Joint Wireless Resource and Computation Offloading Optimization for Energy Efficient Internet of Vehicles

Abstract

The Internet of Vehicles (IoV) is an emerging paradigm, which is expected to be an integral component of beyond-fifth-generation and sixth-generation mobile networks. However, the processing requirements and strict delay constraints of IoV applications pose a challenge to vehicle processing units. To this end, multi-access edge computing (MEC) can leverage the availability of computing resources at the edge of the network to meet the intensive computation demands. Nevertheless, the optimal allocation of computing resources is challenging due to the various parameters, such as the number of vehicles, the available resources, and the particular requirements of each task. In this work, we consider a network consisting of multiple vehicles connected to MEC-enabled roadside units (RSUs) and propose an approach that minimizes the total energy consumption of the system by jointly optimizing the task offloading decision, the allocation of power and bandwidth, and the assignment of tasks to MEC-enabled RSUs. Due to the original problem complexity, we decouple it into subproblems and we leverage the block coordinate descent method to iteratively optimize them. Finally, the numerical results demonstrate that the proposed solution can effectively minimize total energy consumption for various numbers of vehicles and MEC nodes while maintaining a low outage probability.

Full text

1
Joint Wireless Resource and Computation
Offloading Optimization for
Energy Efficient Internet of Vehicles
Dimitrios Pliatsios, Panagiotis Sarigiannidis, Thomas Lagkas, Vasileios Argyriou,
Alexandros-Apostolos A. Boulogeorgos, Peristera Baziana
Abstract—The Internet of Vehicles (IoV) is an emerging
paradigm, which is expected to be an integral component of
beyond-fifth-generation and sixth-generation mobile networks.
However, the processing requirements and strict delay constraints
of IoV applications pose a challenge to vehicle processing units.
To this end, multi-access edge computing (MEC) can leverage the
availability of computing resources at the edge of the network
to meet the intensive computation demands. Nevertheless, the
optimal allocation of computing resources is challenging due to
the various parameters, such as the number of vehicles, the avail-
able resources, and the particular requirements of each task. In
this work, we consider a network consisting of multiple vehicles
connected to MEC-enabled roadside units (RSUs) and propose
an approach that minimizes the total energy consumption of the
system by jointly optimizing the task offloading decision, the
allocation of power and bandwidth, and the assignment of tasks
to MEC-enabled RSUs. Due to the original problem complexity,
we decouple it into subproblems and we leverage the block
coordinate descent method to iteratively optimize them. Finally,
the numerical results demonstrate that the proposed solution
can effectively minimize total energy consumption for various
numbers of vehicles and MEC nodes while maintaining a low
outage probability.
Index Terms—6G, B5G, Block Coordinate Descent, Computa-
tion Offloading, Energy Efficiency, Internet of Vehicles, Mobile
Edge Computing
I. INTRODUCTION
The sixth-generation (6G) of mobile networks aims to
integrate the advances in wireless communication technolo-
gies to deliver enhanced performance compared to fifth-
generation (5G) mobile networks and realize new applications
and services [1], requiring increased computing capabilities
and low computing latency. The Internet of Vehicles (IoV)
is an emerging paradigm derived from the concept of the
Internet of Things and features great potential in the Beyond
This work has received funding from the European Unions Horizon 2020
research and innovation programme under grant agreement No. 957406
(TERMINET).
D. Pliatsios and P. Sarigiannidis are with the Department of Electrical
and Computer Engineering, University of Western Macedonia, Kozani 50100,
Greece; {dpliatsios, psarigiannidis}@uowm.gr
T. Lagkas is with the Department of Computer Science, School of Science,
International Hellenic University, Thessaloniki, Greece; tlagkas@cs.ihu.gr
V. Argyriou is with the Department of Networks and Digital Media,
Kingston University London, Penrhyn Road, Kingston upon Thames, Surrey
KT1 2EE, UK; vasileios.argyriou@kingston.ac.uk
A-A.A. Boulogeorgos is with the Department of Digital Systems, University
of Piraeus, 18534 Piraeus, Greece; al.boulogeorgos@ieee.org
P. Baziana is with the Department of Computer Science and Telecommu-
nications, University of Thessaly, Lamia, Greece; baziana@uth.gr
5G/6G era [2]–[5]. The IoV paradigm aims to deliver an
intelligent and efficient transportation system able to support
applications such as autonomous driving, traffic prediction,
and road security and safety [6]. Such applications often have
strict delay constraints and require intensive computations [7].
Although the computing capabilities of vehicles are higher
than conventional mobile devices, the complex processing
requirements and strict delay constraints of IoV applications
pose a challenge to vehicle processing units. In addition, an
individual vehicle’s available computing resources may not be
able to meet the aforementioned requirements and constraints.
Multi-access edge computing (MEC), formerly known as
mobile edge computing, can leverage the availability of com-
puting resources located at the edge of the network to effi-
ciently realize computing resource sharing, in order to meet
the intensive computing demands posed by IoV applications.
In this direction, a device can offload a task to a MEC-enabled
small cell (SC), where sufficient computation resources exist.
Nevertheless, the orchestration of resource sharing among var-
ious devices and SCs is challenging due to the heterogeneity
of the resources and the time-varying topology of vehicular
networks. Furthermore, the dense deployment of MEC-enabled
SCs will result in higher total energy consumption. Conse-
quently, minimizing the total energy consumption while taking
into account the quality of service (QoS) requirements of the
application, is challenging [8], [9].
A. Related Works
In this direction, research efforts are being focused on
exploiting the ample computing resources of the edge nodes
by offloading the tasks of mobile devices or vehicles. In more
detail, the minimization of the task processing time is the
focus of the research works in [10]–[19]. The authors in [10]
developed a task offloading optimization approach that aims
to minimize task computation delay and energy consumption.
Xu et al. [11] investigated an offloading system, where the
QoS depends on the task response time and developed a deep
reinforcement learning approach that minimizes the response
time. Zhao et al. [12] considered the partial offloading of
vehicle tasks to multiple smart devices, such as drones and
edge nodes, and minimized the execution time of a task taking
into account energy consumption and rental rate of the smart
device. In [13], the authors combined reinforcement learning
and heuristic algorithms to optimize the allocation of user
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content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
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2
applications to vehicular computation resources. Moreover,
Luo et al. [14] designed a dynamic programming-based al-
gorithm that minimizes the processing latency of tasks in het-
erogeneous MEC environments. In [15], the authors leveraged
reinforcement learning to develop a mobile offloading method
aiming to minimize the cost of task migration under energy
constraints. The authors of [16] proposed a federated learning-
based offloading scheme for minimizing the total latency in
vehicular environments, where each task can be divided into
three parts so it can be respectively processed locally, offloaded
to another vehicle, or offloaded to a MEC node. Yadav et
al. [17] developed an algorithm to minimize the task latency
by optimally selecting the tasks to be offloaded to the MEC
nodes. In [18], the authors formulated the minimization of task
latency by jointly optimizing the offloading decision, as well
as the wireless and computing resource allocation in satellite-
assisted vehicle-to-vehicle communications. The authors of
[19] utilized the particle swarm optimization algorithm to
minimize the processing time of each task by offloading
portions of the task to multiple vehicles.
Alternatively, the maximization of the throughput is the
focus of the research works presented in [20]–[22] The authors
in [20] investigated the resource allocation in networks con-
sisting of unmanned aerial vehicles and formulated a mixed-
integer non-linear problem, aiming to maximize the average
throughput while satisfying energy constraints. In addition,
Ning et al. [21] leveraged non-orthogonal multiple access and
MEC technologies to develop a method that maximizes the
link throughput, by optimizing power allocation, subchannel
assignment, and task assignment. Furthermore, Lu et al. [22]
considered a network, where two unmanned aerial vehicles
(UAVs) provide wireless power transfer to two ground devices
and developed a solution based on successive convex program-
ming in order to maximize the sum average transmission rate.
The approaches presented in [23]–[29] are focused on maxi-
mizing the system utility. Specifically, Dai et al. [23] proposed
a low-complexity algorithm to jointly optimize the offloading
decision and resource allocation toward maximizing the sys-
tem utility. In [24], the authors proposed a vehicle-assisted
offloading scheme that aims to maximize the long-term utility
rate of a vehicular network using a reinforcement learning
method. The authors in [25] addressed the maximization of
the system offloading utility rate taking into account the task
execution order and the available computing resources. The au-
thors of [26] designed a collaborative resource allocation and
offloading decision optimization scheme for maximizing the
utility rate of the system. In [27], Zhang et al. adopted a deep
Q-learning method for optimizing the offloading decision and
the data uploading method (i.e., vehicle-to-vehicle, vehicle-to-
base-station) with the aim of maximizing the system utility
rate. The authors in [28] presented a joint resource allocation
and task scheduling scheme for maximizing the system’s util-
ity by formulating the corresponding optimization problem as
a Stackelberg game. Xu et al. [29] leveraged a multi-objective
evolutionary algorithm based on decomposition to minimize
the task processing latency and maximize the utilization of
the system resources.
