research article ecots: efficient and cooperative task sharing...

Research ArticleeCOTS Efficient and Cooperative Task Sharing forLarge-Scale Smart City Sensing Application

Qingyu Li and Panlong Yang

College of Communication Engineering PLA University of Science and Technology Nanjing 210007 China

Correspondence should be addressed to Panlong Yang panlongyanggmailcom

Received 5 July 2013 Revised 23 October 2013 Accepted 3 November 2013 Published 12 January 2014

Academic Editor Yunhuai Liu

Copyright copy 2014 Q Li and P Yang 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

With the pervasive use of mobile devices and increasingly computational ability more concrete and deeper collaborations amongmobile users are becoming possible and needed However most of the studies fail to consider load balancing requirement amongmobile users When tasks are unevenly distributed the processing time as well as energy consumption will be extremely high onsome devices whichwill inevitably counterweight the benefits from incentivemechanism and task scheduling scheme In this workwe propose eCOTS (Efficient and Cooperative Task Sharing for Large-scale Smart City Sensing Application)We leverage the ldquoballsand binsrdquo theory for task assignment where 119889mobile users in contact range are investigated and select the least loaded one amongthe d users It has been proved that such simple case can effectively reduce the largest queueing length from 120579(log 119899 log log 119899) to120579(log log 119899 log 119889) Simulation and real-trace driven studies have shown that eCOTS can effectively improve the balancing effects intypical network scenarios even the energy level and computational capability are diverse In simulation study eCOTS can reducethe gap between the maximum and minimum queueing lengths up to 5times and over 2times in real trace data evaluations

1 Introduction

Recent years have witnessed a significant rise in the usageof smart phone as well as the associated applications Withthe increasing number of mobile devices in network peoplewould share their data with mobile devices and make furthercollaborations with each other Recently crowdsourcing withparticipatory sensing schemes enables more unconsciousand volunteering collaborations among sensing informationshareholders Actually in such mobile computing environ-ment deeper collaborations are needed Mobile users withdifferent number of tasks will share and reassign tasks amongthem taking advantages of computing and energy diversityFor example users with low battery level will offload theirtasks onto the contacted users in communication ranges withhigher battery level Even further tasks should be assigned tonodes with higher computing ability

However previousworks [1ndash5] fail to achieve load balanc-ing among users Under these schemes the queuing lengthmay be extremely high in some particular nodes which willinevitably lead to exhausted energy and long delay The rootreason is that these works are all focusing on the data sharing

efficiency instead of the allocation equilibrium among diverseusers Moreover computational capability and remainingenergy levels are also vitally important for task reallocation

Traditional load balancing schemes cannot be appliedto mobile social network directly because in mobile socialnetwork the information collection and task assignmentshould be distributed Centralized schemes will suffer fromoverwhelmingly communication overhead and time delayEven though the distributed features are applied such assome of the distributed algorithms the transitory inter-contact time and dynamic queueing length [6 7] makingthis task assignment fail to balance the tasks among usersproperly

Actually a simple and effective method is called forbalancing the tasks among mobile users which is criticallyimportant for smart phone based large-scale urban sensingapplications Unfortunately balancing the tasks allocationamongmobile users is not trivial First task balancing amongmobile users needs accurate buffering information for eachuser which will cost significant amount of bandwidthSecond multiple task-assignment users and unpredictabletask completion time will incur dynamic buffer-length

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 463876 14 pageshttpdxdoiorg1011552014463876

2 International Journal of Distributed Sensor Networks

which makes the balanced queue length difficult to achieveThird it is difficult tomeasure the intercontact time inmobilesocial network which makes it difficult to evaluate the taskcompletion time Also the remaining energy level andcomputational diversity among users should be consideredfor fair and balanced task allocation

In this work we propose eCOTS (Efficient and Coop-erative Task Sharing for Large-scale Smart City SensingApplication)We address the above three challenges with twoimportant techniques First we use the ldquotwo choicesrdquo schemein ldquoballs and binsrdquo theory [8] as fundamental mechanism fortask offloading where queuing lengths of 119889 users are com-pared and userswith the least value are selected Such schemeis simple but effective The root reason is that random walkalso plays the role of random selection Second we leveragethe random walk behavior for random choice and considerthe energy level as well as computational capability for taskreassignment We find that the considerations for energyconsumption and computational capability effectively offsetthe uncertainty inmobility without addingmuch complexityThe root reason is that energy consumption is also an implicitfactor for intercontact time Further the computational capa-bility also dominates the task allocation preference as well asinter contact frequency We verified the effectiveness of theproposed techniques in our extensive experimental study

The contribution of this work is threefold

(i) We propose eCOTS an efficient cooperative taskshared among smartphone users for large-scale urbansensing applications To the best of our knowledgewe are the first systematic study on balanced taskassignment in pure distributed environment

(ii) We incorporate the energy level and computationalcapability in task-assignment scheme which could bein appliance with heterogeneous mobile social net-work eCOTS can deal with these two cases separatelyand jointly with satisfiable performance Also theseconcerns are helpful in achieving the robustness inmobile environment

(iii) We make an extensive experimental study on ourproposed scheme The evaluations include the taskbalancing effects in different traffic load under dif-ferent energy levels and computational capabilitiesExperimental results based on real trace data show thesurprisingly good balancing property even though thevariance and diversity between users are very large

The rest of the paper is organized as follows We describeour system model in Section 2 Section 3 provides problemformation as well as preliminary analysis about it Afterdescribing our algorithm design in Section 4 We evaluatethe performance of eCOTS by simulation in Section 5 andmake real trace driven study in Section 6 Finally we discussrelated work in Section 7 and conclude the work in Section 8

2 Preliminary and System Model

21 ldquoBalls and Binsrdquo Theory The ldquoballs and binsrdquo problem isclassic and simple being widely used in many applications

in computer science such as hashing [9 10] shared memoryemulations in DMM (Distributed Memory Machines)[11 12] and load balancing with limited information Thebasic problem is very simple Given 119899 nodes are to be throwninto 119899 bins where each ball is chosen to each bin uniformlyand independently the focus is themaximum loaded bin thatis the largest number of balls in all the bins is approximately

log 119899log log 119899

(1)

If the balls are thrown sequentially and each ball is placedin the least loaded bins of 119889 ge 2 the maximum load is

log log 119899

log 119889+ Θ (2)

with high probability We call this method ldquo119889-choiceparadigmrdquo

When the number of balls 119898 is larger than 119899 especially119898 ≫ 119899 log 119899 the maximum load of random choice is

119898

119899+ radic

119898 log 119899119899

(3)

while for the ldquo119889-choice paradigmrdquo the maximum load is

119898

119899+log log 119899

log 119889 (4)

Notably there is also a very interesting and beneficialproperty in ldquo119889-choice paradigmrdquo This property motivatesus to take this method into task assignment and balancingscheme where increasing the number of tasks will notincrease the variance of the queue length

