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Performance Guaranteed Partial Ofﬂoading for

Mobile Edge Computing

Umber Saleem∗, Yu Liu∗, Sobia Jangsher†, Yong Li∗

∗Beijing National Research Center for Information Science and Technology (BNRist),

Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

†Department of Electrical Engineering, Institute of Space Technology (IST), Islamabad 44000, Pakistan

Email: liyong07@tsinghua.edu.cn

Abstract—In this paper, we jointly consider partial ofﬂoading

and resource allocation to minimize the sum latency with energy

efﬁciency for multi-user mobile-edge computation ofﬂoading

(MECO) system based on orthogonal frequency-division mul-

tiple access (OFDMA). We formulate mixed integer non-linear

programming (MINLP) sum latency minimization problem con-

sidering the edge execution delay, desired energy consumption for

local computation, OFDMA, QoS, transmission power in uplink

and edge computation capacity constraints. We propose that a

user can make use of multi-channel transmissions to reduce

the transmission delay for task with large data size. We ﬁrst

derive an expression to determine optimal ofﬂoading fraction

such that edge computing delay is less than the local execution

delay and energy consumed for local execution does not exceed

the desired limit. Then, we transform the original problem into

communication and computation resource allocation problem

and propose a suboptimal low complexity algorithm to ﬁnd

the resource allocation. The simulation results show that the

proposed scheme achieves 17% and 25% better performance

than random and complete ofﬂoading schemes, respectively.

I. INTRODUCTION

With the technological evolution of smart phones and

Internet of Things (IoT), new applications such as online

gaming, image/video editing, face/speech recognition, aug-

mented reality, etc. are emerging rapidly. These consumer

oriented services demand for real time communication and

intensive computations. However, the explosive growth of

mobile data trafﬁc and ﬁnite computation resources of devices

pose signiﬁcant challenges to realize the millisecond-scale

latency requirement in 5G network [1].

Mobile-edge computing (MEC) is seen as a promising

paradigm which provides cloud services close to the mobile

edge. It enables the mobile users to ofﬂoad their computation

intensive tasks to the edge server, referred to as mobile-edge

computation ofﬂoading (MECO)[2]. In order to minimize the

energy consumption and the latency for MECO, the commu-

nication and computation resources require to be optimally

allocated among the users and the edge. Hence, designing

effective computation ofﬂoading schemes have attracted huge

attention. Most of the research works focus on energy efﬁcient

resource allocation for single user and multi-user MECO, and

consider latency as a constraint [3],[4],[5].

There are few works which investigate latency minimization

problem for single user [6], [7] and multi-user [8], [9] MECO

systems. In [6], a power constrained delay minimization

problem was formulated based on average delay of each task

and average power consumption of the mobile device. A one

dimensional search algorithm was proposed to ﬁnd the optimal

stochastic computation ofﬂoading policy. On the other hand,

execution cost as a function of execution latency and task

failure was the performance metric in [7] for green MEC.

A dynamic computation ofﬂoading policy based on Lyapunov

optimization was proposed which reduced the execution delay

and task failure at the cost of execution delay performance

degradation. In [8], the allocation of the communication and

remote computational resources in uplink and downlink was

investigated to minimize the average latency of the worst case

user, while saving energy as compared to the local execution.

Power consumption minimization problem was formulated

to investigate the tradeoff between power consumption and

task execution delay in [9]. An algorithm based on Lya-

punov optimization was devised to achieve the objective by

effectively allocating transmit power, bandwidth and local

execution frequency.

It is important to note that the aforementioned works

considered complete ofﬂoading, while partial ofﬂoading can

signiﬁcantly improve the latency as the network becomes

dense and the edge resources are limited. In a recent work

[10], partial ofﬂoading for weighted sum latency minimization

was investigated by optimally allocating the communication

and computation resources. However, the fundamental energy

constraint of the devices is ignored and the data segmentation

strategy is derived irrelevant of the resulting local execution

cost. In order to improve the performance for practical sce-

narios for MECO, there is need to jointly address the aspects

of partial ofﬂoading, latency minimization, energy efﬁciency

and resource allocation.

In this paper, we address the sum latency minimization

problem with partial ofﬂoading for multi-user orthogonal

frequency-division multiple access (OFDMA) MECO system.

