Received June 27, 2020, accepted July 13, 2020, date of publication July 22, 2020, date of current version August 5, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.3011167

Energy Efficient Communication andComputation Resource Slicing for eMBBand URLLC Coexistence in 5G and BeyondYAN KYAW TUN 1, DO HYEON KIM 1, MADYAN ALSENWI 1,NGUYEN H. TRAN 2, (Senior Member, IEEE), ZHU HAN 1,3, (Fellow, IEEE),AND CHOONG SEON HONG 1, (Senior Member, IEEE)1Department of Computer Science and Engineering, Kyung Hee University, Yongin 17104, South Korea2School of Computer Science, The University of Sydney, Sydney, NSW 2006, Australia3Electrical and Computer Engineering Department, University of Houston, Houston, TX 77004, USA

Corresponding author: Choong Seon Hong (cshong@khu.ac.kr)

This work was supported in part by the Ministry of Science and ICT (MSIT), South Korea, through the Grand Information TechnologyResearch Center Support Program supervised by the Institute for Information and communications Technology Planning andEvaluation (IITP) under Grant IITP-2020-2015-0-00742, and in part by the IITP grant funded by the MSIT (Evolvable Deep LearningModel Generation Platform for Edge Computing) under Grant 2019-0-01287.

ABSTRACT Multi-access edge computing (MEC) enables mobile users to offload their computation tasksto the server located at the edge of the cellular network. Thereby, MEC prolongs the battery lifespan ofmobile devices and significantly enhances their computation capacities. However, a significant challengeis to offload the computation tasks to the MEC server in an energy-efficient manner. Meanwhile, in thefifth-generation (5G) networks, mobile users with different service requirements classified as enhancedmobile broadband (eMBB) and ultra-reliable low-latency communications (URLLC) users will coexist inthe current cellular network. Therefore, it is important to appropriately multiplex these users in the cellularnetwork. In this work, we address the issues of these two promising technologies together. Firstly, we for-mulate an energy-efficient task offloading, and scheduling of eMBB and URLLC users as a mixed-integernon-linear problem. Then, we decompose the problem into multiple sub-problems in order to transform intoconvex form and alternately solve them until converging to the desired solutions by using the block coordinatedescent (BCD) algorithm. Finally, we demonstrate numerical results to prove the superior effectiveness inthe performance of our proposed algorithm over classical existing schemes.

INDEX TERMS Multi-access edge computing (MEC), resource slicing, eMBB-URLLC coexistence, blockcoordinate descent (BCD).

I. INTRODUCTIONWith the explosive growth of the Internet of Things (IoT)devices, computation-intensive applications (e.g., Aug-mented Reality (AR), face recognition, Virtual Reality (VR),online gaming, and traffic monitoring) are appearing as anintegral part of our daily activities. However, as the compu-tation capacity (i.e., central processing unit (CPU) capacity)and battery lifetime of IoT devices are limited, processingdata on the local device becomes a challenging issue. Oneof the promising solutions to address the above argumentis the mobile cloud computing (MCC) [1], [2]. In MCC,

The associate editor coordinating the review of this manuscript and

approving it for publication was Zhenhui Yuan .

the energy consumption at the resource-constrained devicescan be reduced by offloading its computation-intensive tasksto the cloud server via a cellular network. Then, the cloudserver executes offloaded tasks and sends the output back tothe devices. However, the cloud server is far from the mobiledevices, and the delay experienced by the services at thedevices can be significantly increased. Recently, the wirelesscommunication industry and academic research communityhave introduced the new technology called multi-access edgecomputing (MEC) [3]. In MEC, a server is deployed at theedge of the radio access network, e.g., at the small cell, macrobase station, relay station, and an access point, and providescomputation services to the mobile devices [4]. Comparedwith MCC, MEC can reduce the delay of the mobile devices

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Y. K. Tun et al.: Energy Efficient Communication and Computation Resource Slicing for eMBB and URLLC Coexistence

as the computing resource is nearer to the devices than thecloud server. Notably, computation capacity of a MEC serveris limited when compared with the cloud server; therefore,efficient resource allocation in MEC system comes up asa challenge. To address this issue, several current researchworks have discussed an efficient computation-intensivetask offloading and resource allocation algorithms inMEC [5]–[8].

According to the 3GPP latest release, multiple com-munication services such as enhanced mobile broadband(eMBB), massive machine-type communications (mMTC),and ultra-reliable and low latency communication (URLLC)will be provided in 5G. To summarize, eMBB service isthe advancement of the existing mobile broadband servicein the current LTE networks with higher throughput fordelay-sensitive applications. URLLC is the new service forhighly reliable and low latency applications, e.g., self-drivingcar, industrial automotive, and remote surgery, and mMTC isfor IoT devices employed in smart city. Though new wirelessservices will be available in 5G, there remains several chal-lenging issues to be addressed. Amongst them, one crucialchallenge is to schedule services with different QoS require-ments in the existing cellular network. In the previous works,authors addressed the scheduling of eMBB and URLLC traf-fic in 5G new radio access networks [9]–[12].

