Joint Task Offloading Scheduling and Transmit Power Allocation for Mobile-Edge Computing Systems

0.28 MB·

by  Yuyi Mao

Joint Task Offloading Scheduling and Transmit Power
Allocation for Mobile-Edge Computing Systems
Yuyi Mao†, Jun Zhang†, and Khaled B. Letaief†∗, Fellow, IEEE
†Dept. of ECE, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
∗Hamad bin Khalifa University, Doha, Qatar
Email: {ymaoac, eejzhang, eekhaled}@ust.hk
7
Abstract—Mobile-edge computing (MEC) has emerged as a proposedin [6]. For multi-userMEC systems, a decentralized
1
prominenttechniquetoprovidemobileserviceswithhighcompu- computation offloading policy was proposed in [7], and joint
0
tationrequirement,bymigratingthecomputation-intensivetasks
sub-carrier and CPU time allocation was investigated in [8].
2 fromthemobiledevicestothenearbyMECservers.Toreducethe
n execution latency and device energy consumption, in this paper, Inspired by the fact that many applications can be divided
a wejointlyoptimizetaskoffloadingschedulingandtransmitpower into a set of dependent sub-tasks, fine-grained computation
J allocation for MEC systems with multiple independent tasks. A offloading(a.k.a.codepartitioning)hasalsobeenwidelystud-
low-complexity sub-optimal algorithm is proposed to minimize ied most recently [9]-[14]. Assuming serial implementation
8
the weighted sum of the execution delay and device energy
1 of communication and computation, a heuristic offloading
consumption based on alternating minimization. Specifically,
algorithmwasproposedin [9], while thejointoptimizationof
given the transmit power allocation, the optimal task offloading
] scheduling,i.e.,to determinethe order of offloading, isobtained radio resource and code partitioning was investigated in [10].
T
withthehelpofflowshopschedulingtheory.Besides,theoptimal Besides, a dynamic code partitioning algorithm was proposed
I
. transmitpowerallocationwithagiventaskoffloadingscheduling in[11],whichisadaptivetothetime-varyingwirelessdatarate
s decisionwillbedeterminedusingconvexoptimizationtechniques.
and the random application requests. In order to reduce the
c
Simulation results show that task offloading scheduling is more
[ execution latency, parallel implementation of communication
critical whentheavailable radioand computational resourcesin
1 MECsystemsarerelativelybalanced.Inaddition,itisshownthat and computation was adopted in [12]-[14], where the code
the proposed algorithm achieves near-optimal execution delay partitioning policy design becomes much more challenging.
v
5 along with a substantial device energy saving. In[12],a codepartitioningalgorithmwasdevelopedbasedon
IndexTerms—Mobile-edgecomputing,taskoffloadingschedul-
5 dynamic programming for applications with a tree topology.
ing, power control, flow shop scheduling, convex optimization.
0 This study was extended to applications with general topolo-
5 giesin[13],wherethesolutionhasexponentialcomplexity.By
0 I. INTRODUCTION
leveraging the structures of the application topology, a code
. The rapid development of mobile applications with ad-
1 partitioningalgorithmwasproposedtoreducethecomputation
0 vanced features has brought great pressure on mobile com- complexitybased on message passing in [14]. However,these
7 puting systems. However, the limited processing capability
studies assume that each offloaded sub-task is allocated with
1 of mobile devices becomes an obstacle to fulfill such a
certainamountofcommunicationbandwidthandcomputation
: requirement. Mobile-edge computing (MEC) has emerged as
v resource at the MEC server, i.e., transmitting the input data
Xi a promising technique to resolve this issue, which offers ofmultipletasks(executingmultipletasksattheMECserver)
computation capability within the radio access network in
concurrentlyis allowed.Althoughsuch assumptionmakesthe
r contrast to conventional cloud computing systems that use
a designmoretractable,itmaybeimpracticalforMECsystems
remote public clouds [1], [2]. By offloading the computation-
with limited resources, e.g., for MEC servers with a single
intensive tasks from the mobile devices to the nearby MEC
communication channel and a single-core CPU.
servers, the quality of computation experience, including the
In this paper, we consider a single-user MEC system with
latency and device energy consumption, could be greatly
multipleindependentcomputationtasksrequestingformobile-
improved [3].