We assume a client server model, where the base station is

the resourceful MEC server with ﬁnite computation capacity

and users have limited computation resources. Each user has

a computation intensive task to perform where the data size of

each task is assumed to be large [11]. We formulate mixed in-

teger non-linear programming (MINLP) optimization problem

Fig. 1. Partial ofﬂoading Scenario.

with objective to minimize the sum latency of all users under

the expected energy consumption, edge computation latency,

communication and computation resources constraints. First,

an optimal ofﬂoading fraction based on the local energy

consumption and edge computation latency is derived for

each user. The original problem is then decomposed and a

centralized low complexity suboptimal communication and

computation resource allocation algorithm is proposed to

decide the partial ofﬂoading policy. Performance analysis

shows that the proposed solution has promising performance.

Moreover, the comparison shows that the proposed scheme

outperforms some baseline schemes including random ofﬂoad-

ing and complete ofﬂoading.

The rest of the paper is organized as follows. Section II,

presents the system model and discusses the communication

and partial ofﬂoading model in detail. In Section III, we

formulate the MINLP sum latency minimization problem for

multiple users. Section IV discusses the proposed solution

and a suboptimal communication and computation resource

allocation algorithm. Section V presents simulation results and

the conclusion provided in Section VI.

II. SY ST EM MO DE L

We consider a multiuser MECO system with the BS as the

ﬁnite capacity edge server and denote M={1,2, ..., M }

as a set of mobile users. Each user has a delay sensitive

computationally intensive task to be executed, while the user’s

computation resource is limited. A user partially ofﬂoads its

task to the BS for remote execution through a wireless channel

and executes the rest of the task locally. Thus, the total task

computation latency for a user is the sum of the ofﬂoading,

edge computation and local computation delays as shown in

Fig. 1. The BS is assumed to have a perfect knowledge of the

multiuser channel gains, size of input computation data, local

computing energy per bit and expected energy cost of the local

computation. Based on this information, the BS determines the

amount of data to be ofﬂoaded at each user, assigns subcarriers

and allocates power to all the users with aim to minimize

the ofﬂoading and edge computation latency. We ignore the

downloading latency for our problem keeping in view that

computation results have relatively smaller sizes [12].

A. Partial Ofﬂoading Model

Each user m∈ M has a computation task denoted as Tm

∆

=

(Dm, cm), where Dmdenotes the data size of the task in bits

and cmdenotes CPU cycles required for computing one bit at

user m. For an optimal ofﬂoading decision, we assume that a

user mcan ofﬂoad a fraction αm∈[0,1] of its computation

data, hence the ofﬂoaded data is given by Doff

m=αmDm.

In the following discussion, we introduce the local computing

model, communication model and edge computing model.

1) Local Execution Model: For each user we deﬁne a

desired energy consumption value ϵm, from which we can

determine an energy baseline to ofﬂoad at the edge. Therefore,

the ofﬂoading fraction should be decided according to the

expected energy consumption. We assume that each user has

a ﬁxed CPU frequency, which may vary over different users.

Let ωmdenote the energy consumption per cycle for local

computing at user m. Then ωmcmgives the computing energy

per bit. After ofﬂoading Doff

mbits, user mneeds to compute

(1 −αm)Dmbits locally. Then the energy consumption for

local computing at user mis given by

Eloc

m=ωmcm(1 −αm)Dm.(1)

Let Fmdenote the computation capacity of user mmea-

sured in CPU cycles per second. Then the local execution

latency can be obtained as

Lloc

m=cm(1 −αm)Dm

Fm

.(2)

2) Communication Model: Here, we discuss the communi-

cation model and the cost of computation ofﬂoading process.

We assume an OFDMA system where the total bandwidth

Bis divided in Northogonal subcarriers and their set is

denoted as N={1,2, ..., N }. A single subcarrier can be

assigned to one user at a particular instant, hence there will

be no interference. Moreover, a user can transmit on more

than one subcarrier. We deﬁne ρn

m∈ {0,1}and ρas the

subcarrier assignment parameter and subcarrier assignment

matrix, respectively. ρn

m= 1 indicates that a user m∈ M is

assigned the subcarrier n∈ N , and verse vice. The subcarrier

assignment matrix is denoted as ρ. We assume Rayleigh

fading channel and the channel gain for user mon subcarrier

nis denoted as hn

mcorresponding to a white Gaussian noise

channel which incorporates distance based path loss model.