The ldquo119889-choice paradigmrdquo has been widely studied andextended for many interesting aspects For example manystudies [8] focus on the weighted balls and bins which ispractical and useful in real task assignment For computersystem and networks the parallel execution studies withoverhead considerations are very useful and get manyconcentrations [6 7]

In our study the ldquo119889-choice paradigmrdquo is useful butshould be tailored for our investigated problem We willintroduce our system model and the investigated problem inthe following paragraphs

22 Modeling the Users and Tasks We consider a mobilesocial network where 119899 users in user set 119880 = 1 2 119899will share their tasks among them For each task there isa metric in evaluating its difficulty which corresponds tothe weight of a task 0 le 119908

119894119895le 1 is the weight of the

119895th task on user 119894 The weight can be represented as thedifficulty for completing a task which is directly relevant totask completion time as well as energy consumption Eachuser 119894 isin 119880 holds a task set 119879

119894= 1198791198941 119879

119894119898 For each task

from user 119894 when it is reallocated to another user 119895 it willbe processed at 119895 without being further forwarded We donot consider multiforwarding case in this study We put it tofuture work and social mapping technologyThe tasks in user

International Journal of Distributed Sensor Networks 3

Tasks

Tasks

Tasks

Tasks

Tasks

User 2Compare

User 1

User 3

Communication

Energy level

range

Communication

range

Figure 1 Basic scheme of task offloading and reassignment

119894have not been given priority here andwe donot consider theldquodequeueingrdquo and ldquoenqueueingrdquo technologies for task prioritybecause in social task offloading network there should bevery few urgent tasks for reassignmentThe tasks with higherpriority should be processed on local device

The tasks getting from other users are listed in queue119876119894=

1199021198941 1199021198942 119902

119894119898 and the queueing length is 119876

119894

23 Modeling the Energy Level and Computational CapabilityEach user 119894 has an energy level 119864

119894 For each processing of

the reallocated task a corresponding amount of energy isconsumed In our model it is proportional to task weightMore difficult tasks will cost more energy and we set theenergy-cost model linear here For example the energy costfor task 119879

119894119895is 119864119894119895

= 120572119908119894119895 where 120572 is a scaling factor and

depends on the user device We assume energy consumptionmodel among users is identical The root reason is thatwe are focusing on the load balancing scheme in networkAlso we discuss the tasks and devices with different weightswhich can be easily and reasonably extended to energy levelCombining the resources allocation and task reassignmentwill be left for future work

Another fact is that the execution time is inverselyproportional to the computational capability which willaccordingly affects the queueing length In our model thetask queue is processed according to usersrsquo capability thatis the queuing length 119876 is inversely proportional to thecomputational capability

24 Modeling the Mobile Social Network Each user performsrandom walk in a finite area There are totally 119899 users ran-domly roaming in an area where a communication range119877 isset for each mobile user When two nodes are in the commu-nication range of each other the tasks can be reallocated Asthe data transmission rate is comparatively high with the task

information we assume the task reallocation period is suffi-cient when two nodes are roaming in communication rangeWe also assume that the inherent parameters in each user forexample the energy level queueing length and the compu-tational capabilities can also be exchanged during the inter-contact time between users The basic scheme is shown inFigure 1 In this picture we can see our model of task offload-ing and reassignment more clearly When User 1 is doing theallocation he or she is considered as the center of his or hercommunication circle For example there are in total 5 userswithin the communication range User 1 just picks randomlytwo of them (User 2 andUser 3) and deliver the task to the lessloaded one (User 2)More extensively User 1 can also reassigntasks to other users according to different metrics

3 Problem Formation

31 Basic Problem We investigate the task of offloading andbalancing scheme for mobile social network In particularbalancing among users means an even distribution of thetasks The goal is to minimize the sum of queueing lengthdifference between each one and the average value which canbe given by

minsum

119894isin119880

1003816100381610038161003816119876119894 minus 119864 [119876119894]1003816100381610038161003816 (5)

where 119864[sdot] is the average value for random variables

32 Evaluating theGap betweenMaximumand theAverage Itcan be formulated byminimizing the gap between the averagevalue and the maximum queueing length achievable withhigh probability This evaluation has two advantages Firstit is simple Instead of computing the gap between averagevalue and all the queues the maximum queueing length isinvestigated which saves large amount of communication


Inputthe number of users 119899the number of time slots119898communication range 119903location edge (usersrsquo locations canrsquot go beyond the edge) 119890119889119892119890number of choice 119889

Outputqueue length 119888

1 1198882 119888

119899

queue length (considering task weight and usersrsquo ability) 1199081 1199082 119908

119899

(1) Initialize 1198881 1198882 119888

119899 = 0

1199081 1199082 119908

119899 = 0 119888119900119906119899119905 = 0

(2) while 119888119900119906119899119905 lt 119898 do(3) randomly generate usersrsquo locations (119883

119894 119884119894)

0 lt 119883 lt 119890119889119892119890 0 lt 119910 lt 119890119889119892119890 1 le 119894 le 119899

(4) for every user 119895 1 le 119895 le 119899(5) if (119883

119894minus 119883119895)2+ (119884119894minus 119884119895)2lt 1199032 then

(6) record that (119883119894 119884119894) is in communication range of user 119895

(7) end if(8) if number of users in range ge 119889 then(9) randomly choose 119889 of them(10) 119904 = the one with shortest length among the 119889-choice(11) else if 0 lt the number of users in range lt 119889 then(12) 119904 = the one with shortest length in range(13) else if nobody is in range then(14) continue allocation(15) end if(16) 119888

119904= 119888119904+ 1

(17) 119908119904= 119908119904+ 119905119886119904119896119908119890119894119892ℎ119905(119888119900119906119899119905)119886119887119894119897119894119905119910(119904)

(18) 119888119900119906119899119905 = 119888119900119906119899119905 + 1

(19) end while(20) return 119888

1 1198882 119888

119899 1199081 1199082 119908

119899

Algorithm 1 eCOTS algorithm for large-scale smart city sensing application

overhead in distributed mobile networks Without loss ofgenerality such evaluation is also reasonable Second it isalso an importantmetric in evaluating theworst case betweenthe average cases For example we need to know the taskfinishing time in average and the worst Also in batched taskoffloading case the task finishing time depends on the latestone which corresponds to the longest queueing lengthThussuch evaluation can be given by

minmax119894isin119880

10038171003817100381710038171198761198941003817100381710038171003817 minus 119864119894isin119880

[119876119894] (6)

33 Allocate withWeighted Tasks andDifferent ComputationalCapability We investigate the allocation scheme A whereeach task is given different weights Similarly the evaluationcan be represented by

minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896) minus 119864119894isin119880

[119882 (119876119894)] (7)

where119882(119876119894) = sum

119876119894

119896119908(119902119894119896)

When the nodes are given different computational capa-bilities the representation can be given by

minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896)