A. RESEARCH CONTRIBUTIONSAll of the existing works have discussed an efficient taskoffloading, and computation resource allocation mechanismin the MEC system and further on the scheduling of theeMBB and URLLC users separately. However, these tworesearch issues are coupled because eMBB users will needhigh computation service due to their limited computationcapacity (i.e., CPU resources) and battery lifetime. In thiswork, different from the previous works, we jointly consideran energy-efficient task offloading, and multiplexing of theURLLC and eMBB users. In summary, the contributions ofthis work can be expressed as follows:

• We formulate an efficient joint task offloading, andscheduling of eMBB and URLLC users problem thatminimizes energy consumption and maximizes theachievable data rate of the eMBB users subject tothe latency of eMBB users, the CPU capacity of theMEC server, the maximum transmit power of eMBBusers, the reliability of the URLLC traffic, and theresource block allocation to the eMBB users constraints.The above optimization problem is a non-convex andNP-hard problem, which has the combinatorial com-plexity.

• To solve the proposed problem, we first relax the binaryvariable and decompose the problem into multiple sub-problems. Then, an iterative algorithm, block coordinatedescent (BCD), is applied to solve the relaxed problem.

• In the simulation section, firstly, the convergence rateof our proposed algorithm is demonstrated. Then, we

compare the performance of our proposed algorithmwith other schemes: equal resource sharing, all localcomputing, and all offloading schemes. There, our pro-posed scheme achieves a significant performance gain.

The remainder of this paper is organized as follows:Section III describes the related works and Section IIIpresents the system model and problem formulation. Theproposed solution approach for the formulated problem isintroduced in Section IV and Section V discusses the sim-ulation results. Finally, Section VI concludes the paper.

II. RELATED WORKSThe existing works can be categorized into two groups:i) energy efficient task offloading in the multi-access edgecomputing, and ii) resource slicing for eMBB and URLLCtraffic.

(i) Energy-efficient task offloading in multi-access edgecomputing: The work of [13] introduced a wirelesspowered-enabled multi-user MEC system where the wirelessaccess point integrated with multiple antennas and MECserver is installed to provide wireless power and computationresources to the mobile users in its coverage area. In [14],authors have proposed energy efficient task offloading prob-lem in the mobile edge computing-enabled radio access net-work where they considered multiple base stations scenariowith the consideration of the inter-cell interference. Then,they developed an artificial fish swarm algorithm-basedscheme to solve the proposed problem. In [15], the authorsintroduced the communication-computation tradeoff studyin the multi-server MEC system and proposed an optimaloffloading policy where each user can offload its computa-tion tasks to multiple servers at the same time. The workof [16] considered the performance guaranteed computa-tion offloading in multi-cell networks where they tried tominimize the energy consumption of the mobile users inthe network. In [17], authors introduced an efficient onlinealgorithm in order to make joint base station sleeping andcomputation task offloading decisions in the ultra densecellular networks. In this work, authors assumed that themobile edge computing servers are deployed at the macrobase stations to which mobile users offloaded their compu-tation tasks. However, authors did not take into account theinter-cell interference between the base stations. The work in[18] proposed game theory-based data offloading from themobile devices (MDs) to the MEC servers where authorsdeployed coalitions to manage MDs data offloading as wellas to demonstrate the relationship between MDs and MECservers. Then, the pricing scheme was applied to stimulatethe MDs for data offloading. In [19], the authors proposedan auction-based resource allocation problem in the hierar-chical mobile edge computing where they tired to maximizethe profit of the service providers. Moreover, the work in[20] proposed the radio and computation resource allocationproblem in the multi-access edge computing system. Then,the authors decomposed the proposed problem into upper and

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lower problems. Finally, they exploited the potential gameand evolutionary game in order to address both upper-leveland lower-level problems with the aim of minimizing thecost of the mobile users and maximizing the profit of theMEC servers. In [21], the authors proposed a hierarchicalsystem of three layers to address the problems facing in thefog computing networks. Then, they implemented the pro-posed system as the Stackelberg subgame for the interactionbetween authorized data service subscribers (ADSSs) anddata service providers (DSOs), moral hazard modeling for theinteraction between the fog nodes (FNs) and DSOs, and thestudent project allocation matching game for the interactionbetween FNs and ADSSs. The work of [22] introduced adistributed computation task offloading and radio resourceallocation problem in the mobile edge computing system.In that work, authors considered the multi-cell scenario andthe inter-cell interference was also taken into account. Then,they applied thematching game in order to solve the proposedproblem.

(ii) Resource slicing of eMBB and URLLC traffic: Thework of [23] studied the efficiency of both orthogonal andnon-orthogonal multiple access in the uplink of a multi-cellCloudRadioAccessNetwork (C-RAN) system formultiplex-ing of eMBB and URLLC users. In [10], the authors stud-ied the joint eMBB and URLLC traffic scheduling problemwith the aim of maximizing the achievable data rate of theeMBB users while satisfying the reliability constraint of theURLLC traffic. Moreover, the authors in [24] studied uplinkcommunication resource slicing for eMBB and grant-freeURLLC traffic. The work of [25] proposed a RAN slic-ing problem that enables synchronized multipoint (CoMP)transmissions for multicast eMBB and bursty URLLC ser-vice as a multi-time optimization problem. Then, the pro-posed multi-time scale problem is transformed into the mul-tiple single-time problems and the authors applied the itera-tive algorithm to address the transformed problem. In [26],the authors proposed the problem of downlink multiplexingof eMBB and URLLC traffic in the 5G networks, then,an indicator-free approach is applied to solve the problem.The authors in [27] proposed the deep reinforcement learn-ing based radio resource slicing for eMBB and URLLCtraffic. The work of [28] proposed a resource schedulingframework for eMBB and URLLC based on the puncturingapproach. They leveraged the Deep Reinforcement Learn-ing (DRL) to find the number of punctured mini-slots fromall eMBB users. Then, [29] proposed the use cases of theURLLC traffic in the 5G new radio and the authors in [30]proposed the AI-enabled radio resource slicing for eMBB andURLLC users.