Finally, the research works in [30]–[40] are focused on
minimizing the system energy consumption through the op-
timal allocation of the available resources. Particularly, the
authors in [30] formulated the computation offloading as a
mixed-integer non-linear programming problem and proposed
a genetic algorithm that minimizes the energy consumption.
In [31], the authors leveraged a deep reinforcement learning
approach for minimizing the energy consumption through
the joint optimization of the offloading decision and the
assignment of tasks to the MEC nodes. The authors in
[32] investigated the trade-off between the task latency and
energy consumption and developed an approach to find the
optimal task offloading decision and the allocation of wireless
resources. Zhou et al. [33] developed a scheme based on
the alternating direction method of multipliers for minimizing
the total energy consumption of the system by finding the
optimal offloading decision for each task. In [34], the authors
presented a method based on the Lagrange dual decomposition
method for minimizing the energy consumption through the
joint optimization of the offloading decision, the allocation of
transmission power, and the scaling of computing resources.
The authors in [35] proposed an approach that maximizes the
system energy efficiency by optimally allocating the offloading
transmission power and time, as well as scaling the device
chip computing frequency. Jang et al. [36] investigated the
energy consumption assuming partial and complete offloading
in vehicular edge computing environments and proposed a
solution for optimally assigning the offloading of the task in
time-slots. The authors in [37] developed an energy-efficient
fog computation offloading scheme in order to meet the
stringent requirements of the industrial internet of things. The
scheme leverages an accelerated gradient descent algorithm
that optimizes the offloading ratio, the transmission power and
time, and the local central processing unit (CPU) computation
speed. Wang et al. [38] focused on the energy consumption
of an edge system and proposed an imitation learning-enabled
scheduling algorithm that takes into account the latency con-
straints of the tasks. In [39], the authors presented a deep
reinforcement learning method to minimize the long-term
energy consumption and task processing latency through the
optimization of the offloading decision and the allocation of
computing resources. Lagkas et al. [40] developed a joint
allocation scheme, involving three optimization phases for the
edge, radio, and optical resources, respectively.
B. Contributions
The aforementioned works presented some interesting re-
sults, however, some of them are focused on optimizing only a
particular aspect of the offloading process (e.g., the offloading
decision), while most of the are focused on jointly optimizing
the offloading decision and the allocation of the transmission
power. Furthermore, some of the research works are focused
on the joint optimization of the wireless and computing
resources. Of note, the solutions presented in most of the
works are based on deep learning or reinforcement learning
algorithms to optimize the long-term system performance.
However, these algorithms are considered computationally
expensive. Moreover, deep learning algorithms require large
datasets volumes to achieve high performance.
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content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
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3
Motivated by these remarks, we develop a solution that aims
to minimize the total energy consumption of the system by
optimally offloading the tasks to the MEC-enabled roadside
units (RSUs), taking into account the latency requirements
and the availability of wireless and computing resources.
In particular, the solution aims to jointly optimize the task
offloading decision, the allocation of power and bandwidth
resources, the assignment of tasks to MEC-enabled RSUs, and
the frequency scaling of MEC-enabled RSUs. In more detail,
the contributions of this work are as follows:
•We present a scenario consisting of multiple vehicles
that are served by a number of RSUs. In the considered
scenario, each vehicle may choose to compute its task
locally or offload a portion of it in a MEC-enabled RSU.
Additionally, the scenario supports task migration, mean-
ing that a task can be migrated from a RSU to another,
based on the computation requirements and availability
of resources.
•We formulate the minimization of the total energy con-
sumption as a joint optimization of the task offloading
decision, the allocation of power and bandwidth, the
assignment of tasks to MEC-enabled RSUs, and the fre-
quency scaling of MEC-enabled RSUs. We also discuss
the convexity of the original optimization problem and
transform it into convex equivalents.
•As the joint optimization problem is challenging to solve,
we decouple the original optimization problem into three
problems and solve each one in an iterative way by
leveraging the block coordinate descent (BCD) method.
•Particularly, for optimizing the task offloading decision,
we derive closed-form expressions taking into account
each task’s latency constraints. Towards optimizing the
power and bandwidth allocation, as well as the task as-
signment and frequency scaling, the Lagrange multipliers
and subgradient methods are employed.
•We evaluate the performance of the proposed approach
through system-level Monte Carlo simulations in terms
of total energy consumption and outage probability.
•To highlight the impact of the allocation of wireless and
computing resources on the total energy consumption,
we designed three evaluation scenarios. Particularly, in
the first scenario, only the offloading decision is op-
timized, whereas in the second scenario we optimize
the offloading decision and the allocation of wireless
resources. Finally, in the third scenario, the allocation of
both wireless and computing resources is optimized in
addition to the offloading decision.
The remainder of the paper is structured as follows: In
Section II we develop the model and the problem formulation,
while, in Section III, we present the proposed solution. We pro-
vide the evaluation results in Section IV and we conclude the
work in Section V. Additionally, all notations used throughout
the paper are summarized in Table I.
II. SY ST EM MO DE L AN D PROB LE M FOR MU LATI ON
Fig. 1 depicts the considered system model. In particular, a
number of vehicles are served by RSUs equipped with MEC
TABLE I: Summary of Notations
Notations Explanation
NNumber of vehicles
SNumber of RSUs
xnOffloading decision
wnBandwith allocation coefficient
WAvailable bandwidth
an,s Task assigment index
fn,s MEC frequency scaling coefficient
Fmax
sMaximum computation capability of MEC node
RnWireless link capacity
BnTotal system bandwidth
pnVehicle transmission power
d−δ
n,s Distance-based pathloss
σ2Noise variance
LnTask size
CnRequired cycles
Tmax
nMaximum latency
floc
nLocal computing capability
Tloc
nLocal computation time
Tup
nUpload time
Toff
nOffloaded computation time
Eloc
nEnergy consumed locally
Eup
nEnergy consumed during the upload
Tmec
nMEC processing time
ϕloc
nLocal energy consumption coefficient
ϕmec
sMEC energy consumption coefficient
βn, κn,s, λn, µsLagrange multipliers
ξn,s, πn, τsLagrange multipliers

Fig. 1: Computation Offloading for Internet of Vehicles
capabilities. Each vehicle is served by its nearest RSU via
a wireless link, while RSUs are interconnected using high-
capacity optical backhaul links [41]. The wireless communi-
cation between the RSUs and the vehicles can be enabled by a
mobile network (e.g., B5G or 6G), while the optical backhaul
links can be enabled by the latest optical communications
standards, such as the 10-Gigabit Symmetrical Passive Optical
Network (10GS-PON) or the Next-Generation PON 2 (NG-
PON2), that are able to provide data rates up to 10 Gbps [42],
[43].
Let N={1, ..., N }denote the set of vehicles, while
S={1, ..., S}denotes the set of RSUs. To mitigate the energy
required for the wireless data transmission, each vehicle is
assumed to be connected to the closest RSU in its proximity
and the corresponding distance is denoted by dn,s. We assume
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
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4
that the optimization process takes place in cycles, in which
the vehicles may offload a portion of a task. Consequently,
the terms vehicle and task can be used interchangeably. In
addition, for the duration of the cycle, the vehicle position
is assumed to remain steady. The offloaded tasks can be part
of various IoV applications, including navigation assistance,
image or video recognition, collision or obstacle detection, or
autonomous driving [44], [45]. In addition, task profilers can
be leveraged to provide valuable insights to operators about
the computing and delay requirements of each task [46], [47].
A. Communication Model
The wireless link capacity between a vehicle and an RSU
is calculated by
Rn=wnWlog2(1 + SNRn,s)(1)
where wndenotes the bandwidth portion allocated to vehicle
n, while Wis the total available bandwidth. The respective
signal-to-noise ratio (SNR) is obtained by
SNRn,s =pnd−δ
n,s
σ2(2)
where pnis the power of the transmitted signal, d−δ
n,s is
distance pathloss based on δcoefficient, and σ2is the
noise variance. Orthogonal frequency-division multiple access
(OFDMA) is selected for minimizing interferences among
vehicles.
