a game theory based efficient computation offloading in an

4964 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 5, MAY 2019

A Game Theory Based Efficient ComputationOffloading in an UAV Network

Mohamed-Ayoub Messous , Sidi-Mohammed Senouci , Hichem Sedjelmaci , Member, IEEE,and Soumaya Cherkaoui

Abstract—Recently, solutions based on mobile edge computingparadigm have been widely discussed in academia and industry.This paradigm offers solutions to address limitations, in terms ofbattery lifetime and processing power, of mobile and constraineddevices. Despite the ever-increasing capabilities of these devices,resource requirements of applications can often transcend what isavailable within a single device. Offloading intensive computationtasks to a distant server can help applications reach their desiredperformances. In this work, we tackle the problem of offloadingheavy computation tasks of unmanned aerial vehicles (UAVs) whileachieving the best possible tradeoff between energy consumption,time delay, and computation cost. We focus on a scenario of afleet of small UAVs performing an exploration mission. Duringtheir mission, these constrained devices have to carry-out highlyintensive computation tasks such as pattern recognition and videopreprocessing. We formulate the problem using a non-cooperativetheoretical game with N players and three pure strategies. We pro-vide a comprehensive proof for the existence of a Nash equilibriumand implement accordingly a distributed algorithm that convergesto such an equilibrium. Extensive simulations are performed inorder to provide thorough results and assess the performances ofthe approach compared to three other models. Results show thatour algorithm outperforms all the three approaches. Our approachachieved in average about 19%, 58%, and 55% better results com-pared to local computing, offloading to the edge server, and offload-ing to base station, respectively.

Index Terms—Mobile edge computing, computation offloadingproblem, non-cooperative game, pure-strategies, unmanned arealvehicles (UAVs).

I. INTRODUCTION

UAVs (Unmanned Aerial Vehicles), aka drones, continueto attract much attention. Initially, relatively large drone

platforms played a prominent role in strategic and defense pro-grams. Recent technological advances have led to the emergenceof smaller significantly cheaper UAVs which made them easierto acquire, maintain and handle, thus significantly increasing

Manuscript received October 5, 2018; revised January 15, 2019; acceptedFebruary 26, 2019. Date of publication February 28, 2019; date of currentversion May 28, 2019. The review of this paper was coordinated by Prof. J.Liu. (Corresponding author: Mohamed-Ayoub Messous.)

M.-A. Messous and S.-M. Senouci are with the Departement De RechercheEn Ingenierie Des Vehicules Pour L’environnement EA 1859, UniversityBourgogne Franche Comte, Nevers F58000, France (e-mail:,[email protected]; [email protected]).

H. Sedjelmaci is with the Orange Labs, Chatillon 92320, France (e-mail:,[email protected]).

S. Cherkaoui is with the INTERLAB Research Laboratory, Universite deSherbrooke, Sherbrooke, QC J4K 0A8, Canada (e-mail:, [email protected]).

Digital Object Identifier 10.1109/TVT.2019.2902318

their usage in civilian applications. Indeed, UAVs proved to beuseful in application like rescue missions, target detection, re-mote sensing, surveillance, service delivery, pollution detectionand farming [1]–[9]. Drones can carry out exploration missionsto replace human presence in areas which are inaccessible orhazardous. They can also deliver data to and from areas withno infrastructure [2]. In fact, thanks to the maturity of their un-derlying technology, along with their three-dimensional aerialmobility, drones are expected to play an enabler role in emergingnetworks of the future as aerial base stations to collect/deliverdata from/to ground devices [3].

Even with current advances, research activities are yet toovercome some challenging issues. For instance, UAVs need todetect, classify and identify objects or situations on the spot,in order to be fully operational in surveillance applications.Besides, UAVs are brought to deal with some intensive com-putation tasks such as video preprocessing, pattern recognitionand feature extraction. These kinds of tasks typically require ex-ecuting complex algorithms and demanding calculations, whichcan be computation-intensive and call for dedicated and power-ful processors. At the same time, limited computational powerand energy supply present a major challenge for real-time dataprocessing, networking and decision-making; all requirementsof vital importance to many applications. Despite the ever-increasing capabilities of UAVs, resource requirements for ap-plications can often transcend what is available within a singleUAV. Moreover, performing intensive computation onboard anUAV may result in slow response times, can be detrimental toits battery lifetime, and ultimately can compromise mission suc-cess. In order to address issues caused by the limited resourcesand the intermittent connectivity in UAVs, a cloud-based solu-tion can be adopted [10].