In this paper, we find the critical requirements fre-quently overlooked in the previous works, and for-mulate the joint efficient computation task offloadingand scheduling of eMBB and URLLC traffic. In addi-tion, we employ the block-coordinate descent (BCD)algorithm in order to solve the proposed optimizationproblem.

III. SYSTEM MODEL AND PROBLEM FORMULATIONA. SYSTEM MODELAs shown in Fig. 1, we focus on the multiuser mobile edgecomputing system with a single base station (BS) attachedwith the MEC server and eMBB users (i.e., AR and VR)in the set {1, 2, . . . ,U} defined by U . The BS is operatingon the system bandwidth F and is orthogonally sliced [31]into two static portions, such as Fb for eMBB users andFs = F−Fb for the traffic of URLLC users. However, in thiswork, dynamic resource slicing is studied, where we considerthe scenariowith high traffic ofURLLCusers. In other words,the portion of available resourceFs is not sufficient to provideservices to all URLLC users. In such a case, the BSwill punc-ture the resource allocated to the eMBB users, meanwhileensuring the QoS requirement of each eMBB user. The frac-tion of the system bandwidth for eMBB users Fb is dividedinto a set of resource blocks (RBs) B = {1, 2, . . . ,B}, whereeach RB has bandwidth δ. Moreover, the time duration ofeach resource block is one millisecond. Here, we consider thescenario where eMBB users are required to compute differentcomputation tasks under different latency constraints. In thismultiuser MEC network, each eMBB user has a computationtask defined as γu = {du, cu,Tu}, where du is the total datasize of the input data of the eMBB user u, cu denotes the totalnumber of CPU cycles required to accomplish one bit of thecomputation task, and Tu is the maximum tolerable latencyor the execution deadline of the task of user u. We assumethat the BS has complete information on the channel stateinformation (CSI), local energy consumption, and requiredCPU cycles to execute one bit of data. We also assume that

FIGURE 1. System Model.

FIGURE 2. Communication and computation latency.

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TABLE 1. Summary of key notations.

the size of the input data of all eMBB users can be obtained bythe feedback signal [5]. For each eMBB user, its task can beexecuted locally or offloaded to the MEC server, and then theserver executes it. In this work, we consider the partial taskoffloading scenariowhere the total input data size of each useris divided into remote computing and local computing as luand (du − lu), respectively.1) Local computing: Let us define the maximum compu-

tation capacity (CPU cycles per second) of eMBB user u asf lu . If user u executes a portion of its task locally, the taskexecution time (i.e., latency) to accomplish the task is asfollows:

tLu =cu(du − lu)

f lu, ∀u ∈ U . (1)

Then, the energy consumption at eMBB user u for localcomputing can be expressed as follows:

ELu = k(f lu )2 cu(du − lu), ∀u ∈ U, (2)

where k is the system constant which depends on the chiparchitecture of the eMBB users’ device, and set as k = 5 ×10−27.

2) Mobile Edge Computing: When eMBB users offloadinput data to the MEC server, the BS will allocate resourceblocks to the eMBB users. Let us introduce a new variableybu ∈ {0, 1} as the resource block assignment variable, whichindicates whether or not resource block b is assigned to

eMBB user u:

ybu =

1, if eMBB user u is assgined to resource

block b ,0, otherwise.

(3)

Here, the minislots produced through dividing each resourceblock of the time slot are represented as M . Meanwhile,the traffic of URLLC users may happenwithin the time slot ofwhich the RBs are already allocated to the eMBB users. Dueto the hard latency requirements, the traffic of URLLC userscannot be postponed to the next time slot. Hence, the arrivingtraffic of URLLC users is scheduled in order to transmitin the next minislot and the zero transmit power for theoverlapped eMBB users. Let us consider Lm as the variablethat represents the traffic of URLLC users, which comes at aminislot, denoted by m. Lm can be represented as a Bernoullidistribution with success probability p (i.e. the likelihood ofURLLC transmission at a minislot).

There is a direct relation between the loss rate of user dataof eMBB within each time slot and the punctured resourcesof eMBB user [10]. Let wu define the weight of puncturingeMBB user u, i.e., wu ∈ [0, 1], where u ∈ U and w =(w1,w2, . . . ,wU ). The higher the wu value, the higher theprobability of eMBB users being punctured by the traffic ofURLLC users. Therefore, the achievable data rate of eMBBuser u on resource block b with puncturing weight wu is [9]:

Ru,b = δ(1− wu ×

LLmax

)log2

(1+

Pbugbu

N0

),

∀b ∈ B,∀u ∈ U, (4)

where L =∑

m∈M Lm follows the binomial distribution withparameter M and p. The maximum traffic of URLLC usersthat can be served at each time slot is represented by Lmax,Pbu and g

bu are the uplink transmit power and achieved channel

gain of eMBB user u on resource block b, respectively, andN0 represents the additive white Gaussian noise power. Thetermwu× L

Lmaxis the estimation of the punctured resources of

eMBB user u by the traffic of URLLC users. Then, the totalachievable instantaneous data rate of eMBB user u is asfollows:

Ru =B∑b=1

ybuRu,b, ∀u ∈ U . (5)

The uplink transmission delay/time of eMBB user u to theMEC server is:

tupu =luRu, ∀u ∈ U . (6)

