Research Article A Novel Execution Mode Selection Scheme ...

Research ArticleA Novel Execution Mode Selection Schemefor Wireless Computing

Jiadi Chen and Wenbo Wang

Wireless Signal Processing and Network Lab Key Laboratory of Universal Wireless CommunicationMinistry of Education Beijing University of Posts amp Telecommunications Beijing 100876 China

Correspondence should be addressed to Jiadi Chen chenjdbupteducn

Received 11 September 2014 Accepted 25 December 2014

Academic Editor Feifei Gao

Copyright copy 2015 J Chen and W WangThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Computation offloading is an effective way to alleviate the resource limited problem of mobile devices However the offloading isnot an always advantageous strategy for under some circumstances the overhead in time and energy may turn out to be greaterthan the offloading savings Therefore an offloading decision scheme is in demand for mobile devices to decide whether to offloada computation task to the server or to execute it in a local processor In this paper the offloading decision problem is translated intoa dynamic execution mode selection problem the objective of which is to minimize the task execution delay and reduce the energyconsumption of mobile devices A novel executionmode adjustment mechanism is introduced tomake the execution process moreflexible for real-time environment variation Numerical results indicate that the proposed scheme can significantly reduce the taskexecution delay in an energy-efficient way

1 Introduction

Nowadays advancements in computing technology havemade mobile devices more and more smart and powerfulfor example smart phones handheld computers ambientsensors and autonomous robots The increasing processingand storage capacity have made it possible for them to runcomplex applicationsHowevermobile devices are inherentlyresource limited and energy constrained [1] for the morecomplex and energy-intensive programs are emerging in anexplosive speed [2]

Advanced computing architectures for example wire-lessmobile computing [3] and cloud computing [4] canprovide attractive solutions to alleviate the resource limita-tion problem These solutions all introduce a new strategythat is the task offloading also known as task migrationwhere the mobile terminals (MTs) can make use of theample computing resources of the wireline domain sendingtheir computation tasks to remote computation servers andreceiving the computation results afterwards

Is the offloading really beneficial From the perspectiveof saving time the relatively faster server processor can accel-erate the execution speed however overheads are introducedby wireless communication between MTs and the server

On the other hand it is hard to conclude whether theoffloading can reduce the MTrsquos energy consumption or notMost energy is consumed by the MTrsquos CPU when the task isexecuted locally If offloaded this part of energy can be savedbut the MTrsquos transceiver will consume additional energy toaccomplish the uplink and downlink data transmission

Therefore the offloading decision problem needs to beconsidered from many aspects for example task propertieswireless bandwidth and MTrsquos CPU capacity As [5] con-cludes offloading is beneficial when large amounts of com-putation are needed with relatively small amounts of com-munication Except typical applications which are suitable foroffloading (chess games face recognition applications etc)there are many computation tasks that are hard to be clas-sified as ldquotasks suitable for offloadingrdquo or ldquotasks suitable forlocal processingrdquo for example the online file editing or therelatively simple image processing the local computation vol-ume and offloading communication volume which are com-parative and the wireless bandwidth plays an important rolein the offloading decision process A weak wireless link canslow down the communication and raise power consumptionat the transceiver the overhead in time and energy may turnout to be greater than the offloading savings

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 106053 12 pageshttpdxdoiorg1011552015106053

2 International Journal of Antennas and Propagation

In this paper we consider the computing architecturewhich has been introduced in [6] The MT can execute thecomputation task in one of the following three modes (1)locally executing the task at the MTrsquos local processor (2)remotely offloading the task to a remote server by wirelesstransmission and (3) combinedly executing the task in theformer two ways simultaneously Before task execution theMT has to decide which mode to adopt Therefore theoffloading decision problem is equivalent to an executionmode selection problem

Based on the previous description an adaptive executionmode selection scheme (AEMSS) is proposed to help MTsmake offloading decisions Main contributions of this paperare described as follows

(i) For the existing offloading schemes decisions aremade in advance and cannot be changed once theexecution has begun The proposed AEMSS allowsthe task to change executionmode during processingwhich can make the task execution more flexible forthe changing wireless condition

(ii) The execution mode selection problem is formulatedas a finite-horizon Markov decision process (MDP)and the userrsquos tolerance for execution delay is subtlyformulated as the last decision epoch of the modelA heavy penalty factor for timeout can guarantee thedelay performance of the proposed scheme

(iii) The MDP is solved by the backward induction algo-rithm (BIA) and numerical results indicate that theproposedAEMSS can achieve a good performance onexecution delay and energy efficiency

The remainder of this paper is organized as followsThe related work is summarized in Section 2 System modeland the problem formulation of AEMSS are presented inSection 3 The detailed finite-horizon MDP model and thesolution are described in Section 4 In Section 5 some imple-mentation issues are discussed Simulation assumptions andthe numerical results are presented in Section 6 Finally theconclusions are drawn in Section 7

2 Related Work

In this section we provide a discussion on the existing algo-rithms for offloading decision which can be partitioned intotwo categories that is the static decisions and the dynamicdecisions [7]

Static decision is that the program is partitioned duringdevelopmentmdashwhich part to execute locally and which partto offload Algorithms to make static offloading decisionsmostly appear in the work of earlier years [8ndash10] In [8] analgorithm is proposed to divide the program into server tasksand client tasks such that the energy consumed at the clientis minimized Reference [9] presents a task partition andallocation scheme to divide the distributed multimedia pro-cessing between the server and a handheld device Authors in[10] introduce a strategy that executes the program initiallyon the mobile system with a timeout If the computationis not completed after the timeout it is offloaded These

static offloading decisions have the advantage of lowoverheadduring execution However this kind of approach is validonly when the parameters for example wireless transmissioncapacity can be accurately predicted in advance

In contrast dynamic decisions can adapt to various run-time conditions for example fluctuating network band-widths and varying server load Prediction mechanisms areusually used in dynamic approaches for decisionmaking Forexample the bandwidth is monitored and predicted using aBayesian scheme in [11] Offloading decision algorithms inrecent work are most dynamic ones [12ndash16] In [12] a theo-retical framework of energy-optimalmobile cloud computingunder stochastic wireless channel is provided In [13] a studyon the feasibility of applying machine learning techniquesis presented to address the adaptive scheduling problemin mobile offloading framework Reference [14] presents acollaborative WiFi-based mobile data offloading architecturetargeted at improving the energy efficiency for smartphonesReference [15] proposes a fine grained application model anda fast optimal offloading decision algorithm where multipleoffloading decisions are made per module based on theexecution paths leading to the module Authors in [16] alsoformulate the offloading decision problem based on MDPand solve it by using a linear programming approach Theyaddress the problem of extending the lifetime of a batterypowered mobile host in a client-server wireless network byusing task migration and remote processing

The work in this paper is inspired by [6] where atask migration jointly with the terminal power managementmechanism is formulated in the framework of dynamicprogramming The solution is a policy specifying when theterminal should initiate task migration versus executing thetask locally in conjunction with the power managementAlthough there have been various offloading decision algo-rithms proposed in the literature our work has some originaland advanced characters We put the focus on the offloadingdecision making phase with the optimization objective ofimproving the task execution efficiency and reducing theenergy consumption of mobile devices by determining theldquobest fitrdquo execution mode at each decision epoch

3 Problem Formulation

31 Computing Architecture In this paper we consider acomputing architecture where the MT can execute its com-putation task in one of the following three modes

(1) locally executing the task at the MTrsquos processor(2) remotely offloading the task to a remote computation

server via the wireless network(3) combinedly executing the task with the former two

options simultaneously

Modes 2 and 3 involve the practice of offloading which ismodeled into a three-step process as follows

(i) Data Uploading MT sends the task specification andinput data to the remote computation server

International Journal of Antennas and Propagation 3

(ii) Server Computing The remote computation serverperforms the task

(iii) Results DownloadingTheMT downloads the compu-tation results from the remote computation server

32 Execution Completion Time Let119862 denote the local com-putation volume of the task 119903119897 is the speed of local processorwhich is a constant value determined by the MTrsquos CPUcapacity The task execution completion time under the localexecution mode can be expressed as

119905119897 =119862

119903119897

(1)

In the remote execution mode let 119863119906 and 119863119889 denotethe data volume for uplink and downlink transmission andthe corresponding average transmission capacities of thewireless system are 119903119906 and 119903119889 respectively 119903119906 and 119903119889 aredetermined by multiple parameters for example the wirelessbandwidth transmission power and average channel fadingcoefficient For simplicity the remote server is assumed tohave a perfect process capacity so that the computation delaycan be ignored Thus the execution completion time underthe remote executionmode can be expressed as the sumof theuplink transmission delay 119905119906 and the downlink transmissiondelay 119905119889 that is

119905119903 = 119905119906 + 119905119889 =119863119906

119903119906

+119863119889

119903119889

(2)

When the task is executed combinedly the local processorand the remote server work simultaneously The executionprocess ends when either of them finishes the task So theexecution completion time can be expressed as

119905119888 = min 119905119897 119905119903 = min119862119903119897

119863119906

119903119906

+119863119889

119903119889

(3)

33 Energy Consumption of MT Energy is primary con-straint for mobile devices therefore we only consider theenergy consumption of the MT In the local execution mode119901119897 is the power of the local processor the energy consumptionof the MT is