Several studies recommend offloading from constrained de-vices to remote cloud/edge servers [11]–[13]. In particular, theability of providing unrestricted computing capabilities at theedge of the access networks for mobile devices, aka MobileEdge Computing (MEC), is a paradigm that has received in-creasing attention in academic and industrial communities. In-deed, MEC was revealed as a very promising concept in order toimprove network performance as well as user experience. Whenintensive computation tasks are offloaded to an ES significantperformance enhancement can be achieved [14]–[17]. Existingresearch works [14]–[17] considered computation offloading toservers located either in the cloud or at the edge of the accessnetwork. The work presented in [16] suggested using a cloudlet-

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MESSOUS et al.: GAME THEORY BASED EFFICIENT COMPUTATION OFFLOADING IN AN UAV NETWORK 4965

based infrastructure in order to reduce power consumption andnetwork delay when using mobile cloud computing. Most of theprevious studies only consider two choices for the offloading de-cision: either perform the computation locally or offload it to adistance server. Since computation services can be performedwithin different distant sureggate devices (servers), in this work,we intreduce a third choice for addressing the computation-offloading problem. Besides the obvious choice of locally ex-ecuting a computation task, UAVs in our approach have twopossible offloading choices: (i) they can send their tasks to apowerful nearby BS through a wireless local access network(WLAN), or (ii) they can send them to a more powerful serverat the edge of the cellular access network (called an ES). Theprocessing of intensive tasks will take place in one of these tworemote servers and the execution results are transmitted even-tually to their initiator device (UAV). We formulate this kind ofdecision problem using Game Theory (GT). This analytical toolhas been widely used by the wireless networking communityfor modeling different types of problems [18]. Our objective isto optimize a global utility function, which takes into accounta combination of energy consumption, delay and communica-tion cost. We design therefore a solution that achieves the bestpossible tradeoff between execution time and energy overheadwhile taking communication cost into account. In a previouswork [19], we proposed a computation offloading game for anUAV network in a mobile edge computing environment. Thismanuscript presents an extension of our previous paper. In con-trast to the previous work, we provide an all-new design for thesystem model and the problem formulation. We further extendour study to cover a much generic usecase. Furthermore, a non-cooperative game with N players and 3 pure strategies is adoptedto model the computation offloading problem. We also give amore comprehensive proof for the existence of equilibrium andthe convergence of our distributed algorithm. We performed ex-tensive simulation work, which provided comprehensive resultsto assess the performances of our approach.

This work addresses the challenges related to real-time ap-plications where the drones are required to do computation-intensive tasks in a short amount of time. We tackle the problemof computation offloading and adopt a decentralized mecha-nism in which each drone makes the computation offloadingdecision locally. This can naturally overcome the need to imple-ment a centralized scheme with much overhead compared to adistributed scheme. The main contributions of the present paperare as follow:

� Present a new generic approach for the computation-offloading problem using UAVs in a MEC environment.

� Conceive a non-cooperative game with N players and 3pure strategies to model this decision problem.

� Design and implement a distributed algorithm, where de-cisions are made locally without a centralized entity.

The rest of the paper is organized as follows: we firstsummarize in Section II, research works that influenced ourstudy. We present in Section III the system model and theformulation of our problem. Section IV gives the details ofthe major contributions of this paper. The simulation work andthe results obtained are presented and discussed in Section V.

Finally, Section VI concludes the paper and gives some futuredirections.

II. GT BASED COMPUTATION OFFLOADING

Mobile and distributed applications are facing a rapid growthin demand on computational and storage resources. Eventhough, recent technological advances have considerably im-proved the available resources in mobile devices, they are stillnot sufficient to meet the ever-growing applications demands.The most important challenges are closely related to energymanagement and delay minimization. On the first hand, sincethe energy resource is crucial for mobile devices, its optimalmanagement is vital for network lifetime and to missions’ suc-cess. On the other hand, the time required to achieve a given taskis often very important. This motivated many previous studiesto focus primarily on minimizing delay while optimizing en-ergy [20]. The proposed solutions often offload computationaldemands to more powerful surrogate machines. The most com-mon choice is offloading computation to a neighboring serveror even to a distant cloud server through a dedicated commu-nication interface. Such solutions have significantly succeededin increasing computational capabilities of constrained devices.Nevertheless, overall response times may suffer considerablywhen many devices attempt to offload their computation taskssimultaneously. This may be primarily due to concurrent accessto constrained network resources [21]. The other reason wouldbe the size of data that needs to be offloaded, which can greatlyaffect transmission time as well as energy, especially for lessercomplex computation tasks where it is more efficient to executelocally.

In the following, we gather a set of prominent recent worksthat used theoretical game methodology to tackle computationoffloading problems. [22] presented a generic hybrid architec-ture containing a centralized cloud and a distributed MEC for anIoT environment. The authors defined a computation offloadingproblem and formulated their solution as collaborative gamebetween mobile IoT devices. Authors in [23] proposed a singlewireless channel to access an all-powerful cloud. They used anon-cooperative game model to implement a decentralized al-gorithm for offloading heavily intensive computation tasks tothe cloud servers. The players of this game are all the mobiledevices that have a computation task. Each player has two possi-ble strategies: (i) local computing or (ii) offloading to the server.The authors proved the game to be a potential game and provedits convergence. Then, they extended their model in [24] to amore general use-case scenario with multiple wireless channelsand showed that the game remains a potential game.