The transmission power of user mon subcarrier nis

denoted as pn

mand the total transmission power of a user

is bounded by Pmax

m. The power allocation matrix is denoted

as p. The maximum achievable data rate rn

mof a user mon

subcarrier nis given as

rn

m=Wlog2(1 + pn

mhn

m

N0W),(3)

where N0denotes the power spectral density of white Gaus-

sian channel noise and Wis the bandwidth of each subcarrier.

Accordingly, the data rate of user mis

Rm=

N

n=1

ρn

mWlog2(1 + pn

mhn

m

N0W).(4)

In order to guarantee the reduction in communication cost,

we consider the QoS constraint of each user corresponding

to its computation data size. Hence, we assume that the data

rate of a user should be greater than a minimum threshold of

Rmin

m. Consequently, the number of subcarriers assigned to

each user is bounded such that QoS of all the users is met at

least with equality.

Let Nmdenote the total number of subcarriers assigned to

a user m. For simplicity, we assume that the ofﬂoaded data

Doff

mby user mis uniformly distributed over its assigned

subcarriers. Thus the data ofﬂoaded by user mon its subcar-

rier nis given by dn

m=αmDm/Nm. Due to multi-channel

transmission, the ofﬂoading latency Lmcan be determined by

the transmission delay of worst channel and is expressed as

Loff

m= max(ρn

mdn

m

rn

m

).(5)

Whereas, the energy consumed while ofﬂoading a task can

be expressed in terms of task size, transmission power and

transmission rate as

Eoff

m=

N

n=1

(ρn

mdn

mpn

m

rn

m

).(6)

3) MEC Server Execution Model: We assume that the

BS has ﬁnite computation capacity Fexpressed in number

of CPU cycles per second. Let Fe

mdenote the computation

resource assigned to user m. Then the edge execution latency

is given as

Le

m=cmαmDm

Fe

m

.(7)

Due to the ﬁnite computation capacity of the edge

server, a feasible computation resource allocation must follow

M

m=1

Fe

m≤F. Moreover, we assume that the total time

consumption in case of ofﬂoading must be less than the time

when computation task is executed locally [13].

III. PROB LE M FOR MU LATI ON

In this section, we formulate the resource allocation for

partial ofﬂoading multiuser MECO as an optimization prob-

lem. A user ofﬂoads fraction of task to the edge server and

computes the remaining task locally after downloading the

results from the edge. The delay for execution includes the

transmission time over the channel, remote execution time

and local execution time. Thus, our objective is to minimize

the sum latency:

M

m=1

(Loff

m+Le

m+Lloc

m). The joint latency

minimization and energy efﬁciency partial ofﬂoading problem

can be formulated as

min

α,ρ,p

M

m=1 max(ρn

mdn

m

rn

m

) + cmαmDm

Fe

m

+cm(1 −αm)Dm

Fm,

(8a)

s.t. 0≤αm≤1,∀m∈ M (8b)

Le

m+Loff

m≤Lloc

m,∀m∈ M (8c)

Eoff

m+Eloc

m≤ϵm,∀m∈ M (8d)

ρn

m∈ {0,1},

M

m=1

ρn

m= 1,∀n∈ N (8e)

N

n=1

ρn

m≥1,∀m∈ M (8f)

N

n=1

ρn

mrn

m≥Rmin

m,∀m∈ M (8g)

N

n=1

ρn

mpn

m≤Pmax

m,∀m∈ M (8h)

M

m=1

Fe

m≤F. ∀m∈ M (8i)

Here, (8a) shows our objective function which is sum of the

ofﬂoading, edge computation and local computation latency

of all the users. Constraint in (8b) presents the limits on the

fraction of data to be ofﬂoaded by every user. Constraint (8c)

ensures that ofﬂoading and edge execution together require

less time than the time required for local execution. Constraint

(8d) implies that the energy cost of ofﬂoading must not exceed

the expected energy consumption of a user to ensure that

the ofﬂoading is energy efﬁcient. Constraints (8e) and (8f)

bound the communication resources allocation, where (8e)

shows the exclusive channel allocation due to OFDMA and

(8f) shows that a user should be allocated at least one or

more subcarriers. Constraint (8g) ensures that the sum data

rate of a user must be greater than a minimum threshold

to guarantee QoS. Constraint (8h) shows the bound on total

transmission power of a user in uplink. Constraint (8i) shows

feasible computation resource allocation at the edge server

and means that the computation resources are allocated to

the ofﬂoading users within the computation capacity of edge

server.