119890119897 = 119901119897 sdot 119905119897 (4)

In the remote execution mode the power of transmittingantenna and receiving antenna is 119901119906 and 119901119889 respectivelyTheenergy consumption of the MT is

119890119903 = 119890119906 + 119890119889 = 119901119906 sdot 119905119906 + 119901119889 sdot 119905119889 (5)

where 119890119906 and 119890119889 are power consumption of the data uploadingand results downloading phases respectivelyWhen executedcombinedly the energy consumption of the MT can beexpressed as

119890119888 =

(119901119897 + 119901119906) 119905119906 + (119901119897 + 119901119889) (119905119888 minus 119905119906) 119905119888 gt 119905119906

(119901119897 + 119901119906) 119905119888 119905119888 le 119905119906

(6)

s0 a0 s1 a1 s2 a2

t = 0 middot middot middot T1 2 T minus 1

Observation end time

TimelinesTminus1 aTminus1

Figure 1 Timing in MDP

34 Adaptive Execution Mode Selection Under the previousassumptions the offloading decision problem can be trans-lated into an executionmode selection problem Based on theoptimization object that is minimizing task execution delayas well as reducing MTsrsquo energy consumption an adaptiveexecution mode selection scheme (AEMSS) is proposedFunctions of the offloading decision maker include

(i) determining the most appropriate execution modefor a specific computing task that is local executionremote execution or combined execution

(ii) determining if the execution mode needs to beadjusted during the execution process when theunstable factors for example the wireless environ-ment condition have dramatically changed

The AEMSS makes decisions based on a series of param-eters including the task properties (119862119863119906 119863119889) MTrsquos CPUcapacity and the wireless transmission capacity (119903119897 119903119906 119903119889)The problem is formulated into a finite-horizon Markovdecision process (MDP) model and solved by the backwardinduction algorithm (BIA) Details are elaborated in the nextsection

4 The Finite-Horizon MDP-Based AEMSS

In general an MDP model consists of five elements thatis (1) decision epochs (2) states (3) actions (4) transitionprobabilities and (5) rewards In this section we will describehow the offloading decision problem can be formulated intoa finite-horizon MDP model from these five aspects

41 Decision Epochs and State Space For simplicity the timeis slotted into discrete decision epochs and indexed by 119905 isin

0 1 2 119879 As Figure 1 shows time point 119905 = 119879 denotesthe observation end time in the MDPmodel not the momentthe task is just being completed Time 119879 has another sensethat is the longest task completion time that the user cansustain The task is considered failed if it is still uncompletedupon time 119879

At decision epoch 119905 the system state 119904119905 reflects thecurrent task completion progress and the real-time wirelesscondition which can be expressed as a tuple

119904119905 = (120601119905 1198621015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) (7)

the elements in which are explained below(i) 120601119905 the execution mode adopted in the last time slot

[119905 minus 1 119905) that is

120601119905 =

1 local execution2 remote execution3 combined execution

(8)


Table 1 Subspaces of the state space

S1

1119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 1 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906= 1198631015840

119889= 0 119903 isin R

S22 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906isin 1 2 119863119906 minus 11198631015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 minus 1 119903 isin R

S33 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 3 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906isin 1 2 119863119906 minus 1 119863

1015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)

1003816100381610038161003816 120601 = 3 1198621015840isin 1 2 119862 minus 1 119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 119903 isin R

Sinitial4

119904initial = (0 119862119863119906 119863119889 119903)|119903 isin R

Sterminal5

119904terminal = (4 0 0 0 119903)

1S1 is the set of system states indicating that the task is in the local execution process that is 120601 = 1R = 119903min 119903min +1 119903max where 119903min and 119903max denotethe minimum and maximum transmission capacities the wireless network can provide respectively2S2 is the set of system states indicating that the task is in the remote execution process that is 120601 = 2S2 can be seen as the union of two state sets that is thetask is in the uplink transmission process (1198631015840

119889= 119863119889) and the task is in the downlink receiving process (1198631015840

119906= 119863119906) respectively

3S3 is the set of system states indicating that the task is in the combined executing process that is 120601 = 3S3 can be seen as the union of two state sets that isthe task is in the uplink transmission process (1198631015840


119906= 119863119906) respectively Meanwhile the task is also

under local processing4S4 is the set of initial states which are distinguished by different wireless conditions that is different values of 1199035S5 contains a single state that is 119904terminal indicating that the task execution process is already finished 119903means that when the task has been completed thewireless transmission capacity can be disregarded

(ii) 1198621015840119905 the remaining computation volume for local

processing by time 119905(iii) 1198631015840

119906119905 the remaining data volume for uplink transmis-

sion by decision epoch 119905 if 120601119905 = 1 or the uplinktransmission has already finished1198631015840

119906119905= 0

(iv) 1198631015840119889119905 the remaining data volume for downlink trans-

mission by decision epoch 119905 if 120601119905 = 11198631015840119889119905

= 0(v) 119903119905 the transmission capacity the wireless network can

provide at decision epoch 119905 which is assumed to bestatic within a time slot and iid between slots

In addition there are two kinds of special states in thestate space that is the initial states 119904initial isin 119878initial and aterminal state 119904terminalThe initial states are specific at decisionepoch 119905 = 0 and indicate that the task is untreated while theterminal state indicates that the task execution process hasalready been completed Therefore the state space S can beexpressed as

S = S1 cup S2 cup S3 cupSinitial cupSterminal (9)

whereS1S2S3Sinitial andSterminal are subspaces ofS thedefinitions of which are listed in Table 1

42 Action Space and Policy In this model there are fouractions in the action spaceA that is

A = 0 1 2 3 (10)

At decision epoch 119905 AEMSS chooses an action based onthe current state 119904119905 Different actions represent the differentexecutionmodes the taskwill adopt in the following time slotthat is

119886119905 =

0 null1 local execution2 remote execution3 combined execution

(11)

where 119886119905 = 0 indicates that the task has already beencompleted andnothing needs to be done in the following timeslot

At decision epoch 119905 the decisionmaker chooses an actionfrom the feasible action setA119905 according to the decision rule119889119905(119904119905) = 119886119905 In MDP a policy 120587 = (1198890 1198891 119889119879) specifies thedecision rule to be used at all decision epochs It provides thedecisionmaker with a prescription for action selection underany possible future state [17] In this model the decision rulesat all 119879 decision epochs are different for example when thetask has already been completed 119886119905 = 0 is the only availableaction Therefore the policy obtained is a ldquononstationarypolicyrdquo In the following parts we will show how the actionscan transform the system states

At time 119905 the system state is 119904119905 = (120601119905 1198621015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905)

After action 119886119905 is taken the system will transform to the state119904119905+1 = (120601119905+1 119862

1015840

119905+1 1198631015840

119906119905+1 1198631015840

119889119905+1 119903119905+1) by time 119905+1The feasible

cases of states transformation are listed in Table 2 The casescan be split into two categories that is 119886119905 = 120601119905 (cases 1ndash3 thecurrent executionmodewill continue to be adopted) and 119886119905 =

120601119905 (cases 4ndash9 the current execution mode will be adjusted)In Table 2 cases 4ndash9 indicate that the execution mode is

changed within two successive time slots as follows

(i) In cases 4 and 5 the task is being executed locallyremotely at time 119905 when the decision maker decidesto change the executionmode to the remotelocal oneIn these cases the execution progress before time 119905willbe cleared and the task will be forced to be executedfrom scratch with a different execution mode

(ii) In cases 6 and 7 when the task is being executedlocally or remotely the decision maker wants it tobe executed with both modes simultaneously in thenext time slot In these cases the current executionprogress will be preserved and a new executionprocesswith another executionmodewill begin in thenext slot


Table 2 Actions and states transformation

Number Cases Illustration1 120601119905 = 1 119886119905 = 1 119904

119905= (1 119862

1015840

119905 0 0 119903

119905) 119886119905= 1 rArr 119904

119905+1= (1 119862

1015840

119905minus 119903119897 0 0 119903

119905+1)

2 120601119905 = 2 119886119905 = 2 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

1

3 120601119905 = 3 119886119905 = 3 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3119863

1015840

119906119905minus 119903119905 119863119889 119862

1015840

119905minus 119903119897 119903119905+1)

2

4 120601119905 = 1 119886119905 = 2 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863119906 minus 119903119905 119863119889 119903119905+1)

5 120601119905 = 2 119886119905 = 1 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862 minus 119903119897 0 0 119903119905+1)

6 120601119905 = 1 119886119905 = 3 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119896 = 3 rArr 119904119905+1 = (3 119862

1015840

119905minus 119903119897 119863119906 minus 119903119905 119863119889 119903119905+1)

7 120601119905 = 2 119886119905 = 3 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3 119862 minus 119903119897 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

8 120601119905= 3 119886

119905= 1 119904119905 = (3 119862

1015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862

1015840

119905minus 119903119897 0 0 119903119905+1)

9 120601119905 = 3 119886119905 = 2 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

12119862119863119906119863119889 denote the task properties that is the total computation volume for local processing and the total data volume for wireless transmission while1198621015840