B. Computation Model
Each task nis described by the tuple (Ln, Cn, T max
n),
where Lndenotes the data length in bits to be processed
and Cn(cycles/bit) denotes the number of cycles required
to process a single bit of the task [21], [48]. Consequently,
the total number of cycles required for processing the task
can be obtained by LnCn. Also, Tmax
ndenotes the maximum
tolerable latency for the task.
1) Local Computation: The total time for the local compu-
tation is obtained by
Tloc
n=LnCn
floc
n
(3)
where floc
n(cycles/s) denotes the computing capability of
the n-th vehicle. As in [48], [49], and [50], we model the
energy consumption of the processor as ϕloc
n(floc
n)3(joules
per second), where ϕloc
nstands for the processor’s chip energy
coefficient [49]. By multiplying the aforementioned equation
with the right hand side of (3), we obtain the energy consumed
for the processing of the n-th task as
Eloc
n=LnCn(floc
n)2ϕloc
n(4)
2) Offloaded Computation: The total time for the offloaded
computation consists of the time required for the vehicle to
upload the data to the nearest MEC-enabled RSU and the
time required for the RSU to process the data. Moreover,
the nearest RSU may not have enough available computing
resources and thus, the task will be migrated to another RSU
through the backhaul optical link. Also, since that the size
of the offloaded task is much smaller than the backhaul link
capacity, we can assume that the task migration time is zero in
order to simplify the optimization process. To indicate where
each task is processed, we use the binary variable an,s as
follows:
an,s =(1,the n-th task is proccessed at the s-th node
0,otherwise
(5)
Based on the aformenioned remarks, the upload time is
calculated as
Tup
n=Ln
Rn
(6)
The processing time of the n-th task at the s-th node can
obtained by
Tproc
n,s =LnCn
fn,sFmax
s
(7)
where fn,s is the frequency scaling coefficient that denotes the
utilization ratio of the processor. For example, when fn,s = 1,
the current processor frequency will be equal to Fmax
s, where
Fmax
sdenotes the maximum computing capability of the s-th
RSU (in Hz).
Assuming that the downlink transmission delay is consid-
ered negligible, due to the result of the computation being very
small ( [51], [52]), the total time for the offloaded computation
of the n-th task is
Toff
n=Tup
n+
S
X
s=1
an,sTproc
n,s (8)
The total energy consumed in the offloaded computation
includes the energy consumed at the vehicle for the task upload
and the energy consumed at the RSU for the processing. In
particular, the energy consumed for the task upload will be
the transmission power of the n-th vehicle multiplied by the
time required to upload the task and can be calculated by
Eup
n=pnTup
n(9)
Using the same energy consumption model as in local com-
putation, the energy consumed for the processing of n-th task
at the s-th node is obtained by
Eproc
n,s =LnCn(fn,sFmax
s)2ϕmec
s(10)
where ϕmec
sis the energy consumption coefficient of the RSU.
Eoff
n=Eup
n+
S
X
s=1
an,sEproc
n,s (11)
For the communication between RSUs, a high-capacity passive
optical network is utilized [53], [54]. As a result, in case of
task migration, the respective data can be promptly transferred
among RSUs, with minimal delay, leading to a small energy
overhead.
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5
C. Problem Formulation
We aim to minimize the total power consumption of the
system by jointly optimizing the task offloading decision,
the allocation of power and bandwidth, the assignment of
tasks to MEC-enabled RSUs, and the frequency scaling of
MEC-enabled RSUs. Moreover, we adopt a partial offloading
scheme, meaning that a task can be concurrently computed
locally and in a MEC-enabled RSU. The portion of local and
offloaded computation is denoted by xn. Specifically, when
xn= 0 the whole task is computed locally at a vehicle,
whereas when xn= 1, the whole task is offloaded to a MEC-
enabled RSU. Combining (1) - (11), the total computation time
is expressed as
Tn(xn, pn, wn, an,s, fn,s ) = (1 −xn)Tloc
n+ (xn)Toff
n(12)
Similarly, the total energy consumption is formulated as
En(xn, pn, wn, an,s, fn,s ) = (1 −xn)Eloc
n+ (xn)Eoff
n(13)
Consequently, the optimization problem is expressed as fol-
lows:
P0 : min
x
x
x,p
p
p,w
w
w,a
a
a,f
f
f
N
X
n=1
En(xn, pn, wn, an,s, fn,s )(14a)
subject to:
max{Toff
n, T loc
n} ≤ Tmax
n,∀n(14b)
0≤xn≤1,∀n(14c)
0≤pn≤Pmax
n,∀n(14d)
0≤wn≤1,∀n(14e)
N
X
n=1
wn≤1(14f)
an,s ={0,1},∀n, s (14g)
N
X
n=1
an,s ≤2,∀s(14h)
0≤fn,s ≤1,∀n, s (14i)
N
X
n=1
fn,s ≤1,∀s(14j)
In P0,x
x
xdenotes the vector of the task offloading deci-
sion, while p
p
pand w
w
wdenote the vectors of the transmission
power and bandwidth allocation, respectively. Furthermore, a
a
a
denotes the task-MEC assignment vector, while f
f
fdenotes the
frequency scaling coefficient vector. Constraint (14b) enforces
that the total computation time of the task does not exceed
the maximum tolerable delay. Additionally, constraint (14c)
enforces the task offloading portion in the range [0,1], while
(14d) enforces the transmission power between 0 and the
Pmax
n. Similarly, (14e) and (14f) are employed to limit the
bandwidth coefficient up to 1. Furthermore, (14g) enforces
binary values to an,s, while (14g) limits the tasks computed
in a single RSU up to two. Finally, (14i) and (14j) are imposed
to limit frequency scaling coefficient up to 1.
In P0, the objective function and constraint (14b) are non-
linear due to the logarithm in (1). Moreover, there are product
relationships between the optimization variables in the objec-
tive function. For example, for the offloaded computation case,
xn,pn,fn,s,an,s are multiplied based on (11). Additionally,
(14b) and (14g) make the feasible set non-convex. Therefore,
P0is a non-convex mixed-integer non-linear problem.
III. PROP OS ED SOLUTION
This section presents the solution to the formulated opti-
mization problem. In this direction, the original problem is
decoupled into three problems, which are iteratively optimized
through the BCD method. Particularly, closed-form expres-
sions are derived for solving the task offloading decision.
Moreover, the Lagrange multipliers and subgradient methods
are employed for solving the wireless and computing resource
allocation problems.
A. Optimizing Offloading Decision while Fixing the Rest Op-
timization Variables
In P0, constraint (14b) makes the feasible set non-convex.
Therefore, to transform the feasible set into a convex one, we
propose Lemma 1.
Lemma 1. The equivalent of (14b) is expressed as
1−floc
nTmax
n
LnCn
≤xn≤Tmax
nRn
Ln+RnTproc
n
(15)
Proof: The proof of Lemma 1 is provided in Appendix A.
Assuming fixed p
p
p, w
w
w, a
a
a, f
f
f,P0can be decoupled into Nsub-
problems that can be independently optimized. By leveraging
Lemma 1, the following optimization problem is formulated
for each task:
P1 : min
xn
En(xn)(16a)
subject to 1−floc
nTmax
n
LnCn
≤xn≤Tmax
nRn
Ln+RnTproc
n
(16b)
The first derivative of P1’s objective function is
∂En(xn)
∂xn
=Eoff
n−Eloc
n(17)
According to (17), the objective function is monotonically
increasing or decreasing based on the sign of the first deriva-
tive. By exploiting this monotonocity, xncan be set to the
lower/upper bound of (16b) when the objective function is
increasing/decreasing. Therefore, the following Theorem is
proposed:
Theorem 1. The optimal offloading decision is obtained as
x∗
n=






max{0,1−floc
nTmax
n
LnCn
},if Eoff
n−Eloc
n≥0,
min{1,Tmax
nRn
Ln+RnTproc
n
},otherwise
(18)
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

6
Algorithm 1 Bisection Method for Finding pn
Input: Maximum transmission power Pmax
n
Output: Optimal pn
1: Set pLB
n= 0 and pU B
n=Pmax
n
2: repeat
3: Set X=pLB
n+pUB
n
2
4: if ∂Lp,w (pLB
n)
∂pn
·∂Lp,w (X)
∂pn
<0then
5: pUB
n=X
6: else
7: pLB
n=X
8: end if
9: until |pUB
n−pLB
n|<0.001
10: Return pn
B. Optimizing Wireless Resouces while Fixing the Rest Opti-
mization Variables
After obtaining the optimal offloading decision for each
task, we consider x
x
x, a
a
a, f
f
fto be fixed in order to determine the
optimal power and bandwidth allocation. Consequently, P2is
formulated as
P2 : min
p
p
p,w
w
w
N
X
n=1
En(pn, wn)(19a)
subject to:
Tn(pn, wn)≤Tmax
n,∀n(19b)
0≤pn≤Pmax
n,∀n(19c)
0≤wn≤1,∀n(19d)
N
X
n=1
wn≤1(19e)
To find the optimal power and bandwidth allocation, we
employ the Lagrange multiplier and subgradient methods.