edge execution, assuming parallel implementation of task
Nevertheless, the efficiency of an MEC system largely
offloading and execution. A radio resource limited system is
depends on the adopted computation offloading policy, which
considered, where each time the input data of only one task
should be carefully designed by taking the characteristics
can be offloaded, while different tasks are executed by the
of the computation tasks and wireless channels into account
MEC server sequentially. In this case, the transmission and
[5]-[14]. In [5], energy consumption for mobile execution
execution processes of different tasks are coupled, and the
and computation offloading for single-user MEC systems
task offloading scheduling, i.e., the order of the tasks to be
was minimized via dynamic voltage frequency scaling and
offloaded, becomes a new design dimension. We formulate a
data transmission scheduling, respectively. A delay-optimal
jointtask offloadingschedulingand transmitpowerallocation
task scheduling algorithm for single-user MEC systems was
problem with the objective of minimizing the weighted sum
of the executiondelay and deviceenergyconsumption,which
ThisworkissupportedbytheHongKongResearchGrantsCouncilunder
GrantNo.16200214. is a highly non-trivial mixed integer nonlinear programming
(MINLP)problem.Alow-complexitysub-optimalalgorithmis and σ 6= σ ,j 6= i,∀i,j = 1,··· ,N. The mobile device
i j
proposed based on alternating minimization.In particular, the is equipped with a single antenna and it can transmit the
optimaltaskoffloadingschedulingwithagiventransmitpower input data of one computation task at each time. Thus, the
allocation is obtained with the aid of flow shop scheduling transmission rate for task T can be expressed as
i
theory, while the optimal transmit power allocation with a
g (L /L)θp
giventask offloadingschedulingdecision is determinedbased R(p )=ωlog 1+ 0 0 i , (1)
on convex optimization. Simulation results shall show that i 2 N0ω !
task offloadingschedulingis morecriticalwhen the radioand
where p is the transmit power for task T , g is the path-
computationalresourcesarerelativelybalanced.Besides,near- i i 0
loss constant, θ is the path-loss exponent, L is the reference
optimalexecutiondelayalongwithasubstantialdeviceenergy 0
distance, and N is the noise power spectral density at the
saving can be achieved by the proposed algorithm. 0
receiver of the MEC server.
II. SYSTEMMODEL The MEC server has a single-core CPU and executes the
offloaded tasks one after another. A task buffer is employed
at the MEC server to store the tasks that have been offloaded
(cid:55) (cid:55)N(cid:16)(cid:20) butnotyetexecuted,whichisassumedtobesufficientlylarge
(cid:55) (cid:22) for simplicity. Besides, it executes the computation task with
(cid:20)
(cid:55)(cid:21) (cid:55) … (cid:55)N a first-come-first-serve (FCFS) fashion. Thus, the execution
(cid:23)
orderofthetasksisthesameasthetaskoffloadingorder.The
(cid:38)(cid:82)(cid:80)(cid:83)(cid:88)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:87)(cid:68)(cid:86)(cid:78)(cid:86) (cid:48)(cid:82)(cid:69)(cid:76)(cid:79)(cid:72)(cid:3)(cid:71)(cid:72)(cid:89)(cid:76)(cid:70)(cid:72) (cid:48)(cid:40)(cid:38)(cid:3)(cid:86)(cid:72)(cid:85)(cid:89)(cid:72)(cid:85) CPU-cyclefrequencyatthe MECserverisdenotedasfser (in
Hz). Besides, the computation results are assumed to be of
Fig.1. Amobile-edgecomputingsystemwithamobiledeviceandanMEC small size and thus the feedback delay is ignored.
server. Theexecutiondelayanddeviceenergyconsumptionaretwo
critical design considerations in MEC systems, and both of
We consider a single-user mobile-edge computing (MEC)
them depend on the adopted task offloading scheduling and
system as shown in Fig. 1, which consists of a mobile device
transmit power allocation policy. In the next section, we will
and an MEC server. The MEC server is a small-scale data
formulate an optimization problem to minimize the weighted
center deployed by the telecom operator and communicates
sum of the execution delay and device energy consumption,
withthemobiledevicethroughthewirelesschannel.Acloud-
by jointly designing the offloading scheduling and transmit
cloneassociatedwiththemobiledeviceisrunningattheMEC
power allocation for the computation tasks.
server. Hence, the MEC server can execute the computation
tasksonbehalfof themobiledevice[4]. Besides, thedistance III. PROBLEMFORMULATION
between the mobile device and the MEC server is denoted as In this section, we will first analyze the execution delay
L, and the system bandwidth is represented by ω. and device energy consumption with given task offloading
scheduling decision σ and transmit power allocation vector
A. Computation Task Model
p = [p ,··· ,p ]. The joint task offloading scheduling and
1 N
We assume that the mobile device has N independent transmit power allocation problem will then be formulated.