119905 1198631015840

119906119905 1198631015840

119889119905 are real-time values at decision epoch 119905 that is the remaining computation volume after a period of local processing and remaining data volumeafter a period of transmission Therefore 119904119905 = (2 0119863

1015840

119906119905 119863119889 119903119896) and 119904119896 = (2 0 0119863

1015840

119889119905 119903119896) denote that the task is in uplink transmission process and in

downlink transmission process respectively In this table cases which involve the remote executing are all in the uplink transmission process

(iii) In cases 8 and 9 the task is being executed with localmode and remote mode simultaneously but the deci-sion maker judges that one of them is unnecessary Inthe next time slot the execution progress of this modewill be cleared and another one will continue

43 State Transition Probabilities From Table 2 we can con-clude that when a specific action 119886119905 is selected the systemstate of the next decision epoch can be determined except theelement of wireless transmission capacity 119903119905+1 Therefore thestate transition probability between two successive decisionepochs can be written as

119901 (119904119905+1 | 119904119905 119886119905) = 119901 (119903119905+1 | 119903119905) (12)

The long-term probability distribution of the wirelesstransmission capacities is denoted as 119901

infin(119903min) 119901

infin(119903min +

1) 119901infin(119903max) thus the steady state probability distribu-

tions of each task state at each decision epoch are

119901infin

0(119904initial = (0 119862119863119906 119863119889 1199030)) = 119901

infin(1199030)

1199030 isin 119903min 119903min + 1 119903max

119901infin

119905+1(1199041015840) =

119905

sum

119896=0

sum

1199041199041015840isin119878119878initial119886isin119860119905

119901infin

119896(119904) 119901 (119904

1015840| 119904 119886)

(13)

119901infin

119905(119904) denotes the steady state probability of state 119904 isin S119905

at decision epoch 119905 isin 0 1 119879 minus 1 S119905 denotes the setcontaining all feasible states at time epoch 119905 that is states witha steady state probability of 119901infin

119905(119904) = 0

44 Rewards and Value Function In this model the systemreward functionwithin time interval 119905 sim 119905+1 119905 lt 119879 is definedas

119903119905 (119904 119886) = sum

119904isin1198781199051199041015840isin119878119905+1

119886isin119860119905

119901 (1199041015840| 119904 119886) 119903119905 (119904

1015840| 119904 119886)

119903119905 (1199041015840| 119904 119886) = 120596119889119891119889119905 (119904

1015840| 119904 119886) minus 120596119890119891119890119905 (119904

1015840| 119904 119886) minus 120590119905

(14)

119891119889119896(1199041015840| 119904 119886) is the delay reward function and 119891119890119896(119904

1015840| 119904 119886)

is the energy consumption function120596119889 120596119890 are weight factorssatisfying 120596119889 + 120596119890 = 1 120590119896 is the penalty factor for exceedingthe execution delay limit which is defined as

120590119905 =

0 119905 = 119879

0 119905 = 119879 119904119905 = 119904terminal

120590 119905 = 119879 119904119905 = 119904terminal

(15)

It can be seen that the task will be regarded as a failure if it isstill uncompleted at the final decision epoch 119905 = 119879 The delayreward function is given by

119891119889119905 (1199041015840| 119904 119886) =

120588119905+1 minus 120588119905 120601119905 = 4

120588lowast 120601119905 = 4

(16)

where 119904 isin S119905 1199041015840isin S119905+1 119886 isin A119905 and 120588119905 is the task completion

factor at decision epoch 119905 the definition of which is

120588119905 =

1 minus1198621015840

119905

119862 120601119905 = 1

1 minus1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

120601119905 = 2

1 minusmin1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

1198621015840

119905

119862 120601119905 = 3

(17)

It can be seen that 120588119905 is the percentage completion of the task120588lowast is the extra reward the system gains each time slot after

the task is completed The penalty factor 120590119905 and extra reward120588lowast have the same function that is promoting the task to be

completed as early as possibleAt decision epoch 119905 the energy consumption function is

given by

119891119890119905 (119904119905+1 | 119904119905 119886119905) =

119901119897 119886119905 = 1

119901119906 119886119905 = 2 1198631015840

119906119905= 0

119901119889 119886119905 = 2 1198631015840

119906119905= 0

119901119897 + 119901119906 119886119905 = 3 1198631015840

119906119905= 0

119901119897 + 119901119889 119886119905 = 3 1198631015840

119906119905= 0

0 120601119905 = 4

(18)


It can be seen that under the combined execution mode thetask can be accomplished fastest with the price of the highestenergy consumption During the whole time domain from119905 = 0 sim 119879 the expected total reward that is the valuefunction can be expressed as

V120587 (119904) = 119864120587

119904

119879minus1

sum

119905=0

119903119905 (119904119905 119886119905) 119904 isin Sinitial 119904119905 isin S119905 119886119905 isin A119905

(19)

where 119864120587119904lowast denotes the expectation value of lowast under policy

120587 = (1198890 1198891 119889119879minus1)with the initial state 119904The optimizationobjective is to find an optimal policy 120587lowast = (119889

lowast

0 119889lowast

1 119889

lowast

119879minus1)

which satisfies

V120587lowast

(119904) ge V120587 (119904) (20)

for all initial states 119904 isin Sinitial and all 120587 isin Π Π is the setcontaining all feasible policies

45 Solution for Finite-HorizonMDP For an infinite-horizonMDP there are various mature algorithms available forreference for example value iteration policy iteration andaction elimination algorithms [17] In this part the solutionfor the proposed finite-horizon MDP model is discussed

On time domain 0 sim 119905 sequence ℎ119905 = (1199040 1198860 1199041

1198861 119904119905minus1 119886119905minus1 119904119905) is called a ldquohistoryrdquo of the system andℎ119905+1 = (ℎ119905 119886119905 119904119905+1) Let 119906

120587

119905(ℎ119905) for 119905 lt 119879 denote the

total expected reward obtained by using policy 120587 at decisionepochs 119905 119905 + 1 119879 minus 1 with a history of ℎ119905 that is

119906120587

119905(ℎ119905) = 119864

120587

ℎ119905

119879minus1

sum

119896=119905

119903119896 (119904119896 119886119896) 119904119896 isin S119896 119886119896 isin A119896 (21)

When ℎ1 = 119904 1199061205870(119904) = V120587(119904) From [17] the optimal equations

are given by

119906lowast

119905(ℎ119905) = max

119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886 119904

1015840)

(22)

for 119905 = 0 1 119879 minus 1 and ℎ119905 = (ℎ119905minus1 119886119905minus1 119904) 119904 isin S119905From above we can see that 119906lowast

0(ℎ119879) corresponds to the

maximum total expected reward V120587lowast

(119904) The solutions satis-fying the optimal equations are the actions 119886lowast

119904119905 119904 isin S119905 and

119905 isin 0 1 119879 minus 1 which can achieve the maximum totalexpected reward that is

119886lowast

119904119905= arg max119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886119905 119904

1015840)

(23)

In this paper the BIA [17] is employed to solve theoptimization problem given by (23) as follows

The Backward Induction Algorithm (BIA)

(1) Set 119905 = 119879 minus 1 and

119906lowast

119879minus1(119904) = max119886isin119860119879minus1

119903119879minus1 (119904 119886)

119886lowast

119904119879minus1= arg max119886isin119860119879minus1

119903119879minus1 (119904 119886)

(24)

for all 119904 isin S119879minus1(2) Substitute 119905minus1 for 119905 and compute 119906lowast

119905(119904) for each 119904 isin 119878119905

by

119906lowast

119905(119904) = max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(25)

Set

119886lowast

119904119905= arg max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(26)

(3) If 119905 = 0 stop Otherwise return to step 2

5 Model Implementation Issues

In this section discussions are made on some issues occur-ring when the proposed MDP-based AEMSS is implementedto a real system

51 The Offloading Decision Process Figure 2 illustrates theworkflow of the AEMSS which can be partitioned into twoparts that is the offline policy making and the online actionmapping

(i) Offline Policy Making The execution mode selectionpolicy is calculated offline via BIA the input dataof which includes task properties wireless networkcharacteristics and the MTrsquos capacities Before exe-cution the computation task needs to be profiledfirst to determine the description parameters thatis 119862 119863119906 119863119889 and the time threshold 119879 Then theparameters will be submitted to the server for policydetermination The server will also evaluate the wire-less channel condition to determine the transitionprobability matrix of the wireless capacities In thismodel the optimal policy achieved that is the outputof BIA is a nonstationary policy Thus for eachdecision epoch 119905 there will be a matrix reflecting thecorrespondence between states and actions and all the119879 matrixes can form a 119879-dimension state-to-actionmapping table


Offline policy makingTask

Request

Network parameter collection

BIA

State-to-action mapping table

Online action mapping

Real-time parameter

State recognition

Action mapping

Mobileterminal

Task

Channel state information

CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at

Module at the MT side Module at the server side

Wired domain transmission or logical relation Wireless transmission

120601t

Figure 2 Workflow of the AEMSS

Table 3 Parameters in the simulation for state transition probabil-ities

Parameters ValuesIntercell distance 500mBandwidth 5MHzScheduling algorithm Round RobinTransmitter power of base station 43 dBmMaximum transmitter power of MT 21 dBmPoisson intensity for service requests 5

