new application task offloading algorithms for edge, fog...

Research ArticleNew Application Task Offloading Algorithms for Edge, Fog, andCloud Computing Paradigms

Sungwook Kim

Department of Computer Science, Sogang University, 35 Baekbeom-ro, Sinsu-dong, Mapo-gu, Seoul 04107, Republic of Korea

Correspondence should be addressed to Sungwook Kim; [email protected]

Received 15 March 2020; Revised 15 July 2020; Accepted 21 August 2020; Published 6 October 2020

Academic Editor: Miguel Garcia-Pineda

Copyright © 2020 Sungwook Kim. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In the last few years, we have seen an exponential increase in the number of computation-intensive applications, which haveresulted in the popularity of fog and cloud computing paradigms among smart-chip-embedded mobile devices. These devicescan partially offload computation tasks either using the fog system or using the cloud system. In this study, we design a newtask offloading scheme by considering the challenges of future edge, fog and cloud computing paradigms. To provide aneffective solution toward an appropriate task offloading problem, we focus on two cooperative bargaining gamesolutions—Tempered Aspirations Bargaining Solution (TABS) and Gupta-Livne Bargaining Solution (GLBS). To maximizethe application service quality, a proper bargaining solution should be properly selected. In the proposed scheme, the TABSmethod is used for time-sensitive offloading services, and the GLBS method is applied to ensure computation-orientedoffloading services. The primary advantage of our bargaining-based approach is to provide an axiom-based strategic solution forthe task offloading problem while dynamically responding to the current network environments. Extensive simulation studiesare conducted to demonstrate the effectiveness of the proposed scheme, and the superior performance over existing schemes isobserved. Finally, we show prime directions for future work and potential research issues.

1. Introduction

Currently, billions of smart devices connect to the Internetin the form of the Internet of Things (IoT). IoT is a world-wide network based on standard communication protocolsand a novel paradigm with access to wireless communica-tion systems. It applies various technologies to provide thepromising fifth generation (5G) service applications. Mean-while, the evolution of 5G networks is becoming a majordriving force for the growth of IoT. For the connection ofbillions of smart devices, 5G-based IoT infrastructure isexpected to have extended coverage, higher throughput,lower latency, and connection density of massive bandwidth.However, the management of such different kinds of controlcriteria is cumbersome and challenging for traditional net-work infrastructures that rely on conventional computingparadigms [1, 2].

Despite the advance in the capacity of smart devices,mobile hardware is still resource-poor compared to the sys-

tem server hardware. Constrained by battery life, storagelimitation, computation capacity, and wireless bandwidthscarcity, the resource-poor mobile devices encounter the dif-ficulty of supporting content-rich or computation-intensiveapplications such as real-time image processing for videogames, augmented reality, and location-based services. Cloudcomputing is introduced as a promising paradigm to over-come the above difficulty. By employing this cloud comput-ing method, the computing, data storage, and massinformation processing can be offloaded to the cloud serverswhile ensuring the reliability and availability of the applica-tion services. This new paradigm is termed as the Cloud ofThings (CoT), which helps in creating an extended portfolioof future network architecture [3, 4].

CoT offers an efficient computing model where systemresources can be shared as services through IoT. However,connecting to the remote cloud server causes communicationlatency, and the cloud cannot easily respond in real time tofrequent network dynamics; it turns down the expected

HindawiWireless Communications and Mobile ComputingVolume 2020, Article ID 8888074, 14 pageshttps://doi.org/10.1155/2020/8888074

https://orcid.org/0000-0003-1967-151X

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https://doi.org/10.1155/2020/8888074

advantages of CoT. Usually, mobile devices can no longerafford to wait for the varying response time of a cloud-based computation service, especially with stringentdemands on tolerated delay. Therefore, the rising tide is driv-ing toward a new technology. Fog computing is a solution tosubdue the shortcomings of cloud computing. It is a highlydistributed platform with fog computing nodes, such ascloudlets, located at the edge of the Internet. As a mobility-enhanced small-scale cloud datacenter, the main purpose ofcloudlets is arbitrating resource-intensive and interactivemobile applications with lower latency. It is a new architec-tural structure, called Fog-of-Things (FoT), which extendsthe CoT paradigm to leverage recent developments in futurenetworks [5, 6].

Initially, IoT devices had simply developed to collectand send data for analysis, but lacked system elements toperform complex computations on-site. However, recentadvancements in embedded systems-on-a-chip have signif-icantly increased the number of intelligent devices thatpossess some resources to partially run computation-intensive applications [2]. This trend has extended thepotential of IoT, and paves a way to develop a new para-digm, called the Edge-of-Things (EoT). Actually, there is ahigh possibility that CoT and FoT paradigms will encoun-ter more challenges in relation to network dynamics,resulting in a high overhead in the network response time,leading to time latency and traffic burden. In order toavoid these problems while achieving an efficient resourceutilization, the EoT paradigm may become necessary infuture network services [7].