119888119894

minus 119864119894isin119880

[ (119876119894)] (8)

where (119876119894) = sum119876119894

119896119908(119902119894119896)119888119894

4 Algorithm Design

41 eCOTS Overview Our algorithm is leveraging two basiccharacteristics in random based paradigm with theoreticalguarantees One is the 2-choice paradigm where investigat-ing 2 choices is nearly optimal in practice The other is therandomness inmobile sensor network especially the randomwalk behavior The stationary distribution over the visitingfrequency and diversity among users provides sufficientchoices as well as randomness for task reassignment Insummary our basic idea is simple There are basically twoparts in our algorithm First the algorithm will select theusers in communication range according to the number ofusers in range Second according to the ldquo119889-choice paradigmrdquothe users are selected for task reassignment according to theirqueueing length Notably when the energy level and com-putational capability are considered the problem is similar


0 5 10 15 20 25

Empirical CDF

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

2-choice

(a) Range 119903 = 5

0 5 10 15 20 25 30 35 40

Empirical CDF

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

2-choice

CDF

of u

sers

rsquo que

ue le

ngth

s

(b) Range 119903 = 10

0 5 10 15 20 25 30 35 40

Empirical CDF

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

2-choice

CDF

of u

sers

rsquo que

ue le

ngth

s

(c) Range 119903 = 20

Figure 2 Choice performance in the communication range

to weighted bin case in ldquoballs and binsrdquo theory Howeverconsidering energy level brings negative impact Such prop-erty is different from traditional weighted bin case Whilewe consider the computational capability case it differs fromweighted bin theory because for the traditional weightedbin problem selecting the higher weight bin with higherprobability is not favorable However in our concern as theexecution time is inversely proportional to the computationalcapability selecting users in higher capability with higherprobability accordingly is favorable and reasonable In thefollowing subsection we will describe our algorithm eCOTSin detail

42 Algorithm Description on eCOTS According to theabove derivation we present the algorithm description ontask allocation in mobile case as Algorithm 1 The inputparameters are the number of users 119899 the number of timeslots 119898 the communication range 119903 the location edge 119890119889119892119890(usersrsquo location cannot go beyond the edge) and the choicenumber 119889 The amount of tasks a person has accepted isrecorded as queue length 119888 but considering that tasks are notidentical and usersrsquo ability is in diversity we provide the task

length 119908 Here we do our allocation work according to theapparent queue lengths of users

At the beginning of our Algorithm 1 both queue lengthsand the allocation time slot are initialized with 0 And thenwhen the allocation time slot arrives we first randomly gen-erate usersrsquo locations (119883

119894 119884119894) after that for every single user

119895 we check whether the other users are in communicationrange and record the in-ones If the number of users in rangeis no less than 119889 for example 2 in 2-choice paradigm wearbitrarily choose 119889 users out of them in advance instead ofdelivering the task to a random person After comparison wegive the task to the one who has the shortest length amongthe 119889 selected users When the number of users in range issmaller than 119889 we can also choose the shortest queue amongthem and allocate the task to the chosen one Further ifthere is nobody in communication range we just continuethe task allocation in the next time slot After choosing theright person 119904 to deliver the task let the queue length of 119904 add1 119888119904= 119888119904+ 1

Considering that every task has its own difficulty andeach personrsquos ability to deal with the task is in diversity thetask length is totally different from what we can see it isthe actual complexity of every task queue We measure this


0 20 40 60 80 100 120

Empirical CDF

Random

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice

(a) Task weight random 1ndash5

0 200 400 600 800 1000

Empirical CDF

Random

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice

(b) Task weight random 1ndash50

0 2000 4000 6000 8000 10000 12000

Empirical CDF

Random

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice

(c) Task weight random 1ndash500

Figure 3 2-choice performance with different task weights comparing queue lengths only

with119908 in addition119908 should be added by the correspondingvalue of person 119904 with 119886119887119894119897119894119905119910 (119904) processing the current taskwith 119905119886119904119896119908119890119894119892ℎ119905 (119888119900119906119899119905) When all the users have finishedtheir allocation at time 119888119900119906119899119905 we can continue our taskallocation with above steps until the allocation time slot119888119900119906119899119905 = 119898

5 Simulation Results

In this section we conduct extensive simulations to evaluateeCOTS algorithm The overall methodology and simulationsettings are introduced firstly Afterward we evaluate theperformance of eCOTS in terms of different parametersettings Table 1 summarizes the parameters frequently usedin this paper

51 Implementation Methodology and Simulation SettingsIn this simulation we emulate a realistic and meaningfulscenario for mobile social network as follows For eachtime slot 119894 119899 users randomly walked in a square region of

Table 1 Parameter settings

Parameter SettingTotal number of users 119899 100Communication range 119903 5 10 20mTime slot number 119868 30Task weight 1ndash5 1ndash50 1ndash500Usersrsquo computational ability 1ndash5

100m times 100m As a result for user 119896 the location (119883119906 119884119906) is

randomly generated where 0 lt 119883 lt 100 0 lt 119910 lt 100 1 le

119906 le 119899 Users in the communication range 119903 can contactwith each other switching basic information and reassigningthe tasks In each time slot each user will share only onetask thus 119899 users allocate their respective tasks (in total 119899)in each time slot For each task the person who launchesthe task allocation is considered as the center point of thecommunication circle We calculate the distance with everyother user to find the candidates Among the candidates wepick two of them randomly and compare the queue length


between them delivering the current task to the one withshorter queue length In more practical case the weight oftasks the diversity of usersrsquo ability and energy consumptionare also taken into consideration and we set up the varioussituations for our experimental evaluations

52 Performance Evaluation of eCOTS We compare eCOTSwith the simple random delivering approach based on fourmetrics (1) the communication range (2) tasks with differentdifficulties (3) the users owning diverse abilities (4) energyconsumption We evaluate the impacts of four factors on theperformance of eCOTS as follows Additionally we considerthe most complicated situation

521 Impact of Communication Range We need to compareeCOTS with the initial random allocation in different com-munication ranges Here we choose 100 users and 30 timeslots To show the results more obviously we experimentidentical case where each task has the unit weight (ie 1) andeach user has the same ability to process the task

As shown in Figure 2(a) when the communication rangeis set to 5meters eCOTS and random allocation do not havemuch difference The main reason is that communicationrange 119903was too small to find enough candidates For exampleif we find only one person in each search eCOTS hasnothing different with the random allocation Moreover ifnobody can be found in communication range there is noallocation among users then With the increased commu-nication range 119903 we can discover obviously that eCOTSoutperforms random allocation Let us see Figure 2(b) inwhich the communication rang is set to 10 meters whilerandom allocation brings about the maximum queue lengthof users with 38 and the minimum with 17 the maximumload is twofold high over the minimum load By contrasteCOTS algorithm narrows the difference into 4 and theload of every user approach to the balance level (total taskamountuser) 30 which is a favorable property Moreover asshown in Figure 2(c) the allocation results of 119903 = 30 indicatethat eCOTS is better than random allocation too

Further we also perform the comparison between eCOTSand optimal case (reassign tasks to the least loaded userswithin the communication range) in Figure 4 Since the fullline (eCOTS) almost coincides with the dotted one (optimalcase) we have no doubt to believe that eCOTS algorithmworks perfectly With the eCOTS algorithm no person bearstoo much work to do while some other users have little taskto process