More recently, other noteworthy ideas were presented in [25],where the authors proposed a new paradigm for vehicular net-works in 5G communications environment. The objective wasto support data-heavy applications through a mixed-networkdeployment of small-cells, device-to device (D2D) and hetero-geneous networks combined with cloud computing capabilities.Taking advantage of graph theory modeling, the authors demon-strate the distributed nature of their model and the relationshipbetween cloudlets. Furthermore, they formulated a resource



allocation problem via a non-cooperation matrix game andsolved it though a non-linear concave optimization approach.Authors in [26] consider a dense wireless network where eachindividual device can offload computations via multiple accesspoints to a mobile cloud in order to minimize their computationcosts. The authors provided a game theoretical analysis of thisproblem while considering the set of players to be selfish. Theyproved the existence of a pure strategy Nash equilibrium andprovided an efficient algorithm for computing an equilibriumpoint. The obtained simulation results showed that the equi-librium cost was close to optimal. Likewise, authors in [27]considered a multi-user mobile cloud computing system witha computing access point where each user has multiple depen-dent tasks to process. Since a centralized optimization solutionis non-convex for the problem at hand, the authors formulatedthe problem as an offloading game in order to minimize the over-all energy cost, computation, and the maximum delay amongall users. Additionally, they showed the existence of a Nashequilibrium and proposed an algorithm to attain an equilibriumpoint. Finally, Yu et al. [28] considered a scenario where muchduplicated computation tasks are processed on specific mobileusers and computation results are shared through D2D multi-cast channels. The objective was to find an optimal networkpartition in order to minimize the overall energy consumptionfor the mobile devices. Consequently, the problem was mod-eled as a combinatorial optimization problem. Unlike the worksmentioned previously, the authors in [28] used a different gametheoretic methodology. The proposed solution was implementedusing the concepts of coalitional games in order to find a max-imum weighted bipartite matching. Simulation results showeda significant decrease in energy consumption while grantingfairness among multiple users simultaneously.

In the same context as the related works summarized above,we tackle in our study the problem of offloading highly intensivecomputation tasks in mobile devices. Furthermore, we take asuse-case of a fleet of small UAVs performing an exploration op-eration. In order to fulfill their missions, the drones are requiredto compute very intensive computation tasks, such as image pro-cessing, feature extraction and pattern recognition algorithms.Since, the small drones have limited computation capabilitiesand are powered through an onboard battery, offloading theircomputation tasks to a more powerful distant device would bevery interesting. Nevertheless, this solution is not viable for allthe possible cases, because transmission delays and the energyrequired to send data through the wireless medium can hinderperformances. Therefore, finding the right tradeoff between en-ergy consumption and delay is very tricky, especially in scenar-ios with multiple users in which the solution space can increaseexponentially. To this extent, we formulate this challenging de-cision problem using a GT methodology as a dilemma betweenenergy and delay. Besides, we also consider the communicationcost as a third decision parameter.

As far as we know, we are the first to incorporate a combi-nation of these three previous decision metrics, namely: energy,delay and cost, within the same utility function while also con-sidering three different strategies rather than just two in solvingthe computation-offloading problem. In the following sections,

we provide the details of our system model. After that, we de-scribe a non-cooperative theoretical game where the fleet ofUAVs represents the N players and each of which has threepossible different strategies: (i) local computing, (ii) offload toserver, and (iii) offload to BS. We prove also the existence ofa Nash equilibrium where no player has the incentive to devi-ate from. Moreover, we design a distributed algorithm with anemerging behavior in order to reach equilibrium.

III. SYSTEM MODEL AND PROBLEM FORMULATION

All mobile devices use an onboard battery with limited power.Therefore, an efficient management of the available energy sup-ply is vital for the device’s lifetime and consequently to thesuccess of its mission. Indeed, these constrained devices arerequired to make the most of their available resources throughtheir optimal usage. Energy consumption is an even more criti-cal issue when mobile communication is required, where mobiledevices need to exchange messages via a wireless channel. Inthis context, authors in [29] have shown that a considerableamount of energy can be saved through the usage of the rightcommunication medium. Subsequently, they argued that sinceWi-Fi technology can provide a higher data transmission ratethan traditional cellular networks, Wi-Fi would yield a shorterdata transmission time and therefore lower energy consumption.However, as recent LTE technology can offer a higher or compa-rable data rate to Wi-Fi, the energy efficient offloading problemattracts even more research interest, which is particularly truefor scenarios with two possible interfaces: LTE and Wi-Fi. Manyoffloading schemes aiming to improve the mobile devices’ en-ergy efficiency are summarized in [30]. The most basic idea is toreduce energy consumption used in transmission while grantinga bearable average transfer delay. Furthermore, the data trafficwould be offloaded through a Wi-Fi access point rather than thecellular network if the difference in transmission energy exceedsa predefined threshold. In a similar context, authors in [31] con-sidered using Wi-Fi to handle the traffic explosion problem ina vehicular network environment. They also consider reducingcommunication cost using roadside units to convey or downloaddata freely rather than more expensive cellular links.

Indeed, the problem of computation offloading is very differ-ent from the data-offloading problem. In the latter, the emphasisis on data forwarding towards a distant device, as in [30] and[31], while reducing overhead. Whereas offloading computa-tional tasks focus more on the computation and communicationdelay. However, both approaches try to optimize energy con-sumption since it is a critical resource for all mobile devices.In this context, our aim in this work is to design an optimalapproach for offloading heavy computation tasks to a less con-strained device. We consider both energy consumption and timedelay in order to provide a comprehensive approach to solve thedilemma of jointly addressing these two criteria.