While FoT and EoT paradigms have some similarities,there is a major difference. First, both paradigms involvepushing intelligence and processing capabilities downcloser to where services originate. Therefore, they sharesimilar objectives (i) to reduce the amount of data sentto the cloud, (ii) to decrease network and Internet latency,and (iii) to improve system response time in remotemission-critical applications. However, there is a key dif-ference between FoT and EoT; it is exactly where intelli-gence and computing power is placed. FoT pushesintelligence down to the local area network level of thenetwork architecture, processing data in a fog node orIoT gateway. This approach can achieve a number of ben-efits including on-demand service, resource pooling, andvirtualization. Metaphorically speaking, fog computing sitsbetween physical things and cloud computing, just like innature, where fog exists between the ground and clouds.Contrary to FoT, EoT pushes the intelligence, processingpower, and communication capabilities of an edge gatewayor appliance directly into devices. To ensure Quality ofExperience (QoE) in terms of latency, bandwidth, andsecurity, the applications running on the EoT paradigmwill perform actions locally before connecting to the cloud,thus reducing network overhead issues as well as securityand privacy issues. Therefore, EoT can bring new benefitssuch as early data resolution; responsive management onthe edge; and improved latency, robustness, and security.However, due to cost and energy consumption issues, edgedevices typically have limited capacities [7, 8].

Fortunately, CoT, FoT, and EoT paradigms are notincompatible in nature; in fact, they compensate each other’slimitations. More importantly, the future network concept isthe convergence of CoT, FoT, and EoT paradigms; it hasinspired us to seek a joint solution to maximize the perfor-mance of future networks. In this study, we propose a newtask offloading control scheme by considering the merits ofCoT, FoT, and EoT paradigms. Based on the combineddesign of different paradigm operations, our integratedapproach can obtain a synergy effect while attaining anappropriate performance balance. However, it is anextremely challenging work to combine the CoT, FoT, andEoT paradigms into a holistic scheme. Therefore, a new solu-tion concept is required.

Since the 1950s, game theory has been used to study stra-tegic interactions. Whenever the choices made by two ormore individuals have an effect on each other’s gains orlosses, and hence their actions, the interaction between themis game-theoretic in nature. In recent years, there has been aremarkable increase in work at the interface of game theoryand many academic research fields from economics to com-puter science. Especially, game theory has been playing anincreasingly visible role in network management, in areassuch as resource management, routing mechanism, powercontrol, and traffic modeling. There is a major reason for this;the Internet calls for analysis and design of systems that spanmultiple entities with diverging information and interests.Game theory, for all its limitations, is by far the most devel-oped theory of such interactions [9].

1.1. Motivation. The aim of this study is to propose a noveltask offloading control scheme for a hierarchical future net-work system. To tackle the task offloading problem in mixededge-fog-cloud computing, we employ the CoT, FoT, andEoT paradigms, and jointly consider the combination ofmobile devices, cloudlets, and a cloud system. They needto coexist and synthetically complement each other tomeet the diverse requirements of future networks. Toinvestigate the strategic interactions among cloud, fog,and edge computing paradigms, we formulate mobile devi-ce/cloudlet/cloud-connected cooperative games, and adoptthe Tempered Aspirations Bargaining Solution (TABS)and the Gupta-Livne Bargaining Solution (GLBS). Bothare based on bargaining solution guidelines, and each indi-vidual mobile device and its corresponding cloudlet andcloud server work cooperatively to negotiate their conflict-ing interests while guaranteeing fairness and efficiency.

The main challenge of our game-based task offloadingapproach is to retain generality for future networks. Defi-nitely, future networks will adopt new computing paradigms,and a three-layer hierarchical network system can beextended complicatedly. Therefore, CoT, FoT, and EoT par-adigms could be replaced by new computing fashions. Toadapt to these dynamics, our proposed task offloading con-trol scheme is not fixed to specific computing paradigmsbut is designed to be dynamic and flexible and can adaptivelyrespond to new future network infrastructures. This is themain advantage of our proposed scheme over the traditionaltask offloading scheme.

2 Wireless Communications and Mobile Computing

1.2. Major Contributions. To fulfill the promised advantagesof three-layer hierarchical network platforms, several tech-nical issues and challenges should be addressed. In thisstudy, our work addresses the task offloading problem byadopting TABS and GLBS. To model the interactionsamong mobile devices, cloudlets, and a cloud system, wedesign a new cooperative bargaining game process. Usingtwo different bargaining solutions, the proposed schemeeffectively allocates the hierarchical network resources ina fair-efficient manner. With self-adaptability and real-timeeffectiveness, a well-balanced solution can be obtained whileleveraging the full synergy of the CoT, FoT, and EoT para-digms. In summary, the contributions of this paper are asfollows:

(i) By employing CoT, FoT, and EoT paradigms:motivated by the future IoT environments, weassume a three-layer hierarchical network systemby employing the CoT, FoT, and EoT paradigms.Depending on the different computing characteris-tics, they work together toward an appropriatenetwork performance

(ii) Computation-intensive task offloading based onGLBS: according to GLBS, a computation-intensivetask is offloaded to fog and cloud servers. Thisapproach can investigate the potential benefit gainedfrom its delay-tolerant characteristics

(iii) Time-sensitive task offloading based on TABS: basedon TABS, the time-sensitive task is offloaded to fogand cloud servers. This approach can maximize theexpected payoff obtained from its delay-sensitivecharacteristics

(iv) Jointly designed to leverage the synergistic and com-plementary features: we explore the interaction ofGLBS and TABS methods to balance contradictoryrequirements. The main idea of our approach liesin its responsiveness to the reciprocal combinationof different bargaining solutions

(v) Reciprocal negotiation and self-adaptability: from theviewpoint of practical operations, themain features ofour bargaining-based task offloading scheme arereciprocal negotiation and self-adaptability. Underdynamic hierarchical network environments, thesecharacteristics are generic and applicable for real-world operations while ensuring a fair-efficientsolution

(vi) Performance analysis: the major challenge of ourproposed scheme is to strike the appropriate perfor-mance fairly and efficiently. A numerical simulationstudy shows that a timely effective solution isdynamically obtained based on the jointly bargain-ing solutions

Beyond the feasible combination of optimality and practi-cality, the possible advantages of our approach include adapt-ability, flexibility, and responsiveness to current network

system conditions. To the best of our knowledge, little researchhas been conducted on bargaining-based task offloading algo-rithms for future hierarchical network systems.