computation tasks that need to be executed, where the set of
Themobile-edgeexecutionforacomputationtaskcannotbe
tasks is denoted as T , {T1,··· ,TN}. Each computation started until the following two conditions are satisfied: First,
task is characterized by a two-tuple of parameters, hdi,cii, the task input data is ready at the MEC server. Second, the
where di (in bits) is the amount of task input data, and CPU at the MEC server is available for executinga new task.
ci (in CPU cycles/bit) is the workload. The values of di Denotethereadytimeofthetaskinputdataandthecompletion
and ci depend on the nature of the computation tasks and timeforthe jthtask beingoffloaded(i.e.,T ) astj (σ,p)
can be obtained through off-line measurements [15]. Denote σj ready
and tj (σ,p), respectively. Thus, tj (σ,p) is given by
d = [d ,··· ,d ] and c = [c ,··· ,c ]. In this paper, comp ready
1 N 1 N
we focus on the scenarios that the mobile device has very d
tj (σ,p)= σk ,j =1,··· ,N, (2)
limitedcomputationalresource,andhenceallthecomputation ready R(p )
tasks should be offloaded to the MEC server for mobile-edge Xk≤j σk
execution[16].Thescenariosthatthe mobiledevicehasmore which is the sum transmission time of tasks T ,··· ,T .
σ1 σj
powerfulcomputationcapabilitywill be handledin our future The completion time of task T not only depends on the
σj
work. ready time of its task input data, but also couples with the
completion time of the task being offloaded previously, i.e.,
B. Task Offloading and Mobile-Edge Execution Model T . Consequently, tj (σ,p) can be expressed as the
σj−1 comp
In order to offload the computation tasks for mobile-edge following recursive form:
execution, the task input data should be transmitted to the
tj (σ,p)+d c f−1, j =1
MECserver.Wedenotethetaskoffloadingschedulingdecision ready σj σj ser
for the N tasks as σ ,[σ1,σ2,··· ,σN], which is a permuta- tjcomp(σ,p)=max{tjready(σ,p),tjco−m1p(σ,p)}
tion ofthe task indicesand Tσi isthe ith task beingoffloaded  +dσjcσjfs−er1, j >1,
to the MEC server. Hence, σ satisfies σ ∈ {1,··· ,N} (3)
i

where d c f−1 is the mobile-edge execution time of task d) Permutation scheduling is considered, i.e., the jobs go
σj σj ser
T , and tN (σ,p) is the execution delay for T. through the two machines in the same order, which is
σj comp
The device energy consumption for offloading the N com- encoded as (perm) in the notation.
putation tasks is simply the transmit energy consumption, e) Non-preemptive processing is enforced, i.e., interruption
which is independent with the task offloading scheduling is not allowed once the processing of a job starts, which
decision and can be written as is encoded as (pmtn) in the notation.
f) Each machine has a buffer with infinite capacity to store
N d N d
E (p)= p · i = p · σj . (4) the arrived but not yet processed jobs.
tr i=1 i R(pi) j=1 σj R pσj g) The goal is to minimize the makespan of the N jobs,
X X which is encoded as C in the notation.
Consequently,thejointtaskoffloadingschedulin(cid:0)gand(cid:1)transmit max
power allocation problem can be formulated as We find that the task offloading scheduling problem is a
two-machine flow shop scheduling problem, as demonstrated
P1 :min tNcomp(σ,p)+η·Etr(p) (5) in the follow lemma.
σ,p
Lemma 1: For a given transmit power allocation vector
s.t. σ ∈{1,··· ,N},σ 6=σ ,j 6=i,∀i,j (6)
j i j
p, P is an F2|(perm),(pmtn)|C type of flow shop
0≤p ≤p ,i=1,··· ,N. (7) 1 max
i max scheduling problem.
The objective function in P is the weighted sum of the Proof: In the task offloading scheduling problem, each
1
execution delay and device energy consumption with η (in computation task needs to go through two procedures before
sec · J−1) as the weighting factor, which is able to adjust its completion, which are the transmission of the task input
the tradeoff between the execution delay and device energy dataandthemobile-edgeexecutionattheMECserver.Hence,
consumption performance. (6) guarantees the task offloading thetransmitterofthemobiledeviceandtheMECservercanbe
scheduling decision is valid, and (7) stands for the peak and regarded as M and M in Definition 1, respectively. Thus,
1 2
non-negativetransmitpowerconstraintsforthemobiledevice. the job processing time in the two machines correspond to
It can be easily noticed that P is an MINLP problem as thetransmissiontimeandmobile-edgeexecutiontime,respec-
1
both the integer variables σ and the continuous variables p tively.Byanalogy,itcanbecheckedthatthepropertiesinDef-
need to be optimized, which is very challenging to solve. In inition1alsoholdsforthetaskoffloadingschedulingproblem.
