Research Article - Hindawi Publishing...

Research ArticleOptimal Task Partition with Delay Requirement inMobile Crowdsourcing

Linbo Zhai 1 Hua Wang2 and Xiaole Li 3

1School of Information Science and Engineering Shandong Normal University Jinan 250014 China2School of Computer Science and Technology Shandong University Jinan 250100 China3School of Information Science and Engineering Linyi University Linyi 276000 China

Correspondence should be addressed to Linbo Zhai zhaimailsdueducn and Xiaole Li leo0539163com

Received 13 May 2019 Revised 15 July 2019 Accepted 14 August 2019 Published 12 September 2019

Guest Editor Nhu-Ngoc Dao

Copyright copy 2019 Linbo Zhai et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Mobile crowdsourcing takes advantage of mobile devices such as smart phones and tablets to process data for a lot of applications(eg geotagging for mobile touring guiding monitoring and spectrum sensing) In this paper we propose a mobile crowdsourcingparadigm to make a task requester exploit encountered mobile workers for high-quality results Since a task may be too complex fora single worker it is necessary for a task requester to divide a complex task into several parts so that amobile worker can nish a partof the task easily We describe the task crowdsourcing process and propose the worker arrival model and task model Furthermorethe probability that all parts of the complicated task are executed by mobile workers is introduced to evaluate the result of taskcrowdsourcing Based on these models considering computing capacity and rewards for mobile workers we formulate a taskpartition problem to maximize the introduced probability which is used to evaluate the result of task crowdsourcing en using aMarkov chain a task partition policy is designed for the task requester to realize high-quality mobile crowdsourcing With this taskpartition policy the task requester is able to divide the complicated task into precise number of parts based on mobile workersrsquoarrival and the probability that the total parts are executed by mobile workers is maximized Also the invalid number of taskassignment attempts is analyzed accurately which is helpful to evaluate the resource consumption of requesters due to probingpotential workers Simulations show that our task partition policy improves the results of task crowdsourcing

1 Introduction

In recent years the proliferation of crowdsourcing hasshown signicant potentials for many application areasCrowdsourcing a novel task-solving paradigm means thathuman workers are recruited to solve complicated tasksExtensive researchers are attracted to pay attention tocrowdsourcing due to its success about human intrinsicapplications

Early successful examples are Wikipedia Yahoo An-swers and Yelp As the great potential of crowdsourcing isrealized in recent years several general-purpose platformsincluding oDesk and Amazon Mechanical Turks (AMT)make crowdsourcing more manageable and powerful eseonline systems occur to make requesters dene tasks andhuman workers execute themwith rewards Formany onlinecrowdsourcing systems the common issue is ineciency

For instance no more than 15 tasks in Amazon mTurksystem could be nished within an hour [1]

On the other hand recent years witness the remarkableproliferation of intelligent mobile devices (eg smart phonesand tablets) and the sharp growth of mobile-broadbandservices including data sharing and synchronization ultra-high-resolution video streaming and virtual and augmentedreality All these services continue to drive the demand forhigher data rates and lead to crowdsourcing application inInternet-of-ings (IoT) where pervasive interconnectedsmart objects cooperates together to reach multiple goalsIoT technologies can epoundectively promote the interactionsbetween environments and the human and enhance thereliability and eciency of smart cities [2ndash7]

With the extensive use of mobile devices such as tabletsand smart phones mobile crowdsourcing systems (MCS) isa feasible solution to complete delay-sensitive tasks such as

HindawiWireless Communications and Mobile ComputingVolume 2019 Article ID 5216495 12 pageshttpsdoiorg10115520195216495

geotagging for mobile touring guiding monitoring and localparking space searching which are inevitable in smart citiesTo improve the task-executing efficiency a user tends toassign such delay-sensitive tasks to mobile devices tocomplete them and collect executing results through thewireless communication system which is called mobilecrowdsourcing We should notice that these task-executingresults must come back within delay requirement Howevermobile devices which are portable but with less computingability are difficult to complete complex tasks within delayrequirement Hence this is challenging to mobile devicesand motivates us to develop a mobile crowdsourcing policyto divide large tasks into several small parts suitable formobile devices to execute

In this paper we propose a mobile crowdsourcingparadigm dividing a complicated task into small piecesand assigning small subtasks to mobile devices to obtainhigh-quality executing results which means mobile devicesexecute as many subtasks as possible We design therecruited process and present the worker arrival model andtask model Furthermore the probability that all parts ofthe complicated task are executed by mobile workers isintroduced to evaluate the result of task crowdsourcinge higher probability means the result of the taskcrowdsourcing is better According to these models wetake into consideration other factors such as the com-plexity and rewards of tasks which will influence mobileworkersrsquo execution and formulate a task partition problemto maximize the probability that all parts of the compli-cated task are executed by mobile workers en using theMarkov chain we derive a task division policy to realizehigh-quality results and the invalid number of task as-signment attempts is analyzed accurately based on prob-ability generating function Simulations show that our taskpartition policy improves the results of taskcrowdsourcing

In this paper we study the task partition problem ofcrowdsourcing process in the wireless system consisting ofmany mobile devices e main contributions are sum-marized as follows

(i) Considering the mobility and capacity of mobileworkers we propose a mobile crowdsourcing par-adigm to divide a complicated task into multiplesubtasks and assign these subtasks to mobileworkers e mobile worker decides to execute sucha subtask or not based on its computing capabilityand corresponding requirements

(ii) To describe the attributes of each task the taskmodelis proposed to denote task load delay requirementand monetary reward to the mobile workersMoreover an arrival model of mobile workers isproposed to describe the encountered process be-tween the requester and themobile worker Based onmobile worker features and task attributes we es-tablish the system model and formulate a taskpartition problem to maximize the probability thatall subtasks are executed by mobile workers andguarantee the result of task crowdsourcing

(iii) To realize the high-quality results of task crowd-sourcing using a Markov chain the state transi-tions denoting the number of subtasks executed bymobile workers can be analyzed Based on thesestate transitions within limited period caused bydelay requirement the optimal task partition can beobtained en according to the optimal taskpartition the invalid number of subtask assignmentis analyzed accurately with probability generatingfunction in the total crowdsourcing process

(iv) Simulation results show our proposed policycompared to fix partition policy and the adaptivescheme approaches the optimal solutions

e rest of the paper is organized as follows In Section 2a review about related works is provided In Section 3 wedescribe the task crowdsourcing process and propose thesystem model In Section 4 a Markov chain is developed tosolve the task partition problem and the number of invalidattempts is analyzed In Section 5 the proposed algorithm isevaluated with simulation results Finally conclusions areshown in Section 6

2 Related Works

Human computation has been executed for many centuriesSpecifically if a ldquohumanrdquo serves to ldquocomputerdquo there will be ahuman computation which can be observed is is thereason why there is a history of Human Computation whichis obviously longer than that of the electronic computerWith the rapid development of Internet web service es-pecially those facilitating online labor recruiting and man-aging (eg oDesk and Amazon MTurk) humancomputation begins to experience a new era where thesources of human are not designated exerts or employees butextended to a vast pool of crowds instead is type ofoutsourcing to crowds named crowdsourcing is receivingcountless success in several areas such as logistics fundraising monitoring and so on

