11)



(12057910158402)(2119877120574 minus 120574


into 1199041015840block 119896 and 1199041015840



1198631015840= 3120588

119903 (2119877120574 minus 1205742)

2 (119877 minus 120574)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (12)


1198631015840minus 119863 = 3120588119903 [

(2119877120574 minus 1205742)


21199032)

2 (119877 minus 120575119903)]

=(119877 minus 120575119903) [2119877120574 minus 120574


21199032]

2 (119877 minus 120574) (119877 minus 120575119903)

(13)


1198631015840minus 119863 =

(120574 minus 120575119903) [21198772+ 120574120575119903 minus 119877 (120574 + 120575119903)]

2 (119877 minus 120574) (119877 minus 120575119903)

ge(120574 minus 120575119903) [2119877

2+ 120574120575119903 minus 119877

2]

2 (119877 minus 120574) (119877 minus 120575119903)

=(120574 minus 120575119903) [119877

2+ 120574120575119903]

2 (119877 minus 120574) (119877 minus 120575119903)

(14)


5 Simulation





119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234





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VWTSRGVWTSRIWTSR

(a)


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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





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03

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wor

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VWTSRGVWTSRIWTSR

(b)



minus08

minus06

minus04

minus02

0

02

04

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08

1


minus1

minus08

minus06

minus04

minus02

0

02

04

06

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1

(b)



6 Conclusion






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Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119905



(2) for each tier 119879119896





119898=1119867(119896119898) = 119879

119896


(3) for 119896 = 119889 to 1for 119898 = 1 to ℏ

119896





inner tierend if

end forend for

(4) Output results






119904block 119896 =1205751199032(2119877 minus 120575119903)

2 (119877 minus 120575119903) (9)



119896 119892= 3(1 + 120583) So we get




119863 = 3120588 sdot119903 (2119877120575119903 minus 120575

21199032)

2 (119877 minus 120575119903)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (10)



1198631015840= ℏ1015840

119889(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (11)



(12057910158402)(2119877120574 minus 120574


into 1199041015840block 119896 and 1199041015840



1198631015840= 3120588

119903 (2119877120574 minus 1205742)

2 (119877 minus 120574)(1 + 120583) +

119889minus1

sum

119894=1

(1 + 120583) (12)


1198631015840minus 119863 = 3120588119903 [

(2119877120574 minus 1205742)


21199032)

2 (119877 minus 120575119903)]

=(119877 minus 120575119903) [2119877120574 minus 120574


21199032]

2 (119877 minus 120574) (119877 minus 120575119903)

(13)


1198631015840minus 119863 =

(120574 minus 120575119903) [21198772+ 120574120575119903 minus 119877 (120574 + 120575119903)]

2 (119877 minus 120574) (119877 minus 120575119903)

ge(120574 minus 120575119903) [2119877

2+ 120574120575119903 minus 119877

2]

2 (119877 minus 120574) (119877 minus 120575119903)

=(120574 minus 120575119903) [119877

2+ 120574120575119903]

2 (119877 minus 120574) (119877 minus 120575119903)

(14)


5 Simulation





119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234





minus1

minus08

minus06

minus04

minus02

0

02

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08

1



minus02

minus06

minus04

minus08

04

06

08

02

minus1

0

1







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(a)

minus1

minus08

minus06

minus04

minus02

0

02

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1


(b)



0

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(a)


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12N

etw

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relia

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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





0

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minus1

minus08

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(b)



6 Conclusion






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Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 190258 143240 92219 42201 17180120583 = 2 112324 68276 29240 11210 2186120583 = 4 38327 14321 5252 0219 0183



119901

120583 119901 = 04 119901 = 05 119901 = 06 119901 = 07 119901 = 08

120583 = 1 295303 217288 134273 71249 28234120583 = 2 162378 111348 56312 17267 7240120583 = 4 76456 20381 11330 5273 4234





minus1

minus08

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minus04

minus02

0

02

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08

1



minus02

minus06

minus04

minus08

04

06

08

02

minus1

0

1







0

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umbe

r of p

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(a)

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(a)

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(b)








minus08

minus06

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02

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(a)

minus1

minus08

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minus02

0

02

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08

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(b)



0

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(a)


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etw

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(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





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minus1

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(b)



6 Conclusion






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(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

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220N

umbe

r of p

acke

ts lo

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(a)

180

200

220

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300

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Dela

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(b)


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(a)

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(b)








minus08

minus06

minus04

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0

02

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08

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(a)

minus1

minus08

minus06

minus04

minus02

0

02

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(b)



0

50

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VWTSRGVWTSRIWTSR

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etw

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relia

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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





0

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02

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minus1

minus08

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(b)



6 Conclusion






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(b)



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VWTSRGVWTSRIWTSR

(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minus08

minus06

minus04

minus02

0

02

04

06

08

1

(a)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


(b)



0

50

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Dela

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(a)


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etw

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relia

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VWTSRGVWTSRIWTSR

(b)




120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





120583 = 2 120583 = 4

Schemes 119901 = 04 119901 = 06 119901 = 08 119901 = 04 119901 = 06 119901 = 08





0

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minus1

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(b)



6 Conclusion






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VWTSRGVWTSRIWTSR

(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

50

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minus1

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(b)



6 Conclusion






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(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

50

100

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(tim

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(a)


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Dela

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11

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wor

k re

liabi

lity


VWTSRGVWTSRIWTSR

(b)




Acknowledgments



References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article minimized delay with reliability...

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