522 Impact of Task Weight We need to evaluate the impactof task weight on the eCOTS performance In this experi-ment we make a slight modification on the previous settingswhere every task has its own weight As we all clearly knowthat different tasks have different difficulties we should makethe more difficult tasks owning far more weight than the easyoneThe person we choose to deliver the task actually will notjust add its task length by 1 but also the given task weight

To demonstrate the better performance of eCOTS welet the task weight vary from 1ndash5 1ndash50 1ndash500 If we have

20 21 22 23 24 25 26 27 28 29 30

Empirical CDF

Optimal

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

2-choice

Figure 4 2-choice performance versus optimal case (identical)

access to know about the task length of everyone we canhave the picture as in Figure 5 It shows comparison betweeneCOTS and random allocation in task length Comparingwith Figure 3 the case that users cannot know the task loadof others only knowing the number of tasks The differencebetween the maximum load and minimum load has beennarrowed significantly As shown in Figure 5(a) we find thateCOTS algorithm is almost the same as the optimal casewhich indicates that eCOTS algorithm really works in taskallocation

In summary eCOTS method achieves a much betterperformance rather than random allocation in terms of taskweight

523 Impact of Usersrsquo Computational Ability In social net-work users have diversity in ability An able man alwaysshould do more work we take this factor into our considera-tion To quantify different usersrsquo ability we simply set theirability with 1ndash5 levels That is to say if a personrsquos ability is4 the processing speed will be 4 times faster than the basiclevel that is level one Concretely in our experiments whena person is picked to handle a task the task length is addedby 1119886119887119894119897119894119905119910(119895) where 119895 is the label of user

As shown in Figure 6 we first allocate our tasks accordingto the queue length While it shows great superiority inqueue lengths of users the performance is not satisfactorywhen incorporating into the diverse ability On account ofthis issue we assume that everyonersquos ability is widely knownin our experiments In Figure 7 the full line represents oureCOTS method and the dotted one is on behalf of therandom allocationmethod Obviously our method performsmuch better than the random allocation method because thedistribution of queue length of users is centering at the perfectaverage point

524 The Impact of Energy Consumption Task executionwill cost energy consumption In task allocation we mustconsider the metric of usersrsquo energy Apparently we may notgive the task to the user with limited energy although this


0 20 40 60 80 100 120

Empirical CDF

OptimalRandom

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice


0 200 400 600 800 1000 1200

Empirical CDF

OptimalRandom

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice


0 20001000 40003000 60005000 7000 90008000 10000

OptimalRandom

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice

Empirical CDF


Figure 5 2-choice performance comparing the task length

user may be the one bearing the least load In other words weneed to consider usersrsquo energy levels in advance and the queuelength of every user as well Each user has full energy 100 atthe start of allocation Every time when we allocate a taskwe choose the energetic one (the one who has more energy)from random 2 The chosen user will lose 1 point energy Asshown in Figure 8 eCOTS method (the full line) performsmuch better than random allocation (the dotted line)

525The Impact of Parameter-d Setting After we finished allthe work above we begin to study the impact of parameter-119889setting In the ldquoballs and binsrdquo theory it is well known that ifwe increase the number of119889 the performance of119889-choicewillbe even better Based on this we set parameter-119889 as 2 3 4and the results of identical case are shown in Figure 9 wecan easily find that although the performance of 4-choice isonly a little better than 2-choice considering that seeking twomore usersrsquo information will also cost a lot 2-choice is goodenough for our task allocation in mobile social network

6 Trace Driven Evaluation

According to the simulation results above we find that ldquo2-choicerdquo has shown great superiority in the typical scenarioof mobile social network while simulation is obviously notenough to convince our algorithm As a matter of fact weneed trace-driven performance evaluation to put up theadaptability of ldquo2-choicerdquo in real world

61 Trace Data Processing The trace we use is Rollernet[14] which is the public data collected with iMotes in theroller tour in Paris RollerNet was interested in trackingcontacts between differentmobile usersThe data set has beencollected in August 20 2006 According to organizers andpolice information about 2500 people participated in therollerblading tour The total duration of the tour was aboutthree hours During the tour the iMotes has been deployedto 62 skaters The experiment successfully recorded contactsbetween not only all devices they distributed but also a large


0 10 20 30 40

Empirical CDF

0 10 20 30

Empirical CDF

Task length

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s2-choice

Random2-choice

Figure 6 2-choice performance versus random allocation considering usersrsquo ability comparing queue lengths

Table 2 Contact records of User 1

User 1 User 2 Starting time Ending time Encounter times Duration1 2 1156092016 1156092016 69 421 2 1156092060 1156092071 70 441 2 1156092099 1156092099 71 281 2 1156092143 1156092143 72 441 2 1156092148 1156092148 73 51 2 1156092432 1156092432 74 2841 3 1156084911 1156084911 1 01 3 1156084920 1156084950 2 91 3 1156084987 1156084997 3 371 3 1156085035 1156085035 4 381 3 1156085041 1156085043 5 61 3 1156085064lowast 1156085075 6 211 3 1156085077 1156085077 7 2lowastTime slot (1156085064 minus 1156000000)60asymp1417

amount of external devices (cell phones PDAs) Tomake surethe trace is authentic and faithful we only pick the contactsrecorded between iMotes to continue our work

Part of User 1rsquos original contact file is in Table 2 the firstand second columns give the IDs of the devices which thecontact is reporting The third and fourth columns describerespectively the first and last time when the address of ID2was recorded by ID1 or the address of ID1 was recorded byID2 for this contact The fifth column enumerates contactswith the same ID1 and ID2 as 1 2 The last columndescribes the time difference between the beginning of thiscontact and the end of the previous contact with the sameID1 and ID2

Back to our model we do the allocation task in everytime slot Here we should divide the original time data into aseries of time slots From Table 2 we find that Starting Timeshave a public basic value 1156000000 For convenience letStartingTimes subtract basic value 1156000000 After that wechange the time unit from second tominute and then sort themeeting time in ascending order for example 1156085064 minus1156000000 = 85064 8506460 asymp 1417

62 Algorithm Implementation

621 One User Allocating Tasks Let us start our algorithmin this way First we should find out the users that User 1


0 5 10 15 20 25 30 35

Empirical CDF

CDF

of u

sers

rsquo tas

k le

ngth

s

Random

0

01

02

03

04

05

06

07

08

09

1

Task length

2-choice

Figure 7 2-choice performance versus random allocation consid-ering usersrsquo ability comparing task length

0 10 20 30 40 50 60 70 80

Empirical CDF

Energy level

1

09

08

07

06

05

04

03

02

01

0

Random2-choice

CDF

of u

sers

rsquo ene

rgy

leve

ls

Figure 8 eCOTS performance versus random allocation consider-ing usersrsquo energy