(ii) Online Action Mapping By employing BIA the opti-mal execution mode selection policy can be obtainedand stored in advance At decision epoch 119905 afterthe execution begins the MT evaluates the channelstate information by measuring the fading level ofthe reference signal and reports it to the parametercollectionmodule whichmonitors the task executionprogress and collects necessary parameter values suchas 120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 All the real-time parameter values

are mapped into a certain system state 119904119905 Then bylooking up the state-to-action mapping table theoptimal action 119886119905 can be chosen and the task execu-tion mode in the following time slot is determined

52 Measurement of the State Transition Probabilities Thechanging process of a wireless network is complicated anddifficult to predict There are many factors that can influencethe wireless transmission capacity for example bandwidthuser number and resource allocation scheme In this paper asystem simulation for a typical 3GPP network is conducted toestimate the state transition probabilities where users arriveand depart from the network according to a Poisson processMain parameters in simulation are listed in Table 3 Theproposed scheme is adaptive and applicable to a wide rangeof conditions Different wireless networks have different state

Table 4 Offloading decision policies adopted in the performanceevaluation

Policies Classification Description120587lowast Dynamic The MDP-based AEMSS

120587AL Static Always local

120587AO Static Always offloading

120587AC Static Always combined

120587DY Dynamic

Offloading if network capacity reachesthe average level otherwise it executes

locally

transform situations which can be obtained by changing theparameter set in the simulation

6 Numerical Results and Analysis

In this section the performance of the proposed MDP-basedAEMSS is evaluated with four other offloading schemesincluding three static schemes and a dynamic oneThe policyachieved by solving the finite-horizonMDP is denoted as 120587lowastother policies for comparison are referred to as120587AL120587AO120587ACand 120587

DY the descriptions of which are listed in Table 4Firstly a qualitative analysis on the optimal policy 120587

lowast

is provided to reflect the relationship between the chosenexecution modes and the task characteristics A series ofcomputation tasks with different characteristics (119862 119863119906 and119863119889) are analyzedThe probability of choosing a certain actionis defined as

119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)

where 119889lowast119905(119904) is the action decision rule at decision epoch 119905

The definition of operator 119868[lowast] is

119868 [lowast] = 1 lowast is true0 lowast is false

(28)

8 International Journal of Antennas and PropagationPr

obab

ility

10

08

06

04

02

00030 035 040 045 050

Local executionRemote executionCombined execution

Cl(Du + Dd)

Figure 3 Probability of adopting three execution modes

Table 5 Parameters in performance evaluation

Notation Parameter definition Value120596119889 120596119890 Weight factors in reward function 0sim1119879 Task execution time limit 20119903119897 Speed of MTrsquos processor 1119901119897 Power of MTrsquos processor 2

119901119906 119901119889Power of MTrsquos transmitting and receivingantenna 3 1

119903min 119903maxMinimum and maximum transmissioncapacities of wireless network 1 5

120590 Penalty for timeout 100

Figure 3 shows the probability of adopting the threeexecutionmodes versus the ratio119862119897(119863119906+119863119889) It can be seenthat when 119862 is relatively small to 119863119906 + 119863119889 the probability ofadopting the local execution mode is high With the rising of119862(119863119906+119863119889) the probability of adopting the remote executionmode goes to 1 The conclusion is obvious offloading isbeneficial when large amounts of local computation volumeare neededwith relatively small amounts of data transmissionvolume and vice versa

Next we consider a computation task with a comparativelocal computation volume and data transmission volumeso that making offloading decisions is relying more on thereal-time environmental information The task descriptionparameters adopted in the simulation are

(119862119863119906 119863119889) = (15 20 20) (29)

other parameters are listed in Table 5The performance metric adopted is the expected total

reward defined in Section 4 with different weight factors anddifferent initial states Figure 4 shows the performance of

the MDP-based AEMSS and other four schemes thatis always local always offloading and always combinedschemes and a dynamic scheme that makes offloading deci-sions based on the wireless transmission capacity at thebeginning of the execution (called DY scheme afterwards)

From Figures 4(a)ndash4(d) it can be concluded that (a)with higher wireless transmission capacity the MDP-basedpolicy gains a better performance while the performance ofalways local scheme stays at a consistent level for the wirelesstransmission condition has no effect on the local executionprocess (b) The always offloading scheme gains a prettygood performance almost equivalent with the proposedAEMSS when the wireless transmission capacity is highwhereas when the wireless transmission capacity decreasesthe performance gap between them gets wider (c) Whenthe weight factor of energy consumption function is highthe performance of always combined policy is poor becauseexecuting a task in local and remote modes simultaneouslyis an energy-intensive practice However when the weightfactor of delay reward function increases its performanceimproves and is equal to the AEMSS when the weight factorof delay reward function is 1 Under these circumstancesthe combined execution mode is the optimal mode for itstask completion time is shortest (d) The performance of theDY mechanism is superior to the other three static policiesfor it can react to the real-time environment condition Theperformance gap between it and the AEMSS is causedmainlyby the execution mode adjustment mechanism of AEMSS

We integrate the expected total reward with differentinitial states by

V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)

and the integrated performance of different policies is shownin Figure 5 Figures 4 and 5 reflect a phenomenon that theexpected total reward increases linearlywith theweight factor120596119889 This is driven by the design of the reward function notindicating that a higher weight factor of the delay rewardfunction is better As defined in (16) the system will gain anextra reward 120588

lowast at each time slot after the task execution iscompleted A higher 120596119889 will push the task execution to befinished earlier therefore the system can gain more extrareward until time119879When employing theAEMSS the weightfactors are determined by the designerrsquos preference that isdelay oriented or energy oriented

119904119905 = 119904terminal indicates that the task execution process hasbeen completed at time epoch 119905 Therefore the completionprobability of the task can be estimated by the steady stateprobability of the terminal state at decision epoch 119905 that is

119901119888119905 = 119901infin

119905(119904terminal) (31)

Figure 6(a) depicts the task completion probabilities at eachdecision epoch with different policies when 120596119889 = 120596119890 = 05We can see that the always combined scheme can completethe task fastestThe local computation volume is set as119862 = 15

in the simulation therefore by time 119905 = 15 the always localand always combined schemes can achieve a task completionprobability of 1 The always offloading policy can complete


Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)

Figure 4 Expected total reward with different initial states and different policies

the task with the highest probability when 119905 lt 15 but thismay also leave the task uncompleted when 119905 gt 15 withthe highest probability The delay performance of proposedMDP-based AEMSS is at an intermediate level because it alsotakes the energy consumption into consideration Figure 6(b)illustrates the task completion probabilities with differentweight factors We can see that with a higher weight factor ofthe delay reward function the task execution will be finishedfaster When 120596119889 = 1 the combined execution mode willbe adopted with probability of 1 therefore the task will befinished with probability 1 at time 119905 = 15 (119862119901119897 = 15)

Figure 7 illustrates the tradeoff between the time savingand energy consumption of the AEMSS when the weightfactors are varying At 119905 = 15 the delay performance

and the cumulative energy consumption under the optimalpolicy 120587

lowast are plotted It can be concluded that with ahigher 120596119889 the task will be completed faster and the energyconsumption will increase accordingly This is because thecombined execution mode is more likely to be adopted whenthe delay requirement is strict and executing the task bothlocally and remotely is energy intensive

As described in Section 4 the AEMSS can adjust theexecution mode during the task execution process whenthe wireless condition has dramatically changed That isthe main reason behind the performance improvement inour proposed scheme compared to the general dynamicoffloading schemes An observation is taken on the executionmode adjustment frequency at all the 119879 decision epochs


120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402

Figure 5 Integrated expected total reward

10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty

(a) Task completion probabilities under different policies

00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1

(b) Task completion probability with different weight factors

Figure 6 Task completion probability

At decision epoch 119905 an ldquoexecution mode adjustmentrdquo eventwhich is denoted as 120575 occurs when

119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)

and the occurrence probability of event 120575 at decision epoch 119905

is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)

Figure 8 shows the executionmode adjustment probability atall decision epochs Along with the timeline the execution

mode adjustment probabilities reduce to zero gradually Thereason is that with the growth of the execution progressadjusting the execution mode will cost a heavier price

7 Conclusion

In this paper MTs can execute their computation tasks either(1) locally (2) remotely or (3) combinedly To determinethe most appropriate execution mode a dynamic offloadingdecision scheme that is the AEMSS is proposed Theproblem is formulated into a finite-horizon MDP with theobjectives of minimizing the execution delay and reducingthe energy consumption of MTs Offloading decisions are

International Journal of Antennas and Propagation 11C

ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n

Task completion probability when t = 15(left axis)

Cumulative energy consumption when t = 15(right axis)

120596d

Figure 7 Task completion probability and energy consumptionversus different weight factors when 119905 = 15

006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t

Figure 8 Execution mode adjustment probabilities at all decisionepochs

made by taking the task characteristic and the currentwireless transmission condition into an overall considerationIn the design of reward function an execution thresholdtime is introduced to make sure that the task executioncan be completed with an acceptable delay In addition anovel execution mode adjustment mechanism is introducedto make the task execution process more flexible for thereal-time environment variation By solving the optimizationproblem with the BIA a nonsteady policy describing thecorrespondence of states and actions is obtained The policyis equivalent to a state-to-action mapping table which can bestored for looking up during the decision making phase Theperformance of the proposed scheme is evaluated with otherseveral offloading schemes and the numerical results indicatethat the proposed scheme can outperform other algorithmsin an energy-efficient way