Then, the total task execution time of eMBB user u, includ-ing the uplink transmission time (i.e., offloading time) andcomputation time at the MEC server can be expressed as:

tOffu =luRu+culuf Cu

, ∀u ∈ U, (7)

where f Cu is the CPU capacity of the MEC server that isallocated to eMBB user u. In this work, we consider weighted

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proportional allocation-based computation resource (i.e.,CPU capacity) allocation [32]. Therefore, the CPU capacityof the MEC server allocated to eMBB user u is as follows:

f Cu =lu∑Uu=1 lu

f C ,∀u ∈ U, (8)

where∑U

u=1 lu is the total offloaded data of all eMBB users,and f C is the CPU capacity of the MEC server at the BS.Finally, the energy consumption of eMBB user u for offload-ing data is calculated as:

EOffu =

B∑b=1

ybuPbuluRu,b

, ∀u ∈ U . (9)

Here, the energy consumption for downlink transmission isomitted because the data output from theMEC server is muchsmaller than the input data size.

The purpose of the URLLC scheduler is to get a URLLCplacement weight vector w so that the arriving traffic ofURLLC users can be scheduled. At the same time, the relia-bility of eMBB users transmission is considered. Dependingon the formulation intended for maximizing the total averagedata rate of eMBB users, the URLLC placement weightvector calculation has an effect on eMBB users with a lowdata rate while protecting the users with the high data rate. Forthat reason, the risk on the eMBB transmission is consideredby the URLLC scheduler in order to protect eMBB users witha low data rate. The distribution of the traffic of URLLC usersamong eMBB users by the calculated URLLC placementweight w considers the users with bad channel conditions.To incorporate this, this paper hereby describes conditionalvalue-at-risk (CVaR) as a riskmeasure because of the fact thatit captures the tail of the eMBB users’ data rate. The CVaRsupports the average of potential loss, which is more than theValue-at-Risk (VaR). β -VaR is the β -percentile distributedby random variable given as [33],

VaRβ (R) = arg infν{ν : P(R > ν) ≤ β}, (10)

where R =∑U

u=1∑B

b=1 ybuR

bu and β ∈ (0, 1). The CVaR

function is defined as the expectation of the β function ofthe worst outcomes of R:

CVaRβ (R) = E[R|R > VaRβ (R)]. (11)

Furthermore, from [33]:

ζβ (R, ν) := ν +1

1− βE[(R− ν)+], (12)

and the CVaRβ of the random variable R is formulated asfollows:

CVaRβ (R) = minν∈R

ζβ (R, ν). (13)

Moreover, we rewrite E[R] as follows:

E[R] =U∑u=1

B∑b=1

ybuδ(1− wu ×

E[L]Lmax

)log2

(1+

Pbugbu

N0

)(14)

whereE[L] = Mp. Let us consider a set of URLLC users S ={1, 2, . . . , S}. In this work, we consider that the total incom-ing traffic of the URLLC users is random, and the number ofURLLC users is a discrete finite set. Here, we consider thatthe total punctured resources to the eMBB users are equallydivided among the URLLC users. Therefore, the achievabledata rate of URLLC user s can be expressed as:

Rs =U∑u=1

B∑b=1

ybuλuS

log2

(1+

PsgsN0

), ∀s ∈ S. (15)

Then, the maximum achievable rate of URLLC users can beexpressed as:

Rurllc =S∑s=1

U∑u=1

B∑b=1

ybuλuS

log2

(1+

PsgsN0

), (16)

where λu = (δ × wu LLmax

), S is the total number of URLLCusers, Ps and gs are the transmit power and the achievablechannel gain of URLLC user s, respectively. Then, the outageprobability of URLLC traffic can be expressed as:

P(E) = Pr[Rurllc ≤ L]. (17)

B. PROBLEM FORMULATIONIn this work, we firstly allocate physical resource blocks tothe eMBB users who need to offload their computationaltasks to the MEC server. Then, we propose the risk-sensitiveapproach to assign the resource to the incoming traffic ofURLLC users, ensuring reliability constraint while minimiz-ing the risk of the eMBB users who are offloading their tasks.Here, we want to minimize the overall energy consumptionand maximize the achievable data rate of eMBB users con-sidering the reliability of URLLC users. Therefore, we canwrite an optimization problem as:

miny,l,w

(U∑u=1

EOffu +

U∑u=1

ELu

)− φ

U∑u=1

B∑b=1

ybuRu,b (18)

s.t. C1 :luRu+culuf Cu≤ Tu, u ∈ U, (19)

C2 :cu(du − lu)

f lu≤ Tu, u ∈ U , (20)

C3 : lu ≤ du, ∀u ∈ U , (21)

C4 : 0 ≤ wu ≤ 1, ∀u ∈ U, (22)

C5 : CVaRβ (R) ≤ α, (23)

C6 : Pr[Rurllc ≤ L] ≤ ε, (24)

C7 :U∑u=1

ybu ≤ 1, ∀b ∈ B, (25)

C8 : ybu ∈ {0, 1}, ∀u ∈ U,∀b ∈ B, (26)

where φ is the weight parameter. C1 and C2 represent theexecution latency constraint of the eMBB users and C3 guar-antees that the offloading data size of user u has to be lessthan the total input data size. Constraint C4 states the weightparameter for eMBB user u that can be punctured by the

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traffic of URLLC users, while constraint C5 and C6 showthe reliability constraints of eMBB users and URLLC users,respectively. Constraint C7 ensures that one resource blockcan be allocated to only one eMBB user according to theOFDMA concept. However, each eMBB user can be assignedto more than one resource block. Finally, C8 represents thebinary variable for the resource block allocation. The struc-ture of the aforementioned problem is non-convex becauseof the non-convexity nature of the energy function EOff

u inobjective function (18) and the decision variables such as y,l, and w which are coupling to each other in both objectivefunction and constraints. Moreover, it is a MINLP (mixedinteger non-linear problem) because the problem is mixedwith the continuous variables (l, w) and the binary variable y.Therefore, solving the problem mentioned above will takeexponential time complexity.