24 25 26 27 28 29 30 31

Empirical CDF

d = 2

d = 3

d = 4

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

Figure 9 Impact of parameter-119889 setting

met in the same time slot Then in every time slot if User1 comes across more than 119889 users randomly picks 119889 of themand offload the task to the less loaded one Otherwise if thenumber is smaller than 119889 then just give the task to the leastloaded one among them Setting 119889 in different values we getgraphs as Figure 10 In Figure 10(a) when 119889 = 2 although thefigure is a little undulating comparing with the performanceof the random allocation below 2-choice has a superioritywith no doubt Moreover larger 119889 will lead to better taskbalancing performance Remarkably the value of 119889 cannotreach too high because the number of users encountering ina time slot is limited

622 All Users Allocating Tasks In the social mobile net-work users reassign their tasks distributivelyWe should takeall users into consideration as Figure 11(a) We prefer thatusers do their allocation in the same time slot Of coursethe longer the contact interval is the more people will dotheir allocation in one time slot We set the interval into60 120 and 300 seconds respectively the performance ofeCOTS (119889 = 2) allocation and random allocation is shown inFigure 11We find that the queue length of eCOTS is relativelystable while that of random allocation is highly dynamicWhen time interval is 300 seconds standard deviation isbigger than that of 60 secondsmainly because users will meetmore users in a single time slot and the 119889 users are moreuncertain If the time interval is too small to get enough userto choose we have to give the task to the only one in thecurrent time slot In our experiments the queueing length ofuser with ID23 does not reach the average level most of thetimeAfter checking the original trace data we find the reasonis that the contact records of User 23 are fewer than othersrsquowhen 119889 = 4 the CDF figure of eCOTS and random allocationis shown in Figure 12 As expected eCOTS still performsbetter than random choices With the increased contactinterval eCOTS performs better Notably we also find thatwhen contact interval increases to 300 s the performanceof eCOTS improves significantly where minimum lengthand maximum length are 18 and 35 respectively While forrandom choices although the minimum queueing lengthalso reduces (to 15) the maximum length is not decreasedaccordingly (still over 45)

7 Related Work

Our work relates to the efficient data transfer scheme overdisruption-tolerant networks or opportunistic networks Theintermittent contact between randomly roaming users isuseful for data sharing betweenmobile usersThese networkshave been studied extensively in a variety of settings frommilitary [4] to disasters [5] These settings all assume thatthe fixed infrastructure is unavailable or costly even highlyunreliable With numerous cheap and distributed workingterminals some expensive works can be accomplishedsuccessfully Further the communication links are subjectto disruptions and the opportunistic access will bring morechances for data sharing In summary our work relates tothree research topics which are crowdsourcing schemes


0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

minus5

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

(a) 119889 = 2

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

minus5

(b) 119889 = 4

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

minus5

(c) 119889 = 6

Figure 10 119889-choice in User 1

randomwalk and ldquoballs and binsrdquo theory As ldquoballs and binsrdquotheory has been introduced in Section 2 in this sectionwe mainly introduce the related works on crowdsourcingschemes for cooperative task accomplishment and theliteratures on random walk studies

71 Crowdsourcing Schemes for Cooperative Task Accomplish-ment Many working crowdsourcing systems are concentrat-ing on many researchers and industrial efforts in terms ofdesigning actual platforms like [13 15 16] These workingsystems also need extensive evaluation with solid results like[1 2] Further and more importantly there are many studiesfocusing on pricing schemes for effective crowdsourcing

incentives [3] In smart city sensing applications crowdsourc-ing paradigms leverage the pervasive human behavior forexample walking driving shopping and so forth to providea large-scale urban sensing network with wider coverage intime and space domain Moreover the social relationship forexample the crowd gathering and migrations is also impor-tant for some specific applications for example the flu influ-ence detection air quality traffic monitoring and so forthThepopularity of smartphone also speeds up the crowdsourc-ing based applications for urban sensing Recently the crowd-sourcing based sensing applications are exploited to monitorthe urban environment [17ndash20] More specifically Mun et al[19ndash21] employ the customized and portable sensors on each


0 10 20 30 40 50 60 700

100

200

300

0 10 20 30 40 50 60 700

100

200

300

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth

(a) Contact interval 60 s

0 10 20 30 40 50 60 700

50

100

150

0 10 20 30 40 50 60 700

50

100

150

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth

(b) Contact interval 120 s

0 10 20 30 40 50 60 700

20

40

60

20

40

60

0 10 20 30 40 50 60 700

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth

(c) Contact interval 300 s

Figure 11 Performance of eCOTS (119889 = 2) and random allocation in different contact intervals

participant tomonitor the air quality of the cityThe construc-tions of noise map for the smart city are discussed in [17 22]Leveraging the cell phone microphones of the participantsthese works focus on the implementation of the monitoringsystem However they fail to consider the unreliability andinaccuracy of the observations in the participatory sensing

72 Random Walk The random walk concept was proposedby Pearson [23] We are interested in random walks incity scale where a walker starts from a source node toa destination node and for each step of this travel Notethat in mobile social network the social relationship andhuman behavior dominate the trajectories of the humangraph Although in some specific trajectories it does follow

the random walk character the mass number of users canform a relatively steady distribution of random walk Theinherent reason is the law of large numbers [24]

Fortunately random walks can be put into mobile socialnetwork for exploring the character and opportunities indata transmissions For instance Newman [25] proposes therandom-walk betweenness centrality such kind of metricreasonably defines how often a node in a graph is visited by arandomwalker between all possible node pairs Similar to thebetweenness evaluation Noh and Rieger [26] introduce therandom-walk closeness centrality metric which measureshow fast a node can successfully get a random-walk messagefrom other mobile nodes in the random deployed systemsuch as mobile social networks These works provide us witha guarantee that there are relatively robust closeness between


0 20 40 60 80 100 120

Empirical CDF

eCOTSRandom

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s


0 20 40 60 80 100 120

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom


0 10 15 205 4025 30 35 45

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom



users even if they are randomly mobile users And furtherthe messages can be delivered relatively stable among userswith high probability of convergence

The main focus of this paper is load balancing in dis-tributed crowdsourcing system Different from previouscrowdsourcing based applications we use a pure distributedcomputation and communication model where users neednot transmit any messages for centralized computation Inlarge-scale urban sensing application such property wouldbe welcome because it will not bring much trouble to themobile users Also difficult tasks can be cooperatively sharedby mass number of users which can fully explore the energyusage among users and provide more reasonable usages oncomputational capability

The random walk model in our study is also realistic andapplicable to mobile social networks We use the simulationmodel as well as real trace data Both network scenarios haveshown the effectiveness of our proposed scheme

8 Conclusion

In this work we investigate the task offloading and reassign-ment problem in mobile social network In particular wefocus on the load balancing issue for efficient task executionfor energy constrained mobile device We propose eCOTS(Efficient andCooperativeTask Sharing for Large-scale SmartCity Sensing Application) Our algorithm leverages the ldquo119889-choice paradigmrdquo for ldquoballs and binsrdquo problemWhenmobile


users are in communication range only 2 users are selectedand compared for the least loaded checking Such simplescheme ensures balanced allocation even the energy level andcomputational capability are highly dynamic