With the extensive use of mobile devices such as tabletsand smart phones the new hybrid architecture occurs tosupport a massive ad hoc crowd which is composed ofdistributed mobile nodes and a massive social networkaround a smart city environment [8] erefore mobilecrowdsourcing can be utilized in IoT to complete real-timetasks and improve task efficiency (eg localization servicespectrum sensing and environmental monitoring)

For indoor localization systems a major bottleneck is thetradeoff between both localization accuracy and site surveycosts In [9] a probabilistic radiomap constructionmethod ispropose with crowdsourcing collection taking into accountboth accuracy and survey costs In order to obtain the needfor location labels Jung et al [10] propose the unsupervisedlearning method to calibrate a localization model based on aglobal-local optimization scheme In this hybrid scheme anefficient global-local interaction reduces the task complexitydrastically In [11] a location-aware infrastructure is pro-posed to combine a broad sensing layer centralized cloudfederation support and edge computing With the sensing

2 Wireless Communications and Mobile Computing

capability of mobile devices users can obtain the crowdsensing services in IoT Credible interaction issues amongmobile users however are still hard problems Consideringthe credible interaction An et al focus on assigning thecrowdsourcing sensing tasks [12] In the field of environ-mental monitoring a path planning approach is introducedfor crowd evacuation in buildings [13] Besides there aresome related researches on E-healthcare service for thecrowdsourcing IoT and crowdsourcing industrial-IoT (IIoT)applications [14 15]

To improve the executing efficiency a complicated task isoften divided into smaller pieces in crowdsourcing [16] enthese small pieces can be assigned to a group of undefinedworkers [17] Inmany existing studies there is a central serviceentity which not only collects the information of both workersand requesters but also performs the task-worker assignmentto optimize a global utility [18 19] If someone hopes to use acrowdsourcing system [20 21] inevitably corresponding feemust be paid for using the centralized server

Due to the self-organized nature requesters in mobilenetworks however do not obtain worker information inadvance erefore requesters have to probe worker abilityand make sequential recruitment decision is problemmotivates us to design a task partition policy for mobileworker recruitment

In [22] Tuncay and Helmy use the location visitingfrequency to reflect the worker ability and present a gradientascend policy which assign the task to a user having highervisiting frequency in the destination area However theobjective similar to the traditional routing and data dis-semination is to arrive at the destination as fast as possiblewith minimum replication overhead In [23 24] Chang andGong analyze the schemes for allocating work segmentsamong participants opportunistically When determiningusersrsquo workloads the schemes take into account contactingdelay acceptance probability computing speed and theexistence of resource competition works e purpose is tominimize the task makespan by partitioning the total taskinto suitable subtasks corresponding to the encounteredworker computation power In [25] Pu et al use an onlinealgorithm to maximize the task service quality based onworkerrsquos interest preference Focusing on device-to-devicenetworks the authors study the recruitment problem whenthe crowdsourcing is delay-sensitive [26] In [27] Tong et alstudy a large-scale crowdsourcing task which consists ofthousands or millions of atomic tasks To the best of ourknowledge little work has been done on jointly consideringthe mobile worker features and task partition

3 System Model

In this section at first the task crowdsourcing process isdescribed en the system model involving task attributesand mobile user features is developed and the task partitionproblem is formulated to achieve optimal results

31 RecruitmentDescription Amobile user having a task is arequester e requester can self-organize task crowdsourcing

by recruiting several encountered mobile users who areworkers in real-time Amobile user encountering another usermeans they are close to establish a device-to-device (D2D)link e term of ldquocloserdquo means the distance between twomobile users does not exceed WiFi-direct distance e re-cruitment is described as follows

When a mobile user (requester) launches a task therequester is invoked to recruit some encountered mobileusers (workers) in real-time Since a complicated task isdifficult for a worker to complete in time the requester willdivide the complex task into several subtasks and recruitcorresponding number of workers to complete those sub-tasks e requester sends attributes of a subtask includingthe reward subtask load and delay requirement to an ar-rived worker e worker decides to execute this subtask ornot based on available computing capacity remaining en-ergy subtask reward and delay requirement If the workerdecides to accept this subtask which means it can completethe subtask within delay requirement its worker ability is setto 1 Otherwise it is set to zero en the worker abilityvalue is sent to the requester Finally the requester decides torecruit the worker or not based on its worker ability

If the requester decides to recruit the worker the detailedcontent of a subtask is sent to the worker During the subtaskexecution it is not necessary for the requester and theworker to connect with each other all the time After thesubtask is finished by the worker the corresponding subtaskexecution result will be sent back to the requester by a D2Dlink or cellular link satisfying the delay requirement Oncethe requester receives the result in time the subtask rewardwill be given to the worker Otherwise if the delay re-quirement is not satisfied the requester thinks the worker isfraudulent and does not give the subtask reward to theworker

e key rationale of the recruiting model is that op-portunistic encounters of mobile devices are sufficient andprevalent in modern society [28] which offers lots of op-portunities to exploit nearby intelligent devices [29] If amobile user has a complex task it can self-organize its taskcrowdsourcing by leveraging many encountered mobileusers in real-time and fast response can be realized byinteracting with intelligent workers in proximity directlyFurthermore many mobile crowdsourcing tasks will requirelocation-aware knowledge and information (eg mobiletouring guiding monitoring and local parking spacesearching) Hence nearby intelligent workers are morequalified to execute them than the online workers [22] Inaddition compared to the new emerging paradigm ldquocyberforagingrdquo about mobile computing our framework sharesthe similar spirit so that mobile users can exploit nearbyintelligent devices to facilitate their computational taskprocessing [30]

Figure 1 illustrates the procedure of mobile crowd-sourcing A mobile user (requester R) launching a mobilecrowdsourcing task moves around within the network andencounters a mobile user (worker W1) Requester R dividesthis task and sends subtask attributes to workerW1 througha D2D link at position 1 Worker W1 decides to execute thesubtask and returns the worker ability to requester R en

Wireless Communications and Mobile Computing 3

requester R sends the subtask content to workerW1 Duringthe period of subtask execution workerW1 and requester Rmay continue to move and do not need to connect with eachother When workerW1 finishes the subtask workerW1 andrequester R are at position 3 and position 2 respectivelyedistance between worker W1 and requester R is too long toestablish D2D link erefore workerW1 sends the result torequester R by a cellular link the wireless transmissionthrough mobile communication system [28] at meansworker W1 sends the result to the base station at first enthe base station relays the result to requester R After thatthe subtask reward is granted to worker W1 by requester R

32 System Model

321 Worker Arrival Model We use K to denote the set ofpotential mobile workers who may execute the task Con-sidering worker mobility the inter-encounter time of arequester r and a worker w is important In our system it isnot necessary for the requester r to know the arrival rate λrw

of each worker w e total arrival rate λr 1113936wisinkλrw ob-tained by calculating the number of encountered workersper time unit is adopted instead e current value of totalarrival rate can be estimated based on the value during therecent time units When the total arrival rate is obtained theaverage inter-encounter time of a requester r and a worker w

is 1λr

322 Task Model A mobile requester can describe a task iby a set of attributes ltTaiDi Rigt where Tai denotes the taskload of task i Di represents delay requirement of task i

within which a worker must return the result Ri denotes thetotal reward to workers after the results are returned withinDi

ere are three parameters in the task model Task loadand delay requirement are determined by the category of thecorresponding task such as content creation or informationfinding [31] For the reward similar to online systems thismodel uses a common posted price method where theworkers are provided the explicit price offer [32]