IV. PROPOSED BLOCK COORDINATE DESCENT BASEDSOLUTION APPROACHIn order to address our proposed problem, firstly, we relax theresource block allocation variable in the constraint C8 into acontinuous form, i.e., 0 ≤ ybu ≤ 1. Therefore, the problem in(18) can be rewritten as follows:

miny,l,w

(U∑u=1

EOffu +

U∑u=1

ELu

)− φ

U∑u=1

B∑b=1

ybuRu,b (27)

s.t. (C1)-(C7), (28)

C8 : ybu ∈ [0, 1], ∀b ∈ B, ∀u ∈ U . (29)

However, the problem is still non-convex because the deci-sion variables are coupling in both the objective functionand the constraints. Even though the problem is non-convex,as an example, the subproblem of optimizing variable ywhilefixing the remaining variables such as l, and w is convex.As a conclusion, the proposed problem is in the form ofa multi-convex problem. Therefore, to solve the proposedmulti-convex problem, we decompose the proposed probleminto multiple subproblems such as 1) optimal task offloadingproblem, 2) resource blocks allocation for eMBB users, and3) traffic of URLLC users scheduling problem. Then, BCDalgorithm is adopted to solve the subproblems alternately.

For any given y, andw, the optimal task offloading problemcan be presented as follows:

(P1) : minl

U∑u=1

EOffu +

U∑u=1

ELu (30)

s.t. (C1)-(C3), (31)

where (P1) is the convex problem.Proof: We first set A(l) =

∑Uu=1 E

Offu +

∑Uu=1 E

Lu .

Then, the first-order derivative of A(l) with respect to the luas follows:

dA(l)dlu=

B∑b=1

ybuPbuRbu− k(f lu )

2 cu, ∀u ∈ U . (32)

FIGURE 3. Optimization framework.

Moreover, the second-order derivative is:

d2A(l)dl2u

= 0. (33)

From (33), it is sure that the second order derivative of theobjective function A(l) is positive semi-definite. Therefore,we can conclude that the the objective function in (30) isconvex. Moreover, the constraints (C1)-(C3) are linear con-straints. Therefore, the task offloading problem, (P1), is aconvex problem.Secondly, for any given l, and w, the resource blocks

allocation problem can be described as follows:

(P2) : miny

U∑u=1

EOffu − φ

U∑u=1

B∑b=1

ybuRu,b (34)

s.t. (C1), (C7), and (C8), (35)

where (P2) is the convex problem.Proof: Let G(y) =

∑Uu=1 E

Offu − φ

∑Uu=1

∑Bb=1 y

buRu,b.

The first-order derivative ofG(y) with respect to ybu as follows:

dG(y)dybu

= PbuluRbu− φ

U∑u=1

Ru,b, ∀u ∈ U,∀b ∈ B. (36)

Then, the second-order derivative is given by:

d2G(y)d(ybu)2

= 0, (37)

where (37) demonstrates that G(y) is positive semidefinite.Therefore, we can conclude that the objective function ofthe resource blocks allocation problem in (34) is convex. Letg(ybu) =

luRu+

culuf Cu− Tu, then, we can rewrite the constraint

C2 as follows:

g(ybu) ≤ 0, u ∈ U . (38)

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The first order derivative of g(ybu) with respect to ybu is asfollows:

dg(ybu)dybu=

−lu

(ybu)2ω(1−wu× L

Lmax

)log2

(1+ Pbugbu

N0

) . (39)

Then,

d2g(ybu)d(ybu)2

=2lu

(ybu)3ω(1−wu × L

Lmax

)log2

(1+ Pbugbu

N0

) . (40)

From (40), we can see that d2g(ybu)d(ybu)2

> 0. Therefore, we canconclude that the constraint, C2, is convex [34]. Furthermore,the constraints C7 and C8 are affine. Therefore, the conclu-sion is that the resource blocks allocation problem, (P2), is aconvex problem.

Then, the traffic of URLLC users scheduling problem atgiven l, and y can be formulated as:

(P3) : minw

U∑u=1

EOffu − φ

U∑u=1

B∑b=1

ybuRu,b (41)

s.t. (C4), (C5), and (C6), (42)

where the traffic of URLLC users scheduling problem is aconvex problem.

Proof: LetH (w) be∑U

u=1 EOffu −φ

∑Uu=1

∑Bb=1 y

buRu,b.

The first-order derivative of H (w) with respect to the wu isgiven by:

dH (w)dwu

=L

Lmax

B∑b=1

ybuPbulu

ω(1− wu × LLmax

)2 log2(1+PbugbuN0

)

+φLLmax

B∑b=1

ybuω log2(1+Pbug

bu

N0), ∀u ∈ U . (43)

Then, the second-order derivative is as follows:

d2 H (w)d(wu)2

=2L2

L2max

B∑b=1

ybuPbulu

ω(1− wu × LLmax

)3 log2(1+PbugbuN0

).