1.3. Organization. The remainder of this article is organizedas follows. In Section 2, some related researches about cloudand fog computing-based task offloading problems are dis-cussed. In Section 3, we provide a three-layer hierarchicalnetwork system infrastructure for the task offloading prob-lem and formulate two cooperative bargaining gamemodels for different kinds of application services. Then,we design our proposed scheme aiming at maximizingthe system performance. We also provide the primarysteps of the proposed scheme for readers’ convenience.In Section 4, we evaluate the performance of our proposedscheme through extensive simulations. Finally, concludingremarks are drawn in Section 5 with future work.

2. Related Work

Cloud, fog, and edge computing mechanisms, which arekinds of Internet-based paradigms, have attracted greatattention with a large quantity of literatures. In [10], the Fairand Energy-Minimized Task Offloading (FEMTO) algorithmis proposed based on a fairness scheduling metric, takingthree important characteristics into consideration, whichinclude the task offloading energy consumption, the fognode’s historical average energy, and fog node priority. Basedon the fairness scheduling metric, the FEMTO algorithmdetermines the task offloading solution including the targetfog node, the terminal node transmission power, and the sub-task size in a fair and energy-minimized manner. Finally,extensive simulations are carried out in a fog-enabled IoTnetwork to investigate the performance of the proposedFEMTO algorithm [10].

The article [11] studies the problem of dynamic off-loading and resource allocation with prediction in a fogcomputing system with multiple tiers. By formulating it asa stochastic network optimization problem, the PredictiveOffloading and Resource Allocation (PORA) algorithm isdeveloped. The PORA algorithm exploits predictive offload-ing to minimize power consumption with queue stabilityguarantee. Theoretical analysis and simulation results showthat the PORA algorithm incurs near-optimal power con-sumptions with a guarantee of queue stability. Furthermore,it requires only a mild value of predictive information toachieve a notable latency reduction, even with the predictionerrors [11].

Yousefpour et al. introduced a general framework forIoT-fog-cloud applications and proposed a delay-minimizingcollaboration and offloading policy for fog-capable devicesthat is aimed at reducing the service delay for IoT applications[12]. The authors developed an analytical model to evaluatetheir policy and showed how the proposed framework helpsto reduce IoT service delay. In contrast to the existingschemes, their proposed policy considers IoT-to-cloud andfog-to-cloud interactions and also employs fog-to-fog com-munications to reduce the service delay by sharing load.For load sharing, it considers not only the queue length

3Wireless Communications and Mobile Computing

but also different request types that have various processingtimes [12].

The authors in [13] designed a more efficient and securecloud storage based on fog computing. By offloading part ofthe computing and storage work to the fog servers, theReed-Solomon code is also introduced to protect the privacyof users. Therefore, data privacy can be guaranteed. Todecrease the communication cost and reduce latency, theydeveloped a differential synchronization algorithm, whichprovides a feasible solution but increases the workload onthe users’ devices and the cloud server. By offloading partof the work to the fog server, the efficiency of the entire pro-cess can be improved. Finally, the experiment results showthat their architecture is feasible and has better performancethan the other methods [13].

The Joint User equipment and Fog Optimization (JUFO)scheme is designed to minimize the energy consumption ofthe user’s equipment and fog system based on the prioritydistribution of cloud tasks while maintaining service timeconstraints [14]. It is based on the popularity distributionof cloud tasks and energy consumption model. A networksystem consisting of a user’s equipment, a fog server,and a remote cloud server is considered, where the user’sequipment sends requests for cloud services, and the fogserver and the remote cloud server process the requestedservice. In order to solve the optimization problem, theenergy consumption and service time of each networkcomponent are mathematically modeled. The advantageof the JUFO scheme comes from using the profile of eachcloud task in the optimized fog server offloading controlscheme. Simulation results show that the JUFO schemecan provide a significant savings in energy consumptionwhile supporting real-time service requirements in regionswith burdening workloads [14].

The authors in [15] proposed the Joint Radio andComputational Resource Allocation (JRCRA) scheme.The JRCRA scheme investigates a joint radio and computa-tional resource allocation problem to optimize the systemperformance and improve user satisfaction. By communicat-ing with the users, cloud providers try to find suitable fognodes for offloading users’ computation tasks, together withthe assignment of a radio spectrum, to satisfy users’ require-ments. With the objective of optimizing the users’ satisfac-tion, they formulate this joint resource allocation as a mixinteger nonlinear programming problem. Therefore, theinteractions among the IoT users, service providers, and fognodes have been modeled based on the matching gameframework, and the transmission quality, service latency,and maximum power requirement have been effectivelyaddressed. Through the simulation results, they conform thattheir proposed approach achieves the distributive, close-to-optimal performance from both the users’ perspective andthe system’s view [15].