323 Task Partition Formulation Since a task may be toocomplex for a mobile worker with less computing ability tocomplete in time the task can be divided into many subtasksby the task requester en each subtask of the task issuitable for a worker to finish

Assume that task i is averagely divided into N subtasksen the load of each subtask is

STai(N) Tai

N (1)

e reward for a worker finishing a subtask is

Ri(N) Ri

N (2)

e requester sends the subtask attributes includingRi(N) STai(N) and delay requirement Di to a worker w eworker w evaluates whether STai(N) can be completedwithin Di with satisfying reward Ri(N)

Let Ew denote the remaining energy of worker w Bw

denote the computing capacity of worker w and Piw denotethe probability that worker w accepts the subtask of task iWithout loss of generality it is defined that the probabilitythat a worker accepts a subtask is related to Ri(N) Ew Bwand STai(N)Di Intuitively Ri(N) Ew and Bw will havepositive impact on the accepting probability while STai(N)Di will have negative impact on the accepting probabilityHowever the accepting probability is not simply defined as afunction which is proportional to Ri(N) Ew and Bw andinversely proportional to STai(N)Di since the real case ismore complicated Let RE denote the expectation reward of amobile worker If a mobile worker can gain the reward Ri(N)exceeding its expectation RE it will paymore attention to theratio between the subtask load STai(N)Di and its computingcapacity Bw Otherwise if the reward it can gain is less thanits expectation RE it will focus on the real reward it can gainAdditionally a workerrsquos remaining energy Ew also influencesthe probability of accepting the subtask On the one handthe larger value of Ew will result in the higher acceptingprobability On the other hand the value of Ew will influencethe pace of the probability variety When the remainingenergy of a mobile worker is high it is sensitive and itsaccepting probability will change drastically as other pa-rameters including Ri(N) Bw and STai(N)Di change Whena mobile worker has the low remaining energy its acceptingprobability will change slowly as other parameters change

Based on the aforementioned description the acceptingprobability should be the piecewise function When thereward Ri(N) exceeds its expectation RE STai(N)DiBw has

Base station

A worker W1

A requester R

D2D link

Cellular linkMovement trace

Position 1

Position 2

Position 3

Figure 1 Process of mobile crowdsourcing


more influence on the probability and the probability willdecrease as STai(N)DiBw increases When the rewardRi(N) is lower than its expectation RE the reward will havegreater influence on the probability and the probability willincrease as RE increases To clearly reflect the influence ofSTai(N)DiBw and Ri(N) on the trend of the function va-riety we use the square of them rather than their originalforms in the piecewise function Besides the value of theaccepting probability should be in the range (0 1) Hencethe exponential function is used to guarantee the acceptingprobability Piw in this range en Piw can be defined as

Piw

exp minus CSTai(N)

DiBw

1113888 1113889

2 1Ri(N)Ew

⎛⎝ ⎞⎠Ri(N)geRE

exp minus CSTai(N)

DiBw

1113888 11138891

Ri(N)2Ew

1113888 1113889Ri(N)ltRE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where C is an adjustable constant to control the changingspeed of accepting probability

Using (1) and (2) the probability Piw in Equation (3) canbe rewritten as

Piw

exp minus C1N

Tai

DiBw

1113888 1113889

2 1RiEw

⎛⎝ ⎞⎠N leRi

RE

exp minus CNTai

DiBw

1113888 11138891

Ri2Ew

1113888 1113889NgtRi

RE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

Since accepting probability Piw is the piecewise functionbased on the relationship between Ri(N) and RE and Equation(3) only describes the relationship between Ri(N) and RE usingequation (2) we can obtain the relationship between Ri and REFrom Equation (4) it can be observed that the acceptingprobability Piw increases with the growth of subtask number Nwhen N is less than RiRE On the contrary the acceptingprobability Piw decreases with the growth of the subtask numberNwhenN is higher thanRiREis can be explained as followsWhen the subtask number N is smaller the worker is able togain reward more than its expectation RE As N increases asubtask load decreases and the worker is more likely to acceptsuch a subtask After N exceeds RiRE the worker is not able toachieve its expected reward RE and it mainly focuses on thecurrent reward As N increases the current reward of a subtaskdecreases and the worker is less likely to accept such a subtask

Additionally each worker needs some time to complete asubtask e duration is determined by STai(N) and theworker computing capacity Let Bmin Bw ∣ w isin K de-note the minimum computing capacity of potential workerswhere K is the set of total mobile workers en themaximum duration for executing a subtask is derived as

SDi STai(N)

B (5)

erefore the requester should assign subtasks toworkers within Di minus SDi Otherwise the delay requirementcannot be guaranteed Let Ti (Ti leDi minus SDi) denote the

duration of subtask assignment To maximize the servicequality the requester should find as many workers executingsubtasks as possible within Ti us λrTi denotes the totalnumber of workers which a requester encounters within TiSince workers may accepting the subtasks following Piw thenumber of accepting workers must be less than λrTi Let ndenote the number of workers accepting subtasks If n ex-ceeds the total number of subtasks which is denoted byN allsubtasks are executed by workers and the service quality isguaranteed

To evaluate the result of task crowdsourcing theprobability P(ngeN) denoting that all subtasks of a com-plicated task are executed by mobile workers is introducede higher the probability that n exceeds N is the betterservice quality is

e task partition policy for task i is to divide task i intoN subtasks which are suitable for workers to execute eobjective is to obtain the optimal task partition Nlowast tomaximize the probability that all subtasks are executed byworkers within Ti erefore the optimal task partitionproblem can be formulated as

Nlowast ≜ argmaxN

P(ngeN)

subject to Ti leDi minus SDi(6)

4 Partition Policy

In this section a Markov chain is used to describe the statetransitions denoting subtasks assignment and calculate theoptimal task partition en using the transition matrixthe unsuccessful number of subtask assignment attemptsbefore the crowdsourcing end can be analyzed Further-more the time complexity of proposed algorithm isanalyzed

41 Optimal Task Partition According to the description inSection 3 for task i a requester should receive the executingresults from encountered workers within delay requirementDi Additionally each worker needs a duration SDi tocomplete a subtaske duration is determined by STai(N)Berefore the requester needs to assign subtasks to workerswithin Di minus SDi to satisfy the delay requirement of task i

It is defined that each slot duration is Ts 1λr where λr

denotes the arrival rate of total mobile workers en arequester encounters one mobile worker in a slot on averageSince each slot duration Ts equals 1λr Di minus SDi can bedivided into the m slots We can obtain

m Di minus SDi

Ts

(7)