Consequently, the respective Lagrangian of P2is obtained
by (22) shown at the top of the next page. In (22), set
Xp,w ={βn, λn, µ, πn}denotes the non-negative Lagrange
multipliers. Therefore, the dual function is written as follows:
D1(Xp,w) = min
pn,wn
L(pn, wn,Xp,w)(20)
subject to: (19b)−(19e)
Consequently, the dual problem is expressed as
max
βn,λn,µ,πn
D1(Xp,w)(21)
subject to: Xp,w ⪰0,∀n
In accordance to the Karush–Kuhn–Tucker (KKT) condi-
tions, the derivative of the Lagrangian function with respect
to pnis provided in (23). Since it is challenging to obtain
a closed-form expression for (23), we utilize the bisection
method for finding the root. The bisection method for finding
pnis presented in Algorithm 1.
To obtain the optimal bandwidth allocation, we calculate
the first derivative of the Lagrangian with respect to wn. The
Algorithm 2 Subgradient Method for Optimizing p
p
p, w
w
w
Input: Maximum transmission power Pmax
n,∀nand system
bandwidth W
Output: Optimal p
p
p, w
w
w
1: Initialize pn=Pmax
nand wn=W
|N|,∀n
2: Initialize the Lagrange multipliers: βn, λn, µ, πn
3: set t= 0
4: repeat
5: for n= 1 to Ndo
6: Calculate pnusing Algorithm 1
7: Calculate wnaccording to (25)
8: Update the Lagrange multipliers using (26) - (29)
9: end for
10: Set E[t] = PN
n=1 En(pn, wn)
11: until |E[t]− E[t−1]|<0.01
12: Return p
p
p, w
w
w
result is provided by (24), shown at the top of the next page.
Solving for wn, the root can be obtained by
wn=v
u
u
t
xnLn(pn+λn) ln 2
(βn+µ)Wlog2[1 + pnd−δ
n,s
σ2]
(25)
After obtaining the solution for problem D1through Algo-
rithm 1 and (25), the Lagrange multipliers are updated as
λt+1
n=λt
n+s1(xnLn
Rn
+xnTproc
n−Tmax
n)+
(26)
πt+1
n=πt
n+s2(pn−Pmax
n)+
(27)
βt+1
n=βt
n+s3(wn−1)+
(28)
µt+1 =µt+s4(
N
X
n=1
wn−1)+
(29)
where s1,s2,s2, and s4are the positive step sizes. The subgra-
dient method for optimizing the wireless resource allocation
is presented in Algorithm 2.
C. Optimizing Computing Resources while Fixing the Rest
Optimization Variables
Having obtained the optimal offloading decision and wire-
less resource allocation, we will determine the optimal MEC
assignment, as well as the optimal MEC frequency allocation
to each task. Therefore, in this step, x
x
x,p
p
p,w
w
ware assumed to
be fixed. Also, to address the non-convexity introduced by the
binary constraint (14g), we relax it by setting it in [0,1] range.
This relaxation can be perceived as dividing the offloaded
portion of the task into multiple parts and processing them
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content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
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7
Lp,w(pn, wn,Xp,w ) =
N
X
n=1
En(pn, wn) +
N
X
n=1
λnTn(pn, wn) +
N
X
n=1
πn(pn−pmax)
+
N
X
n=1
βn(wn−1) + µ(
N
X
n=1
wn−1) (22)
∂Lp,w (pn, wn,Xp,w )
∂pn
=πn+
xnLn(log2[1 + pnd−a
n,s
σ2]−pn+λn
ln 2(pn+d−δ
n,sσ2))
wnWlog2[1 + pnd−a
n,s
σ2]2
(23)
∂Lp,w (pn, wn,Xp,w )
wn
=βn+µ−xnLn(pn+λn)
wnRn
(24)
in different RSUs. Consequently, P3is expressed as
P3 : min
a
a
a,f
f
f
N
X
n=1
En(an,s, fn,s )(30a)
subject to:
Tn(an,s, fn,s )≤Tmax
n,∀n(30b)
0≤an,s ≤1,∀n, s (30c)
N
X
n=1
an,s ≤2,∀s(30d)
0≤fn,s ≤1,∀n, s (30e)
N
X
n=1
fn,s ≤1,∀s(30f)
To solve P3, the Lagrage multiplier and subgradient meth-
ods can be employed. The Lagrangian of P3is given
by (39), shown at the top of the next page. In (39), set
Xa,f ={κn, λn,s, µs, ξn,s , τs}denotes the non-negative La-
grange multipliers. Thus, the dual function is written as
follows:
D2(Xa,f ) = min
an,s,fn,s
La,f (an,s, fn,s ,Xa,f )(31)
subject to: (30b)−(30f)
Consequently, the dual problem is expressed as
max
κn,λn,s,µs,ξn,s ,τs
D2(Xa,f )(32)
subject to: Xa,f ⪰0,∀n, s
To obtain the optimal task assignment, we take the first
derivative of La,f (an,s, fn,s , κn, λn,s, µs)with respect to an,s .
According to (40), the n-th task can be assigned to the s-th
RSU as follows:
an,s = 1|s= arg min
s
∂La,f (an,s , fn,s,Xa,f )
∂an,s
(33)
Using (33), binary values for an,s can be obtained without
introducing errors due to the relaxation of (14g).
On the other hand, we utilize the bisection method shown
in Algorithm 3 to obtain the optimal frequency scaling.
Algorithm 3 Bisection Method for Finding fn,s
Input: Maximum RSU frequency Fmax
s
Output: Optimal fn,s
1: Set fLB
n,s = 0 and fU B
n,s = 1
2: repeat
3: Set X=fLB
n,s +fUB
n,s
2
4: if ∂La,f (wUB
n)
∂fn,s
·∂La,f (X)
∂fn,s
<0then
5: fUB
n,s =X
6: else
7: fLB
n,s =X
8: end if
9: until |fUB
n,s −fLB
n,s |<0.001
10: Return fn,s
After problem D2is solved and the optimal task assigment
and frequency vectors are obtained, the Lagrange multipliers
are updated as
λt+1
n=λt
n+s1(xnLn
Rn
+xnTproc
n−Tmax
n)+
(34)
κt+1
n,s =κt
n,s +s2(an,s −1)+
(35)
µt+1
s=µt
s+s3(
N
X
n=1
an,s −2)+
(36)
ξt+1
n,s =ξt
n,s +s4(fn,s −1)+
(37)
τt+1
s=τt
s+s5(
N
X
n=1
fn,s −1)+
(38)
where s1,s2,s3,s4and s5are the positive step sizes.The
subgradient method for optimizing the computing resource
allocation is presented in Algorithm 4.
D. Iterative Optimization using Block Coordinate Descent
The solution to the joint optimization problem is achieved
by iteratively optimizing the subproblems. The employed BCD
method is presented in Algorithm 5. During the initialization
phase, the initial values for the optimization variables and the
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

8
La,f (an,s, fn,s ,Xa,f ) =
N
X
n=1
En(an,s, pn,s ) +
N
X
n=1
λnTn(an,s, pn,s ) +
N
X
n=1
S
X
s=1
κn,s(an,s −1)
+
S
X
s=1
µs(
N
X
n=1
an,s −2) +
N
X
n=1
S
X
s=1
ξn,s(fn,s −1) +
S
X
s=1
τs(
N
X
n=1
fn,s −1) (39)
∂La,f (an,s , fn,s,Xa,f )
an,s
=κn,s +µs+xnLnCn(λn+ (fn,sFmax
s)3ϕs)
fn,sFmax
s
(40)
∂La,f (an,s , fn,s,Xa,f )
fn,s
=ξn,s +τs+an,sxnCnLn(−λn+ 2(fn,s Fmax
s)3ϕs)
f2
n,sFmax
s
(41)
Algorithm 4 Subgradient Method for Optimizing a
a
a, f
f
f
Input: Maximum RSU frequency Fmax
s,∀s
Output: Optimal a
a
a, f
f
f
1: Initialize an,s = 1 and fn,s = 1,∀n, s
2: Initialize the Lagrange multipliers: κn, λn,s, µs, ξn,s , τs
3: set t= 0
4: repeat
5: for n= 1 to Ndo
6: Calculate an,s using (33)
7: Calculate fn,s using Algorithm 3
8: Update the Lagrange multipliers using (34) - (38)
9: end for
10: Set E[t] = PN
n=1 En(an,s, fn,s )
11: until |E[t]− E[t−1]|<0.01
12: Return a
a
a, f
f
f
Algorithm 5 Block Coordinate Descent for the Joint Opti-
mization
1: Initialize the optimization variables and the Lagrange
multipliers
2: Set t=0;
3: repeat
4: Find xn,∀nusing (18)
5: Find pnand wnusing Algorithm 2
6: Find an,s and fn,s using Algorithm 4
7: Set E[t] = PN
n=1 En(xn, pn, wn, an,s, fn,s )
8: Set t=t+ 1
9: until t>tmax or |E[t]− E[t−1]|
E[t−1] <0.01
10: Return x
x
x, p
p
p, w
w
w, a
a
a, f
f
f
Lagrange multipliers are set. In each step, the corresponding
optimal value for each optimization variable is calculated
and the algorithm ends after tmax iterations or if the energy
consumption improvement is lower than 1%.