principle, the optimal solution for P can be obtained via Asaresult,P withagivenpisanF2|(perm),(pmtn)|C
1 1 max
exhaustive search, which, however, is practically infeasible type of flow shop scheduling problem.
due to high complexity. For instance, there will be 20! ≈ Since the task offloading scheduling problem is an
2.43×1018 different permutations for N =20, and for each F2|(perm),(pmtn)|C typeofflowshopschedulingprob-
max
permutation,theoptimaltransmitpowerallocationneedstobe lem, the Johnson’s Algorithm can be applied to find the
determined.Asaresult,insteadoffindingtheoptimalsolution, optimal solution [17]. In the Johnson’s Algorithm, the task
we will propose a low-complexity sub-optimal algorithm for set T is partitioned into two disjoint subsets F and G, where
P1 based on alternating minimization in the next section. F , {Ti ∈ T|R(dpii) < dfisecri} and G , Ti ∈ T|R(dpii) ≥
IV. SUB-OPTIMAL JOINT TASKOFFLOADING SCHEDULING dfisecri}. The tasks in set F will be sched(cid:8)uled before those
AND TRANSMIT POWERALLOCATION in G according to the ascending order of the value of di/
R(p ),T ∈ F, and the tasks in set G will be scheduled
In this section, we will propose a low-complexity sub- i i
accordingtothedescendingorderofd c /f ,T ∈G.Details
optimal algorithm for P based on the idea of optimizing the i i ser i
1 of the Johnson’s Algorithm are summarized in Algorithm 1,
task offloading scheduling and the transmit power allocation
where the computationoverheadmainly comes from the sort-
alternately.
ingproceduresinLine4.Hence,iftheQuicksortAlgorithmis
A. Optimal Task Offloading Scheduling usedasthesortingalgorithm,thecomplexityofAlgorithm1is
O(NlogN)[18],i.e.,thetaskoffloadingschedulingproblem
We first develop an optimal task offloading scheduling
can be solved optimally in polynomial time.
algorithm for a given transmit power allocation vector by
invokingtechniquesfromflowshopschedulingtheory[17].To
beginwith,weintroduceanotationforatypeoftwo-machine
B. Optimal Transmit Power Allocation
flow shop scheduling problems in the following definition.
Definition 1: F2|(perm),(pmtn)|Cmax denotes the type Inthissubsection,weinvestigatetheoptimaltransmitpower
of flow shop scheduling problems that satisfy the following allocationforthe computationtaskswitha giventask offload-
properties: ing schedulingdecisionσ. Note that boththe executiondelay
a) There are N independent jobs and each of them should and the device energy consumption depend on the transmit
be processed sequentially by two machines M and M . power allocation vector p, and tN (σ,p) is given in a
1 2 comp
b) AlljobsareavailableforM fromthebeginning,andthey recursive form, while the objective function in P given σ
1 1
willbeavailableforM immediatelyafterthecompletion is non-differentiable, which makes it difficult to solve. To
2
of the processing at M . overcome this issue, we introduce a set of auxiliary variables
1
c) Each machine can only process one job at each time. ˜t , t˜ ,··· ,t˜ and formulate a modified version of the
σ σ1 σN
(cid:2) (cid:3)
Algorithm 1 The Johnson’sAlgorithmFor The OptimalTask similar to the one used in [10]. In particular,by introducinga
Offloading Scheduling Decision set of new variables ξ = 1/R(p ),i = 1,··· ,N, P can
σi σi 2
1: Input: T, d, c, p, and fser. be rephrased as
2: Output: σopt.
3: Obtain set F and G. N 1
4: Stoortthteheacsocemnpduintagtioonrdtearsksofinthseet tFranasnmdissseitonG aticmcoerdainndg P3 :m˜tσi,nξ t˜σN +C·Xi=1dσiξσi(cid:16)2ωξσi −1(cid:17) (12)
s.t. (10)
the descending order of the execution time at the MEC
server, respectively, i.e., d[1]/R p[1] ≤ ··· ≤ d[|F|]/ ξσi ≥D,i=1,··· ,N (13)
·R··p≥[|Fd|] ,Tc[i] ∈f−F1,,iT= 1∈,·G·,·j,(cid:0)=|F1|,(cid:1)a·n·d· ,d|Gh1|i.ch1ifs−er1 ≥ t˜ ≥ i d ξ + dσicσi,i=1,··· ,N, (14)
5: σo(cid:0)pt =[h[|(cid:1)1G]|i,·h·|G·|,i[|sFer|],hh1jii,··· ,h|G|i]. σi j=1 σj σj fser
X
where C , ηN0ω and D , 1 . In
transmit power allocation problem as the followinggl0e(mL0m/La),θwe show thaωtlPog2(cid:16)is1+agc0o(NLn00v/ωeLx)θpprmoabx(cid:17)lem.
