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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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