(44)

From (44), we notice that d2 H (w)d(wu)2

> 0. Therefore,the objective function of the URLLC users’ traffic schedulingproblem is a convex function. In addition, the constraint C4 isaffine, and C5 and C6 are convex. Hence, the URLLC users’traffic scheduling problem is a convex problem.

We can see that all of the above subproblems are convexproblems. Therefore, we can use ECOS solver in the CVXPYto solve each subproblem.

A. COMPLEXITY OF PROPOSED SOLUTIONAlthough the objective function and feasible set arenon-convex in multiple blocks of variables, they are convex ineach block of variables. It means that when we fix two amongthree blocks of variables, the problem becomes convex in theremaining block of variables, and it is called a multi-convexproblem [35]. To solve this kind of multi-convex problem,

we apply the block coordinate descent (BCD) algorithm andit guarantees to converge to the stationary point (i.e., sub-optimal solution). According to [36], with the flexible blockupdate rule, the BCD algorithm has a sub-linear convergencerate, O(1/k), where k is the index of iteration.Likewise, even though our proposed problem is non-

convex, as an example, the subproblem of optimizing theblock of variable y while fixing the remaining blocks ofvariables such as l, and w is convex. As a conclusion, the pro-posed problem is in the form of a multi-convex problem. Thecomputation complexity of our proposed block coordinatedescent based solution approach, Algorithm 1, in a singleiteration is O(|U | × |B|) which depends on the dimensionsof the blocks of variables in each subproblem. Therefore,the total complexity (i.e., execution time) of the proposedalgorithm is K × O(|U | × |B|) where K is the total numberof iterations that the proposed algorithm takes to converge tothe suboptimal solution.

Algorithm 1 Iterative Algorithm for the Relaxed Problem

1: Initialization: Set k = 0, ε1, ε2, ε3 > 0, and initialsolutions (l(0), y(0),w(0));

2: repeat3: Compute l(k+1) from (P1) at given yk , and wk ;4: Compute y(k+1) from (P2) at given l(k+1), and wk ;5: Compute w(k+1) from (P3) at given l(k+1), and y(k+1);6: k = k + 1;7: until ‖ l(k+1) − l(k) ‖ ≤ ε1, ‖ y(k+1) − y(k) ‖ ≤ ε2, and‖ w(k+1)

− w(k)‖ ≤ ε3;

8: Then, set(l(k+1), y(k+1), w(k+1)

)as the desired solution.

V. SIMULATION RESULTSIn this section, we evaluate the performance of our pro-posed iterative algorithm-based communication and com-putation resource slicing for eMBB and URLLC users in5G networks.

A. SIMULATION SETUPTo figure out the performance of our proposed scheme,we consider a multiuser MEC system with a single BS wherethe MEC server having a maximum computation capacityof 1GHz is deployed. The maximum system bandwidth of theBS is 10MHz. The eMBBusers are randomly scatteredwithinthe radius of the cell r = 1000 m, and every eMBB user hascomputation tasks to be executed. The input data size of tasksof eMBB users and the required CPU cycles to execute onebit of input data are randomly generated between [0.1, 0.4]MB and [10, 25] cycles, respectively. Then, the maximumtolerable latency to execute a computation task of each useris between [30, 100] s. We set the maximum computationcapacity of eMBB users between [0.1, 0.72] MHz and themaximum transmit power of each eMBB user as 100 mW.In this work, we consider a small scale fading model, and the

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back noise of the system is -174 dBm/Hz. The details of theparameters used in our simulation are presented in Table 2.

TABLE 2. Summary of simulation parameters.

B. NUMERICAL RESULTSIn this section, we focus primarily on the proposed algo-rithm’s performance gain. In addition, we compare the effi-ciency of our proposed iterative algorithm with the followingtwo baseline schemes.• Equal resource sharing: The communication resource(i.e., resource blocks) and the computation capacity (i.e.,CPU capacity (cycles/s)) of the MEC server are equallyallocated to all eMBB users.

• All local computing: In this scheme, all eMBB usersexecute their computation tasks locally.

• All offloading: In this scheme, all eMBB users offloadall of their computation tasks to the MEC server.

FIGURE 4. Convergence rate of proposed algorithm.

In Fig. 4, we demonstrate the converge rate of the proposedalgorithm with 5 eMBB users where Q =

∑Uu=1 E

Offu +∑U

u=1 ELu − φ

∑Uu=1

∑Bb=1 y

buRu,b. From there, we observe

that our proposed algorithm takes 95 iterations to convergeto the optimal solution. In Fig. 5, the optimal value of Q

for a different number of eMBB users is described. More-over, we compare the performance of our proposed algorithmwith other schemes such as equal resource sharing, all localcomputing, and all offloading. Under equal resource sharingscheme, the BS allocates its physical resource blocks and thecomputation capacity of the MEC server to all eMBB usersequally, and all eMBB users execute their computation taskslocally and offload their computation tasks to theMEC serverunder all local computing and all offloading schemes. FromFig. 5, we observe that our proposed scheme outperforms theother three schemes. The performance gap between our pro-posed scheme and other schemes is higher when the numberof users increases. Therefore, our proposed scheme is moreefficient when there is a large number of users in the system.

Fig. 6 compares the total energy consumption under dif-ferent number of users through different algorithms: equalresource sharing, all local computing, all offloading and ourproposed algorithm. From Fig. 6, we observe that the energyconsumption is minimum under our proposed scheme. Thereason is that the equal allocation of resource blocks and com-putation capacity of theMEC server cannot be effective for alleMBB users. This is because all eMBB users have differentachievable channel gains and different sizes of offloaded data.