Figure 2 shows the slot division within Di minus SDiTo realize the optimal task partition we use a Markov

chain to describe state transitions within task assignmentduration Di minus SDi For task i which is divided into N sub-tasks averagely we use S0 S1 S2 SN to denote N+ 1states where Sj(j isin [0 N]) means j subtasks have beenassigned to workers successfully


e encountered worker will accept a subtask of task iwith the probability Piw and refuse the subtask with theprobability 1 minus Piw If the encountered worker accepts thesubtask the system moves to new state Sj+ 1 (jleN minus 1) fromstate Sj Otherwise the system still stays at state Sj if theworker refuses the subtask When the system moves to stateSN which means all subtasks of task i have been accepted by

workers the state will not change no matter the requesterencounters new workers or not erefore the one-steptransition probability matrix Q which is a square matrixwith order equaling N+ 1 can be derived as follows

(i) When the system is currently in the state Sj(0le jleN minus 1) after one-step transition the systemwill move to state Sj+ 1 with the probability Piw orstay at Sj with the probability 1 minus Piw us for0le jleN minus 1 Qj j+ 1 Piw and Qj j 1 minus Piw

(ii) When the system is currently in the state Sj (jN)the system must stay at Sj after one-step transitionus for jN Qj j 1

e one-step transition probability matrix Q is a sparsematrix We can obtain

Q

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)

From the initial slot to the last slot the system witnessesm minus 1 transition e system stays at state S0 at the initial slotbecause no subtask is assigned Hence the initial distributionis η [1 0 01113980radicradicradic11139791113978radicradicradic1113981

N

] Let Pi(N) denote the probability that a

requester has assigned total N subtasks of task i successfullywithin the duration Di minus SDi Within the delay requirementthere arem slots We use a Markov chain to describe the statetransition from the first slot to the mth slot Hence there arem minus 1 steps For each step the transition probability matrix isQ erefore Qmminus 1 denotes the transition probability matrixof m minus 1 steps en we can obtain

Pi(N) ηQmminus 1R (9)

where R [0 0 1]T Pi(N) is related to the task partitionnumber N

Tomaximize Pi(N) by solving the KarushndashKuhnndashTucker(KKT) conditions [33] we obtain

z

zNPi(N) 0 (10)

en using (4) (5) (9) and (10) we can derive the optimaltask partition Nprime in theory Considering the practical limitationof partition number the optimal task partition Nlowast is derived as

Nlowast

min Nprime Nmax1113864 1113865 (11)

where Nmax denotes the allowable maximum partitionnumber After Nlowast is determined the maximal value Pi(Nlowast)

of successful assignment probability can be calculated basedon (9)

For a complicated task we use a Markov chain and thestate transition matrix to obtain the optimal task partitionWhen the optimal partition Nlowast is determined the proba-bility Pi(Nlowast) that all parts of the complicated task are ex-ecuted by mobile workers can be obtained Based on thevalue of probability Pi(Nlowast) we know how often this totalassignment occurs e higher value of Pi(Nlowast) means thistotal assignment will occur more often e proposed al-gorithm for task partition is described as Algorithm 1

Theorem 1 6e proposed task partition is optimal

Proof Since a complex task is difficult for a mobile device toexecute we divide a complex task into N subtasks and assigneach subtask to a mobile device If each subtask is acceptedby a mobile device the crowdsourcing process is completedUsing a Markov chain we aim to obtain the optimal value ofN to maximize the completed probability of the crowd-sourcing process

At first the states of the Markov chain are defined Weuse S0 S1 S2 SN to denote N+ 1 states where Sj means jsubtasks have been accepted by mobile devices S0 means nosubtask is assigned while SN means all subtasks have beenassigned successfully Hence these states describe howmanysubtasks are accepted

Di

SDi

m2 m ndash 11

t

Figure 2 Slot division


If the encountered worker accepts the subtask with theprobability Piw the system moves to new state Sj+ 1(jleN minus 1) from state Sj Otherwise the system still stays atstate Sj if the worker refuses the subtask with the probability1 minus Piw When the system moves to state SN which means allsubtasks of task i have been accepted by workers the statewill not change no matter the requester encounters newworkers or not erefore we can obtain one-step transitionprobability matrixQ shown in equation (8) to describe statetransitions

Within the delay requirement the crowdsourcing pro-cess is completed if the system moves from S0 to SN whichmeans all subtasks are accepted by workers We use Pi(N)shown in equation (9) to denote this completed probabilitythat the system moves from S0 to SN is probability isdetermined by the partition valueN Hence the proper valueof N will result in the maximized completed probability Wesolve this problem based on equations (10) and (11) andobtain the optimal value Nlowast to maximize the completedprobability which means optimal partition is obtained

42 Unsuccessful Assigned Attempts Before a requester as-signs all subtasks successfully there may be some un-successful assignment attempts for the requester becausesome encountered workers do not accept the subtaskseseinvalid attempts consume the requesterrsquos resources such asenergy and probing time Based on the optimal task partitionNlowast the invalid attempt number can be obtained accuratelyas follows

After the optimal task partition Nlowast is derived thecorresponding one-step transition probability matrixQNlowast + 1 with order equaling Nlowast + 1 is determined Let Udenote the unsuccessful number of subtask assignment at-tempts before the system reaches state SNlowast To derive theaverage unsuccessful attempt number E[U] the invalid at-tempts should be distinguished from the state transition

us we introduce the matrix QNlowast + 1(x) associated toQNlowast + 1 with dummy variables x e QNlowast + 1(x) is de-fined as follows

(i) For 0le jleNlowast minus 1 QNlowast + 1(x)j j+1 Piw andQNlowast + 1(x)j j x(1 minus Piw)

(ii) For j Nlowast QNlowast + 1(x)j j 1

Note that QNlowast + 1(x) QNlowast + 1 if we take x 1 ento describe invalid attempts among the state transitions wecan define

y(x) ηQNlowast+1(x)mminus 1

R (12)

Let v(x) y(x)Pi(Nlowast) en we can obtain

v(x) ηQNlowast+1(x)mminus 1R

Pi Nlowast( ) (13)

Considering that y(x) Pi(Nlowast) when x equals 1 basedon (13) v(x) can also be expressed by

v(x) 1113944mminus 1

q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)

where the coefficient f(q) denotes the probability the systemreaches state SNlowast with q unsuccessful subtask assignmentattempts after (m minus 1)-step transitions from slot 1 So v(x)

is the probability generating function of the unsuccessfulnumber of subtask assignment attempts within Di minus SDi

Let E[U] be the average unsuccessful number of subtaskassignment attempts within Di minus SDi We can obtain

E[U] z

zxv(x) ∣ x1 (15)

In this section ldquodummy variable xrdquo is introduced tocalculate the number of unsuccessful assigned attempts

InputTotal mobile workersrsquo arrival rate λr

Delay requirement DiTask load TaiMonetary reward Ri to a workerMobile workersrsquo computing capacity B

Outpute optimal task partition Nlowast and the maximal value Pi(Nlowast)

(1) Based on equation (1) STai(N)⟵Each subtask load(2) Based on equation (3) Piw⟵e probability that worker w accepts the subtask of task i(3) With Piw transition probability matrix Q is obtained based on Equation (8)(4) Based on equation (5) SDi⟵Duration for each worker to complete a subtask(5) Based on equation (7) m⟵e number of slots within Di minus SDi

(6) Within m slots Pi(N) is obtained based on equation (9)(7) Using equation (10) Nprime⟵ the optimal task partition in theory(8) Using equation (11) Nlowast⟵ the practical optimal task partition(9) Based on equation (9) and Nlowast Pi(Nlowast)⟵ the maximal value of successful assignment probability