3
N d Lemma 4: P3 is a convex optimization problem.
P2 :m˜tsσ.ti,np. (t˜σ7N) +η·Xi=1pσiR(pσiσi) (8) derivPatriovoefo:fDψe(nξo)teisψgi(vξe)n,byξd(cid:16)2dψ2ξ(2ωξ1ξ) −=12(cid:17)ω1.ξ ωTln2h2ξe23 s≥ec0o,n∀dξ-o>rd0er,
i.e.,ψ(ξ)isaconvexfunctionofξ(ξ >0).Sincetheobjective
t˜ ≥ i dσj + dσicσi,i=1,··· ,N (9) function is a summation of convex and linear functions, and
σi j=1 R pσj fser theconstraintsarelinear,P3 isaconvexoptimizationproblem
X [19].
t˜ ≥t˜ +(cid:0)dσi(cid:1)cσi,i=2,··· ,N, (10) Hence, the optimal transmit power allocation vector can be
σi σi−1 f
ser obtained numerically using convex optimization solvers such
which is a relaxed version of P given σ as t˜ ≥ as CVX [20]. Interestingly, we find that the optimal transmit
max{ ij=1 R(dpσσjj),t˜σi−1}+dσfisecrσi,i1≥2andt˜σ1 ≥ R(dpσσσi11)+ speoqwueernaclel,ocaastidoenmvoencsttorra,tie.de.,inpoσtp1ht,e·f·o·l,lopwoσpNitn,giscoarnoollna-riyn.creasing
dσ1cσ1P. In the followinglemma, we show such a relaxationis Corollary 1: Suppose 1 ≤ i < j ≤ N, then popt ≥ popt,
fser σi σj
tight. wherepopt is the optimalpowerallocationvectorforP (also
Lemma 2: If hpopt,˜toσpti is an optimal solution for P2, for P1 given σ). 2
dsthceehlaneydp.uolipntgisdeaclsiosioonptσim,aalndfot˜roσpNPt 1iswthitehcaorgreivspenontdaisnkgoefxfleocaudtiionng iSi<ncjeP≤ξrσoioNf=:. W1L/eeRtfih(rξpsoσtpiwt),,˜triioσttpeitisthebqeeupivtahraetlieanoltpLttoaimgsrhaaolnwgsoiξalσonupittifoo≤nrξPfσoopjtr,a1Ps≤3.
3
Proof: With the optimaltransmit powerallocation vector
popt, we can construct a new feasible ˜t′ for P as N
dσi + dσicσi, σ 2 i=1 L ξ,˜tσ,λσ =t˜σN +C· dσiξσi 2ωξ1σi −1
t˜′ = R(poσpit) fser (11) (cid:0) (cid:1) Xi=1 (cid:16) (cid:17)
σi max{t˜′ , i dσj }+ dσicσi, i>1, N i d c
 σi−1 j=1 R(poσpjt) fser + ασi dσjξσj + σfi σi −t˜σi (15)
wPgi2hv.eernTehpt˜e′σorpNetf,oiisr.een.,,obt˜yoσlpaNtargp=epPrlyt˜t′σihnNagnapanondpythtopofopPtth,1e˜t′σgfiievaeissnibaσlles,ot˜tσhoNep’tsvimafloaurlefPoo2fr +Xi=N1βσkt˜Xjσ=k1−1 −t˜σk + dσfskercσk , 
the objectivefunctionValP1 equals ValoPp2t, where ValoPp2t is the Xk=2 (cid:18) ser (cid:19)
optimal value for P2. Since P2 is a relaxation of P1 given where α = [α ,··· ,α ] (cid:23) 0 and β =
VtwhaietlhPt1aVs=kaloPVop1fatflloPoaps1at,dtiihn.eeg.,ospcphotipemtdiausllionvpgatliumdeeaclfiosfiorornPP,1i1.egg.i,ivveVennaloPσσp1t,. ≥weVhaaloPvpe2t [[cαβoσnσ2s,,tβr·a·σi·n].,tsσβσSN(i1n]4c)e(cid:23)aPnd30σ1(ai1sre0),atherecσsoNLpneavcgetrxiavneglpyira.onbDlememfiu,nlteipwliλeeσσrscofno,-r
Thus, we may concentrate on P2 in order to obtain the sider its dual problem maxλσ(cid:23)0g(λσ), where g(λσ) =
sotpiltlimdiaflfitcrualntstmoistoplvoewdeurealtloocitastinoonnv-ceocntovre.xNityev,ewrhthicehlesiss,shPo2wins ginivft˜eσni,bξσyiλ≥Dop,t∀,ithLeoξp,t˜timσ,aλlpσrim.Iafltvhaerioapbtliemsaξlodptucaalnvbareiaobblteasinaerde
in the following lemma. σ (cid:0) (cid:1)
by solving
Lemma 3: P is a non-convex optimization problem.