Conflict of Interests

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

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities (no 2014ZD03-02) National Key Scientific Instrument and EquipmentDevelopment Project (2013YQ20060706) and National KeyTechnology RampD Program of China (2013ZX03003005)

References

[1] M Satyanarayanan ldquoFundamental challenges in mobile com-putingrdquo in Proceedings of the 15th Annual ACM Symposium onPrinciples of Distributed Computing pp 1ndash7 ACM Press May1996

[2] K W Tracy ldquoMobile application development experiences onApples iOS and Android OSrdquo IEEE Potentials vol 31 no 4 pp30ndash34 2012

[3] D Datla X Chen T Tsou et al ldquoWireless distributed com-puting a survey of research challengesrdquo IEEE CommunicationsMagazine vol 50 no 1 pp 144ndash152 2012

[4] N Fernando S W Loke and W Rahayu ldquoMobile cloudcomputing a surveyrdquo Future Generation Computer Systems vol29 no 1 pp 84ndash106 2013

[5] K Kumar and Y H Lu ldquoCloud computing for mobile users canoffloading computation save energyrdquo Computer vol 43 no 4Article ID 5445167 pp 51ndash56 2010

[6] S Gitzenis and N Bambos ldquoJoint task migration and powermanagement in wireless computingrdquo IEEE Transactions onMobile Computing vol 8 no 9 pp 1189ndash1204 2009

[7] N I Md Enzai and M Tang ldquoA taxonomy of computationoffloading in mobile cloud computingrdquo in Proceedings of the2nd IEEE International Conference onMobile Cloud ComputingServices and Engineering pp 19ndash28 Oxford UK April 2014

[8] Z Li C Wang and R Xu ldquoComputation offloading to saveenergy on handheld devices a partition schemerdquo in Proceedingsof the International Conference on Compilers Architecture andSynthesis for Embedded Systems (CASES rsquo01) pp 238ndash246November 2001

[9] Z Li C Wang and R Xu ldquoTask allocation for distributed mul-timedia processing on wirelessly networked handheld devicesrdquoin Proceedings of the 16th International Parallel and DistributedProcessing Symposium (IPDPS rsquo02) pp 79ndash84 2002

[10] C Xian Y H Lu and Z Li ldquoAdaptive computation offload-ing for energy conservation on battery-powered systemsrdquo inProceedings of the 13th International Conference on Parallel andDistributed Systems pp 1ndash8 December 2007

[11] R Wolski S Gurun C Krintz and D Nurmi ldquoUsing band-width data to make computation offloading decisionsrdquo in Pro-ceedings of the 22nd IEEE International Parallel and DistributedProcessing Symposium (PDPS rsquo08) pp 1ndash8 April 2008

[12] W Zhang Y Wen K Guan D Kilper H Luo and D OWu ldquoEnergy-optimalmobile cloud computing under stochasticwireless channelrdquo IEEE Transactions on Wireless Communica-tions vol 12 no 9 pp 4569ndash4581 2013

[13] H Eom P S Juste R Figueiredo O Tickoo R Illikkal andR Iyer ldquoMachine learning-based runtime scheduler for mobileoffloading frameworkrdquo in Proceedings of the IEEEACM 6thInternational Conference on Utility and Cloud Computing (UCCrsquo13) pp 17ndash25 December 2013

[14] A YDing BHan Y Xiao et al ldquoEnabling energy-aware collab-orative mobile data offloading for smartphonesrdquo in Proceedings


of the 10th Annual IEEE Communications Society Conference onSensing and Communication in Wireless Networks (SECON rsquo13)pp 487ndash495 June 2013

[15] B Jose and SNancy ldquoAnovel applicationmodel and an off load-ing mechanism for efficient mobile computingrdquo in Proceedingsof the IEEE 10th International Conference onWireless andMobileComputing Networking and Communications (WiMob rsquo14) pp419ndash426 Larnaca Cyprus October 2014

[16] P Rong and M Pedram ldquoExtending the lifetime of a networkof battery-powered mobile devices by remote processing aMarkovian decision-based approachrdquo in Proceedings of the 40thDesign Automation Conference pp 906ndash911 June 2003

[17] M Puterman Markov Decision Processes Discrete StochasticDynamic Programming Wiley Hoboken NJ USA 1994

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



In this paper we consider the computing architecturewhich has been introduced in [6] The MT can execute thecomputation task in one of the following three modes (1)locally executing the task at the MTrsquos local processor (2)remotely offloading the task to a remote server by wirelesstransmission and (3) combinedly executing the task in theformer two ways simultaneously Before task execution theMT has to decide which mode to adopt Therefore theoffloading decision problem is equivalent to an executionmode selection problem

Based on the previous description an adaptive executionmode selection scheme (AEMSS) is proposed to help MTsmake offloading decisions Main contributions of this paperare described as follows

(i) For the existing offloading schemes decisions aremade in advance and cannot be changed once theexecution has begun The proposed AEMSS allowsthe task to change executionmode during processingwhich can make the task execution more flexible forthe changing wireless condition

(ii) The execution mode selection problem is formulatedas a finite-horizon Markov decision process (MDP)and the userrsquos tolerance for execution delay is subtlyformulated as the last decision epoch of the modelA heavy penalty factor for timeout can guarantee thedelay performance of the proposed scheme

(iii) The MDP is solved by the backward induction algo-rithm (BIA) and numerical results indicate that theproposedAEMSS can achieve a good performance onexecution delay and energy efficiency

The remainder of this paper is organized as followsThe related work is summarized in Section 2 System modeland the problem formulation of AEMSS are presented inSection 3 The detailed finite-horizon MDP model and thesolution are described in Section 4 In Section 5 some imple-mentation issues are discussed Simulation assumptions andthe numerical results are presented in Section 6 Finally theconclusions are drawn in Section 7

2 Related Work

In this section we provide a discussion on the existing algo-rithms for offloading decision which can be partitioned intotwo categories that is the static decisions and the dynamicdecisions [7]

Static decision is that the program is partitioned duringdevelopmentmdashwhich part to execute locally and which partto offload Algorithms to make static offloading decisionsmostly appear in the work of earlier years [8ndash10] In [8] analgorithm is proposed to divide the program into server tasksand client tasks such that the energy consumed at the clientis minimized Reference [9] presents a task partition andallocation scheme to divide the distributed multimedia pro-cessing between the server and a handheld device Authors in[10] introduce a strategy that executes the program initiallyon the mobile system with a timeout If the computationis not completed after the timeout it is offloaded These

static offloading decisions have the advantage of lowoverheadduring execution However this kind of approach is validonly when the parameters for example wireless transmissioncapacity can be accurately predicted in advance

In contrast dynamic decisions can adapt to various run-time conditions for example fluctuating network band-widths and varying server load Prediction mechanisms areusually used in dynamic approaches for decisionmaking Forexample the bandwidth is monitored and predicted using aBayesian scheme in [11] Offloading decision algorithms inrecent work are most dynamic ones [12ndash16] In [12] a theo-retical framework of energy-optimalmobile cloud computingunder stochastic wireless channel is provided In [13] a studyon the feasibility of applying machine learning techniquesis presented to address the adaptive scheduling problemin mobile offloading framework Reference [14] presents acollaborative WiFi-based mobile data offloading architecturetargeted at improving the energy efficiency for smartphonesReference [15] proposes a fine grained application model anda fast optimal offloading decision algorithm where multipleoffloading decisions are made per module based on theexecution paths leading to the module Authors in [16] alsoformulate the offloading decision problem based on MDPand solve it by using a linear programming approach Theyaddress the problem of extending the lifetime of a batterypowered mobile host in a client-server wireless network byusing task migration and remote processing

The work in this paper is inspired by [6] where atask migration jointly with the terminal power managementmechanism is formulated in the framework of dynamicprogramming The solution is a policy specifying when theterminal should initiate task migration versus executing thetask locally in conjunction with the power managementAlthough there have been various offloading decision algo-rithms proposed in the literature our work has some originaland advanced characters We put the focus on the offloadingdecision making phase with the optimization objective ofimproving the task execution efficiency and reducing theenergy consumption of mobile devices by determining theldquobest fitrdquo execution mode at each decision epoch

3 Problem Formulation

31 Computing Architecture In this paper we consider acomputing architecture where the MT can execute its com-putation task in one of the following three modes

(1) locally executing the task at the MTrsquos processor(2) remotely offloading the task to a remote computation

server via the wireless network(3) combinedly executing the task with the former two

options simultaneously

Modes 2 and 3 involve the practice of offloading which ismodeled into a three-step process as follows

(i) Data Uploading MT sends the task specification andinput data to the remote computation server





119905119897 =119862

119903119897

(1)


119905119903 = 119905119906 + 119905119889 =119863119906

119903119906

+119863119889

119903119889

(2)


119905119888 = min 119905119897 119905119903 = min119862119903119897

119863119906

119903119906

+119863119889

119903119889

(3)


119890119897 = 119901119897 sdot 119905119897 (4)