IV. PERFORMANCE EVALUATION
To evaluate the performance of our proposed solution, we
utilize system-level Monte Carlo simulations. Table II sum-
marizes the simulation parameters. The numbers of vehicles
is set to {5,10,15,20,25}, while the number of RSUs is
set to {1,5,10,15,20}. The maximum available transmission
power of each vehicle is 36 dBm, while the available system
bandwidth is 20 MHz. Additionally, the path loss coefficient is
set to 2 and 4, while noise variance is set to 10−8. Regarding
the computation model, the task size is uniformly distributed
in the range [500,3500] Kbits, while the required cycles to
process 1 bit and maximum latency are respectively set to
297.6 cycles/bit and 0.5s-3.5s ( [30], [37], [46]). The energy
consumption coefficients for the vehicles and RSUs are set
to 10−28. Furthermore, the computing frequency of vehicles
ranges from 500 MHz to 800 MHz, while the maximum
computing frequency of RSUs is set to 10 GHz.
Three evaluation scenarios are designed in order to high-
light the impact of the allocation of wireless and computing
resources on the total energy consumption in addition to the
optimization of the offloading decision. In more detail, Sce-
nario 1 is focused on optimizing only the offloading decision
is optimized, whereas Scenario 2 is focused on optimizing the
offloading decision and the allocation of wireless resources.
Finally, in Scenario 3, the allocation of both wireless and
computing resources is optimized in addition to the offloading
decision.
TABLE II: Simulation Parameters
Parameter Value
Number of vehicles N{5,10,15,20,25}
Number of SCs S{1,5,10,15,20}
Maximum vehicle transmission power Pmax
n36 dBm
Pathloss coefficient δ{2, 4}
Noise variance σ210−8
Total system bandwidth W20 MHz
Task size Ln[500, 3500] Kbits
Required cycles to process 1 bit Cn297.6 cycles/bit
Maximum tolerable latency Tmax
n0.5s - 3.5 s
Consumption coefficients ϕloc
n, ϕmec
s10−28
Computing capability floc
n[500, 800] MHz
Maximum computing capability Fmax
s10 GHz
Fig. 2 shows the total energy consumption as a function of
the number of vehicles, for various numbers of RSUs. The
task size is randomly selected in the range [500,3500] Kbits,
while the maximum delay tolerance is randomly selected in
the range [0.5,3] seconds. In particular, Fig. 2-(a) shows the
total energy consumption when the path loss exponent is
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

9
5 10 15 20 25
0
10
20
30
40
50
60
70
80
Total Energy Consumption
Number of Vehicles
RSUs
5
10
15
20
(a) Path loss exponent δ= 2
5 10 15 20 25
0
20
40
60
80
100
120
140
160
Total Energy Consumption
Number of Vehicles
RSUs
5
10
15
20
(b) Path loss exponent δ= 4
Fig. 2: Total energy consumption as a function of the number of vehicles for various numbers of RSUs
set to 2, whereas Fig. 2-(b) shows the corresponding energy
consumption when the path loss exponent is set to 4. It is
apparent that as the number of vehicles is increased, the total
consumption also increases. This is expected because there
exist more tasks to be computed leading to increased energy
consumption. Furthermore, for a given number of vehicles, the
total energy consumption is slightly increased as the number of
RSUs increases. Thus, the number of RSUs has a small effect
on the energy consumption for fixed vehicle numbers. Note
that, the MEC-enabled RSUs have the capability to scale the
allocated computing resources, therefore increasing the energy
efficiency. With respect to the path loss exponent, for a given
number of vehicles and RSUs, the total energy consumption
of the system is increased as the path loss exponent increases.
This is expected as additional power will be needed for
uploading the respective tasks. Also, higher path loss will lead
to lower channel capacity. Therefore, additional processing
resources will be employed in order to timely process the task,
resulting in higher energy consumption.
Fig. 3 presents the outage probability as a function of the
number of vehicles, for various numbers of RSUs. The maxi-
mum latency is randomly selected in the range of [0.5,3.5]
seconds, while the outage probability is calculated as the
number of tasks that have not been computed in the required
time to the total number of tasks. According to the results,
the number of vehicles does not have a considerable impact
on the outage probability. On the other hand, when there exist
more RSUs, more tasks can be offloaded, leading to a reduced
outage probability.
Fig. 4 shows the total energy consumption as a function
of the maximum tolerable latency. The numbers of vehicles
and RSUs are set to 20 and 10, respectively. Also, the energy
consumption is evaluated for two cases of path loss exponents,
particularly when δ= 2 and δ= 4. Based on the results,
the total energy consumption is decreasing as the maximum
5 10
15
20 25
5
6
7
8
9
10
11
12
13
14
15
Outage Probability (%)
Number of Vehicles
RSUs
5 10 15 20
Fig. 3: Outage probability as a function of the number of
vehicles for various numbers of RSUs
tolerable latency is increased. This is due to the fact that
lower computing resources are allocated, leading to reduced
energy consumption. As far as the task size is concerned,
it is expected that when the task size is increased, more
computing resources should be allocated, leading to increased
energy consumption. Regarding the path loss exponents, the
total energy consumption is increased for higher values of δ
because of the additional transmission power and computing
resources that will be employed.
Fig. 5 depicts a comparison between the three scenarios in
terms of the total energy consumption for a varying number
of devices. The task sizes are randomly selected in the range
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content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
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10
0,5 1,0 1,5 2,0 2,5 3,0
3,5
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
Total Energy Consumption
Maximum Tolerable Latency
Task Size
0.5 Mbits
2.0 Mbits
3.5 Mbits
! "! # ! "! #
! "! $
Fig. 4: Total energy consumption as a function of the maxi-
mum task latency for various task sizes
5 10 15 20
25
0
200
400
600
800
1000
Total Energy Consumption
Number of Vehicles
RSUs
10
20
Scenario 2
Scenario 1
Scenario 3
Fig. 5: Comparison between three scenarios in terms the total
energy consumption for varying number of devices
[500,3500] Kbits, while the maximum delay tolerance values
are randomly selected in the range [0.5,3] seconds. Also, the
number of RSUs is set to 10 and 20. In all cases, when the
number of vehicles is increased the total energy consumption
is also increased since there are more tasks to be processed,
thereby consuming more energy (both for the upload and pro-
cessing). Particularly, Scenario 1 results in the highest energy
consumption as only the offloading decision is optimized. As
a result, the vehicles transmit with the highest power (i.e.,
36 dBm), while the RSUs process each task by assigning all
available computing resources. On the other hand, Scenario
2 results in lower energy consumption as the allocation of
wireless resources has been optimized, thus, lower levels of
vehicle transmission power are required. Finally, Scenario 3
features the lowest total energy consumption since, in addition
to the offloading decision, it optimizes the allocation of both
0,5 1,0 1,5 2,0 2,5 3,0
3,5
0
200
400
600
800
1000
1200
1400
Total Energy Consumption
Maximum Tolerable Latency
Scenario 1
Scenario 2
Scenario 3
Fig. 6: Comparison between three scenarios in terms the total
energy consumption for varying tolerable delay
wireless and computing resources.