2
Proof: The proof can be obtained by verifying the con- N N i
cavFiotyrtuonfaRte(plpy), (wpe>a0re),awbhleichtoistroamnsitftoerdmfoPr2brienvtioty.a convex ξσim≥iDn,∀iC·Xi=1dσiξσi(cid:16)2ωξ1σi −1(cid:17)+Xi=1αoσpitXj=1dσjξσj,
optimization problem with the change-of-variable technique  (16)
for which the optimal solution is given by ξ⋆ λopt = whichisobtainedbyAlgorithm1.Arandomschedulingalgo-
σi σ
max{D,ϕ N αopt }. Here, when x = 0, ϕ(x) , +∞, rithmisadoptedastheperformancebenchmark,wherethetask
j=i σj (cid:0) (cid:1) offloading scheduling decision σ is a random permutation of
and when(cid:16)xP> 0, (cid:17)ϕ(x) denotes the root of equation the task indices. Three scenarios with R= fser ≈1.25 Mbps,
d−ψdψ(ξ(σξiσ)i/)d/ξdσξiσiis=an1in−cre2aωsiξ1nσgi (cid:16)f1un−ctiωolnξnσ2io(cid:17)f ξ=σi x(/ξσCi. >Sin0c)e, cRon=sid2ecfravsegerd,≈wh2e.5re1tMhebpasv,eraangdeRtran=sm2ficssaesvrgio≈ncatvi0gm.6e3oMf bthpes,taasrke
lim dψ(ξ )/dξ = −∞ and lim dψ(ξ )/
dξσξiσi=→00, weσican sσhiow that for i < ξjσ,i→ξσo+pit∞≤ ξσopjσti as isneprvuetrdinatatheeqfiurasltsctahsee.average processing time at the MEC
αopt ≥0,∀l=1,··· ,N, which completes the proof.
σl
An intuitive explanationfor Corollary1 is that the comple- 70
Random task offloading scheduling
tion time of T will affect those of all the subsequent tasks, Optimal task offloading scheduling
i.e., T ,···σ,iT . Thus, it is desirable to allocate a higher 60 1.9 %
σi+1 σN R = f /2c
transmit power in order to reduce its transmission time. 50 ser avg
ms)
Cde.cIniTshitoehneAlaptnerodrnpaothtsieendgtraMalngisonmrimitihtizmap,toiowthneerAtlaagslolkorciotahftflmioonadvinegctoscrhwedilullinbge Execution delay (3400 R = fser/cavg 6.1 % 1.7 %
updatedin an alternatingmanner,for which,the key steps are 20
summarized in Algorithm 2. Since the Johnson’s Algorithm
determinestheoptimaltaskoffloadingschedulingwithagiven 10 R = 2fser/cavg
transmitpowerallocationvector,andthesolutionforP offers
3 0
5 10 15 20 25 30 35 40
theoptimaltransmitpowerallocationwithagiventaskoffload- Number of computation tasks
ing scheduling decision, the value of the objective function Fig.2. Execution delayvs.thenumberofcomputation tasks.
in P decreases after each update, i.e., the convergence of
1
Algorithm 2 is guaranteed. In Fig. 2, we show the relationship between the execution
delayandthenumberofcomputationtasks.Itcanbeseenthat
Algorithm 2 Sub-Optimal Joint Task Offloading Scheduling theexecutiondelayincreaseslinearlywiththenumberoftasks,
and Transmit Power Allocation Algorithm and a larger transmission rate results in a lower execution
1: Input: pprop = pmax1, σprop = [1,··· ,N], itermax = delay, which agree with intuitions. However, increasing the
50, Val =tN (σprop,pprop)+η·E (pprop), Val = transmission rate from 0.63 to 1.25 Mbps brings a significant
new comp tr old
Val +10, ǫ=10−7, and I =0. delayreduction,whilethedelayreductionbyfurtherdoubling
new
2: Output: pprop and σprop. thetransmissionrateshrinks.Thisisbecauseinthelattercase,
the system bottleneck turns into the limited computational
3: While Valold−Valnew ≥ǫ and I ≤itermax do
resource at the MEC server. Besides, the proposed optimal
4: Set I =I+1.
task offloading scheduling algorithm outperforms the random
5: Set Valold =Valnew.