The Hierarchical Fog-Cloud Computation Offloading(HFCCO) scheme in [16] focuses on the allocation of fog com-puting resources to the IoT users in a hierarchical comput-ing paradigm including fog and remote cloud computingservices. The major goal of this scheme is to determinethe offloading decision for each task arriving to the IoT

users, where each user is interested in maximizing its ownQoE. Utilizing a potential game model, the HFCCO schemeproves the existence of a pure Nash Equilibrium (NE) anddevelops an algorithm to obtain NE. To mitigate the timecomplexity of obtaining NE, a near-optimal resource alloca-tion algorithm is also provided and shows that it reaches ε-NE in polynomial time. Numerical analysis shows that theIoT users can obtain a higher QoE, and the computation timeof delay-sensitive IoT applications is reduced significantlywhen utilizing the computing resources of fog nodes. Theseresults demonstrate the ability of fog nodes in providinglow-latency computing services in IoT systems [16].

In [17], the Fog-Cloud Optimal Workload Allocation(FCOWA) scheme is proposed for the tradeoff betweenpower consumption and transmission delay in the fog-cloud computing system. To provide a systematic frameworkof computation and communication codesign in the fog-cloud computing system, the FCOWA scheme models thepower consumption function and delay function of each partof the fog-cloud computing system and formulates the work-load allocation problem. This problem can be decomposedinto three subproblems of three corresponding subsystems,which are solved via existing optimization techniques. Exten-sive simulations show that the fog computing mechanismcan significantly improve the performance of the cloud com-puting mechanism while sacrificing modest computationresources to save communication bandwidth and reducetransmission latency [17].

Chen et al. developed a novel traffic-flow predictionalgorithm that is based on long short-term memory withan attention mechanism to train mobile-traffic data in asingle-site mode [18]. The proposed algorithm is capableof effectively predicting the peak value of the traffic flow.This predicted peak value is sent to a remote cloud. At theremote cloud, resources are dispatched and allocated dynam-ically based on traffic adaptation using a cognitive engine andan intelligent mobile-traffic module to balance the networkload. For a multisite case, they also presented an intelligentIoT-based mobile-traffic prediction-and-control architecturecapable of dynamically dispatching communication andcomputing resources. With the support of the cognitiveengine and mobile-traffic control modules, the mobile-traffic flow for the entire network is predicted and controlledintelligently [18].

The paper [19] proposes an intelligent task offloadingscheme, called the iTask-Offloading scheme, for a cloud-edge collaborative system. The architecture of iTask-Offloading includes the local device layer, the edge cloudlayer, the remote cloud layer, and the cognitive engine; itcan not only recognize the resources from the local device,the edge cloud, and the remote cloud, but it also under-stands the task of intelligent application. The iTask-Offloading scheme is designed to combine the cognitiveengine with the traditional cloud-edge collaborative sys-tem, and provides fine-grained task offloadings for theseparability of intelligent application tasks to enable per-sonalized task offloading. Finally, a real testbed is built toshow that the iTask-Offloading scheme has less latencythan traditional cloud computing [19].


In [20], the authors proposed a new Edge CognitiveComputing (ECC) architecture that deploys cognitive com-puting at the edge of the network to provide dynamic andelastic storage and computing services. In addition, they pro-posed an ECC-based dynamic cognitive service-migrationmechanism that considers both the elastic allocation of thecognitive computing services and user mobility, to providea mobility-aware dynamic service-adjustment scheme.Finally, they developed an ECC-based test platform to evalu-ate system performance; the results effectively demonstratethat edge cognitive computing realizes the cognitive informa-tion cycle for human-centered reasonable resource distribu-tion and optimization [20].

Chen and Hao investigated the task offloading problemin an ultradense network aiming to minimize the delaywhile saving the battery life of a user’s equipment [21].Specifically, they formulated a task offloading problem asa mixed integer nonlinear program and transformed thisoptimization problem into two subproblems, i.e., a taskplacement subproblem and a resource allocation subprob-lem. Based on the solution of the two subproblems, theyproposed an efficient offloading scheme. Simulation resultshave shown that their proposed scheme is more efficientcompared to the random and uniform computation off-loading schemes [21].

The paper [22] proposes a new mobile cloudlet-assisted service mode named Opportunistic task Schedul-ing over Co-located Clouds (OSCC), which achieves flexi-ble cost-delay tradeoffs between the conventional remotecloud service mode and the mobile cloudlet service mode.Then, this work performs detailed analytic studies for theOSCC mode and solves the energy minimization problemby compromising between the remote cloud mode, themobile cloudlet mode, and the OSCC mode. In addition,this study introduces two different kinds of task allocationschemes, i.e., dynamic allocation and static allocation.Under both the mobile cloudlet mode and the OSCCmode, dynamic allocation exhibits lower cost than staticallocation [22].

3. The Bargaining-Game-Based TaskOffloading Algorithms

In this section, we describe the three-layer hierarchical net-work architecture based on the CoT, FoT, and EoT paradigms.It presents the different emerging technologies, which can becombined to approximate the optimal system performance.According to the cooperative game approach, we can get aneffective bargaining solution while adapting the fast changingfuture network environments.

3.1. Hierarchical Network Architecture for Task OffloadingServices. In this study, we consider a future network systemwith a hierarchical computing structure and discuss thefunctional capabilities of different computing paradigmswith their physical properties. The main objective of thehierarchical architecture is to provide a better QoE for endusers. Edge devices may either perform their tasks locally oroffload them to computing servers, which are the cloudlets

in close proximity and the remote cloud server. In our pro-posed scheme, we address the task offload problem accordingto cooperative bargaining models, which are formulated bycooperation, coordination, and collaboration of the device,the cloudlet, and the cloud server.