In future work we are going to investigate the multilevelforwarding case for efficient and balanced load allocationAlso trace-driven performance evaluations are needed formore convincible algorithm validation

Conflict of Interests

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

Acknowledgments

This research is partially supported by NSF China underGrants nos 61003277 61232018 61272487 61170216 and61172062 NSF CNS-0832120 NSF CNS-1035894 andChina 973 Program under Grants nos 2009CB3204002010CB328100 2010CB334707 and 2011CB302705

References

[1] M S Bernstein J Brandt R C Miller and D R KargerldquoCrowds in two seconds enabling realtime crowd-poweredinterfacesrdquo in Proceedings of the 24th Annual ACM Symposiumon User Interface Software and Technology (UIST rsquo11) pp 33ndash42October 2011

[2] M S Bernstein G Little R C Miller et al ldquoSoylent a wordprocessorwith a crowd insiderdquo inProceedings of the 23rdAnnualACM Symposium on User Interface Software and Technology(UIST rsquo10) pp 313ndash322 October 2010

[3] P G Ipeirotis F Provost and J Wang ldquoQuality managementon Amazon Mechanical Turkrdquo in Proceedings of the HumanComputationWorkshop 2010 (HCOMP rsquo10) pp 64ndash67 July 2010

[4] P Marshall ldquoDARPA progress towards affordable dense andcontent focused tactical EDGE networksrdquo in Proceedings ofthe IEEE Military Communications Conference (MILCOM rsquo08)November 2008

[5] K Fall G Iannaccone and J Kannan ldquoA disruption-tolerantarchitecture for secure and efficient disaster response com-municationsrdquo in Proceedings of the International Conferenceon Information Systems for Crisis Response and Management(ISCRAM rsquo10) 2010

[6] L Rudolph M Slivkin-Allalouf and E Upfal ldquoA simple loadbalancing scheme for task allocation in parallel machinesrdquo inProceedings of the 3rd Annual ACM Symposium on ParallelAlgorithms and Architectures pp 237ndash245 1991

[7] V Stemann ldquoParallel balanced allocationsrdquo in Proceedings of the1996 8th Annual ACM Symposium on Parallel Algorithms andArchitectures pp 261ndash269 June 1996

[8] M Michael A W Richa and R Sitaraman The Power of TwoRandom Choices A Survey of Techniques and Results 2005

[9] A Broder and M Mitzenmacher ldquoUsing multiple hash func-tions to improve ip lookupsrdquo Tech Rep Department ofComputer ScienceHarvardUniversity CambridgeMass USA2000

[10] A Broder and A Karlin ldquoMulti-level adaptive hashingrdquo inProceedings of the First Annual ACM SIAM Symposium onDiscrete Algorithms 1990

[11] A Czumaj F Meyer A der Heide and V Stemann ldquoSharedmemory simulations with triple-logarithmic delayrdquo in Algo-rithms Lecture Notes in Computer Science pp 46ndash59 1995

[12] R M Karp M Luby and F Meyer ldquoEfficient PRAM simulationon a distributed memory machinerdquo Algorithmica vol 16 no 4-5 pp 517ndash542 1996

[13] Crowd flower httpscastingwordscom[14] P U Tournoux J Leguay F Benbadis V Conan M D

De Amorim and J Whitbeck ldquoThe accordion phenomenonanalysis characterization and impact on DTN routingrdquo in Pro-ceedings of the 28th Conference on Computer Communications(IEEE INFOCOM rsquo09) pp 1116ndash1124 April 2009

[15] Casting words httpscastingwordscom[16] Crowd spring httpwwwcrowdspringcom[17] R K Rana C T Chou S S Kanhere N Bulusu and W Hu

ldquoEar-phone an end-to-end participatory urban noise mappingsystemrdquo in Proceedings of the 9th ACMIEEE InternationalConference on Information Processing in Sensor Networks (IPSNrsquo10) pp 105ndash116 April 2010

[18] M FaulknerMOlson R Chandy J Krause KM Chandy andA Krause ldquoThe next big one detecting earthquakes and otherrare events from community-based sensorsrdquo in Proceedings ofthe 10th ACMIEEE International Conference on InformationProcessing in Sensor Networks (IPSN rsquo11) pp 13ndash24 April 2011

[19] W Willett P Aoki N Kumar S Subramanian and AWoodruff ldquoCommon sense community scaffolding mobilesensing and analysis for novice usersrdquo in Pervasive Computingvol 6030 pp 301ndash318 2010

[20] P Volgyesi A Nadas X Koutsoukos and A Ledeczi ldquoAirquality monitoring with SensorMaprdquo in Proceedings of theInternational Conference on Information Processing in SensorNetworks (IPSN rsquo08) pp 529ndash530 April 2008

[21] M Mun S Reddy K Shilton et al ldquoPEIR the personalenvironmental impact report as a platform for participatorysensing systems researchrdquo in Proceedings of the 7th ACMInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo09) pp 55ndash68 June 2009

[22] NMaisonneuveM Stevens andBOchab ldquoParticipatory noisepollution monitoring using mobile phonesrdquo Information Polityvol 15 no 1 pp 51ndash71 2010

[23] K Pearson ldquoThe problem of the random walkrdquo Nature vol 72no 1865 p 294 1905

[24] P K Sen and J M Singer Large Sample Methods in StatisticsChapman amp Hall New York NY USA 1993

[25] M E J Newman ldquoA measure of betweenness centrality basedon random walksrdquo Social Networks vol 27 no 1 pp 39ndash542005

[26] J D Noh andH Rieger ldquoRandomwalks on complex networksrdquoPhysical Review Letters vol 92 no 11 pp 118701ndash1 2004

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



which makes the balanced queue length difficult to achieveThird it is difficult tomeasure the intercontact time inmobilesocial network which makes it difficult to evaluate the taskcompletion time Also the remaining energy level andcomputational diversity among users should be consideredfor fair and balanced task allocation

In this work we propose eCOTS (Efficient and Coop-erative Task Sharing for Large-scale Smart City SensingApplication)We address the above three challenges with twoimportant techniques First we use the ldquotwo choicesrdquo schemein ldquoballs and binsrdquo theory [8] as fundamental mechanism fortask offloading where queuing lengths of 119889 users are com-pared and userswith the least value are selected Such schemeis simple but effective The root reason is that random walkalso plays the role of random selection Second we leveragethe random walk behavior for random choice and considerthe energy level as well as computational capability for taskreassignment We find that the considerations for energyconsumption and computational capability effectively offsetthe uncertainty inmobility without addingmuch complexityThe root reason is that energy consumption is also an implicitfactor for intercontact time Further the computational capa-bility also dominates the task allocation preference as well asinter contact frequency We verified the effectiveness of theproposed techniques in our extensive experimental study

The contribution of this work is threefold

(i) We propose eCOTS an efficient cooperative taskshared among smartphone users for large-scale urbansensing applications To the best of our knowledgewe are the first systematic study on balanced taskassignment in pure distributed environment