6: Updateσprop usingAlgorithm1withthetransmitpower taskoffloadingschedulingforallcases,whiletheperformance
allocation vector pprop. gain achieved by the optimal algorithm is most obvious
7: Update pprop with the task offloading scheduling when R = cfasvegr (e.g. 6.1% for N = 35). In other words,
decision σprop by solving P . the optimal task offloading scheduling is more critical when
3
8: Set Valnew =tNcomp(σprop,pprop)+η·Etr(pprop). the available radio resource and computational resource are
9: End while relatively balanced, i.e., neither of them dominates the other.
B. Joint Task Offloading Scheduling and Transmit Power
Allocation
V. SIMULATION RESULTS
We evaluate the proposed joint task offloading scheduling
Inthissection,wefirstinvestigatetheimpactoftheoptimal and transmit power allocation algorithm by setting g =
0
task offloading scheduling on the delay performance. The −40 dB, L = 1 m, L = 100 m, θ = 4, ω = 1 MHz,
0
proposed joint task offloading scheduling and transmit power N =−174 dBm/Hz, p =100 mW, and N =20.
0 max
allocation algorithm will then be evaluated. In simulations, By varying η, the values of the objective function in P
1
the task inputdata size and the task workload are assumed to undertheproposedalgorithmandabenchmarkalgorithmwith
be uniformly distributed, i.e., d ∼ Unif([0,2d ]) and c ∼ random task offloading scheduling and maximum transmit
i avg i
Unif([0,2c ])whered =1kbitsandc =797.5cycles/ power are shown in Fig. 3. From the curves, we see a
avg avg avg
bit [15]. The CPU speed at the MEC server is set to be significant performance improvement achieved by the pro-
f =1 GHz unless otherwise specified. posedalgorithm.Besides,theperformancegainbecomesmore
ser
dramatic as η increases since the transmit power allocation
A. Impact of The Optimal Task Offloading Scheduling
vector used in the benchmark scheme is non-adaptive to η.
We investigate the impact of the optimal task offloading The relationship between the device energy consumption
scheduling on the execution delay by setting η =0 sec·J−1, andtheexecutiondelayisshowninFig.4,fromwhich,wesee
optimal algorithm to minimize the weighted sum of the
7
Randomtaskoffloadingscheduling,pi=pmax,∀i executiondelay and device energyconsumption.It was found
6 Proposedalgorithm that the optimal task offloading scheduling achieves the most
P1 noticeabledelayperformanceimprovementwhentheavailable
functionin45 rAaldsioo, naneadr-ocopmtimpuatlatdieolnaayl preesrfoourrmceasncaeretorgeeltahteivrelwyithbaalanlacregde.
objective3 dtheevipcreopeonseerdgyalgcoornisthumm.ptFioonr fruetduurectiinovnesctaignatiboen,aicthwieovueldd bbye
the interestingtoextendthisworkformobiledeviceswithcertain
of
Value2 computationcapability,wherethetaskoffloadingdecision,i.e.,
whethertooffloadataskornot,thetaskoffloadingscheduling
1
decision, as well as the transmit power allocation need to be
0 jointly optimized.
0 5000 10000 15000
η(sec·J−1)
Fig.3. Valueoftheobjective functioninP1 vs.η. REFERENCES
[1] EuropeanTelecommunications Standards Institute (ETSI),“Mobile-edge
computing-Introductory technical whitepaper,” Sep.2014.
10x 10−5 [2] Y. Mao, C. You, J. Zhang, K. Huang, and K. B. Letaief, “Mobile
9.5 η=10−3sec·J−1 Mfseirni=mu1mGeHxzecutiondelay ehdttgpes://caormxipv.uotrign/gp:dfS/1u7rv0e1y.01a0n9d0vr1e.spedafrch outlook,” [Online.] Available:
fser=500MHz [3] K.Kumar,J.Liu,Y.H.Lu,andB.Bhargava,“Asurveyofcomputation
9 fser=250MHz offloading for mobile systems,” Mobile Netw. Appl., vol. 18, no. 1, pp.
mption (J)8.85 η=100sec·J−1 η=10−3sec·J−1 [4] M1v2m.9--Sb1aa4ts0ye,adnFcaelroba.uyda2nl0ea1tns3,.inP.mBoabhill,eRco.mCpaucteirnegs,,”aInEdEEN.PeDravvaiseisv,e“CTohmepcuats.,evfoolr.
Energy consu7.75 η=10−3sec·J−1 [5] oW8p,.tniZmo.haa4ln,mgp,opbY.i.l1e4Wc-2leo3nu,,dOKcc.otm.G2pu0ua0nti9,n.gDu.nKdielrpesrt,ocHh.asLtiucow, iarnedlesDs.chWaun,ne“lE,”nIeErgEyE-
Trans.Wireless Commun.,vol.12,no.9,pp.4569-4581, Sep.2013.