119890119903 = 119890119906 + 119890119889 = 119901119906 sdot 119905119906 + 119901119889 sdot 119905119889 (5)


119890119888 =

(119901119897 + 119901119906) 119905119906 + (119901119897 + 119901119889) (119905119888 minus 119905119906) 119905119888 gt 119905119906

(119901119897 + 119901119906) 119905119888 119905119888 le 119905119906

(6)

s0 a0 s1 a1 s2 a2














119904119905 = (120601119905 1198621015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) (7)


[119905 minus 1 119905) that is

120601119905 =


(8)



S1

1119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 1 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906= 1198631015840

119889= 0 119903 isin R

S22 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906isin 1 2 119863119906 minus 11198631015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 minus 1 119903 isin R

S33 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 3 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906isin 1 2 119863119906 minus 1 119863

1015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)

1003816100381610038161003816 120601 = 3 1198621015840isin 1 2 119862 minus 1 119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 119903 isin R

Sinitial4

119904initial = (0 119862119863119906 119863119889 119903)|119903 isin R

Sterminal5

119904terminal = (4 0 0 0 119903)



119906= 119863119906) respectively









119906119905= 0









A = 0 1 2 3 (10)


119886119905 =


(11)




119905 1198631015840

119906119905 1198631015840

119889119905 119903119905)


1015840

119905+1 1198631015840

119906119905+1 1198631015840










119905= (1 119862

1015840

119905 0 0 119903

119905) 119886119905= 1 rArr 119904

119905+1= (1 119862

1015840

119905minus 119903119897 0 0 119903

119905+1)

2 120601119905 = 2 119886119905 = 2 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

1

3 120601119905 = 3 119886119905 = 3 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3119863

1015840

119906119905minus 119903119905 119863119889 119862

1015840

119905minus 119903119897 119903119905+1)

2

4 120601119905 = 1 119886119905 = 2 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863119906 minus 119903119905 119863119889 119903119905+1)

5 120601119905 = 2 119886119905 = 1 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862 minus 119903119897 0 0 119903119905+1)

6 120601119905 = 1 119886119905 = 3 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119896 = 3 rArr 119904119905+1 = (3 119862

1015840

119905minus 119903119897 119863119906 minus 119903119905 119863119889 119903119905+1)

7 120601119905 = 2 119886119905 = 3 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3 119862 minus 119903119897 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

8 120601119905= 3 119886

119905= 1 119904119905 = (3 119862

1015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862

1015840

119905minus 119903119897 0 0 119903119905+1)

9 120601119905 = 3 119886119905 = 2 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)


119905 1198631015840

119906119905 1198631015840


1015840

119906119905 119863119889 119903119896) and 119904119896 = (2 0 0119863

1015840





119901 (119904119905+1 | 119904119905 119886119905) = 119901 (119903119905+1 | 119903119905) (12)


infin(119903min) 119901

infin(119903min +



119901infin

0(119904initial = (0 119862119863119906 119863119889 1199030)) = 119901

infin(1199030)

1199030 isin 119903min 119903min + 1 119903max

119901infin

119905+1(1199041015840) =

119905

sum

119896=0

sum


119901infin

119896(119904) 119901 (119904

1015840| 119904 119886)

(13)

119901infin



119905(119904) = 0


119903119905 (119904 119886) = sum

119904isin1198781199051199041015840isin119878119905+1

119886isin119860119905

119901 (1199041015840| 119904 119886) 119903119905 (119904

1015840| 119904 119886)

119903119905 (1199041015840| 119904 119886) = 120596119889119891119889119905 (119904

1015840| 119904 119886) minus 120596119890119891119890119905 (119904

1015840| 119904 119886) minus 120590119905

(14)


1015840| 119904 119886)


120590119905 =

0 119905 = 119879

0 119905 = 119879 119904119905 = 119904terminal

120590 119905 = 119879 119904119905 = 119904terminal

(15)


119891119889119905 (1199041015840| 119904 119886) =

120588119905+1 minus 120588119905 120601119905 = 4

120588lowast 120601119905 = 4

(16)



120588119905 =

1 minus1198621015840

119905

119862 120601119905 = 1

1 minus1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

120601119905 = 2

1 minusmin1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

1198621015840

119905

119862 120601119905 = 3

(17)




given by

119891119890119905 (119904119905+1 | 119904119905 119886119905) =

119901119897 119886119905 = 1

119901119906 119886119905 = 2 1198631015840

119906119905= 0

119901119889 119886119905 = 2 1198631015840

119906119905= 0

119901119897 + 119901119906 119886119905 = 3 1198631015840

119906119905= 0

119901119897 + 119901119889 119886119905 = 3 1198631015840

119906119905= 0

0 120601119905 = 4

(18)



V120587 (119904) = 119864120587

119904

119879minus1

sum

119905=0


(19)



lowast

0 119889lowast

1 119889

lowast

119879minus1)

which satisfies

V120587lowast

(119904) ge V120587 (119904) (20)





120587



119906120587

119905(ℎ119905) = 119864

120587

ℎ119905

119879minus1

sum

119896=119905

119903119896 (119904119896 119886119896) 119904119896 isin S119896 119886119896 isin A119896 (21)


are given by

119906lowast

119905(ℎ119905) = max

119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886 119904

1015840)

(22)





119904119905 119904 isin S119905 and


119886lowast

119904119905= arg max119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886119905 119904

1015840)

(23)



(1) Set 119905 = 119879 minus 1 and

119906lowast


119903119879minus1 (119904 119886)

119886lowast


119903119879minus1 (119904 119886)

(24)


119905(119904) for each 119904 isin 119878119905

by

119906lowast

119905(119904) = max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(25)

Set

119886lowast

119904119905= arg max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(26)








Request


BIA



Real-time parameter

State recognition

Action mapping

Mobileterminal

Task


CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at



120601t





1015840

119905 1198631015840

119906119905 1198631015840









120587DY Dynamic


locally





lowast


119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)




(28)


obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119905119897 =119862

119903119897

(1)


119905119903 = 119905119906 + 119905119889 =119863119906

119903119906

+119863119889

119903119889

(2)


119905119888 = min 119905119897 119905119903 = min119862119903119897

119863119906

119903119906

+119863119889

119903119889

(3)


119890119897 = 119901119897 sdot 119905119897 (4)


119890119903 = 119890119906 + 119890119889 = 119901119906 sdot 119905119906 + 119901119889 sdot 119905119889 (5)


119890119888 =

(119901119897 + 119901119906) 119905119906 + (119901119897 + 119901119889) (119905119888 minus 119905119906) 119905119888 gt 119905119906

(119901119897 + 119901119906) 119905119888 119905119888 le 119905119906

(6)

s0 a0 s1 a1 s2 a2














119904119905 = (120601119905 1198621015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) (7)


[119905 minus 1 119905) that is

120601119905 =


(8)



S1

1119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 1 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906= 1198631015840

119889= 0 119903 isin R

S22 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906isin 1 2 119863119906 minus 11198631015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 minus 1 119903 isin R

S33 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 3 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906isin 1 2 119863119906 minus 1 119863

1015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)

1003816100381610038161003816 120601 = 3 1198621015840isin 1 2 119862 minus 1 119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 119903 isin R

Sinitial4

119904initial = (0 119862119863119906 119863119889 119903)|119903 isin R

Sterminal5

119904terminal = (4 0 0 0 119903)



119906= 119863119906) respectively









119906119905= 0









A = 0 1 2 3 (10)


119886119905 =


(11)




119905 1198631015840

119906119905 1198631015840

119889119905 119903119905)


1015840

119905+1 1198631015840

119906119905+1 1198631015840










119905= (1 119862

1015840

119905 0 0 119903

119905) 119886119905= 1 rArr 119904

119905+1= (1 119862

1015840

119905minus 119903119897 0 0 119903

119905+1)

2 120601119905 = 2 119886119905 = 2 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

1

3 120601119905 = 3 119886119905 = 3 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3119863

1015840

119906119905minus 119903119905 119863119889 119862

1015840

119905minus 119903119897 119903119905+1)

2

4 120601119905 = 1 119886119905 = 2 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863119906 minus 119903119905 119863119889 119903119905+1)

5 120601119905 = 2 119886119905 = 1 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862 minus 119903119897 0 0 119903119905+1)

6 120601119905 = 1 119886119905 = 3 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119896 = 3 rArr 119904119905+1 = (3 119862

1015840

119905minus 119903119897 119863119906 minus 119903119905 119863119889 119903119905+1)

7 120601119905 = 2 119886119905 = 3 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3 119862 minus 119903119897 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

8 120601119905= 3 119886

119905= 1 119904119905 = (3 119862

1015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862

1015840

119905minus 119903119897 0 0 119903119905+1)

9 120601119905 = 3 119886119905 = 2 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)


119905 1198631015840

119906119905 1198631015840


1015840

119906119905 119863119889 119903119896) and 119904119896 = (2 0 0119863

1015840





119901 (119904119905+1 | 119904119905 119886119905) = 119901 (119903119905+1 | 119903119905) (12)


infin(119903min) 119901

infin(119903min +



119901infin

0(119904initial = (0 119862119863119906 119863119889 1199030)) = 119901

infin(1199030)