(ii) We incorporate the energy level and computationalcapability in task-assignment scheme which could bein appliance with heterogeneous mobile social net-work eCOTS can deal with these two cases separatelyand jointly with satisfiable performance Also theseconcerns are helpful in achieving the robustness inmobile environment

(iii) We make an extensive experimental study on ourproposed scheme The evaluations include the taskbalancing effects in different traffic load under dif-ferent energy levels and computational capabilitiesExperimental results based on real trace data show thesurprisingly good balancing property even though thevariance and diversity between users are very large

The rest of the paper is organized as follows We describeour system model in Section 2 Section 3 provides problemformation as well as preliminary analysis about it Afterdescribing our algorithm design in Section 4 We evaluatethe performance of eCOTS by simulation in Section 5 andmake real trace driven study in Section 6 Finally we discussrelated work in Section 7 and conclude the work in Section 8

2 Preliminary and System Model

21 ldquoBalls and Binsrdquo Theory The ldquoballs and binsrdquo problem isclassic and simple being widely used in many applications

in computer science such as hashing [9 10] shared memoryemulations in DMM (Distributed Memory Machines)[11 12] and load balancing with limited information Thebasic problem is very simple Given 119899 nodes are to be throwninto 119899 bins where each ball is chosen to each bin uniformlyand independently the focus is themaximum loaded bin thatis the largest number of balls in all the bins is approximately

log 119899log log 119899

(1)

If the balls are thrown sequentially and each ball is placedin the least loaded bins of 119889 ge 2 the maximum load is

log log 119899

log 119889+ Θ (2)

with high probability We call this method ldquo119889-choiceparadigmrdquo

When the number of balls 119898 is larger than 119899 especially119898 ≫ 119899 log 119899 the maximum load of random choice is

119898

119899+ radic

119898 log 119899119899

(3)

while for the ldquo119889-choice paradigmrdquo the maximum load is

119898

119899+log log 119899

log 119889 (4)

Notably there is also a very interesting and beneficialproperty in ldquo119889-choice paradigmrdquo This property motivatesus to take this method into task assignment and balancingscheme where increasing the number of tasks will notincrease the variance of the queue length

The ldquo119889-choice paradigmrdquo has been widely studied andextended for many interesting aspects For example manystudies [8] focus on the weighted balls and bins which ispractical and useful in real task assignment For computersystem and networks the parallel execution studies withoverhead considerations are very useful and get manyconcentrations [6 7]

In our study the ldquo119889-choice paradigmrdquo is useful butshould be tailored for our investigated problem We willintroduce our system model and the investigated problem inthe following paragraphs

22 Modeling the Users and Tasks We consider a mobilesocial network where 119899 users in user set 119880 = 1 2 119899will share their tasks among them For each task there isa metric in evaluating its difficulty which corresponds tothe weight of a task 0 le 119908

119894119895le 1 is the weight of the

119895th task on user 119894 The weight can be represented as thedifficulty for completing a task which is directly relevant totask completion time as well as energy consumption Eachuser 119894 isin 119880 holds a task set 119879

119894= 1198791198941 119879

119894119898 For each task

from user 119894 when it is reallocated to another user 119895 it willbe processed at 119895 without being further forwarded We donot consider multiforwarding case in this study We put it tofuture work and social mapping technologyThe tasks in user


Tasks

Tasks

Tasks

Tasks

Tasks

User 2Compare

User 1

User 3

Communication

Energy level

range

Communication

range




1199021198941 1199021198942 119902


119894




119894119895is 119864119894119895






3 Problem Formation


minsum

119894isin119880

1003816100381610038161003816119876119894 minus 119864 [119876119894]1003816100381610038161003816 (5)






1 1198882 119888

119899


119899

(1) Initialize 1198881 1198882 119888

119899 = 0

1199081 1199082 119908

119899 = 0 119888119900119906119899119905 = 0


119894 119884119894)

0 lt 119883 lt 119890119889119892119890 0 lt 119910 lt 119890119889119892119890 1 le 119894 le 119899





119904= 119888119904+ 1

(17) 119908119904= 119908119904+ 119905119886119904119896119908119890119894119892ℎ119905(119888119900119906119899119905)119886119887119894119897119894119905119910(119904)

(18) 119888119900119906119899119905 = 119888119900119906119899119905 + 1


1 1198882 119888

119899 1199081 1199082 119908

119899




10038171003817100381710038171198761198941003817100381710038171003817 minus 119864119894isin119880

[119876119894] (6)


minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896) minus 119864119894isin119880

[119882 (119876119894)] (7)

where119882(119876119894) = sum

119876119894

119896119908(119902119894119896)


minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896)

119888119894

minus 119864119894isin119880

[ (119876119894)] (8)

where (119876119894) = sum119876119894

119896119908(119902119894119896)119888119894

4 Algorithm Design



0 5 10 15 20 25

Empirical CDF

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

2-choice

(a) Range 119903 = 5

0 5 10 15 20 25 30 35 40

Empirical CDF

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

2-choice

CDF

of u

sers

rsquo que

ue le

ngth

s

(b) Range 119903 = 10

0 5 10 15 20 25 30 35 40

Empirical CDF

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

2-choice

CDF

of u

sers

rsquo que

ue le

ngth

s

(c) Range 119903 = 20










0 20 40 60 80 100 120

Empirical CDF

Random

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice


0 200 400 600 800 1000

Empirical CDF

Random

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice


0 2000 4000 6000 8000 10000 12000

Empirical CDF

Random

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice




















20 21 22 23 24 25 26 27 28 29 30

Empirical CDF

Optimal

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

2-choice








0 20 40 60 80 100 120

Empirical CDF

OptimalRandom

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice


0 200 400 600 800 1000 1200

Empirical CDF

OptimalRandom

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice


0 20001000 40003000 60005000 7000 90008000 10000

OptimalRandom

Task length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s

2-choice

Empirical CDF









0 10 20 30 40

Empirical CDF

0 10 20 30

Empirical CDF

Task length

Random

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo tas

k le

ngth

s2-choice

Random2-choice










0 5 10 15 20 25 30 35

Empirical CDF

CDF

of u

sers

rsquo tas

k le

ngth

s

Random

0

01

02

03

04

05

06

07

08

09

1

Task length

2-choice


0 10 20 30 40 50 60 70 80

Empirical CDF

Energy level

1

09

08

07

06

05

04

03

02

01

0

Random2-choice

CDF

of u

sers

rsquo ene

rgy

leve

ls


24 25 26 27 28 29 30 31

Empirical CDF

d = 2

d = 3

d = 4

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s




7 Related Work



0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

minus5

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

(a) 119889 = 2

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

minus5

(b) 119889 = 4

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

minus5

(c) 119889 = 6






0 10 20 30 40 50 60 700

100

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0 20 40 60 80 100 120

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of u

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8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tasks