6.5 [6] J.Liu,Y.Mao,J.Zhang,andK.B.Letaief,“Delay-optimalcomputation
taskscheduling formobile-edge computingsystems,”inProc.IEEEInt.
6 Symp.Information Theory(ISIT),Barcelona, Spain,Jul.2016.
η=15000sec·J−1 [7] X.Chen, “Decentralized computation offloading gameformobile cloud
5.5
10 20 30 40 50 60 70 80 computing,” IEEETrans.ParallelDistrib. Syst.,vol.26,no.4,pp.974-
Execution delay (ms)
983,Apr.2015.
Fig.4. Deviceenergyconsumptionvs.execution delay.(Thedeviceenergy [8] Y. Yu, J. Zhang, and K. B. Letaief, “Joint subcarrier and CPU time
consumptionwithpi=pmax is4.21×10−4 J.) allocation formobile edge computing,” inProc. IEEEGlobal Commun.
Conf.(GLOBECOM),Washington, DC,Dec.2016.
[9] M.Jia,J.Cao,andL.Yang,“Heuristicoffloadingofconcurrenttasksfor
computation-intensive applications inmobilecloudcomputing,”inProc.
the device energy consumption decreases while the execution IEEE Int. Conf. Comput. Commun. Workshops (INFOCOM WKSHPS),
delay increases with η. It is also shown that allocating the Toronto,Canada, Apr.2014.
[10] P. D. Lorenzo, S. Barbarossa, and S. Sardellitti “Joint optimization
transmission energy beyond a threshold has no effect on
of radio resources and code partitioning in mobile edge computing,”
improving the delay performance. This indicates that a large [Online]. Available: http://arxiv.org/pdf/1307.3835v3.pdf
deviceenergyconsumptionreductioncanbeachievedwithout [11] D. Huang, P. Wang, and D. Niyato, “A dynamic offloading algorithm
for mobile computing,” IEEE Trans. Wireless Commun., vol. 11, no. 6,
loss of the optimal delay performance under the proposed
pp.1991-1995, Jun.2012.
algorithm with a suitable choice of η. For instance, with [12] Y. H. Kao and B. Krishnamachari, “Optimizing mobile computational
η = 100 sec·J−1, 78% of the device energy consumption is offloadingwithdelayconstraints,”inProc.IEEEGlobalCommun.Conf.
(GLOBECOM),Austin,TX,Dec.2014.
saved for f =1 GHz. This is due to the fact that the delay
ser [13] S. E. Mahmoodi, R. N. Uma, and K. P. Subbalakshmi, “Optimal joint
performanceis limited by the computationalresource, similar scheduling and cloud offloading for mobile applications,” IEEE Trans.
to what was observed in Fig. 2. In addition, when the device CloudComput.,toappear.
[14] S.KhaliliandO.Simeone,“Inter-layerper-mobileoptimizationofcloud
energy consumption becomes sufficiently small (η becomes
mobile computing: A message passing approach,” [Online] Available:
largeenough),thecurvesfordifferentCPUspeedsattheMEC http://arxiv.org/pdf/1509.01596v1.pdf
sever converge, i.e., the delay performance is constrained by [15] A.P.MiettinenandJ.K.Nurminen,“Energyefficiencyofmobileclients
incloudcomputing,”inProc.USENIXConf.HotTopicsCloudComput.
theradioresource.Thisrevealsafundamentaldesignprinciple
(HotCloud), Boston,MA,Jun.2010.
for MEC systems: Once the system is constrained by the [16] K. Wang, K. Yang, and C. Magurawalage, “Joint energy minimization
available radio resource, there is no need to deploy too much andresourceallocationinC-RANwithmobilecloud,”IEEETrans.Cloud
Comput.,toappear.
computational resources.
[17] H. Emmons and G. Vairaktarakis, Flow shop scheduling: Theoretical
results,algorithms, andapplications. NewYork,USA:Springer, 2013.
VI. CONCLUSIONS [18] T.H.Cormen,C.E.Leiserson,R.L.Rivest,andC.Stein,Introduction
toalgorithm. Cambridge, MA:TheMITPress,2009.
In this paper, we investigated joint task offloading schedul- [19] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge, UK:
ing and transmit power allocation for MEC systems with CambridgeUniversity Press,2004.
[20] CVX Research, Inc., “CVX: Matlab software for disciplined convex
multiple independent tasks. Based on flow shop scheduling
programming,version2.0(beta),” 2013.
and convexoptimization, we proposed a low-complexitysub-