FIGURE 5. Optimal value of Q under different number of users.

FIGURE 6. Energy consumption under different number of users.

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Therefore, more resource blocks are needed to be allocated tolower channel gain users and users with the higher offloadeddata size need to get more fraction of the CPU capacity of theMEC server. Furthermore, there will not be enough resourceblocks to allocate to all eMBB users when users offload allof their computation tasks to the MEC server. Therefore,all offloading scheme is not efficient when compared withour proposed algorithm. In addition, all users’ battery life islimited, and so it is not effective for the users to perform allof their computation tasks locally.

FIGURE 7. Energy consumption under different number of resourceblocks.

Furthermore, Fig. 7 shows the energy consumption of theeMBB users under different number of resource blocks. FromFig. 7, we may note that, under all local computing scheme,energy consumption is the same even though the number ofresource blocks increases. This is because all users do notoffload their computation tasks to the MEC server and exe-cute their computation tasks locally under all local computingscheme, therefore increasing the number of resource blocksdoes not impact the users’ energy usage. Moreover, whenthe number of resource blocks is small, the users’ energyconsumption under proposed algorithm is high. However,when the number of resource blocks is large, our proposedalgorithm does perform better. This is because a user’s energyconsumption decreases according to (9) when the user’s datarate increases and the user’s data rate increases when thenumber of resource blocks allocated to it increases per (5).In conclusion, it is clear from Fig. 7 that our proposed algo-rithm outperforms equal sharing and all offloading schemes.Moreover, our proposed algorithm performs far better thanall local computing scheme when the number of resourceblocks is sufficiently large. In addition, Fig. 8 provides thetotal achievable data rate of the eMBB users under differentnumber of resource blocks. From there, we can note that thedata rate increases with an increase in the number of resourceblocks. Finally, it is clear in Fig. 8 that the attainable data rateunder our proposed algorithm is higher than that under equalsharing scheme.

FIGURE 8. Data rate of eMBB users under different number of resourceblocks.

FIGURE 9. Offloaded data size under different tolerable latencies.

Fig. 9 demonstrates the offloaded data size of the task fromeach eMBB user to the MEC server. From Fig. 9, we observethat users offload more data to the server when the tolerablelatency (i.e., computation deadline) of the task is low. It isbecause each user has limited computation capacity whencompared with the MEC server, and it is difficult for eachuser to complete their task execution within the deadline.When the tolerable latency is high enough, each eMBB userwill offload less data to the server and will do more localcomputing.

We show the optimal weight of puncturing resources ofeach eMBBusers under different traffic of URLLC users (i.e.,different p) in Fig. 10. We observe that the resource of theeMBB users has been punctured more when the incomingtraffic of URLLC users is high (i.e., higher p). As an example,the allocated resource of the eMBB user-1 will be puncturedmore in p = 0.7 when compared with p = 0.2 and p = 0.5.Moreover, we see that resources from the eMBB user-1 mustbe punctured more than from eMBB user-5. The reason isthat the achievable channel gain of user-1 is higher thanthat of user-5 or the QoS requirement of user-5 is higherthan that of user-1. Then, Fig. 11 presents the achievable

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FIGURE 10. Optimal weight of puncturing resources of eMBB users.

FIGURE 11. Data rate of URLLC users on the puncturing resource of eMBBusers.

FIGURE 12. Achieved data rate of eMBB users.

data rate of the URLLC users on the puncturing resourceof each eMBB user. We see that the achievable data rate ofthe URLLC users on the puncturing resource of user-1 ishigher than others because more resource from the user-1 ispunctured for the traffic of URLLC users. Moreover, we canobserve that the achievable data rate of the URLLC users isthe highest at p = 0.7 (i.e., highest traffic of URLLC users).

Finally, we demonstrate the achievable data rate of eMBBusers in Fig. 12. From Fig. 12, we observe that the achievabledata rate of user-5 is the highest compared with other eMBBusers. The reason is that the allocated resource of user-1 is lesspunctured when compared with the resources of other users.Moreover, it can be seen that the achievable instantaneousdata rate of all eMBB users is lowest when the incomingtraffic of URLLC users is the highest (i.e., highest p). The factis that more resources of the eMBB users will be puncturedwhen the incoming traffic of URLLC users is high.

VI. CONCLUSIONSIn this work, we have formulated an energy-efficient jointcommunication and computation resource allocation prob-lem for eMBB, and URLLC users in 5G networks. Then,we have decomposed the formulated problem into multiplesubproblems and solved them alternately until convergence.The superior effectiveness in the performance of our proposedalgorithm over other existing schemes has been proven withsimulation results. In the future, we will consider multiplebase stations scenario and take into account the power controlof the users.

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YAN KYAW TUN received the B.E. degree inmarine electrical systems and electronics engi-neering from Myanmar Maritime University,Thanlyin, Myanmar, in 2014. He is currentlypursuing the Ph.D. degree in computer scienceand engineering with Kyung Hee University,South Korea, for which he received a scholarship,in 2015. His research interests include networkeconomics, game theory, network optimization,wireless communication, wireless network virtu-

alization, mobile edge computing, and wireless resource slicing for 5G.

DO HYEON KIM received the B.S. degree incommunication engineering from Jeju NationalUniversity, in 2014, and the M.S. degree fromKyung Hee University, in 2017, where he is cur-rently pursuing the Ph.D. degree with the Depart-ment of Computer Science and Engineering. Hisresearch interests include multi-access edge com-puting and wireless network virtualization.