It can be observed that the objective function in (8a) is a

MINLP problem. The binary assignment variable ρmresults

in non-convex feasible set and the non-linear constraints (8c),

(8d), (8g) and (8h) make the objective function in (8a) non-

convex due to product of the binary and continuous terms.

Hence, our problem is a mixed discrete and non-convex

optimization problem, which renders the problem NP-hard

[14].

IV. LOC AL EX EC UT IO N AN D PARTIAL OFFLOA DI NG

POLICY

In this section we derive an expression for the ofﬂoading

fraction and then transform the original problem into resource

allocation problem. We then propose a centralized low com-

plexity algorithm to allocate the communication resources for

reducing the ofﬂoading latency and computation resources at

the edge to reduce the edge computation latency.

A. Optimal Ofﬂoading Fraction

The optimal data segmentation strategy in the proposed

problem is inﬂuenced by two assumptions. Firstly, the data of-

ﬂoaded should not require the energy consumption more than

the desired value at each user. Secondly, the ofﬂoaded fraction

should improve the ofﬂoading performance as compared to the

local execution. Therefore, we derive an expression for αm

based on constraints (8b), (8c) and (8d) as

α∗

m≤minFe

mNmrmin

mcm

FmFe

m+ (Fm+Fe

m)Nmrmin

mcm

,

(ϵm−ωmcmDm)Nm

N

n=1

(ρn

mpn

m/rn

m)Dm−ωmcmDmNm(9)

Here, rmin

mdenotes the maximum achievable data rate among

all the subcarriers of a user and it corresponds to the maximum

value of ofﬂoading latency.

B. Optimal Resource Allocation

After obtaining the expression for αm, the original problem

is transformed into latency minimization problem by optimal

communication and computation resource allocation and pre-

sented as

min

ρ,p

M

m=1 max(ρn

mdn

m

rn

m

) + cmα∗

mDm

Fe

m

+cm(1 −α∗

m)Dm

Fm,

(10a)

s.t. (8e),(8f),(8g),(8h),and (8i).(10b)

The problem in (10a) still has non-convex objective func-

tion and non-linear constraints due to the binary variable

ρn

m, which makes the problem intractable and a global op-

timum solution is difﬁcult to obtain. Therefore, we propose a

centralized low complexity algorithm for communication and

computation resource allocation with aim to minimize the sum

latency.

C. Communication and Computation Resource Allocation

Here, we propose Algorithm 1 by decomposing our problem

into two parts. First we assign subcarriers and allocate power

to all the users keeping in view the fact that maximizing the

data rate per subcarrier would result in minimum ofﬂoading

latency. After allocating the communication resources, we

allocate computation resources according to the computation

capacity of the edge server.

In the ﬁrst iteration, a single subcarrier is assigned to

each user. From the marginal rate function with respect to

subcarrier, to maximize the data rate a subcarrier nshould

be assigned to a user msuch that m= arg max

i(rn

i)[15].

Therefore, we select the subcarrier and user pair such that

the ratio between the data rate of user over the average data

rate on that subcarrier is maximized. As there is only one

subcarrier per user, we allocate maximum power to all the

subcarriers. Next, we assign the remaining subcarriers such

that a user with the smallest Rm/Rmin

mvalue will be optimally

assigned a subcarrier. Each time a subcarrier assignment is

performed, the power allocation is also updated and the sum

rate is calculated for all the users. We perform uniform power

allocation for a user motivated by the fact that each subcarrier

carries same amount of data. The subsequent iterations aim to

improve the sum rate of all the users which leads to reduced

ofﬂoading delay. Finally, the edge computation resources are

equally distributed among all the users as the edge execu-

tion latency is already taken care of while determining the

ofﬂoading fraction.