Return Nlowast and Pi(Nlowast)

ALGORITHM 1 Optimal task partition for task i


During the state transition based on y(x) in (12) all un-successful assignments are labeled by the dummy variable xTo calculate the unsuccessful assignment number we use theproperties of generation function Hence we usey(x)Pi(Nlowast) in (13) to guarantee the coefficient of each termincluding dummy variable x is in the range (0 1) based ongeneration function format en (13) can be rewritten as(14) which is the expression of the probability generatingfunction for the unsuccessful number Based on the prop-erties of generation function the average unsuccessfulnumber of subtask assignment attempts is equivalent to thefirst derivative of v(x) at the point x 1 Here the invalidnumber of subtask assignment attempts is analyzed accu-rately which is helpful to evaluate the resource consumptionof requesters due to probing potential workers

e proposed algorithm for unsuccessful assignmentattempts is described as Algorithm 2

43 Analysis of Time Complexity e complexity of pro-posed algorithm is computed as follows

We first discuss computation complexity of optimal taskpartition In line 7 of Algorithm 1 the solution of optimaltask partition determines the complexity of Algorithm 1Considering the allowable maximum partition numberNmax the practical partition number cannot exceed thisthreshold Meanwhile the primary computation is matrixmultiplication based on (9) and allowable maximum par-tition number Nmax limits the matrix size us the solutioncomplexity is O((Nmax)3m) where m denotes the number ofslots within delay requirement Based on (7) m is de-termined by the arrival rate λr of total mobile workers andthe delay requirement Di minus SDi of task i erefore com-putation complexity of Algorithm 1 is O((Nmax)3m) which isdetermined by the allowable maximum partition numberthe total arrival rate and the delay requirement

en we analyze the computation complexity of un-successful assignment attempts In line 2 of Algorithm 2 thecalculation of y(x) determines the complexity of Algo-rithm 2 Based on slot number m and optimal partition Nlowast

obtained in Algorithm 1 the calculation complexity ofAlgorithm 2 is O((Nlowast)3m) It seems that slot number m andoptimal partitionNlowast determine the computation complexityof Algorithm 2 Actually since slot number m and optimalpartitionNlowast are the results of Algorithm 1 the complexity ofAlgorithm 2 is also determined by the allowable maximumpartition number the total arrival rate and the delayrequirement

5 Simulations

In this section our proposed task partition policy is eval-uated by extensive simulations Compared to the fixedpartition scheme and adaptive scheme in [23] our policy canrealize high task service quality

51 Comparison Metric For efficient comparison in thissection we adopt two metrics task service quality and in-valid number of subtask assignment attempts

e first metric task service quality is denoted by theratio between the real completed subtasks and the totalsubtasks Obviously the more subtasks have been finishedthe better task service quality can be realizedis metric canclearly illustrate how many subtasks are accepted and exe-cuted by mobile workers within the duration Di minus SDi Byusing this metric we can observe different methods lead tovarious impacts on real completed subtasks

e second metric calculates unsuccessful number ofsubtask assignment attempts within delay requirementDuring the process of probing potential workers someworkers do not accept subtasks us these assignmentattempts are unsuccessful is leads to useless resourceconsumption of requesters and workers e larger invalidsubtask assignment attempts are the higher invalid resourceconsumption is is metric can clearly illustrate how manysubtask assignment attempts are not accepted by mobileworkers within the duration Di minus SDi By using this metricit is helpful for us to understand the resource consumptionof requesters and workers in the mobile crowdsourcingsystem

e simulation environments are described as followsAs the user mobility model is widely used and validated byresearch works [34 35] we use the same parameters of themobility model as in these studiesemobile workers comefollowing exponential distribution and the total arrival rateis denoted by λr Note that our task model fits several mobilecrowdsourcing tasks including location-based informationfinding tasks and content creation tasks Here we do thesimulation based on the content creation tasks and all taskparameters are the same as in [25] B TaiDi and Ri are all inthe unit of slots e requester and workers are able tocommunicate with others by cellular links or D2D links

52 Simulation Results With the total arrival rate λr 1Figure 3 depicts the result of task crowdsourcing as the taskload Tai increases from 300 to 400 In Figure 3 parametersare set as Di 100 Ri 10 Ew 02 C 6 and B 2 Asshown in Figure 3 compared to the fix partition policieswhich divide the task into 3 subtasks (N 3) and 8 subtasks(N 8) and the adaptive scheme in [23] our partition policycan achieve higher service quality As the total task loadchanges our policy divides the task into various number ofsmall subtasks to improve the accepting probability ofmobile workers while the fix partition method divides thetask into fixed number leading to the low acceptingprobability of mobile workers Also our partition policy isbetter than the adaptive scheme because the adaptive schemedoes not take into consideration the mobile feature ofworkers As the task load Tai increases the service qualitydecreases because it is difficult for workers with limitedcomputing capacity to complete complex subtasks

Figure 4 depicts the result of task crowdsourcing as thedelay requirement Di increases from 80 to 100 In Figure 4parameters are set as follows Ri 10 Ew 02 C 6 B 2and Tai 350 As shown in Figure 4 the service qualityincreases as the delay requirement Di increases becausemore time is permitted for workers to finish subtasks


Compared to the fix partition policies (N 3 and 8) and theadaptive scheme our policy achieves higher quality Basedon the change of delay requirement our policy adjusts the

length of each subtask by task partition to increase theaccepting probability of mobile workers while the fix par-tition method divides the task into fixed number which doesnot consider the accepting probability of mobile workersAlso our partition policy is better than the adaptive schemesince the adaptive scheme does not take into considerationthe mobile feature of workers Besides the fix partitionpolicy of N 8 realizes higher service quality than that ofN 3 when the delay requirement is small e policy ofN 8 means each subtask is smaller than that of N 3Intuitively a smaller subtask is more likely to be completedwithin strict delay requirement Hence the fix partitionpolicy of N 8 realizes higher service quality under smalldelay requirement As the delay requirement increases thecompleted probability of a bigger subtask also grows Whena bigger subtask is completed it brings more impact on theservice quality Hence under the large delay requirementthe fix partition policy of N 3 realizes higher servicequality

Figure 5 depicts the result of task crowdsourcing as thereward Ri increases In Figure 5 parameters are set as fol-lows Tai 350 Di 80 C 6 and B 2 As shown in Fig-ure 5 we can see the service quality increases when the taskreward Ri increases e reason is that the probability thatworkers accept subtask becomes higher with the larger RiOur partition policy even under the lower reward conditioncan realize higher task service quality because our policydivides the task into small pieces based on the current re-ward to increase the workerrsquos accepting probability of eachsubtask Furthermore the fix partition policy of N 8 growssharply as the reward increases Initially the total reward islow and each subtask is given a small reward Hence theaccepting probability is low and the service quality is smallWhen the reward increases each subtask is corresponding tohigher reward For fix partition policy ofN 8 the acceptingprobability increases sharply than others leading to higherservice quality

When total arrival rate of mobile workers changes thetask service quality of our partition policy also changes InFigure 6 we set task load Tai 350 and 400 respectivelyOther parameters are set as follows Ri 10 Di 80 C 6and B 2 As shown in Figure 6 we can see the servicequality increases when there is higher total arrival rate of