1199030 isin 119903min 119903min + 1 119903max

119901infin

119905+1(1199041015840) =

119905

sum

119896=0

sum


119901infin

119896(119904) 119901 (119904

1015840| 119904 119886)

(13)

119901infin



119905(119904) = 0


119903119905 (119904 119886) = sum

119904isin1198781199051199041015840isin119878119905+1

119886isin119860119905

119901 (1199041015840| 119904 119886) 119903119905 (119904

1015840| 119904 119886)

119903119905 (1199041015840| 119904 119886) = 120596119889119891119889119905 (119904

1015840| 119904 119886) minus 120596119890119891119890119905 (119904

1015840| 119904 119886) minus 120590119905

(14)


1015840| 119904 119886)


120590119905 =

0 119905 = 119879

0 119905 = 119879 119904119905 = 119904terminal

120590 119905 = 119879 119904119905 = 119904terminal

(15)


119891119889119905 (1199041015840| 119904 119886) =

120588119905+1 minus 120588119905 120601119905 = 4

120588lowast 120601119905 = 4

(16)



120588119905 =

1 minus1198621015840

119905

119862 120601119905 = 1

1 minus1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

120601119905 = 2

1 minusmin1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

1198621015840

119905

119862 120601119905 = 3

(17)




given by

119891119890119905 (119904119905+1 | 119904119905 119886119905) =

119901119897 119886119905 = 1

119901119906 119886119905 = 2 1198631015840

119906119905= 0

119901119889 119886119905 = 2 1198631015840

119906119905= 0

119901119897 + 119901119906 119886119905 = 3 1198631015840

119906119905= 0

119901119897 + 119901119889 119886119905 = 3 1198631015840

119906119905= 0

0 120601119905 = 4

(18)



V120587 (119904) = 119864120587

119904

119879minus1

sum

119905=0


(19)



lowast

0 119889lowast

1 119889

lowast

119879minus1)

which satisfies

V120587lowast

(119904) ge V120587 (119904) (20)





120587



119906120587

119905(ℎ119905) = 119864

120587

ℎ119905

119879minus1

sum

119896=119905

119903119896 (119904119896 119886119896) 119904119896 isin S119896 119886119896 isin A119896 (21)


are given by

119906lowast

119905(ℎ119905) = max

119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886 119904

1015840)

(22)





119904119905 119904 isin S119905 and


119886lowast

119904119905= arg max119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886119905 119904

1015840)

(23)



(1) Set 119905 = 119879 minus 1 and

119906lowast


119903119879minus1 (119904 119886)

119886lowast


119903119879minus1 (119904 119886)

(24)


119905(119904) for each 119904 isin 119878119905

by

119906lowast

119905(119904) = max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(25)

Set

119886lowast

119904119905= arg max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(26)








Request


BIA



Real-time parameter

State recognition

Action mapping

Mobileterminal

Task


CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at



120601t





1015840

119905 1198631015840

119906119905 1198631015840









120587DY Dynamic


locally





lowast


119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)




(28)


obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











S1

1119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 1 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906= 1198631015840

119889= 0 119903 isin R

S22 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906isin 1 2 119863119906 minus 11198631015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 2 119862

1015840= 0119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 minus 1 119903 isin R

S33 119904 = (120601 119862

1015840 1198631015840

119906 1198631015840

119889 119903)|120601 = 3 119862

1015840isin 1 2 119862 minus 1 119863

1015840

119906isin 1 2 119863119906 minus 1 119863

1015840

119889= 119863119889 119903 isin R

cup 119904 = (120601 1198621015840 1198631015840

119906 1198631015840

119889 119903)

1003816100381610038161003816 120601 = 3 1198621015840isin 1 2 119862 minus 1 119863

1015840

119906= 0119863

1015840

119889isin 1 2 119863119889 119903 isin R

Sinitial4

119904initial = (0 119862119863119906 119863119889 119903)|119903 isin R

Sterminal5

119904terminal = (4 0 0 0 119903)



119906= 119863119906) respectively









119906119905= 0









A = 0 1 2 3 (10)


119886119905 =


(11)




119905 1198631015840

119906119905 1198631015840

119889119905 119903119905)


1015840

119905+1 1198631015840

119906119905+1 1198631015840










119905= (1 119862

1015840

119905 0 0 119903

119905) 119886119905= 1 rArr 119904

119905+1= (1 119862

1015840

119905minus 119903119897 0 0 119903

119905+1)

2 120601119905 = 2 119886119905 = 2 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

1

3 120601119905 = 3 119886119905 = 3 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3119863

1015840

119906119905minus 119903119905 119863119889 119862

1015840

119905minus 119903119897 119903119905+1)

2

4 120601119905 = 1 119886119905 = 2 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863119906 minus 119903119905 119863119889 119903119905+1)

5 120601119905 = 2 119886119905 = 1 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862 minus 119903119897 0 0 119903119905+1)

6 120601119905 = 1 119886119905 = 3 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119896 = 3 rArr 119904119905+1 = (3 119862

1015840

119905minus 119903119897 119863119906 minus 119903119905 119863119889 119903119905+1)

7 120601119905 = 2 119886119905 = 3 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3 119862 minus 119903119897 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

8 120601119905= 3 119886

119905= 1 119904119905 = (3 119862

1015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862

1015840

119905minus 119903119897 0 0 119903119905+1)

9 120601119905 = 3 119886119905 = 2 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)


119905 1198631015840

119906119905 1198631015840


1015840

119906119905 119863119889 119903119896) and 119904119896 = (2 0 0119863

1015840





119901 (119904119905+1 | 119904119905 119886119905) = 119901 (119903119905+1 | 119903119905) (12)


infin(119903min) 119901

infin(119903min +



119901infin

0(119904initial = (0 119862119863119906 119863119889 1199030)) = 119901

infin(1199030)

1199030 isin 119903min 119903min + 1 119903max

119901infin

119905+1(1199041015840) =

119905

sum

119896=0

sum


119901infin

119896(119904) 119901 (119904

1015840| 119904 119886)

(13)

119901infin



119905(119904) = 0


119903119905 (119904 119886) = sum

119904isin1198781199051199041015840isin119878119905+1

119886isin119860119905

119901 (1199041015840| 119904 119886) 119903119905 (119904

1015840| 119904 119886)

119903119905 (1199041015840| 119904 119886) = 120596119889119891119889119905 (119904

1015840| 119904 119886) minus 120596119890119891119890119905 (119904

1015840| 119904 119886) minus 120590119905

(14)


1015840| 119904 119886)


120590119905 =

0 119905 = 119879

0 119905 = 119879 119904119905 = 119904terminal

120590 119905 = 119879 119904119905 = 119904terminal

(15)


119891119889119905 (1199041015840| 119904 119886) =

120588119905+1 minus 120588119905 120601119905 = 4

120588lowast 120601119905 = 4

(16)



120588119905 =

1 minus1198621015840

119905

119862 120601119905 = 1

1 minus1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

120601119905 = 2

1 minusmin1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

1198621015840

119905

119862 120601119905 = 3

(17)




given by

119891119890119905 (119904119905+1 | 119904119905 119886119905) =

119901119897 119886119905 = 1

119901119906 119886119905 = 2 1198631015840

119906119905= 0

119901119889 119886119905 = 2 1198631015840

119906119905= 0

119901119897 + 119901119906 119886119905 = 3 1198631015840

119906119905= 0

119901119897 + 119901119889 119886119905 = 3 1198631015840

119906119905= 0

0 120601119905 = 4

(18)



V120587 (119904) = 119864120587

119904

119879minus1

sum

119905=0


(19)



lowast

0 119889lowast

1 119889

lowast

119879minus1)

which satisfies

V120587lowast

(119904) ge V120587 (119904) (20)





120587



119906120587

119905(ℎ119905) = 119864

120587

ℎ119905

119879minus1

sum

119896=119905

119903119896 (119904119896 119886119896) 119904119896 isin S119896 119886119896 isin A119896 (21)


are given by

119906lowast

119905(ℎ119905) = max

119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886 119904

1015840)

(22)





119904119905 119904 isin S119905 and


119886lowast

119904119905= arg max119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886119905 119904

1015840)

(23)



(1) Set 119905 = 119879 minus 1 and

119906lowast


119903119879minus1 (119904 119886)

119886lowast


119903119879minus1 (119904 119886)

(24)


119905(119904) for each 119904 isin 119878119905

by

119906lowast

119905(119904) = max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(25)

Set

119886lowast

119904119905= arg max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(26)








Request


BIA



Real-time parameter

State recognition

Action mapping

Mobileterminal

Task


CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at



120601t





1015840

119905 1198631015840

119906119905 1198631015840









120587DY Dynamic


locally





lowast


119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)




(28)


obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119905= (1 119862

1015840

119905 0 0 119903

119905) 119886119905= 1 rArr 119904

119905+1= (1 119862

1015840

119905minus 119903119897 0 0 119903

119905+1)

2 120601119905 = 2 119886119905 = 2 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

1

3 120601119905 = 3 119886119905 = 3 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3119863

1015840

119906119905minus 119903119905 119863119889 119862

1015840

119905minus 119903119897 119903119905+1)

2

4 120601119905 = 1 119886119905 = 2 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863119906 minus 119903119905 119863119889 119903119905+1)

5 120601119905 = 2 119886119905 = 1 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862 minus 119903119897 0 0 119903119905+1)