The proposed algorithm has Miterations in ﬁrst step of

initial subcarrier assignment and Niterations for assigning

the remaining subcarriers. Therefore, assuming N >> M the

complexity of Algorithm 1 can be expressed as O|N |, which

shows that it achieves lower computation complexity.

V. PERFORMANCE EVAL UATIO N

In this section, we evaluate the performance of our proposed

scheme by analyzing the numerical results and comparing

with other baseline schemes, namely complete ofﬂoading and

random ofﬂoading as there is no other existing scheme which

considers latency minimization and guarantees energy efﬁ-

ciency at the same time for partial ofﬂoading. The simulation

parameters are as follows unless stated otherwise. The BS

has radius of 500 m and there are 35 users randomly located

Algorithm 1 Joint resource allocation scheme

1: Input: N,M, Channel gain matrix H,F

2: Output: Subcarrier assignment matrix ρ, Power alloca-

tion matrix p.

3: Initialize: U, U ′=M, S =N, Rm= 0 ∀m∈M.

4: while U=ϕdo

5: Find

(m∗, n∗) = arg max

n∈S,m∈U

rn

m

1

M

m′∈U′

rn

m′

6: ρ(m∗, n∗)= 1,U=U− {m∗},S=S− {n∗}

7: p(m∗, n∗)=Pmax

mand Rm(m∗) = rn∗

m∗

8: end while

9: while S=ϕdo

10: Find

m′= arg min

m∈URm

Rmin

m

11: Find

n∗= arg max

n∈S

rn

m′

1

M

m∈U′

rn

m′

12: ρ(m′, n∗)= 1 and S=S− {n∗}

13: For (m′, n∗)calculate pn∗

m′by Pmax

m′/Nm′

14: Update Rm(m′) = Rm(m′) + rn∗

m′from updated p

15: end while

16: for each user min U′do

17: Fe

m=F/M

18: end for

5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

Average Latency (msec)

Proposed Scheme

Random Offloading Scheme

Complete Offloading

Fig. 2. Effect of number of users on sum latency of the system for ﬁxed

number of subcarriers.

in the network. The total bandwidth Bis 20 MHz, which

is divided into N= 64 orthogonal subcarriers. The channel

gain hn

mis modeled as independent Rayleigh fading channel

which incorporates the path loss and shadowing effects [15].

The noise power is set as N0=−100 dB. For each task,

the data size and required CPU cycles per bit are uniformly

distributed as Dm∈[100,500] KB and cm∈[500,1500]

cycles/bit, while Rmin

mis chosen randomly from the range

{100,200}KB/s based on the data size of each user’s task.

The expected energy consumption for each user is randomly

chosen from {1,1.5,2}J. The local computation capacity Fm

and local computation energy per cycle ωmfollow uniform

distribution between [0.1,1.0] GHz and [0.5,2x10−10]J/cycle,

respectively. We model computing capabilities of the users as

independent variables. Last, the ﬁnite edge capacity is set as

F= 10x109GHz.

We ﬁrst compare the performance of proposed scheme with

random ofﬂoading which randomly segments the computation

data for ofﬂoading and complete ofﬂoading which ofﬂoads

the complete data for remote execution. Fig. 2 shows the

average latency versus number of users in the three different

cases. The average latency increases with the number of users

for all the three schemes as the communication and edge

computation resources become scarce. For small number of

users, partial ofﬂoading scheme performs better than random

ofﬂoading, while complete ofﬂoading achieves the minimum

latency due to sufﬁcient computation resources at the edge.

However, partial ofﬂoading outperforms the other schemes

as the number of users increases in the network. This can

be explained by the fact that our proposed scheme allows

multi-channel transmission and jointly considers the com-

munication and computation resources allocation resulting in

reduced communication and edge execution latency. Hence,

it is evident that the proposed scheme is effective for delay

sensitive tasks especially when the network becomes dense.

In Fig. 3, we compare the performance of the three schemes

from energy consumption perspective. It can be seen that as

the task size increases, the energy consumption also increases

for all the three cases due to limited communication and

computation resources, while the proposed scheme consumes

0.5 1 1.5 2 2.5

Task Size (MB)

2

4

6

8

10

Average Energy Consumption (J)

Proposed Scheme

Random Offloading Scheme

Complete Offloading

Fig. 3. Effect of task size on local energy consumption.

less energy as compared to random and complete ofﬂoading.