This section provides the problem formulation and highlightsthe system model that we have used to implement our computa-tion offloading approach. We consider a set of drones N = {1,2, . . . , n} collocated in the same area of interest (see Figure 1).In order to achieve its mission, each UAV is required to execute



Fig. 1. System architecture.

a highly intensive and delay sensitive computation task, whilepreserving its available energy. Different choices are availablefor these constrained mobile devices. They can either: (i) per-form their tasks locally, (ii) offload them via a local wirelessconnection to a neighboring BS, or finally (iii) through a cellu-lar connection to an ES. The computational tasks that need to beexecuted are characterized by the number of CPU cycles Ci re-quired to perform the calculation and the size of necessary dataDi. Besides the input parameters necessary for the computation,the data to be sent can even include the program code if it needsto be executed remotely.

In the following subsections, we start by presenting the utilityfunction and the different inputs required to compute its values.Then, we show the communication model used by the drones inorder to communicate. Finally, we give the details related to thethree possible computation models.

A. Utility Funtion

We defined our payoff function as the combination of energyconsumption, delay time and communication cost. Since the vastmajority of mobile devices have limited energy resources, theoptimal management of this critical asset is quite beneficial forthe onboard battery lifetime. Moreover, intensive computationtasks are known to necessitate a considerable amount of timeto complete their execution, even with slightly powerful pro-cessors. The third entry for our performance metric is the com-munication cost, which would play a decisive role in choosinga suitable communication interface, because cellular networksare never freely available. Furthermore, cellular operators of-ten charge according to the amount of data transmitted, whileWi-Fi access is perceived as a local network and are mostlyfree of charge. For these reasons, we implement a global payofffunction as a joint equation of: (i) delay overhead, (ii) energyoverhead and (iii) communication cost overhead. The resultingfunction for all the users is given as:

Utility = α

N∑

i=1

T i + βN∑

i=1

Ei + γN∑

i=1

Ci (1)

Where: N is the number of tasks, T represents Time, E standsfor Energy overhead and C is the communication Cost. Addi-tionally, α, β and γ represent respectively the weighting param-eters of delay, energy consumption and communication cost,and α + β + γ = 1. Moreover, in order to form this globaloverhead metric, a specific normalization method was adoptedin order to be able to add these different measures together.Furthermore, using a weighted function provide a much higherflexibility and answer a wide range of applications with spe-cific requirements. Accordingly, depending on the envisionedapplication or even the current system status, different tasks canhave different weighting parameters. For instance, if the devicebattery is running low, the value of the weight β should beincreased in order to save more energy. Whereas, for a delaysensitive task, the weight α is increased in order to reduce thedelay. Finally, the weight γ would to be increased or decreasedaccording to the availability cellular communication offer.

B. Communication Models

Wi-Fi is the most recognized wireless technology that usesa set of standards for implementing a WLAN communication.It allows an interface between a wireless client and a BS orbetween two wireless clients. This technology has been widelyused in UAV related applications [4], [32]–[35]. For instance,[32] used Wi-Fi for achieving a flight control with a real-timedata such as photo and video transmission between UAVs anddevices on the ground. Moreover, authors in [33] have developedan UAV-carried, on-demand Wi-Fi prototype system where theUAV carries the Wi-Fi signal to the emergency areas. While tra-ditional Wi-Fi signal is transmitted around 100 meters, this newprototype for a UAV-carried system can extend the signal up to25 kilometers using special directional antennas. This line ofwork supports the feasibility of offering Wi-Fi services throughflexible UAV platforms. Another study, presented in [34], fo-cused on enhancing Wi-Fi bandwidth for communications be-tween UAV and ground stations. Furthermore, the results of theexperimental work in [35] showed the viability of using 802.11interfaces for UAV-based networking.

Since cellular access is widely spread, the small drones shownin Figure 1 are considered to have a cellular network accessalong with a second 802.11 wireless interface. This latter isused to access the BS while the connection to the ES is achievedthrough a cellular network (3G/LTE). We denote di� {0, 1, 2}as the computation offloading decision for node i. Explicitly, wehave di = 0 if n chooses to compute its task locally. Otherwise,we would have di = 1 or di = 2 if it chooses to offload thecomputation, respectively, to the ES via the cellular networkor to the BS via Wi-Fi connectivity. It worth mentioning thatif too many devices choose to offload their computation taskssimultaneously, via the same medium, some severe interferencemay incur. It leads subsequently to low data rates, which wouldnegatively affect the overall network performances. In a con-trolled environment and knowing the decisions of all the mobiledevices (d1 , d2 , . . . , dN ), it is eventually possible to computethe conceivable data rates for each node. Moreover, commu-nication delay contains the network propagation delay and the



data transmission delay. In our case, P, the network propagationdelay, is determined by transmission distance, while the datatransmission delay is jointly determined by Di , the amount ofdata being trnsfered, and Ri , the link badwidth.

C. Computation Model

For the computation aspects of the proposed approach, weconsider that each device has one or more computation intensivetasks. Each task Ti is defined through (Ci, Di) which are re-spectively the number of computation cycles required to achievea result and the size of data that needs to be forwarded. Datacan include the input parameters necessary for the computationand the program code to be executed. The devices have to de-cide whether to execute their computation tasks either locallyor offload them to a remote station. Three possible choices areavailable and for each of which a different value for the utilityfunction is assumed. The details related to how to compute thesevalues are given in the following paragraphs.