As shown in Figure 1, we assume a three-layer hierar-chical network system comprised of multiple IoT devices,such as smart phones, surveillance cameras, personal digi-tal assistants, laptops, and on-board units, denoted as theset of EoT devices D = fD1,D2,⋯,Dng. D1≤i≤n generates

different application service requests ADi = fADi1 ,ADi

2 ,A

Di3 ,⋯g and may offload certain amounts of computing

tasks to the fog nodes, denoted as the set of cloudlets F =fCL1,CL2 ⋯ ,CLmg, and one cloud server ðℂÞ. D1≤i≤n,CL1≤j≤m, and ℂ have their computation power capacities,

i.e., PDi , PCL j , and Pℂ, respectively, which can be con-sumed by a monotonic increasing function of the compu-tation amount. Whereas in reality, the PDi , PCL j , and Pℂ

resources are limited and raced. When a lot of computation-intensive applications are executed, these resources willbecome exhausted rapidly. Due to the resource scarcity, it isimpossible to guarantee all applications’ needs. To maximizethe overall system performance, it is necessary to effectivelyutilize these computation resources for different applicationrequests.

Despite the obvious advantages of using offloading ser-vices to process IoT applications, the future network systemstill suffers from the degraded QoE from service delays.Different application services not only require differentcomputation intensities, but also have different delay sensi-tivities. Since the future network system covers a large geo-graphical area from the edge device (D) to the central cloud(ℂ), the communication delay should be taken into account.According to the required QoE, various application servicescan be categorized into two classes: computation-intensiveapplications and delay-sensitive applications. To make off-loading decisions, we must consider the required QoE.Therefore, resource management strategy becomes a key fac-tor in enhancing the future network system performancewhile ensuring service constraints.

To tackle the future network task offloading problem, weadopt two cooperative bargaining solutions: Tempered Aspi-rations Bargaining Solution (TABS) and Gupta-Livne Bar-gaining Solution (GLBS) [23]. Each individual mobiledevice offloads its application task ðAÞ while partitioningthe computation amount ðΓA Þ into three parts, i.e., PD

A ,PCL

A , andPℂA ; they are assigned to its own deviceD, the cor-

responding CL , and ℂ, respectively. To adaptively partitionits ΓA , the main ideas of TABS and GLBS are applied. Basedon two bargaining solutions, we can take various benefits in afair-efficient way.

3.2. Tempered Aspirations and Gupta-Livne BargainingSolutions. Let N be the set of potential bargainers, and ℝ,ℝ+, and ℝ++ are denoted as the sets of all, nonnegative andpositive real numbers, respectively.ℝn is the n-fold Cartesianproduct of ℝ. We use conventional notation for comparisonof vectors: x ≥ y means that x1≤i≤n ≥ y1≤i≤n, x > y indicates


that x ≥ y, and x ≠ y and x≫ y means x1≤i≤n > y1≤i≤n. Let coðAÞ denote the convex hull of setA inℝn; it is mathematicallyexpressed as coðAÞ = fZ ∈ℝn ∣Z = ðα × xÞ + ðð1 − αÞ × yÞ,x, y ∈ A and α ∈ ½0, 1�g. Let cchðAÞ denote the convex andcomprehensive hull of A, cchðAÞ = fy ∈ℝn ∣ y ≤Z,Z ∈ coðAÞg. If N has more than one member, for every x ∈ℝn

and every i ∈N, define x−i = xN\fig [23, 24]. A disagreementpoint (d) is a vector d = ðd1,⋯, dnÞ that is expected to bethe result if bargainers cannot reach an agreement. A bargain-ing problem forN is a pair ðS, dÞ such that S is a bargaining setfor N , d ∈ S, and there exists an x ∈ S satisfying x≫ d. Let theaspiration vector aðS, xÞ be defined by [23].

ai S, xð Þ =max t ∈ℝ ∣ t, x−ið Þ ∈ Sf g for every i ∈N: ð1Þ

The ideal point of the problem ðS, dÞ represents bar-gainers’ expectations before bargaining negotiation and it isdefined by aðS, dÞ . Denote the family of all bargaining prob-lems for N by ΣN . The reference point r ∈ S satisfies r ≥ d. Asolution concept on ΣN is a function ϕ that associates witheach triple ðS, d, rÞ ∈ ΣN , and a unique outcome of ϕ isdenoted as ϕðS, d, rÞ ∈ S [23].

In 2011, P.V. Balakrishnana et al. proposed a new bar-gaining solution, called Tempered Aspirations BargainingSolution (TABS). With the reference point ðrÞ, TABS isdefined for every ðS, d, rÞ ∈ ΣN as [23]:

TABS S, d, rð Þ = λ∗ × a S, rð Þ½ � + 1 − λ∗ð Þ × d½ �s:t: λ∗ =max λ ∈ 0, 1½ � ∣ λ × a S, rð Þ½ �ðf

+ 1 − λð Þ × d½ �Þ ∈ Sg:ð2Þ

If a bargaining problem is translated so that the dis-agreement point is at the origin, TABS is the only pointalong the frontier of S proportional to the aspirationsvector aðS, rÞ. TABS can be axiomatically characterizedby using the following axioms: Weak Pareto-Optimality,

Symmetry, Scale Invariance axioms, r-RestrictedS-Monoto-nicity, Irrelevance of Trivial Reference Points, and S-Conti-nuity [23].