The total energy consumed is due to the local execution and

then data transmission over the channel. In our scheme, we

decide the optimal ofﬂoading fraction based on the expected

energy cost and edge execution latency due to which less

energy is consumed locally. Moreover, the optimized sub-

carrier and power allocation reduces the energy consumption

for communication. Complete ofﬂoading consumes energy for

communication only, which is still larger as the data size of

tasks is assumed to be large and communication resources are

not allocated optimally. Random ofﬂoading performs worst

as the data segmentation and communication is not optimal,

which leads to higher energy consumption for both locally

execution and ofﬂoading.

Next, we analyse the effect of increase in task size on

communication cost in order to provide more insight into the

optimal communication resource allocation policy. We assume

that each user has different task size and QoS requirement, and

plot the average communication cost in Fig. 4 by increasing

the task size for each user. It can be observed that the time

consumed for ofﬂoading in all the three compared cases

increases with the increase in task size. This can be explained

as each user has a limited computation capacity due to which

it tends to ofﬂoad more computation on the edge server. On

the other hand, with increase in ofﬂoading data the communi-

cation resources also become scarce, which leads to increased

transmission delay. The comparison of the communication

cost for the three different cases shows that the proposed

algorithm achieves minimum communication delay due to

optimal subcarrier assignment and power allocation. Whereas,

the communication cost in case of complete ofﬂoading is

highest due to the data rate bottleneck. Although, random

ofﬂoading is better than complete ofﬂoading, the communica-

tion resource allocation is not optimal due to which the partial

ofﬂoading does not pay off.

Finally, we analyse the effect of edge computation capacity

on sum latency of the system in Fig. 5. The results show that

by increasing the edge capacity the performance is improved

for all the three schemes. This trend is obvious as the users

will tend to ofﬂoad and perform most of the computation

remotely on the resourceful edge. However, exceeding the

0 50 100 150 200 250

Increase in task size (%)

10

20

30

40

50

Average Communication Cost (msec)

Proposed Scheme

Random Offloading Scheme

Complete Oflloading

Fig. 4. Effect of task size on time cost of local computing, ofﬂoading and

edge computing.

edge capacity beyond a certain limit does not improve the

performance any further, which shows that there exists a

critical value of edge computation capacity beyond which the

latency can not be reduced any more. Moreover, the compar-

ison shows that the proposed scheme achieves minimum sum

latency as compared to the other two schemes due to optimal

ofﬂoading and resource allocation. Whereas, beyond a critical

value of computation capacity the sum latency and becomes

invariant with further increase in computation capacity. It is

important to note that the edge capacity beyond 10 GHz is

hard to realise, thus the results for edge capacity above 10

GHz are insigniﬁcant.

VI. CONCLUSION

In this paper, we jointly investigated partial ofﬂoading and

resource allocation for an OFDMA based multi-user MECO

system. To enhance the system performance and ensure energy

efﬁciency, we formulated sum latency minimization prob-

lem considering the constraints on edge computing latency,

expected energy cost for local computing, communication

and edge computation resources. We determined the optimal

ofﬂoading fraction at every user to improve edge performance

and save local energy, and then proposed a low complexity

algorithm for optimal communication and computation re-

source allocation. Numerical results showed that our proposed

scheme can achieve better performance both in terms of

sum latency and energy consumption than random ofﬂoading

scheme and complete ofﬂoading.

ACK NOW LE DG ME NT

This work was supported in part by The National Key

Research and Development Program of China under grant

2017YFE0112300, the National Nature Science Foundation of

China under 61861136003, 61621091 and 61673237, Beijing

National Research Center for Information Science and Tech-

nology under 20031887521, and research fund of Tsinghua

University-Tencent Joint Laboratory for Internet Innovation

Technology.

4 6 8 10 12

800

1200

1600

2000

2400

2800

Average Latency (msec)

Proposed Scheme

Random Offloading Scheme

Complete Offloading

Fig. 5. Effect of edge computation capacity on sum latency of the system.

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