Inpute probability Piw denoting that a worker accepts the subtask of taske optimal task partition Nlowast

e maximal value Pi(Nlowast) can be obtainede number m of slots within Di minus SDi

OutputAverage unsuccessful number of subtask assignment attempts E[U]

(1) Based on transition probability matrix Q and the optimal task partition Nlowast in Algorithm 1 QNlowast + 1(x) is obtained(2) Using QNlowast + 1(x) y(x) is defined to describe invalid attempts based on Equation (12)(3) Using equations (13) and (14) y(x) is converted to v(x) denoting the probability generating function of unsuccessful attempts(4) Using Equation (15) average unsuccessful attempts E[U] is obtained

Return E[U]

ALGORITHM 2 Unsuccessful assignment attempts for task i

300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8

Our partition policyAdaptive scheme

Figure 3 Task service quality varies with task load

Task

serv

ice q

ualit

y

N = 3N = 8


80 85 90 95 100Delay requirement

01

02

03

04

05

06

07

08

09

1

Figure 4 e task service quality varies with delay requirement


mobile workers e reason is that the requester will en-counter more workers and the chance for task crowd-sourcing increases When the task load Tai increases theservice quality decreases since it is difficult for workers withlimited computing capacity to complete complex subtasks

Figure 7 depicts the invalid number of subtask as-signment attempts when the task load changes As shownin Figure 7 our partition policy witnesses less invalidnumber of subtask assignment attempts than the fixedpartition policy which divide the task into 5 subtasks(N 5) Our partition policy is able to adjust the partitionnumber of subtasks based on the task load and increasethe accepting probability of mobile workers while thefixed partition policy only divides task into fixed numberno matter how big the task load is erefore our policyrealizes less invalid assignment attempts When the

reward Ri increases from 15 to 20 both our partitionpolicy and the fixed partition policy experience less in-valid number of subtask assignment attempts e reasonis that the workers are willing to accept subtasks with thehigh reward

6 Conclusions

In this paper a mobile crowdsourcing paradigm has beenproposed for a task requester to obtain high-quality re-sults We develop a recruitment process and proposesystem models Jointly considering the mobile workerfeatures (eg the worker computing capacity and mo-bility) and task partition a task partition problem isformulated to maximize the service quality To solve theoptimal task partition problem a Markov chain-basedsolution is developed to model and perform task partitionWith this policy the requester is able to divide a complextask into optimal number of subtasks and maximize theprobability that all subtasks are accepted by workers withinlimited time In addition the invalid number of subtaskassignment is precisely analyzed which is helpful toevaluate the resource consumption of requesters due toprobing potential workers Simulations show that theproposed task partition policy improves the results of taskcrowdsourcing

Conflicts of Interest

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

Acknowledgments

e work was supported in part by Key Research and De-velopment Program of Shandong Province China (no2017GGX10142) and in part by China Scholarship Fund

10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8


Figure 5 e task service quality varies with rewards

50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5

Ri = 15 our partition poicy Ri = 20 our partition poicy

Figure 7 Invalid subtask assignment number

Task

serv

ice q

ualit

y

02 04 06 08 1Arrival rate

Task = 350 our partition policyTask = 350 adaptive schemeTask = 400 our partition policyTask = 400 adaptive scheme

01

02

03

04

05

06

07

08

09

1

0

Figure 6 Task service quality varies with arrival rate


References

[1] P G Ipeirotis ldquoAnalyzing the Amazon mechanical turkmarketplacerdquo XRDS Crossroads 6e ACM Magazine forStudents vol 17 no 2 p 16 2010

[2] J Tian H Zhang D Wu and D Yuan ldquoQoS-constrainedmedium access probability optimization in wireless in-terference-limited networksrdquo IEEE Transactions on Com-munications vol 66 no 3 pp 1064ndash1077 2018

[3] L Zhai H Wang and C Liu ldquoDistributed schemes forcrowdsourcing-based sensing task assignment in cognitiveradio networksrdquo Wireless Communications and MobileComputing vol 2017 Article ID 5017653 2017

[4] C Ji C Zhao S Liu et al ldquoA fast shapelet selection algorithmfor time series classificationrdquo Computer Networks vol 148pp 231ndash240 2019

[5] Y X Yan L Wu W Y Xu H Wang and Z M Liu ldquoIn-tegrity audit of shared cloud data with identity trackingrdquoSecurity and Communication Networks vol 2019 pp 1ndash112019

[6] L Zhai and H Wang ldquoCrowdsensing task assignment basedon particle swarm optimization in cognitive radio networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 4687974 2017

[7] Z Wang J Xu X Song and H Zhang ldquoConsensus problemin multi-agent systems under delayed informationrdquo Neuro-computing vol 316 pp 277ndash283 2018

[8] B Hu H Wang X Yu W Yuan and T He ldquoSparse networkembedding for community detection and sign prediction insigned social networksrdquo Journal of Ambient Intelligence andHumanized Computing vol 10 no 1 pp 175ndash186 2019

[9] Q Jiang Y Ma K Liu and Z Dou ldquoA probabilistic radiomap construction scheme for crowdsourcing-based finger-printing localizationrdquo IEEE Sensors Journal vol 16 no 10pp 3764ndash3774 2016

[10] S Jung B Moon and D Han ldquoUnsupervised learning forcrowdsourced indoor localization in wireless networksrdquo IEEETransactions on Mobile Computing vol 15 no 11pp 2892ndash2906 2016

[11] D Sikeridis B P Rimal I Papapanagiotou andM Devetsikiotis ldquoUnsupervised crowd-assisted learningenabling location-aware facilitiesrdquo IEEE Internet of 6ingsJournal vol 5 no 6 pp 4699ndash4713 2018

[12] J An X Gui Z Wang J Yang and X He ldquoA crowdsourcingassignment model based on mobile crowd sensing in theInternet of thingsrdquo IEEE Internet of 6ings Journal vol 2no 5 pp 358ndash369 2015

[13] H Liu B Xu D Lu and G Zhang ldquoA path planning ap-proach for crowd evacuation in buildings based on improvedartificial bee colony algorithmrdquo Applied Soft Computingvol 68 pp 360ndash376 2018

[14] X Deng Y Zheng Y Xu X Xi N Li and Y Yin ldquoGraph cutbased automatic aorta segmentation with an adaptivesmoothness constraint in 3D abdominal CT imagesrdquo Neu-rocomputing vol 310 pp 46ndash58 2018

[15] J Lian S Hou X Sui F Xu and Y Zheng ldquoDeblurringretinal optical coherence tomography via a convolutionalneural network with anisotropic and double convolutionlayerrdquo IET Computer Vision vol 12 no 6 pp 900ndash907 2018

[16] D C Brabham Crowdsourcing MIT Press Cambridge MAUSA 2013

[17] J J Horton and L B Chilton ldquoe labor economics of paidcrowdsourcingrdquo in Proceedings of the ACM 11th ACM

Conference on Electronic Commerce pp 209ndash218 CambridgeMA USA June 2010

[18] M Karaliopoulos and I Koutsopoulos ldquoUser recruitment formobile crowdsensing over opportunistic networksrdquo in Pro-ceedings of the IEEE Infocom Hong Kong China April 2015