(i) Weak Pareto-Optimality (WPO): for every bargain-ing set S, define its Pareto-optimal set as POðSÞ =fy ∈ S ∣ x > y implies x ∉ Sg. Similarly, its weakPareto-optimal set is defined as WPOðSÞ = fy ∈ S ∣x≫ y implies x ∉ Sg. For every ðS, d, rÞ ∈ ΣN , ϕðS, d,rÞ ∈WPOðSÞ

(ii) Symmetry (SYM): let ΠðNÞ be the set of permuta-tions of set N . For every π ∈ΠðNÞ and every x ∈ℝN , define πðxÞ ∈ℝN as the vector such that forevery i ∈N , ðπðxÞÞπðiÞ = xi. For every X ⊆ℝN define

πðXÞ = fπðxÞ ∣ x ∈ Xg. A problem ðS, d, rÞ ∈ ΣN issaid to be symmetric if, for every π ∈ΠðNÞ, πðSÞ =S, πðdÞ = d, and πðrÞ = r. Therefore, for every ðS, d,rÞ ∈ ΣN , if ðS, d, rÞ is symmetric then, for every i, j∈N , ϕðS, d, rÞ = ϕjðS, d, rÞ

(iii) Scale Invariance (SC.INV): letL be the family of vec-tors of functions ðLiÞi∈N such that for every i ∈N,there exist mi ∈ℝ++ and bi ∈ℝ satisfying, for every t∈ℝ, LiðtÞ =mi × t + bi. For every ðS, d, rÞ ∈ ΣN andevery L ∈L , ϕðLðSÞ, LðdÞ, LðrÞÞ = LðϕðS, d, rÞÞ

(iv) r-Restricted S-Monotonicity (r-REST.S-MON): inthe presence of a reference point, the ideal point,aðS, dÞ, is substituted by the vector of aspirations,aðS, rÞ. For every ðS, d, rÞ and ðS′, d′, r′Þ ∈ ΣN , ðd,rÞ = ðd′, r′Þ, S ⊆ S′, and aðS, rÞ = aðS′, r′Þ, imply ϕðS, d, rÞ ≤ ϕðS′, d′, r′Þ

(v) Irrelevance of Trivial Reference Points (ITR):whenever introducing a reference point does notchange the bargainers’ initial aspirations aðS, dÞ,the reference point might as well be replaced bythe disagreement point. For every ðS, d, rÞ ∈ ΣN , aðS, rÞ = aðS, dÞ, imply ϕðS, d, rÞ = ϕðS, d, dÞ

Cloud server

NAPNAP

Edge devices

Edge devices

Edge devices(EoT)

Edge devices (EoT)NAP

Figure 1: The infrastructure of the three-layer hierarchical network.


(vi) S-Continuity (S-CONT): when a convergence of setsis evaluated using the Hausdorff topology, for everyfðSk, d, rÞgk ⊂ ΣN , such that lim

k→∞Sk = S and ðS, d, rÞ

∈ ΣN , limk→∞

ϕðSk, d, rÞ = ϕðS, d, rÞ

In 1988, Gupta and Livne proposed another bargainingsolution, called the Gupta-Livne Bargaining Solution (GLBS).The solution is “dual” to the TABS in the sense that itexchanges the roles played by the reference and disagreementpoints. In the Gupta-Livne approach, the disagreement pointd has no role to play as a threat in the bargain. It serves onlyto form the aspirations of the players through the construc-tion of the ideal aspiration point. For every ðS, d, rÞ ∈ ΣN ,the GLBS is defined as follows [23]:

GLBS S, d, rð Þ = λ∗ × a S, dð Þ½ � + 1 − λ∗ð Þ × r½ �s:t: λ∗ =max λ ∈ 0, 1½ � ∣ λ × a S, dð Þ½ �ðf

+ 1 − λð Þ × r½ �Þ ∈ Sg:ð3Þ

Gupta and Livne characterize their solution using thealready familiar WPO, SYM, and SC.INV, plus the followingRelevant Domain, d-REST.S-MON, and LIM.d-SENSaxioms [23]:

(i) Relevant Domain (RD): for every ðS, d, rÞ ∈ ΣN , ϕðS, d, rÞ = ϕðcchðfx ∈ Sjx ≥ dgÞ, d, rÞ. This propertystates that the outcome of the negotiation is onlyaffected by points that weakly Pareto-dominatethe disagreement point

(ii) dS-Monotonicity (d-REST. S-MON): for every ðS,d, rÞ, ðS′, d′, r′Þ ∈ ΣN , ðd, rÞ = ðd′, r′Þ, S ⊆ S′, andaðS, dÞ = aðS′, d′Þ, imply ϕðS, d, rÞ ≤ ϕðS′, d′, r′Þ.Therefore, as the bargaining set S grows, the corre-sponding aspirations must remain fixed in order topreserve monotonicity. Originally proposed for

standard bargaining problems by Roth, the d-REST.S-MON axiom can be seen as dual to r-REST.S-MON

(iii) Limitedd-Sensitivity (LIM.d-SENS): for every ðS, d,rÞ, ðS′, d′, r′Þ ∈ ΣN , ðS, rÞ = ðS′, r′Þ, and aðS, dÞ = aðS′, d′Þ, imply ϕðS, d, rÞ = ϕðS′, d′, r′Þ. This axiomwas originally labeled limited sensitivity to changesin the disagreement point. It says that if the disagree-ment point changes without altering the corre-sponding aspirations, then the outcome of thenegotiation is the same

The main difference of TABS and GLBS is the role of dis-agreement point d. In TABS, d is used as a reference vectorfrom which proportional payoffs are measured. However, inGLBS, it is used to set the ideal aspiration point. Both solu-tion concepts are illustrated in Figure 2 [23].