1) Local Computing: Since computation tasks in the “localcomputing” are executed locally, no actual data ought to be sentvia wireless interfaces. Therefore, the utility function wouldonly be impacted by the computation power available in thedevice, i.e., the CPU frequency which is the number of compu-tation cycles per a time unit. Subsequently, the execution timefor a task Ti = (Ci, Di) if the local CPU frequency is FLocal

CP U

is given as:

TLocal = Ci/FLocalCP U (2)

And as for the expected energy consumption, we would have:

ELocal = Ci∗eLocalCP U (3)

Where eLocalCP U is the coefficient value representing the energyconsumed per CPU cycle.

2) Offloading to the ES: The first possible offloading ap-proach is to send the computation task via a compatible cellularaccess network to the ES. This latter will compute the receivedtask instead of the mobile node. Compared to the previous op-tion, the delay or time required to obtain results for the taskbeing executed, in addition to the computation time, will incuran extra overhead. This is due to the additional time necessaryto transmit data up to the ES. Therefore, the equation for thetime function would be written as:

TES = Ci/FESCP U +Di/RCellular (4)

Where FESCP U represents the frequency of the server CPU,

which in practice is very big compared to the running frequencyfor the mobile devices’ CPUs. RCellular is the effective data rateachieved through the cellular network as given in section III.A.

When compared to mobile devices, energy resource is abun-dantly available for the server. So, for the energy cost requiredto achieve a computation task we only consider the energy re-quired for its transmission to the ES. Thus, the energy functionis given as:

EES = Di∗ecellular (5)

Where ecellular denotes the consumption coefficient requiredto send one unit of data through the cellular network to the ES.

CES = Di∗ccellular (6)

Where ccellular represents the communication cost requiredto send one unit of data through the cellular network to the ES.

3) Offloading to the BS: The third possible choice and thesecond offloading approach considered in this work is to offloadthe computation task through a wireless access point to a nearbyBS. This latter would compute the received task on behalf ofthe mobile node. In this case, the time delay and energy cost aregiven respectively as:

TBS = Ci/FBSCP U +Di/Rwi−fi (7)

and:

EBS = Ci∗eBSCP U +Di∗ewi−fi (8)

WhereFBSCP U denotes the CPU’s frequency of the BS,Rwi−f i

is the effective data rate achieved through the WLAN and eBSCP Umeasures the energy required to execute one CPU cycle. Finally,ewi−f i represents the coefficient measuring the energy neededto send one data unit through the available access point networkto the BS.

As many previous studies [23], [24], [26], we neglect thedelay overhead required to send back the computation result toits respective initiator. This is due to the fact that the size ofdata resulting from an intensive computation task is consideredvery small and eventually insignificant compared to the size ofthe input data. This assumption holds for many scenarios suchas video processing, feature extraction and pattern recognitionalgorithms, where the program codes and input parameters sizeare much bigger than the input data.

In the following sections and using the system model pre-sented above as a guideline, we will develop a decentralizedalgorithm based on a GT approach for offloading highly inten-sive computation tasks to more powerful and less constrainednetwork nodes.

IV. GT BASED DISTRIBUTED COMPUTATION

OFFLOADING STRATEGY

We tackle throughout our study the issue of implementing anefficient decentralized algorithm for the offloading of heavycomputation tasks either to an ES or to a neighboring BS.From the computation and communication models presentedin the previous section, it is clear that the decisions made by thedrones are highly coupled. This means that each locally madedecision will have a direct impact on the other devices evolv-ing in the same system. Furthermore, if a significant numberof drones choose simultaneously the same offloading strategythrough the same access network, it would have a direct im-pact on the network performances, which would subsequentlyaffect transmission data rate. Low network throughput wouldlead to higher transmission delay. Moreover, when the datarate is low, much more energy would be consumed to offloaddata. In order to get around this issue, it would be more prof-itable to use another offloading strategy or even choose a local



computation. In the aim of achieving the best possible compu-tation offloading decision, we design and implement a decen-tralized algorithm based on a non-cooperative theoretical gamemodel.

A. Computation Offloading Game

GT is a powerful tool to analyze the interactions betweenmultiple independent entities that are required to work togetherin order to achieve their own goals. Using practical examples,authors in [18] have shown how GT can be used as an enablingtool in resolving wireless networking problems. They alsosummarized the basic notions of non-cooperative games, wherethe players are the devices in the network. The first reason forchoosing GT as an enabling framework for our approach is thedecentralized nature of the decision-making process achievedby the network nodes. Since each entity may have differentrequirements and eventually does not pursue the same interest,a decentralized scheme is required where each player choosesthe best possible strategy to achieve its own goals. Thus,decentralized schemes are formulated with low complexityby leveraging the intelligence of each individual device. Theother reason is the complexity and viability of implementinga centralized approach. The optimization problem that we arefacing is fundamentally difficult. The authors in [24] proved thatthe cardinality for this resource allocation problem is similar tothe bin-packing problem, which is known to be NP-hard [36].

In GT, players ought to self-organize into a mutually satis-factory solution such that no player has the incentive to deviateunilaterally. Therefore, it would ease the burden of implement-ing a more complex centralized system. This mutually satisfac-tory solution where no player has the incentive to unilaterallychange its strategy is called a Nash Equilibrium [37]. In orderto obtain meaningful insights from our analysis study, we makethe common assumption that the number of drones does notchange during a mission [38], [39]. Similar to many previousstudies dealing with mobile cloud computing [40] and mobileedge computing [23], [24], we consider a quasi-static scenariowhere the nodes positions remain unchanged, during a periodof time, while they may move throughout different periods.