[19] L Gao and J Huang ldquoProviding long-term participationincentive in participatory sensingrdquo in Proceedings of the IEEEInfocom 2015

[20] A Kittur E H Chi and B Suh ldquoCrowdsourcing user studieswith Mechanical Turkrdquo in Proceedings of the ACM SIGCHIConference on Human Factors in Computing Systemspp 453ndash456 Hong Kong China April 2008

[21] N Eagle ldquotxteagle mobile crowdsourcingrdquo InternationalConference on Internationalization Design and Global De-velopment Lecture Notes in Computer Science vol 5623pp 447ndash456 2009

[22] G S Tuncay and A Helmy ldquoParticipant recruitment and datacollection framework for opportunistic sensing a compara-tive analysisrdquo in Proceedings of the ACM MobiCom ChantsMiami FL USA September 2013

[23] W Chang and J Wu ldquoProgressive or conservative rationallyallocate cooperative work in mobile social networksrdquo IEEETransactions on Parallel and Distributed Systems vol 26no 7 pp 2020ndash2035 2015

[24] X Gong X Chen J Zhang and H V Poor ldquoExploiting socialtrust assisted reciprocity (star) toward utility-optimal socially-aware crowdsensingrdquo IEEE Transactions on Signal and In-formation Processing Over Networks vol 1 no 3 pp 195ndash2082015

[25] L Pu X Chen J Xu and X Fu ldquoCrowdlet optimal workerrecruitment for self-organized mobile crowdsourcingrdquo inProceedings of the 35th Annual IEEE International Conferenceon Computer Communications San Francisco CA USAApril 2016

[26] Y Han T Luo D Li and H Wu ldquoCompetition-basedparticipant recruitment for delay-sensitive crowdsourcingapplications in D2D networksrdquo IEEE Transactions on MobileComputing vol 15 no 12 pp 2987ndash2999 2016

[27] Y Tong L Chen Z Zhou H V Jagadish L Shou andW LvldquoSLADE a smart large-scale task decomposer in crowd-sourcingrdquo IEEE Transactions on Knowledge and Data Engi-neering vol 30 no 8 pp 1588ndash1601 2018

[28] HWu H Zhang L Cui and XWang ldquoCEPTM a cross-edgemodel for diverse personalization service and topic migrationin MECrdquo Wireless Communications and Mobile Computingvol 2018 Article ID 8056195 2018

[29] X Yu HWang X Zheng and YWang ldquoEffective algorithmsfor vertical mining probabilistic frequent patterns in un-certain mobile environmentsrdquo International Journal of AdHoc and Ubiquitous Computing vol 23 no 34 pp 137ndash1512016

[30] M Sharifi S Kafaie and O Kashefi ldquoA survey and taxonomyof cyber foraging of mobile devicesrdquo IEEE CommunicationsSurveys amp Tutorials vol 14 no 4 pp 1232ndash1243 2012

[31] U Gadiraju ldquoHuman beyond the machine challenges andopportunities of microtask crowdsourcingrdquo IEEE IntelligentSystems vol 30 no 4 pp 81ndash85 2015

[32] A Singla and A Krause ldquoTruthful incentives in crowd-sourcing tasks using regret minimization mechanismsrdquo inProceedings of the 22nd International Conference on WorldWide Web-WWWrsquo13 Rio de Janeiro Brazil May 2013

[33] S Boyd and L Vandenberghe Convex Optimization Cam-bridge University Press Cambridge UK 2004


[34] J Wu andM Xiao ldquoHoming spread community home-basedmulticopy routing in mobile social networksrdquo in Proceedingsof the IEEE Conference on Computer Communications TurinItaly April 2013

[35] A Picu and T Spyropoulos ldquoDTN-meteo forecasting theperformance of DTN protocols under heterogeneous mo-bilityrdquo IEEEACM Transactions on Networking vol 23 no 2pp 587ndash602 2015


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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


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Hindawi

wwwhindawicom Volume 2018

Advances in

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Submit your manuscripts atwwwhindawicom

geotagging for mobile touring guiding monitoring and localparking space searching which are inevitable in smart citiesTo improve the task-executing efficiency a user tends toassign such delay-sensitive tasks to mobile devices tocomplete them and collect executing results through thewireless communication system which is called mobilecrowdsourcing We should notice that these task-executingresults must come back within delay requirement Howevermobile devices which are portable but with less computingability are difficult to complete complex tasks within delayrequirement Hence this is challenging to mobile devicesand motivates us to develop a mobile crowdsourcing policyto divide large tasks into several small parts suitable formobile devices to execute

In this paper we propose a mobile crowdsourcingparadigm dividing a complicated task into small piecesand assigning small subtasks to mobile devices to obtainhigh-quality executing results which means mobile devicesexecute as many subtasks as possible We design therecruited process and present the worker arrival model andtask model Furthermore the probability that all parts ofthe complicated task are executed by mobile workers isintroduced to evaluate the result of task crowdsourcinge higher probability means the result of the taskcrowdsourcing is better According to these models wetake into consideration other factors such as the com-plexity and rewards of tasks which will influence mobileworkersrsquo execution and formulate a task partition problemto maximize the probability that all parts of the compli-cated task are executed by mobile workers en using theMarkov chain we derive a task division policy to realizehigh-quality results and the invalid number of task as-signment attempts is analyzed accurately based on prob-ability generating function Simulations show that our taskpartition policy improves the results of taskcrowdsourcing

In this paper we study the task partition problem ofcrowdsourcing process in the wireless system consisting ofmany mobile devices e main contributions are sum-marized as follows

(i) Considering the mobility and capacity of mobileworkers we propose a mobile crowdsourcing par-adigm to divide a complicated task into multiplesubtasks and assign these subtasks to mobileworkers e mobile worker decides to execute sucha subtask or not based on its computing capabilityand corresponding requirements

(ii) To describe the attributes of each task the taskmodelis proposed to denote task load delay requirementand monetary reward to the mobile workersMoreover an arrival model of mobile workers isproposed to describe the encountered process be-tween the requester and themobile worker Based onmobile worker features and task attributes we es-tablish the system model and formulate a taskpartition problem to maximize the probability thatall subtasks are executed by mobile workers andguarantee the result of task crowdsourcing

(iii) To realize the high-quality results of task crowd-sourcing using a Markov chain the state transi-tions denoting the number of subtasks executed bymobile workers can be analyzed Based on thesestate transitions within limited period caused bydelay requirement the optimal task partition can beobtained en according to the optimal taskpartition the invalid number of subtask assignmentis analyzed accurately with probability generatingfunction in the total crowdsourcing process

(iv) Simulation results show our proposed policycompared to fix partition policy and the adaptivescheme approaches the optimal solutions

e rest of the paper is organized as follows In Section 2a review about related works is provided In Section 3 wedescribe the task crowdsourcing process and propose thesystem model In Section 4 a Markov chain is developed tosolve the task partition problem and the number of invalidattempts is analyzed In Section 5 the proposed algorithm isevaluated with simulation results Finally conclusions areshown in Section 6