MADYAN ALSENWI received the B.E. and M.Sc.degrees in electronics and communications engi-neering from Cairo University, Egypt, in 2011 and2016, respectively. He is currently pursuing thePh.D. degree in computer science and engineeringwithKyungHeeUniversity, SouthKorea. Hewas aResearch Assistant under several research projectsfunded by the Egyptian Government. His researchinterests include wireless communications andnetworking, resource slicing in 5G wireless net-

works, ultra-reliable low-latency communications (URLLC), UAV-assistedwireless networks, and machine learning.

NGUYEN H. TRAN (Senior Member, IEEE)received the B.S. degree in electrical and computerengineering from the Hochiminh City Universityof Technology, in 2005, and the Ph.D. degree inelectrical and computer engineering from KyungHee University, in 2011. He was an Assistant Pro-fessor with the Department of Computer Scienceand Engineering, Kyung Hee University, from2012 to 2017. Since 2018, he has been with theSchool of Computer Science, The University of

Sydney, where he is currently a Senior Lecturer. His research interestincludes distributed computing and learning over networks. He received theBest KHU Thesis Award in engineering, in 2011, and several best paperawards, including the IEEE ICC 2016, APNOMS 2016, and IEEE ICCS2016. He receives the Korea NRF Funding for Basic Science and Research,from 2016 to 2023. He has been an Editor of the IEEE TRANSACTIONS ON

GREEN COMMUNICATIONS AND NETWORKING, since 2016.

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ZHU HAN (Fellow, IEEE) received the B.S.degree in electronic engineering from TsinghuaUniversity, in 1997, and the M.S. and Ph.D.degrees in electrical and computer engineeringfrom the University of Maryland, College Park, in1999 and 2003, respectively. From 2000 to 2002,he was a Research and Development Engineer ofJDSU, Germantown, MD, USA. From 2003 to2006, he was a Research Associate at the Univer-sity of Maryland. From 2006 to 2008, he was an

Assistant Professor at Boise State University, ID, USA. He is currently aJohn and Rebecca Moores Professor with the Electrical and Computer Engi-neering Department and the Computer Science Department, University ofHouston, TX, USA. He is also with the Department of Computer Science andEngineering, Kyung Hee University, Yongin-si, South Korea. His researchinterests include wireless resource allocation and management, wirelesscommunications and networking, game theory, big data analysis, security,and smart grid. He received the NSF Career Award, in 2010, the Fred W.Ellersick Prize of the IEEE Communication Society, in 2011, the EURASIPBest Paper Award for the Journal on Advances in Signal Processing, in 2015,the IEEE Leonard G. Abraham Prize in the field of Communications Systems(Best Paper Award in the IEEE JSAC), in 2016, and several best paperawards in IEEE conferences. He was an IEEE Communications SocietyDistinguished Lecturer, from 2015 to 2018, has been an AAAS fellow, since2019, and has been an ACMDistinguishedMember, since 2019. He has been1% highly cited researcher, since 2017, according to Web of Science. Healso received the 2021 IEEE Kiyo Tomiyasu Award, for outstanding early tomid-career contributions to technologies holding the promise of innovativeapplications, with the following citation: ‘‘for contributions to game theoryand distributed management of autonomous communication networks.’’

CHOONG SEON HONG (Senior Member, IEEE)received the B.S. and M.S. degrees in electronicengineering from Kyung Hee University, Seoul,South Korea, in 1983 and 1985, respectively, andthe Ph.D. degree from Keio University, Tokyo,Japan, in 1997. In 1988, he joined KT, Gyeonggi,South Korea, where he was involved in broadbandnetworks as a Member of Technical Staff. Since1993, he has been with Keio University. He waswith the Telecommunications Network Labora-

tory, KT, as a Senior Member of Technical Staff and as the Director of theNetworking Research Team, until 1999. Since 1999, he has been a Professorwith the Department of Computer Science and Engineering, Kyung HeeUniversity. His research interests include future Internet, intelligent edgecomputing, network management, and network security. He is a member ofthe Association for Computing Machinery (ACM), the Institute of Electron-ics, Information and Communication Engineers (IEICE), the InformationProcessing Society of Japan (IPSJ), the Korean Institute of Information Sci-entists and Engineers (KIISE), the Korean Institute of Communications andInformation Sciences (KICS), the Korean Information Processing Society(KIPS), and the Open Standards and ICT Association (OSIA). He has servedas the General Chair, the TPC Chair/Member, or an Organizing Commit-tee Member of international conferences, such as the Network Operationsand Management Symposium (NOMS), the International Symposium onIntegrated Network Management (IM), the Asia–Pacific Network Opera-tions and Management Symposium (APNOMS), End-to-End MonitoringTechniques and Services (E2EMON), the IEEE Consumer Communicationsand Networking Conference (CCNC), Assurance in Distributed Systemsand Networks (ADSN), the International Conference on Parallel Processing(ICPP), Data Integration and Mining (DIM), the World Conference on Infor-mation Security Applications (WISA), Broadband Convergence Network(BcN), Telecommunication Information Networking Architecture (TINA),the International Symposium on Applications and the Internet (SAINT), andthe International Conference on Information Networking (ICOIN). He wasan Associate Editor of the IEEE TRANSACTIONS ON NETWORK AND SERVICE

MANAGEMENT and the IEEE JOURNAL OF COMMUNICATIONS AND NETWORKS.He currently serves as an Associate Editor for the International Journalof Network Management and an Associate Technical Editor for the IEEECommunications Magazine.

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