6 120601119905 = 1 119886119905 = 3 119904119905 = (1 1198621015840

119905 0 0 119903119905) 119886119896 = 3 rArr 119904119905+1 = (3 119862

1015840

119905minus 119903119897 119863119906 minus 119903119905 119863119889 119903119905+1)

7 120601119905 = 2 119886119905 = 3 119904119905 = (2 0 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 3 rArr 119904119905+1 = (3 119862 minus 119903119897 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)

8 120601119905= 3 119886

119905= 1 119904119905 = (3 119862

1015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 1 rArr 119904119905+1 = (1 119862

1015840

119905minus 119903119897 0 0 119903119905+1)

9 120601119905 = 3 119886119905 = 2 119904119905 = (3 1198621015840

119905 1198631015840

119906119905 119863119889 119903119905) 119886119905 = 2 rArr 119904119905+1 = (2 0 119863

1015840

119906119905minus 119903119905 119863119889 119903119905+1)


119905 1198631015840

119906119905 1198631015840


1015840

119906119905 119863119889 119903119896) and 119904119896 = (2 0 0119863

1015840





119901 (119904119905+1 | 119904119905 119886119905) = 119901 (119903119905+1 | 119903119905) (12)


infin(119903min) 119901

infin(119903min +



119901infin

0(119904initial = (0 119862119863119906 119863119889 1199030)) = 119901

infin(1199030)

1199030 isin 119903min 119903min + 1 119903max

119901infin

119905+1(1199041015840) =

119905

sum

119896=0

sum


119901infin

119896(119904) 119901 (119904

1015840| 119904 119886)

(13)

119901infin



119905(119904) = 0


119903119905 (119904 119886) = sum

119904isin1198781199051199041015840isin119878119905+1

119886isin119860119905

119901 (1199041015840| 119904 119886) 119903119905 (119904

1015840| 119904 119886)

119903119905 (1199041015840| 119904 119886) = 120596119889119891119889119905 (119904

1015840| 119904 119886) minus 120596119890119891119890119905 (119904

1015840| 119904 119886) minus 120590119905

(14)


1015840| 119904 119886)


120590119905 =

0 119905 = 119879

0 119905 = 119879 119904119905 = 119904terminal

120590 119905 = 119879 119904119905 = 119904terminal

(15)


119891119889119905 (1199041015840| 119904 119886) =

120588119905+1 minus 120588119905 120601119905 = 4

120588lowast 120601119905 = 4

(16)



120588119905 =

1 minus1198621015840

119905

119862 120601119905 = 1

1 minus1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

120601119905 = 2

1 minusmin1198631015840

119906119905+ 1198631015840

119889119905

119863119906 + 119863119889

1198621015840

119905

119862 120601119905 = 3

(17)




given by

119891119890119905 (119904119905+1 | 119904119905 119886119905) =

119901119897 119886119905 = 1

119901119906 119886119905 = 2 1198631015840

119906119905= 0

119901119889 119886119905 = 2 1198631015840

119906119905= 0

119901119897 + 119901119906 119886119905 = 3 1198631015840

119906119905= 0

119901119897 + 119901119889 119886119905 = 3 1198631015840

119906119905= 0

0 120601119905 = 4

(18)



V120587 (119904) = 119864120587

119904

119879minus1

sum

119905=0


(19)



lowast

0 119889lowast

1 119889

lowast

119879minus1)

which satisfies

V120587lowast

(119904) ge V120587 (119904) (20)





120587



119906120587

119905(ℎ119905) = 119864

120587

ℎ119905

119879minus1

sum

119896=119905

119903119896 (119904119896 119886119896) 119904119896 isin S119896 119886119896 isin A119896 (21)


are given by

119906lowast

119905(ℎ119905) = max

119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886 119904

1015840)

(22)





119904119905 119904 isin S119905 and


119886lowast

119904119905= arg max119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886119905 119904

1015840)

(23)



(1) Set 119905 = 119879 minus 1 and

119906lowast


119903119879minus1 (119904 119886)

119886lowast


119903119879minus1 (119904 119886)

(24)


119905(119904) for each 119904 isin 119878119905

by

119906lowast

119905(119904) = max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(25)

Set

119886lowast

119904119905= arg max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(26)








Request


BIA



Real-time parameter

State recognition

Action mapping

Mobileterminal

Task


CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at



120601t





1015840

119905 1198631015840

119906119905 1198631015840









120587DY Dynamic


locally





lowast


119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)




(28)


obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











V120587 (119904) = 119864120587

119904

119879minus1

sum

119905=0


(19)



lowast

0 119889lowast

1 119889

lowast

119879minus1)

which satisfies

V120587lowast

(119904) ge V120587 (119904) (20)





120587



119906120587

119905(ℎ119905) = 119864

120587

ℎ119905

119879minus1

sum

119896=119905

119903119896 (119904119896 119886119896) 119904119896 isin S119896 119886119896 isin A119896 (21)


are given by

119906lowast

119905(ℎ119905) = max

119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886 119904

1015840)

(22)





119904119905 119904 isin S119905 and


119886lowast

119904119905= arg max119886isin119860119905

119903119905 (119904 119886) + sum

1199041015840isin119878119905+1

119901 (1199041015840| 119904 119886) 119906

lowast

119905+1(ℎ119905 119886119905 119904

1015840)

(23)



(1) Set 119905 = 119879 minus 1 and

119906lowast


119903119879minus1 (119904 119886)

119886lowast


119903119879minus1 (119904 119886)

(24)


119905(119904) for each 119904 isin 119878119905

by

119906lowast

119905(119904) = max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(25)

Set

119886lowast

119904119905= arg max119886isin119860119878119905

119903119905 (119904119905 119886119905)

+ sum

119904119905+1isin119878119905+1

119901 (119904119905+1 | 119904119905 119886119905) 119906lowast

119905+1(119904119905+1)

(26)








Request


BIA



Real-time parameter

State recognition

Action mapping

Mobileterminal

Task


CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at



120601t





1015840

119905 1198631015840

119906119905 1198631015840









120587DY Dynamic


locally





lowast


119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)




(28)


obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Request


BIA



Real-time parameter

State recognition

Action mapping

Mobileterminal

Task


CDu Dd T

rl pu

rmin rmax

profiling

submitting

collection

execution

pd p(s998400|s a)

C998400t D

998400ut D

998400dt rt t

st

at



120601t





1015840

119905 1198631015840

119906119905 1198631015840









120587DY Dynamic


locally





lowast


119901 (119886) =1

119879

119879minus1

sum

119905=0

sum

119904isinS119905

119901infin(119904) sdot 119868 [119889

lowast

119905(119904) = 119886] 119886 = 1 2 3 (27)




(28)


obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










obab

ility

10

08

06

04

02

00030 035 040 045 050


Cl(Du + Dd)









(119862119863119906 119863119889) = (15 20 20) (29)






V120587 = sum

119904isin1198780

119901infin

0(119904) V120587 (119904) (30)




119901119888119905 = 119901infin

119905(119904terminal) (31)




Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AL r0 = 5

120587AL r0 = 3

120587AL r0 = 1

120596d

(a)

10

8

6

4

2

0

minus2

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AO r0 = 5

120587AO r0 = 3

120587AO r0 = 1

120596d

Expe

cted

tota

l rew

ard

(b)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus6

minus4

00 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587AJ r0 = 5

120587AJ r0 = 3

120587AJ r0 = 1

120596d

(c)

Expe

cted

tota

l rew

ard

10

8

6

4

2

0

minus2

minus400 02 04 06 08 10

120587lowast r0 = 5

120587lowast r0 = 3

120587lowast r0 = 1

120587DY r0 = 5

120587DY r0 = 3

120587DY r0 = 1

120596d

(d)








120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120596d

120587lowast

120587AL

120587AO

120587AC

120587DY

Inte

grat

ed ex

pect

ed to

tal r

ewar

d

8

6

4

2

0

minus2

minus4

minus600 1008060402


10

08

06

04

02

006 8 10 12 14 16 18 20 22

Decision epoch

120587lowast

120587AL

120587AO

120587AC

120587DY

Com

plet

ion

prob

abili

ty


00

10

08

06

04

02

8 10 12 14 16 18 20 22

Decision epoch

Com

plet

ion

prob

abili

ty

120596d = 0

120596d = 06

120596d = 08120596d = 1




119889lowast

119905(119904) = 119886119905 = 120601119905 119904 = (120601119905 119862

1015840

119905 1198631015840

119906119905 1198631015840

119889119905 119903119905) isin S119905 (32)


is defined as

119901119905 (120575) = sum

119904isin119878119905

119901infin

119905(119904) sdot 119868 [119889

lowast

119905(119904) = 120601119905] 119905 isin 0 1 119879

(33)



7 Conclusion



ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ompl

etio

n pr

obab

ility

100

098

096

094

092

090

088

086

08400 02 04 06 08 10

60

55

50

45

40

35

30

Ener

gy co

nsum

ptio

n



120596d


006

005

004

003

002

001

0002 4 6 8 10 12 14 16 18 20

Exec

utio

n m

ode a

djus

tmen

t pro

babi

lity

Decision epoch t





Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article A Novel Execution Mode Selection Scheme ...

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