In this study, we use a strategic form non-cooperative gamedenoted as μ(N,S,U), which consists of: (i) a finite set ofplayers representing the set N = {1, . . . N}, where N is thenumber of drones in the fleet, (ii) Strategy space S, repre-senting the set of actions that each player can take. S = {s1 ,s2 , s3}, (iii) Utility function Ui for each player i. The strat-egy selected by the UAVj could be either local computing,offload to the ES or offload to the BS. Therefore, Si canbe defined as Si = {sj ; ∀ j ∈ (0 � Local computing, 1 �Offload toES, 2 � Offload toBS)}. The strategies of allthe other players excluding UAVi are denoted S−j . The utilityfunction of UAVi represents the overhead generated through oneof the previous strategies while taking into account the strategiesof all the other players. This is called a strategy profile and isdenoted (Sj , S−j ). Details about the possible values of Ui are

shown in Eq. (9).

U i (sj ,S−j) =⎧⎨

⎩

ULocal = αELocal + βTLocal + γCLocal if si = 0UES = αEES + βTES + γCES if si = 1UBS = αEBS + βTBS + γCBS if si = 2

(9)

In this type of strategic form games, the underlying assump-tion is that preferences of players are captured through the utilityfunctions, i.e., the strategy profile (s′j , S′−j ) is more profitablethan the strategy profile (s′j , S

′−j ) for the player i if and only if

Ui ′(sj ′, S−j ′) > U ′i(s

′j , S

′−j ). Moreover, players in our game

are assumed to be non-cooperative, such that each player actsindependently to improve its own utility function. They are alsoconsidered to be rational in the sense that they utilize strategieswith better utility. These three assumptions lead eventually to anequilibrium state for all the players called the Nash Equilibrium(NE), where no player has the incentive to deviate unilaterally[41], [42].

B. Nash Equilibrium

In order to achieve a stable convergence state in a non-cooperative game, all the players need to reach a common con-sensus status, namely a Nash Equilibrium. This optimal staterepresents a stable point where no player has the incentive todeviate from. This means that no player can further improve hisutility function by unilaterally changing his strategy. Further-more, a NE is a strategy profile from which no player can unilat-erally deviate and improve its payoff [41], [42]. NE representsa stable outcome for a strategic form game. When equilibriumis reached, rational players cannot deviate from this strategyprofile. This makes NE one of the most frequently used solutionconcepts for games. A formal definition is provided below.

Definition 1 (Nash Equilibrium):

A strategy profile S∗ : (s∗1, . . . s∗N) is a Nash equilibrium

⇔ U ∗i

(s∗j , S

∗−j

) ≤ Ui(sj , S

∗−j

) ∀ i ∈ N, ∀ sj ∈ S

Where N is the number of players participating in the game,S is the set of the strategies of each player and Ui is the valueof the utility function defined in eq. (9).

In order to proof the existence of a NE and eventually theconvergence of our game, we resort to the concept of potentialgames, presented for the first time in [43]. Since a potential gamehas at least one NE solution [23], [24], we can prove whether ouroffloading game may achieve a NE. Potential games are definedas non-zero-sum games in which the determination of a NE canbe equivalently posed as the optimization by all the players of asingle function, called a potential function. This latter is used foranalyzing equilibrium properties of games because all players’objectives are aligned with a global objective. Furthermore, po-tential games are special class of theoretical games in which allplayers’ preferences are coupled into the same function. Thisfeature is profitable since it makes potential games easier toanalyze and it also ensures the convergence of the game to an



equilibrium through simple dynamics. A formal definition for apotential game is given in the following.

Definition 2 (Potential Game): A game μ(N,S,U) is a po-tential game if there exist a potential function P:S→R suchthat, for all i�N, all s−j εS−j and sj , s′j εSj , Ui (sj , S−j ) −Ui (s′j , S−j )) = P (sj , S−j ) − P (s′j , S−j )

Now, in order to proof the convergence of our approach, weneed to proof the existence of a NE. Since, it has been alreadyproven that every potential game has a NE [23], [24], [44], weonly need to prove that our game μ(N,A,G) is a potential game.

Proof: A game G is a potential game if its utility function Ucan be expressed as a Potential function P (sj , S−j ). This latteris defined as.

P (sj , S−j ) − P (s′j , S ′−j ) = Ui (sj , S−j) − Ui (s′j , S ′−j)

P (sj , S−j ) = arg minsj ∈Si Ui (sj , S−j ) = ψi (S−j ) ;

P (s′j , S ′−j ) = ψi (S ′−j ) ;

Where ψi(S−j ) is the best possible payoff for a player i giventhe strategy profile S−j . It is also defined as a best-responsepotential game [44], which is equal to Eq. (10).

ψi (S−j) =

⎧⎨

⎩

arg minsj∈SiULocal, if si = 0

arg minsj∈SiUES , if si = 1

arg minsj∈SiUBS , if si = 2

(10)

μ(N,S,U) is a potential game since Eq. (10) satisfies the def-inition of a potential function and it provides an optimal so-lution that ensures the best tradeoff between a low overheadand achieving the requested task. Therefore, the NE solutionis unique and it is equal to ψi(S−j ). In the real experiment,the players choose the strategy that corresponds to the mini-mum from the three possible values of U: arg minsj ∈Si ULocal ,arg minsj ∈Si UES and arg minsj ∈Si UBS .