Finally, Fig. 6 shows a comparison between the scenarios
with respect to the total energy consumption as a function of
the maximum tolerable latency. The numbers of vehicles and
RSUS are respectively set to 25 and 20, while the task sizes
are randomly selected in the range [500,3500] Kbits. Similarly
to Fig. 4, the total energy consumption is decreased as the
maximum tolerable latency of each task is increased. However,
Scenario 1 features the highest overall energy consumption
followed by Scenario 2, while Scenario 3 results in the lowest
overall energy consumption. This is expected, as in Scenario 3
all the system variables are optimized, in contrast to Scenarios
2 and 3 where only a subset of the variables is optimized.
V. CONCLUSION
In this work, we considered the energy consumption mini-
mization of a vehicular network. Specifically, we formulated
the optimization problem as a joint optimization of the task
offloading decision, the allocation of power and bandwidth, the
assignment of tasks to MEC-enabled RSUs, and the frequency
scaling of MEC-enabled RSUs. Since the optimization of the
aforementioned problem is challenging, we decoupled it into
three problems and leveraged the BCD method to iteratively
optimize them. For the performance evaluation, we carried out
system-level Monte Carlo simulations and evaluated the total
energy consumption and the outage probability. The simulation
results show that the proposed BCD-based approach can mini-
mize the system energy consumption while maintaining a low
outage probability. Moreover, three evaluation scenarios have
been designed in order to highlight the impact of optimizing
the allocation of both wireless and computing resources in
addition to the offloading decision.
In the future, we aim to extend this work towards mini-
mizing the average energy consumption over time, taking into
account the mobility of the vehicles, as well as the arrival of
new tasks. Furthermore, we aim to leverage our previous work
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

11
in [55] in order to incorporate UAVs to provide on-demand
computation offloading. In this direction, the design of the
offloading policy and resource allocation should also consider
the limited energy reserves of the UAVs. Finally, in light of
the exponential increase of internet of things devices, we will
also evaluate the impact of novel multiple access methods in a
scenario consisting of numerous devices and vehicles sharing
the same wireless and computing resources.
APPENDIX A
For a given xnthe required time for the local computation
is expressed as
xn(Ln
Rn
+Tproc
n)≤Tmax
n⇒xn≤Tmax
nRn
Ln+RnTproc
n
(42)
On the other hand, the required time for the offloaded com-
putation is expressed as
(1 −xn)(LnCn
floc
n
)≤Tmax
n⇒xn≥1−floc
nTmax
n
LnCn
(43)
Combining (42) and (43) Lemma 1 is proved.
REFERENCES
[1] I. Tomkos, D. Klonidis, E. Pikasis, and S. Theodoridis, “Toward the 6G
network era: Opportunities and challenges,” IT Professional, vol. 22,
no. 1, pp. 34–38, Jan. 2020.
[2] Y. Lu and X. Zheng, “6G: A survey on technologies, scenarios,
challenges, and the related issues,” Journal of Industrial Information
Integration, vol. 19, p. 100158, Sep. 2020.
[3] M. Giordani, M. Polese, M. Mezzavilla, S. Rangan, and M. Zorzi, “To-
ward 6G networks: Use cases and technologies,” IEEE Communications
Magazine, vol. 58, no. 3, pp. 55–61, Mar. 2020.
[4] J. Wang, K. Zhu, and E. Hossain, “Green internet of vehicles (IoV) in the
6G era: Toward sustainable vehicular communications and networking,”
IEEE Transactions on Green Communications and Networking, vol. 6,
no. 1, pp. 391–423, Nov. 2022.
[5] D. P. Moya Osorio, I. Ahmad, J. D. V. S ´
anchez, A. Gurtov, J. Scholliers,
M. Kutila, and P. Porambage, “Towards 6G-enabled internet of vehicles:
Security and privacy,” IEEE Open Journal of the Communications
Society, vol. 3, pp. 82–105, Jan. 2022.
[6] L.-M. Ang, K. P. Seng, G. K. Ijemaru, and A. M. Zungeru, “Deployment
of IoV for smart cities: Applications, architecture, and challenges,” IEEE
Access, vol. 7, pp. 6473–6492, 2019.
[7] A. Sacco, F. Esposito, and G. Marchetto, “Resource inference for
sustainable and responsive task offloading in challenged edge networks,”
IEEE Transactions on Green Communications and Networking, vol. 5,
no. 3, pp. 1114–1127, Sep. 2021.
[8] T. Lagkas, G. Papadimitriou, P. Nicopolitidis, and A. Pomportsis, “A
new approach to the design of MAC protocols for wireless LANs:
combining QoS guarantee with power saving,” IEEE Communications
Letters, vol. 10, no. 7, pp. 537–539, Jul. 2006.
[9] L. D. Nguyen, H. D. Tuan, and T. Q. Duong, “Energy-efficient signalling
in QoS constrained heterogeneous networks,” IEEE Access, vol. 4, pp.
7958–7966, 2016.
[10] T. Q. Dinh, J. Tang, Q. D. La, and T. Q. S. Quek, “Offloading in mobile
edge computing: Task allocation and computational frequency scaling,”
IEEE Transactions on Communications, vol. 65, no. 8, pp. 3571–3584,
Aug. 2017.
[11] X. Xu, B. Shen, S. Ding, G. Srivastava, M. Bilal, M. R. Khosravi,
V. G. Menon, M. A. Jan, and M. Wang, “Service offloading with deep
Q-network for digital twinning-empowered internet of vehicles in edge
computing,” IEEE Transactions on Industrial Informatics, vol. 18, no. 2,
pp. 1414–1423, Feb. 2022.
[12] L. Zhao, K. Yang, Z. Tan, H. Song, A. Al-Dubai, A. Y. Zomaya,
and X. Li, “Vehicular computation offloading for industrial mobile
edge computing,” IEEE Transactions on Industrial Informatics, vol. 17,
no. 11, pp. 7871–7881, Nov. 2021.
[13] S.-S. Lee and S. Lee, “Resource allocation for vehicular fog computing
using reinforcement learning combined with heuristic information,”
IEEE Internet of Things Journal, vol. 7, no. 10, pp. 10 450–10 464,
Oct. 2020.
[14] J. Luo, X. Deng, H. Zhang, and H. Qi, “Ultra-low latency service
provision in edge computing,” in 2018 IEEE International Conference
on Communications (ICC), 2018, pp. 1–6.
[15] F. Brandherm, L. Wang, and M. M ¨
uhlh¨
auser, “A learning-based frame-
work for optimizing service migration in mobile edge clouds,” in Pro-
ceedings of the 2nd International Workshop on Edge Systems, Analytics
and Networking - EdgeSys '19. ACM Press, 2019.
[16] H. Wang, X. Li, H. Ji, and H. Zhang, “Federated offloading scheme
to minimize latency in mec-enabled vehicular networks,” in 2018 IEEE
Globecom Workshops (GC Wkshps), 2018, pp. 1–6.
[17] R. Yadav, W. Zhang, O. Kaiwartya, H. Song, and S. Yu, “Energy-
latency tradeoff for dynamic computation offloading in vehicular fog
computing,” IEEE Transactions on Vehicular Technology, vol. 69, no. 12,
pp. 14 198–14 211, Nov. 2020.
[18] G. Cui, Y. Long, L. Xu, and W. Wang, “Joint offloading and resource
allocation for satellite assisted vehicle-to-vehicle communication,” IEEE
Systems Journal, vol. 15, no. 3, pp. 3958–3969, Sep. 2021.
[19] S. Chen, Y. Zheng, W. Lu, V. Varadarajan, and K. Wang, “Energy-
optimal dynamic computation offloading for industrial IoT in fog com-
puting,” IEEE Transactions on Green Communications and Networking,
vol. 4, no. 2, pp. 566–576, Jun. 2020.
[20] H. Wang, J. Wang, G. Ding, L. Wang, T. A. Tsiftsis, and P. K. Sharma,
“Resource allocation for energy harvesting-powered D2D communica-
tion underlaying UAV-assisted networks,” IEEE Transactions on Green
Communications and Networking, vol. 2, no. 1, pp. 14–24, Mar. 2018.
[21] Z. Ning, X. Wang, J. J. P. C. Rodrigues, and F. Xia, “Joint computation
offloading, power allocation, and channel assignment for 5G-enabled
traffic management systems,” IEEE Transactions on Industrial Infor-
matics, vol. 15, no. 5, pp. 3058–3067, May 2019.
[22] W. Lu, P. Si, Y. Gao, H. Han, Z. Liu, Y. Wu, and Y. Gong, “Trajectory
and resource optimization in OFDM-based UAV-powered IoT network,”
IEEE Transactions on Green Communications and Networking, vol. 5,
no. 3, pp. 1259–1270, Sep. 2021.