Tasks

Tasks

Tasks

Tasks

User 2Compare

User 1

User 3

Communication

Energy level

range

Communication

range




1199021198941 1199021198942 119902


119894




119894119895is 119864119894119895






3 Problem Formation


minsum

119894isin119880

1003816100381610038161003816119876119894 minus 119864 [119876119894]1003816100381610038161003816 (5)






1 1198882 119888

119899


119899

(1) Initialize 1198881 1198882 119888

119899 = 0

1199081 1199082 119908

119899 = 0 119888119900119906119899119905 = 0


119894 119884119894)

0 lt 119883 lt 119890119889119892119890 0 lt 119910 lt 119890119889119892119890 1 le 119894 le 119899





119904= 119888119904+ 1

(17) 119908119904= 119908119904+ 119905119886119904119896119908119890119894119892ℎ119905(119888119900119906119899119905)119886119887119894119897119894119905119910(119904)

(18) 119888119900119906119899119905 = 119888119900119906119899119905 + 1


1 1198882 119888

119899 1199081 1199082 119908

119899




10038171003817100381710038171198761198941003817100381710038171003817 minus 119864119894isin119880

[119876119894] (6)


minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896) minus 119864119894isin119880

[119882 (119876119894)] (7)

where119882(119876119894) = sum

119876119894

119896119908(119902119894119896)


minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896)

119888119894

minus 119864119894isin119880

[ (119876119894)] (8)

where (119876119894) = sum119876119894

119896119908(119902119894119896)119888119894

4 Algorithm Design



0 5 10 15 20 25

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Queue length

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CDF

of u

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(a) Range 119903 = 5

0 5 10 15 20 25 30 35 40

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(b) Range 119903 = 10

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07

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of u

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(c) Range 119903 = 20










0 20 40 60 80 100 120

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of u

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of u

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of u

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0 20001000 40003000 60005000 7000 90008000 10000

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of u

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0 10 20 30 40

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01

02

03

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05

06

07

08

09

1

Task length

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0 10 20 30 40 50 60 70 80

Empirical CDF

Energy level

1

09

08

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06

05

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0

Random2-choice

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of u

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24 25 26 27 28 29 30 31

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d = 2

d = 3

d = 4

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1

09

08

07

06

05

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of u

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7 Related Work



0 10 20 30 40 50 60 70

0

5

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eCOTS allocation

Random allocation

minus5

0 10 20 30 40 50 60 70

0

5

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User ID

Que

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minus5

(a) 119889 = 2

0 10 20 30 40 50 60 70

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5

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0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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(c) 119889 = 6






0 10 20 30 40 50 60 700

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0 20 40 60 80 100 120

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of u

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8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1 1198882 119888

119899


119899

(1) Initialize 1198881 1198882 119888

119899 = 0

1199081 1199082 119908

119899 = 0 119888119900119906119899119905 = 0


119894 119884119894)

0 lt 119883 lt 119890119889119892119890 0 lt 119910 lt 119890119889119892119890 1 le 119894 le 119899





119904= 119888119904+ 1

(17) 119908119904= 119908119904+ 119905119886119904119896119908119890119894119892ℎ119905(119888119900119906119899119905)119886119887119894119897119894119905119910(119904)

(18) 119888119900119906119899119905 = 119888119900119906119899119905 + 1


1 1198882 119888

119899 1199081 1199082 119908

119899




10038171003817100381710038171198761198941003817100381710038171003817 minus 119864119894isin119880

[119876119894] (6)


minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896) minus 119864119894isin119880

[119882 (119876119894)] (7)

where119882(119876119894) = sum

119876119894

119896119908(119902119894119896)


minmax119894119895isin119880

119876119894

sum

119896=1

119908 (119902119894119896)

119888119894

minus 119864119894isin119880

[ (119876119894)] (8)

where (119876119894) = sum119876119894

119896119908(119902119894119896)119888119894

4 Algorithm Design



0 5 10 15 20 25

Empirical CDF

Random

Queue length

1

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08

07

06

05

04

03

02

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0

CDF

of u

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(a) Range 119903 = 5

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0 200 400 600 800 1000

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of u

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20 21 22 23 24 25 26 27 28 29 30

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Optimal

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of u

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0 20 40 60 80 100 120

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Task length

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0 200 400 600 800 1000 1200

Empirical CDF

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of u

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0 20001000 40003000 60005000 7000 90008000 10000

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Task length

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0 10 20 30 40 50 60 70

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minus5

0 10 20 30 40 50 60 70

0

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0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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(c) 119889 = 6






0 10 20 30 40 50 60 700

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20

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0 20 40 60 80 100 120

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07

06

05

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03

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8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25

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7 Related Work



0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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0 10 20 30 40 50 60 70

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(c) 119889 = 6






0 10 20 30 40 50 60 700

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0 10 20 30 40 50 60 700

20

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20

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0 10 20 30 40 50 60 700

User ID

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Random allocation

User ID

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Acknowledgments


References




























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Journal of



RotatingMachinery





VLSI Design



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Volume 2014


SensorsJournal of





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8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















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8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



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Journal of



Volume 2014


SensorsJournal of





Propagation










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8 Conclusion







Acknowledgments


References




























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Journal of



Volume 2014


SensorsJournal of





Propagation










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8 Conclusion







Acknowledgments


References




























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Journal of



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VLSI Design



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Volume 2014


SensorsJournal of





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ue le

ngth

minus5

minus5

(b) 119889 = 4

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

0 10 20 30 40 50 60 70

0

5

10

15

User ID

Que

ue le

ngth

minus5

minus5

(c) 119889 = 6






0 10 20 30 40 50 60 700

100

200

300

0 10 20 30 40 50 60 700

100

200

300

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth


0 10 20 30 40 50 60 700

50

100

150

0 10 20 30 40 50 60 700

50

100

150

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth


0 10 20 30 40 50 60 700

20

40

60

20

40

60

0 10 20 30 40 50 60 700

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth








0 20 40 60 80 100 120

Empirical CDF

eCOTSRandom

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s


0 20 40 60 80 100 120

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom


0 10 15 205 4025 30 35 45

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom






8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 700

100

200

300

0 10 20 30 40 50 60 700

100

200

300

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth


0 10 20 30 40 50 60 700

50

100

150

0 10 20 30 40 50 60 700

50

100

150

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth


0 10 20 30 40 50 60 700

20

40

60

20

40

60

0 10 20 30 40 50 60 700

User ID

Que

ue le

ngth

eCOTS allocation

Random allocation

User ID

Que

ue le

ngth








0 20 40 60 80 100 120

Empirical CDF

eCOTSRandom

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s


0 20 40 60 80 100 120

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom


0 10 15 205 4025 30 35 45

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom






8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 80 100 120

Empirical CDF

eCOTSRandom

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s


0 20 40 60 80 100 120

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom


0 10 15 205 4025 30 35 45

Empirical CDF

Queue length

1

09

08

07

06

05

04

03

02

01

0

CDF

of u

sers

rsquo que

ue le

ngth

s

eCOTSRandom






8 Conclusion







Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














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









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