C. Decentrelized Offloading Algorithm

The analysis study provided above shows the stable profilefor the player’s decisions when the equilibrium is reached. Nev-ertheless, a decentralized algorithm is required to implement ourdistributed computation-offloading scheme and eventually en-able the UAVs to attain a mutually satisfactory goal. The mainidea behind our algorithm is to use the convergence propertyreached thanks to the NE theorem presented in the previous sec-tion. Since, a finite number of iterations is needed to achievethis plateau status. The decision-making process is executedsimultaneously all over the network devices before launchingthe computation tasks. Similar algorithms have been proposedfor cloudlet-based [16] and mobile cloud computing [23], [24].To implement the concurrently selfish behavior of the differentplayers, we proposed in our case a simple message exchangeprotocol. In the latter, each drone initiates a request message toupdate its status if a better strategy is attainable. Nonetheless,at each iteration, one single update request is approved via anacknowledgment message, so that only one decision is made ata time. The flowchart in Figure 2 summarizes the main steps ofthe proposed algorithm.

Fig. 2. Computation offloading algorithm.

For higher number of nodes, the concurrent nature of ourscheme and the number of iterations required to reach the equi-librium might eventually rise a scaling problem, especially invery dense networks. This issue can be handled by adopting ahierarchical multi-tier scheme in order to resolve the contention[45]. However, it should be noted that, based on the hypothe-sis initially presented in the system model section, the proposedscheme as it is currently presented does not suffer from this scal-ing issue for the following reasons: (i) Only a limited numberof UAVs can be used at the same time in the same explorationmission. (ii) In order to offload tasks to the BS, we only con-sider one wireless access point serving a predetermined numberof users in the same region (as shown in figure 1).

V. EXPERIMENTAL RESULTS AND DISCUSSIONS

We evaluate, in this section, the performances of the approachbased on a theoretic game compared to three other strategies:(i) Local Computing, (ii) Offloading to ES, and (iii) Offloadingto BS. In the first model, all the computation tasks are executedlocally. However, they are offloaded to ES via a cellular accessnetwork in the second approach and to the BS via a WLAN in thethird approach. We evaluated the system-wide overhead, whichis defined in the previous sections as a combination of delayoverhead, energy overhead and communication cost. Differentscenarios are considered in our simulation while varying eachtime the possible entries. Specifically, we evaluate the impact ofthe size of the UAV network on the performances by changingthe number of drones. Furthermore, since the global overhead isdirectly affected by the size of data that need to be transmittedand the CPU cycles required of computing a task, these two



TABLE ISIMULATION SCENARIOS

TABLE IISIMULATION PARAMETERS

Fig. 3. Average system-wide overhead.

parameters need to be taken into consideration. Therefore, westudy also the impact that data sizes and computation cycles mayhave on the overall overhead. The set of simulation scenarios andthe main simulation parameters are summarized respectively inTable I and Table II.

We consider FESCPU the CPU capability of the ES to be six

times more powerful than BS frequency FBSCPU , which is five

time more powerful than the local processing frequency FLocalCP U

available within the drone. As for energy coefficients, we se-lected realistic parameters similar to those used in the literature[46]–[49]. We consider that sending one data unit to the BSthrough the WLAN interface ewi−fi consumes more than com-puting one CPU cycle locally eLocalCP U [48]. This latter is twice theenergy consumed if the calculation is executed in the BS eBS

CPU .As for the energy coefficient of the server, we consider it un-limited, thus eES

CPU = 0. Furthermore, we consider that the useof cellular network to offload data consume 20% more energythan Wi-Fi, therefore, eCellular and ewi−fi needs 1200 units and1000 units respectively to send a single packet of data [46], [49].Finally, to introduce the communication cost in our simulation,we consider that Wi-Fi is free (Costwi−fi = 0) whereas cellularnetwork is not (Costcellular = 1 unit).

The diagram shown in Figure 3 represents the average systemwide overhead. It reveals that our approach outperforms thethree models in terms of global overhead. This is due to the fact

that our model always chooses the most efficient strategy whiletaking time overhead, energy consumption and communicationcost into consideration.

Moreover, in order to investigate the impact of the networksize on the model performances, we evaluate scenarios withdifferent number of UAV. The results shown in Figure 4(a) rep-resent the system-wide overhead achieved, when we vary thenetwork size, through our model compared to the three differentstrategies. We can notice the continuous growth in the values ofglobal overhead at the same time with the size of the network.This is quite normal, since with the increase of the numberof drones, the number of computation tasks increases accord-ingly, therefore, much more resources are needed which wouldtranslate in greater values for the system-wide overhead. Nev-ertheless, within the same graph, the values achieved throughthe theoretical game approach were always better than the threeother models. We also considered, in our evaluation study, theimpact that different computation cycles have on our approach.Thus, we performed new simulations while fixing the numberof CPU cycles Ci for each scenario and changing the size ofdata and the number of drones. We than calculated the averagevalues for the system-wide overhead that correspond to eachcomputation cycles. Results are shown in Figure 4(b). We cansee that the average system overhead achieved through our theo-retical game approach outperforms the three other models in allthe considered scenarios. The achieved results were even bet-ter for highly intensive computation tasks. Indeed, the averagesystem overhead for the theoretical game model increases muchslower, compared to other models, because as the number ofprocessing cycles increases, more UAVs choose to offload theirtasks to mitigate the computation delays of local computing.Additionally, Figure 4(b) also shows that the local computing ismost suitable for less intensive computation tasks, namely forvalues that are less than 5x106 CPU cycles. Inversely, offload-ing to server is more appropriate for highly intensive tasks withmore than 10x106 CPU cycles. Between these two intervals,local computing and both offloading strategies achieved closerperformances.