[23] Y. Dai, D. Xu, S. Maharjan, and Y. Zhang, “Joint offloading and resource
allocation in vehicular edge computing and networks,” in 2018 IEEE
Global Communications Conference (GLOBECOM), 2018, pp. 1–7.
[24] Y. Liu, H. Yu, S. Xie, and Y. Zhang, “Deep reinforcement learning
for offloading and resource allocation in vehicle edge computing and
networks,” IEEE Transactions on Vehicular Technology, vol. 68, no. 11,
pp. 11 158–11 168, Nov. 2019.
[25] J. Sun, Q. Gu, T. Zheng, P. Dong, A. Valera, and Y. Qin, “Joint
optimization of computation offloading and task scheduling in vehicular
edge computing networks,” IEEE Access, vol. 8, pp. 10 466–10 477,
2020.
[26] J. Zhao, Q. Li, Y. Gong, and K. Zhang, “Computation offloading
and resource allocation for cloud assisted mobile edge computing
in vehicular networks,” IEEE Transactions on Vehicular Technology,
vol. 68, no. 8, pp. 7944–7956, Aug. 2019.
[27] K. Zhang, Y. Zhu, S. Leng, Y. He, S. Maharjan, and Y. Zhang, “Deep
learning empowered task offloading for mobile edge computing in urban
informatics,” IEEE Internet of Things Journal, vol. 6, no. 5, pp. 7635–
7647, Oct. 2019.
[28] X. Jianbin, H. Qingchun, A. Yaning, and W. Lu, “Joint task offloading
and resource allocation in vehicle-assisted multi-access edge comput-
ing,” Computer Communications, vol. 177, pp. 77–85, Sep. 2021.
[29] X. Xu, X. Zhang, X. Liu, J. Jiang, L. Qi, and M. Z. A. Bhuiyan,
“Adaptive computation offloading with edge for 5G-envisioned internet
of connected vehicles,” IEEE Transactions on Intelligent Transportation
Systems, vol. 22, no. 8, pp. 5213–5222, Aug. 2021.
[30] F. Guo, H. Zhang, H. Ji, X. Li, and V. C. M. Leung, “An efficient com-
putation offloading management scheme in the densely deployed small
cell networks with mobile edge computing,” IEEE/ACM Transactions
on Networking, vol. 26, no. 6, pp. 2651–2664, Dec. 2018.
[31] Z. Ning, P. Dong, X. Wang, L. Guo, J. J. P. C. Rodrigues, X. Kong,
J. Huang, and R. Y. K. Kwok, “Deep reinforcement learning for
intelligent internet of vehicles: An energy-efficient computational of-
floading scheme,” IEEE Transactions on Cognitive Communications and
Networking, vol. 5, no. 4, pp. 1060–1072, Dec. 2019.
[32] C. Yang, Y. Liu, X. Chen, W. Zhong, and S. Xie, “Efficient mobility-
aware task offloading for vehicular edge computing networks,” IEEE
Access, vol. 7, pp. 26 652–26 664, 2019.
[33] Z. Zhou, J. Feng, Z. Chang, and X. Shen, “Energy-efficient edge
computing service provisioning for vehicular networks: A consensus
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

12
ADMM approach,” IEEE Transactions on Vehicular Technology, vol. 68,
no. 5, pp. 5087–5099, May 2019.
[34] S. Guo, J. Liu, Y. Yang, B. Xiao, and Z. Li, “Energy-efficient dynamic
computation offloading and cooperative task scheduling in mobile cloud
computing,” IEEE Transactions on Mobile Computing, vol. 18, no. 2,
pp. 319–333, Feb. 2019.
[35] H. Sun, F. Zhou, and R. Q. Hu, “Joint offloading and computation
energy efficiency maximization in a mobile edge computing system,”
IEEE Transactions on Vehicular Technology, vol. 68, no. 3, pp. 3052–
3056, Mar. 2019.
[36] Y. Jang, J. Na, S. Jeong, and J. Kang, “Energy-efficient task offloading
for vehicular edge computing: Joint optimization of offloading and
bit allocation,” in 2020 IEEE 91st Vehicular Technology Conference
(VTC2020-Spring), 2020, pp. 1–5.
[37] C. Chen, L. Chen, L. Liu, S. He, X. Yuan, D. Lan, and Z. Chen, “Delay-
optimized V2V-based computation offloading in urban vehicular edge
computing and networks,” IEEE Access, vol. 8, pp. 18 863–18873, 2020.
[38] X. Wang, Z. Ning, S. Guo, and L. Wang, “Imitation learning enabled task
scheduling for online vehicular edge computing,” IEEE Transactions on
Mobile Computing, vol. 21, no. 2, pp. 598–611, Feb. 2022.
[39] W. Zhan, C. Luo, J. Wang, C. Wang, G. Min, H. Duan, and Q. Zhu,
“Deep-reinforcement-learning-based offloading scheduling for vehicular
edge computing,” IEEE Internet of Things Journal, vol. 7, no. 6, pp.
5449–5465, Jun. 2020.
[40] T. Lagkas, D. Klonidis, P. Sarigiannidis, and I. Tomkos, “Optimized joint
allocation of radio, optical, and MEC resources for the 5G and beyond
fronthaul,” IEEE Transactions on Network and Service Management,
vol. 18, no. 4, pp. 4639–4653, Dec. 2021.
[41] A. Ebrahimzadeh and M. Maier, “Cooperative computation offloading
in FiWi enhanced 4G HetNets using self-organizing MEC,” IEEE
Transactions on Wireless Communications, vol. 19, no. 7, pp. 4480–
4493, Jul. 2020.
[42] T. Sizer, D. Samardzija, H. Viswanathan, S. Thai Le, S. Bidkar, P. Dom,
E. Harstead, and T. Pfeiffer, “Integrated solutions for deployment of 6G
mobile networks,” Journal of Lightwave Technology, vol. 40, no. 2, pp.
346–357, Jan. 2022.
[43] H. Guo, Y. Wang, J. Liu, and N. Kato, “Super-broadband optical access
networks (OANs) in 6G: vision, architecture, and key technologies,”
IEEE Wireless Communications, pp. 1–11, 2022.
[44] C. Zhu, G. Pastor, Y. Xiao, and A. Ylajaaski, “Vehicular fog computing
for video crowdsourcing: Applications, feasibility, and challenges,” IEEE
Communications Magazine, vol. 56, no. 10, pp. 58–63, Oct. 2018.
[45] H. Lu, Q. Liu, D. Tian, Y. Li, H. Kim, and S. Serikawa, “The cognitive
internet of vehicles for autonomous driving,” IEEE Network, vol. 33,
no. 3, pp. 65–73, May/Jun. 2019.
[46] X. Lyu, H. Tian, L. Jiang, A. Vinel, S. Maharjan, S. Gjessing, and
Y. Zhang, “Selective offloading in mobile edge computing for the green
internet of things,” IEEE Network, vol. 32, no. 1, pp. 54–60, Jan./Feb.
2018.
[47] Y. Mao, C. You, J. Zhang, K. Huang, and K. B. Letaief, “A survey
on mobile edge computing: The communication perspective,” IEEE
Communications Surveys Tutorials, vol. 19, no. 4, pp. 2322–2358, 4th
Quart. 2017.
[48] W. Zhang, Y. Wen, K. Guan, D. Kilper, H. Luo, and D. O. Wu, “Energy-
optimal mobile cloud computing under stochastic wireless channel,”
IEEE Transactions on Wireless Communications, vol. 12, no. 9, pp.
4569–4581, Sep. 2013.
[49] Y. Wang, M. Sheng, X. Wang, L. Wang, and J. Li, “Mobile-edge com-
puting: Partial computation offloading using dynamic voltage scaling,”
IEEE Transactions on Communications, vol. 64, no. 10, pp. 4268–4282,
Oct. 2016.
[50] S. Bi and Y. J. Zhang, “Computation rate maximization for wireless
powered mobile-edge computing with binary computation offloading,”
IEEE Transactions on Wireless Communications, vol. 17, no. 6, pp.
4177–4190, Jun. 2018.
[51] M. Chen and Y. Hao, “Task offloading for mobile edge computing in
software defined ultra-dense network,” IEEE Journal on Selected Areas
in Communications, vol. 36, no. 3, pp. 587–597, Mar. 2018.
[52] S.-W. Ko, K. Han, and K. Huang, “Wireless networks for mobile edge
computing: Spatial modeling and latency analysis,” IEEE Transactions
on Wireless Communications, vol. 17, no. 8, pp. 5225–5240, Aug. 2018.