2 Related Works

Human computation has been executed for many centuriesSpecifically if a ldquohumanrdquo serves to ldquocomputerdquo there will be ahuman computation which can be observed is is thereason why there is a history of Human Computation whichis obviously longer than that of the electronic computerWith the rapid development of Internet web service es-pecially those facilitating online labor recruiting and man-aging (eg oDesk and Amazon MTurk) humancomputation begins to experience a new era where thesources of human are not designated exerts or employees butextended to a vast pool of crowds instead is type ofoutsourcing to crowds named crowdsourcing is receivingcountless success in several areas such as logistics fundraising monitoring and so on

With the extensive use of mobile devices such as tabletsand smart phones the new hybrid architecture occurs tosupport a massive ad hoc crowd which is composed ofdistributed mobile nodes and a massive social networkaround a smart city environment [8] erefore mobilecrowdsourcing can be utilized in IoT to complete real-timetasks and improve task efficiency (eg localization servicespectrum sensing and environmental monitoring)

For indoor localization systems a major bottleneck is thetradeoff between both localization accuracy and site surveycosts In [9] a probabilistic radiomap constructionmethod ispropose with crowdsourcing collection taking into accountboth accuracy and survey costs In order to obtain the needfor location labels Jung et al [10] propose the unsupervisedlearning method to calibrate a localization model based on aglobal-local optimization scheme In this hybrid scheme anefficient global-local interaction reduces the task complexitydrastically In [11] a location-aware infrastructure is pro-posed to combine a broad sensing layer centralized cloudfederation support and edge computing With the sensing






3 System Model










32 System Model



is 1λr






STai(N) Tai

N (1)


Ri(N) Ri

N (2)





Base station

A worker W1

A requester R

D2D link


Position 1

Position 2

Position 3




Piw

exp minus CSTai(N)

DiBw

1113888 1113889

2 1Ri(N)Ew


exp minus CSTai(N)

DiBw

1113888 11138891

Ri(N)2Ew

1113888 1113889Ri(N)ltRE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)



Piw

exp minus C1N

Tai

DiBw

1113888 1113889

2 1RiEw

⎛⎝ ⎞⎠N leRi

RE

exp minus CNTai

DiBw

1113888 11138891

Ri2Ew

1113888 1113889NgtRi

RE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



SDi STai(N)

B (5)





Nlowast ≜ argmaxN

P(ngeN)


4 Partition Policy





m Di minus SDi

Ts

(7)









Q

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


N






z

zNPi(N) 0 (10)


Nlowast

min Nprime Nmax1113864 1113865 (11)







Di

SDi

m2 m ndash 11

t












R (12)



Pi Nlowast( ) (13)



q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)




E[U] z

zxv(x) ∣ x1 (15)
















5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






3 System Model










32 System Model



is 1λr






STai(N) Tai

N (1)


Ri(N) Ri

N (2)





Base station

A worker W1

A requester R

D2D link


Position 1

Position 2

Position 3




Piw

exp minus CSTai(N)

DiBw

1113888 1113889

2 1Ri(N)Ew


exp minus CSTai(N)

DiBw

1113888 11138891

Ri(N)2Ew

1113888 1113889Ri(N)ltRE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)



Piw

exp minus C1N

Tai

DiBw

1113888 1113889

2 1RiEw

⎛⎝ ⎞⎠N leRi

RE

exp minus CNTai

DiBw

1113888 11138891

Ri2Ew

1113888 1113889NgtRi

RE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



SDi STai(N)

B (5)





Nlowast ≜ argmaxN

P(ngeN)


4 Partition Policy





m Di minus SDi

Ts

(7)









Q

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


N






z

zNPi(N) 0 (10)


Nlowast

min Nprime Nmax1113864 1113865 (11)







Di

SDi

m2 m ndash 11

t












R (12)



Pi Nlowast( ) (13)



q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)




E[U] z

zxv(x) ∣ x1 (15)
















5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



32 System Model



is 1λr






STai(N) Tai

N (1)


Ri(N) Ri

N (2)





Base station

A worker W1

A requester R

D2D link


Position 1

Position 2

Position 3




Piw

exp minus CSTai(N)

DiBw

1113888 1113889

2 1Ri(N)Ew


exp minus CSTai(N)

DiBw

1113888 11138891

Ri(N)2Ew

1113888 1113889Ri(N)ltRE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)



Piw

exp minus C1N

Tai

DiBw

1113888 1113889

2 1RiEw

⎛⎝ ⎞⎠N leRi

RE

exp minus CNTai

DiBw

1113888 11138891

Ri2Ew

1113888 1113889NgtRi

RE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



SDi STai(N)

B (5)





Nlowast ≜ argmaxN

P(ngeN)


4 Partition Policy





m Di minus SDi

Ts

(7)









Q

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


N






z

zNPi(N) 0 (10)


Nlowast

min Nprime Nmax1113864 1113865 (11)







Di

SDi

m2 m ndash 11

t












R (12)



Pi Nlowast( ) (13)



q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)




E[U] z

zxv(x) ∣ x1 (15)
















5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Piw

exp minus CSTai(N)

DiBw

1113888 1113889

2 1Ri(N)Ew


exp minus CSTai(N)

DiBw

1113888 11138891

Ri(N)2Ew

1113888 1113889Ri(N)ltRE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)



Piw

exp minus C1N

Tai

DiBw

1113888 1113889

2 1RiEw

⎛⎝ ⎞⎠N leRi

RE

exp minus CNTai

DiBw

1113888 11138891

Ri2Ew

1113888 1113889NgtRi

RE

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



SDi STai(N)

B (5)





Nlowast ≜ argmaxN

P(ngeN)


4 Partition Policy





m Di minus SDi

Ts

(7)









Q

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


N






z

zNPi(N) 0 (10)


Nlowast

min Nprime Nmax1113864 1113865 (11)







Di

SDi

m2 m ndash 11

t












R (12)



Pi Nlowast( ) (13)



q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)




E[U] z

zxv(x) ∣ x1 (15)
















5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Q

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw

1 minus Piw Piw 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


N






z

zNPi(N) 0 (10)


Nlowast

min Nprime Nmax1113864 1113865 (11)







Di

SDi

m2 m ndash 11

t












R (12)



Pi Nlowast( ) (13)



q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)




E[U] z

zxv(x) ∣ x1 (15)
















5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











R (12)



Pi Nlowast( ) (13)



q0f(q)x

q

1113944

mminus 1

q0f(q) 1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)




E[U] z

zxv(x) ∣ x1 (15)
















5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








5 Simulations

















Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Return E[U]


300 320 340 360 380 40004

05

06

07

08

09

1

Task load

Task

serv

ice q

ualit

y

N = 3N = 8



Task

serv

ice q

ualit

y

N = 3N = 8



01

02

03

04

05

06

07

08

09

1






6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





6 Conclusions




Acknowledgments


10 12 14 16 1801

02

03

04

05

06

07

08

09

Rewards

Task

serv

ice q

ualit

y

1

N = 3N = 8



50 60 70 80 90 1005

10

15

20

25

30

35

Task load

Inva

lid su

btas

k as

singm

ent n

umbe

r

Ri = 15 N = 5Ri = 20 N = 5



Task

serv

ice q

ualit

y



01

02

03

04

05

06

07

08

09

1

0



References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Research Article - Hindawi Publishing...

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