Furthermore, to evaluate the impact of data sizes that com-putation tasks need to send, we finally run different simulationswith the same data sizes while changing each time the compu-tation cycles and the number of UAVs. Figure 4(c) shows thatthe system-wide overhead increases as the data size increasesin the two offloading approaches, due to the fact that big datainduce high transmission overhead. Nevertheless, system over-head in the theoretical game approach increases slowly whendata size increases. This is because more UAVs choose to avoidthe heavy cost of offloading via wireless interfaces and computetheir tasks locally. In this last case, the size of data has a di-rect impact on communication cost, communication delay andeven the amount of energy required for packet’s transmissionusing the cellular link. Moreover, the local computing approachdelivers much better results compared to the offloading strate-gies for computation task that require transmitting more than50 × 103 packets. Whereas, offloading approaches always out-perform the local approach when the size of data is less than25 × 103 packets.



Fig. 4. Impact of different evaluation parameters on the average overhead.

Fig. 5. System wide average overhead.

The results shown in the previous figures only provide aunique angle each time. For a more comprehensive analysis ofour simulation results, we consider the impact that changingdata sizes and computation cycles at the same time may have.This duality is thoroughly examined in Figure 5 and 6, wherewe evaluate respectively the average values of overhead forthe different approaches than delay and energy for GT model.Figure 5 confirms that the GT based approach (Figure 5(d))

clearly outperforms the three other models in terms of averageoverhead. Furthermore, we notice that values of average over-head in the local computing approach (Figure 5(a)) are more cor-related with the computation intensity of tasks. Consequently,this means that the data size does not have any impact of theoverall overhead since tasks do not require to be transferredto a distant device. Whereas, both of the offloading strategiesin Figure 5(b) and Figure 5(c) are more affected by data sizes



Fig. 6. Evaluation of average delay and average energy achieved by GT based apporach.

rather than the required computation cycles. Nevertheless, sinceES has more computation power than BS, CPU cycles have lessimpact on the overhead when offloading to ES compared to of-floading to BS. Whereas, inversely data size influences moretransmitting tasks to ES rather than sending data to BS. This isbecause cellular network consumes more energy compared toWi-Fi while providing less data rate.

Since the overhead function comprises disjoint parameters, aglobal overview is still missing. In order to fully examine theperformances of the proposed model, we provide even morecomprehensive analysis in Figure 6. Specifically, we assess theimpact of the GT based approach on the communication andcomputation time in Figure 6(a) and its impact on energy con-sumption in Figure 6(b). It can be seen that a stronger correla-tion between computation complexity, expressed in CPU cycles,with average energy consumption and delay compared to datasizes. However, the size of data still has an important impactof the offloading decision. As a summery, we can say that theGT based approach made its offloading decisions based on themost efficient choice based on global overhead expressed incommunication cost, time delay and energy consumption.

VI. CONCLUSION

Thanks to the recent technological advances, UAVs are cur-rently emerging as versatile nascent paradigm that can be usedin exploration and surveillance missions. However, the corre-sponding span of applications requires very often complex com-puting in a limited amount of time. Nonetheless, on the one hand,due to the limited computation and energy resources availablewithin UAVs, time delay and energy consumption for these con-strained devices are still a major challenge. On the other hand,services and functionalities offered through the concept of mo-bile edge computing (MEC) provide feasible alternatives to mit-igate the issues facing these constrained and mobile devices. Inthis paper, we consider the problem of offloading highly inten-sive computation tasks in a fleet of small UAVs to decrease theexecution delay while optimizing the energy overhead. We for-mulate the problem using a non-cooperative theoretical gamewith N players and three pure strategies, which are: (i) localcomputing, (ii) offload to an ES, or (iii) offload to a powerfulBS. Additionally, we define an all-new utility function that com-bines energy overhead, computation and communication delayswhile taking the communication cost into account. We also

provide a comprehensive proof for the existence of a NE andimplement accordingly a distributed algorithm that convergesto such an equilibrium. To gauge the effectiveness of our pro-posal, extensive experimental work was achieved. Simulationresults show that our model outperforms other approaches, pro-vides better performances and significantly reduces the averagesystem-wide overhead.

As future direction to our work, we intend to implementand assess the performances of our computation-offloading ap-proach through a cooperative game. We plan also to furtherevaluate the impact that the weighting parameters used in ourutility function may have on the overall overhead. In the samecontext, considering a dynamic selection of the weighting pa-rameters, depending on the requirements of each computationtask, would make our scheme even more generic and provideadditional setting for the final user.

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a game theory based efficient computation offloading in an

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