[53] D. Pliatsios, P. Sarigiannidis, S. Goudos, and G. K. Karagiannidis,
“Realizing 5G vision through cloud RAN: technologies, challenges, and
trends,” EURASIP Journal on Wireless Communications and Network-
ing, vol. 2018, no. 1, May 2018.
[54] S. Huang, C. Yang, S. Yin, Z. Zhang, and Y. Chu, “Latency-aware task
peer offloading on overloaded server in multi-access edge computing
system interconnected by metro optical networks,” Journal of Lightwave
Technology, vol. 38, no. 21, pp. 5949–5961, Nov. 2020.
[55] D. Pliatsios, P. Sarigiannidis, S. K. Goudos, and K. Psannis, “3D place-
ment of drone-mounted remote radio head for minimum transmission
power under connectivity constraints,” IEEE Access, vol. 8, pp. 200 338–
200 350, 2020.
Dimitrios Pliatsios (Graduate Student Member,
IEEE) received his diploma degree from the De-
partment of Electrical and Computer Engineering,
Aristotle University of Thessaloniki, Greece. Cur-
rently, he is a Ph.D. Candidate in the Department
of Electrical and Computer Engineering, University
of Western Macedonia, Kozani, Greece. His research
interests lie in the areas of wireless communications,
mobile networks, virtualization technologies, and
computer and network security, while his Ph.D.
research is funded by the Greek State Scholarship
Foundation. He has participated as a research associate of UOWM in European
and National research projects. Finally, he is a member of the IEEE and the
Technical Chamber of Greece.
Prof. Panagiotis Sarigiannidis (Member,
IEEE) is the Director of the ITHACA lab
(https://ithaca.ece.uowm.gr/), co-founder of the 1st
spin-off of the University of Western Macedonia:
MetaMind Innovations P.C. (https://metamind.gr),
and Associate Professor in the Department of
Electrical and Computer Engineering in the
University of Western Macedonia, Kozani, Greece.
He received the B.Sc. and Ph.D. degrees in
computer science from the Aristotle University of
Thessaloniki, Thessaloniki, Greece, in 2001 and
2007, respectively. He has published over 260 papers in international journals,
conferences and book chapters, including IEEE Communications Surveys and
Tutorials, IEEE Transactions on Communications, IEEE Internet of Things,
IEEE Transactions on Broadcasting, IEEE Systems Journal, IEEE Wireless
Communications Magazine, IEEE Open Journal of the Communications
Society, IEEE/OSA Journal of Lightwave Technology, IEEE Transactions
on Industrial Informatics, IEEE Access, and Computer Networks. He has
been involved in several national, European and international projects. He is
currently the project coordinator of three H2020 projects, namely a) H2020-
DS-SC7-2017 (DS-07-2017), SPEAR: Secure and PrivatE smArt gRid, b)
H2020-LC-SC3-EE-2020-1 (LC-SC3-EC-4-2020), EVIDENT: bEhaVioral
Insgihts anD Effective eNergy policy acTions, and c) H2020-ICT-2020-1
(ICT-56-2020), TERMINET: nexT gEneRation sMart INterconnectEd ioT,
while he coordinates the Operational Program MARS: sMart fArming
with dRoneS (Competitiveness, Entrepreneurship, and Innovation) and the
Erasmus+ KA2 ARRANGE-ICT: SmartROOT: Smart faRming innOvatiOn
Training. He also serves as a principal investigator in the H2020-SU-
DS-2018 (SU-DS04-2018), SDN-microSENSE: SDN-microgrid reSilient
Electrical eNergy SystEm and in three Erasmus+ KA2: a) ARRANGE-ICT:
pArtneRship foR AddressiNG mEgatrends in ICT, b) JAUNTY: Joint
undergAduate coUrses for smart eNergy managemenT sYstems, and c)
STRONG: advanced firST RespONders traininG (Cooperation for Innovation
and the Exchange of Good Practices). His research interests include
telecommunication networks, internet of things and network security. He is
an IEEE member and participates in the Editorial Boards of various journals.
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

13
Dr. Thomas D. Lagkas (Senior Member, IEEE) is
an Assistant Professor at the Department of Com-
puter Science of the International Hellenic Univer-
sity. In 2002, he graduated with honors from the
Department of Informatics, Aristotle University of
Thessaloniki, and he was awarded PhD on Wireless
Networks from the same Department in 2006. He
has been scholar of the Aristotle University Research
Committee, as well as postdoctoral scholar of the
National Scholarships Institute of Greece. His re-
search interests are in the areas of IoT communi-
cations with more than 100 publications at a number of widely recognized
international scientific journals and conferences. Dr. Lagkas is IEEE Senior
Member and Fellow of the Higher Education Academy in UK. Moreover, he
actively participates in the preparation, management, and implementation of
several EU funded research projects.
Vasileios Argyriou (Member, IEEE) received his
BSc degree in computer science from Aristotle Uni-
versity of Thessaloniki, Greece, in 2001 and his
MSc and PhD degrees from the University of Surrey,
in 2003 and2006, respectively, both in electrical
engineering working on registration. From 2001 to
2002, he held a research position at Aristotle Univer-
sity, working on image and video watermarking. He
joined the Communications and Signal Processing
(CSP) Department, Imperial College, London, in
2007, where he was a Research Fellow working on
3D object reconstruction. Now, he is a Professor at Kingston University,
working on computer vision and AI for crowd and human behaviour analysis,
computer games, entertainment, and medical applications. Also, research is
conducted on educational games and on HCI for augmented and virtual reality
(AR/VR) systems.
Alexandros-Apostolos A. Boulogeorgos (Senior
Member, IEEE) was born in Trikala, Greece, in
1988. He received the Diploma degree in electrical
and computer engineering and the Ph.D. degree in
wireless communications from the Aristotle Uni-
versity of Thessaloniki (AUTh) in 2012 and 2016,
respectively. In 2017, he joined the Department of
Digital Systems, University of Piraeus, where he
conducts research in the area of wireless commu-
nications. From October 2012 to September 2016,
he was a Teaching Assistant with the Department
of ECE, AUTh, and from February 2017, he serves as an Adjunct Professor
with the Department of ECE, University of Western Macedonia, and as an
Visiting Lecturer with the Department of Computer Science and Biomedical
Informatics and Department of Computer Science both at University of
Thessaly and with the Department of Computer Science, International Hellenic
University, Greece.
Dr Boulogeorgos has authored and coauthored more than 90 technical
papers, which were published in scientific journals and presented at prestigious
international conferences. Furthermore, he has submitted two (one national
and one European) patents. His current research interests span the area of
wireless communications and networks with emphasis in high frequency
communications, optical wireless communications, and signal processing and
communications for biomedical applications. He was awarded the Distinction
Scholarship Award from the Research Committee of AUTh in 2014, and
was recognized as an Exemplary Reviewer for IEEE COMMUNICATION
LETTERS in 2016 (top 3% of reviewers). Moreover, he was named a Top Peer
Reviewer (top 1% of reviewers) in Cross-Field and Computer Science in the
Global Peer Review Awards 2019, which was presented by the Web of Science
and Publons. Finally, in 2021, he received the best oral presentation award in
the International Conference on Modern Circuits and Systems Technologies
(MOCAST) 2021.
He has been involved as a member of organizational and technical program
committees in several IEEE and non-IEEE conferences and served as a
reviewer and guest editor in various IEEE and non-IEEE journals and
conferences. He is an IEEE Senior Member and a Member of the Technical
Chamber of Greece. He is currently an Editor for IEEE COMMUNICATIONS
LETTERS, an Associate Editor for the Frontier in Communications and
Networks, and for the MDPI Telecom.
Peristera Baziana (Member, IEEE) received her
Dr.-Ing. degree in Electrical and Computer Engi-
neering from the National Technical University of
Athens (NTUA), Greece. She is currently serving as
an Assistant Professor at the Department of Com-
puter Science and Telecommunications, University
of Thessaly, Greece. Her research interests include
optical communications, networks architectures and
transmission protocols, networks analytical model-
ing and optimization, and telecommunication net-
works simulation. She has several publications in
international journals and conferences proceedings with reviewers, related to
these fields. During the period 2000-2002, she was a research fellow of the
University of Patras, Greece, while from 2002 to 2015 she was a researcher
of the NTUA. During the period 2015-2019 she was an adjunct lecturer at the
Department of Engineering Informatics and Telecommunications, University
of Western Macedonia, Greece and at the Department of Computer Science
and Telecommunications, University of Thessaly, Greece.
This article has been accepted for publication in IEEE Transactions on Green Communications and Networking. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TGCN.2022.3189413
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/