3.3. The Proposed Application Task Offloading Algorithms.In this study, we design two bargaining games for task off-loading services. First, the idea of TABS is adopted toimplement the time-sensitive application offloading algo-rithm. To fair-efficiently offload the task computation, the

offload decision process for ADik is formulated as a cooper-

ative bargaining game GTABS = ffDi,CL j,ℂg, fPDi ,

PCL j ,Pℂg,ADik , ΓAk , fSDi

, SCL j, Sℂg, fUDi

,UCL j,Uℂg,

rDi ,CL j ,ℂðS, xÞ, aDi ,CL j ,ℂðS, xÞg:

(i) Players: in GTABS, a smart device Di ∈D, the corre-sponding cloudlet CL j ∈ F, and the cloud server ℂare assumed as game players fDi,CL j,ℂg to pro-cess the task offloading service

(ii) Computation powers of players: Di, CL j, and ℂ

have PDi , PCL j , and Pℂ computation powers,respectively; they are assumed as total CPU capaci-ties of game players

U2

U1

S

a(S,r)

TABS (S,d,r)

Reference point r

Disagreement point

(a) TABS

U2

U1

S

a(S,r)

GLBS (S,d,r)

Reference point r

Disagreement point

(b) GLBS

Figure 2: Tempered aspirations and Gupta-Livne bargaining solutions.


(iii) Application task and computation amount: the

application ADik is generated from the Di, and total

computation amount of ADik is ΓAk

(iv) Strategies: each player has a finite computationcapacity. The set of strategies for each player con-sists of its discrete computation power levels. Let

SDi= fCDi

1≤k≤r ≤PDi ∣ fCDi1 ,⋯,CDi

r gg be Di’s

strategy set, SCL j= fCCL j

1≤k≤e ≤PCL j ∣ fCCL j

1 ,⋯,

CCL je gg be CL j’s strategy set, and Sℂ = fCℂ

1≤k≤l≤Pℂ ∣ fCℂ

1 ,⋯,Cℂl gg be ℂ’s strategy set

(v) Utility functions: Di, CL j, and ℂ players have

their own utility functions UAkDi, UAk

CL j, and UAk

ℂ ,

respectively, to process the offload service of task

ADik . Each utility function maps the player’s satis-

faction to a real number, which represents theresulting payoff in the game GTABS

(vi) Reference point: the reference point of Di, CL j,and ℂ is denoted as rDi ,CL j ,ℂðS, xÞ; it satisfies twofeatures, namely, (a) rDi ,CL j,ℂ ∈ S/WPOðSÞ, and (b)

rDi ,CL j ,ℂ > d

(vii) Aspiration point: the aspiration point of Di, CL j,and ℂ is denoted as aDi ,CL j,ℂðS, xÞ; it is defined

based on the reference point

To quantify service satisfaction, the utility functions ofplayers in TABS can be derived as follows:

UAkDi

χAkDi

� �=ψDi

ηDi

× log 1 + ηDi×χAkDi

ΓAk

! !,

UAkCL j

χAkCL j

� �=ψCL j

ηCL j

× log 1 + ηCL j×χAkCL j

ΓAk

0@

1A

0@

1A,

UAkℂ χAk

ℂ

� �=ψℂ

ηℂ× log 1 + ηℂ ×

χAkℂ

ΓAk

! !,

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

s:t: ηDi=

βDiC

PDi

ηCL j=

βCL j

C

PCL j

ηℂ =βℂC

Pℂ

ΓA k = χAkDi

+ χAkCL j

+ χAkℂ

� �:

ð4Þ

where χAkDi, χ

AkCL j

, and χAkℂ are assigned computation

amounts to Di, CL j, and ℂ, respectively. ψDi, ψCL j

, and

ψℂ are coefficient parameters to represent the QoE of Di,

CL j, and ℂ computation services, respectively. βDiC , β

CL j

C ,

and βℂC are the current computation loads of Di, CL j, and

ℂ, respectively. In the developed bargaining game, eachplayer is a member of a team willing to compromise withother players. According to their utility functions andexpected payoffs, team players make a collective decision togain a total optimal solution. In GTABS, the reference point,i.e., rDi ,CL j ,ℂðS, xÞ, is defined as follows:

rDi ,CL j,ℂ S, xð Þ = UrDi,Ur

CL j,Ur

ℂ

� �

s:t: UrDi

=UAk

DimAk� �

φD

UrCL j

=UAk

CL jmAk� �

φCL

Urℂ χAk

ℂ

� �=UAk

ℂ mAk� �φℂ

,

ð5Þ

where φD, φCL , and φℂ are the control factors to decide thereference point values of Di, CL j, and ℂ, respectively. mAk

is the minimum computation capacity for the Ak task off-loading service. In GTABS, the aspiration point of TABS, i.e.,aDi ,CL j ,ℂðS, xÞ, is defined as follows:

aDi ,CL j ,ℂ S, xð Þ = aDiS, xð Þ, aCL j

S, xð Þ, aℂ S, xð Þ� �

s:t:

aDiS, xð Þ =max t ∈ℝ ∣ t,Ur

CL j,Ur

ℂ

� �∈ S

n o

aCL jS, xð Þ =max t ∈ℝ ∣ t,Ur

Di,Ur

ℂ

� �∈ S

n o

aℂ S, xð Þ =max t ∈ℝ ∣ t,UrDi,Ur

CL j

� �∈ S

n o:

8>>>>><>>>>>:

ð6Þ

Based on the disagreement point d as a starting point, theline (L) forward of the aspiration point aDi ,CL j ,ℂðS, xÞ is

defined as follows:

L = UUAk

DiχAkDi

� �

aDiS, xð Þ =

UAkCL j

χAkCL j

� �

aCL jS, xð Þ =

UAkℂ χAk

ℂ

� �

aℂ S, xð Þ

��

8<:

9=;: ð7Þ

Simply, we can think that TABS is a weak Pareto-optimalsolution located in S as well as in line L in (7). Geometrically,TABS is the intersection point ðUAk

Diðχ∗

DiÞ,UAk

CL jðχ∗

CL jÞ,

UAkℂ ðχ∗

ℂÞÞ between the bargaining set S and line L. Therefore,TABS must satisfy


UAkDi

χ∗Di

� �

aDiS, xð Þ

0@

1A =

UAkCL j

χ∗CL j

� �

aCL jS, xð Þ

0@

1A =

UAkℂ χ∗

ℂð Þaℂ S, xð Þ

!: ð8Þ

Second, the idea of GLBS is adopted to develop thecomputation-intensive application offloading algorithm. Toadaptively offload the delay-tolerant task computation, the

offload decision process for ADik is formulated as another

cooperative game model GGLBS = ffDi,CL j,ℂg, fPDi ,PCL j ,Pℂg,ADi

k , ΓAk , fSDi, SCL j

, Sℂg, fUDi,UCL j

,Uℂg,rDi ,CL j ,ℂðS, xÞ, aDi ,CL j ,ℂðS, xÞg. In the GGLBS game, only util-

ity functions and aspiration points are defined differently,and the other game elements are the same as GTABS. InGGLBS, aDi ,CL j ,ℂðS, xÞ is dynamically calculated according to

(1), and Di, CL j, and ℂ’s utility functions for the task ADik

can be derived as follows:

where ωAkDi, ωAk

CL j, and ωAk

ℂ are computation delay factors

of Di, CL j, and ℂ, respectively. ξDiCL j

and ξDiℂ are com-

munication delay factors of CL j and ℂ, respectively. σis the system’s basic time unit for the task offloading ser-

vice. ΤAk is the time deadline of Ak. Based on the refer-ence point rDi ,CL j,ℂðS, xÞ as a starting point, the line (L)forward of the aspiration point aDi ,CL j ,ℂðS, xÞ is defined

as follows:

UAkDi

χAkDi

� �=ψDi

ηDi

× log 1 + ηDi×χAkDi

ΓAk

! !×F

AkDi

χAkDi

� �

s:t: FAkDi

χAkDi

� �=

χAkCL j

1 + ωAkDi/σ

� �� × ΓAk

, if ωAkDi

×χAkDi

mAk

!≤

χAkDi

ΓAk× ΤAk

!,

0, otherwise,

8>>><>>>:

ð9Þ

UAkCL j

χAkCL j

� �=ψCL j

ηCL j

× log 1 + ηCL j×χAkCL j

ΓAk

0@

1A

0@

1A ×F

AkCL j

χAkCL j

� �

s:t: FAkCL j

χAkCL j

� �=

χAkCL j

1 + ξDiCL j

+ ωAkCL j

� �+ ωAk

Di

� �/σ

� �� × ΓAk

, if ξDiCL j

+ ωAkCL j

� �+ ωAk

Di

� �×χAkCL j

mAk

0@

1A ≤

χAkCL j

ΓAk× ΤAk

0@

1A,

0, otherwise,

8>>><>>>:

ð10ÞUAk

ℂ χAkℂ

� �=ψℂ

ηℂ× log 1 + ηℂ ×

χAkℂ

ΓAk

! !×F

Akℂ χ

Akℂ

� �

s:t: FAkℂ χ

Akℂ

� �=

χAkℂ

1 + ξDiℂ + ω

Akℂ

� �+ ω

AkDi

� �/σ

� �� × ΓAk

, if ξDiℂ + ωAk

ℂ

� �+ ωAk

Di

� �×

χAkℂ

mAk

!≤

χAkℂ

ΓAk× ΤAk

!,

0, otherwise:

8>><>>:

ð11Þ

L = UUAk

DiχAkDi

� �−Ur

DiχAkDi

� �

aDiS, xð Þ −Ur

DiχAkDi

� � =UAk

CL jχAkCL j

� �−Ur

CL jχAkCL j

� �

aCL jS, xð Þ −Ur

CL jχAkCL j

� � =UAk

ℂ χAkℂ

� �−Ur

ℂ χAkℂ

� �

aℂ S, xð Þ −Urℂ χAk

ℂ

� ��

8<:

9=;: ð12Þ


Simply, we can think that GLBS is a weak Pareto-optimalsolution located in S as well as in line L in (12). Geometrically,GLBS is the intersection point ðUAk

Diðχ∗

DiÞ,UAk

CL jðχ∗

CL jÞ,UAk

ℂ

ðχ∗ℂÞÞbetween thebargaining setS and lineL. Therefore,GLBS

must satisfy

UAkDi

χ∗Di

� �−Ur

DiχAkDi

� ��

aDiS, xð Þ −Ur

DiχA kDi

� �� =UAk

CL jχ∗CL j

� �−Ur

CL jχAkCL j

� ��

aCL jS, xð Þ −Ur

CL jχAkCL j

� ��

=UAk

ℂ χ∗ℂð Þ −Ur

ℂ χAkℂ

� ��

aℂ S, xð Þ −Urℂ χAk

ℂ

� �� :

ð13Þ

3.4. Main Steps of Proposed Task Offloading Algorithm. Inthis study, we design a novel task offloading scheme for dif-ferent kinds of applications, which can be categorized intotwo classes according to the required QoE: computation-intensive or time-sensitive applications. Different types ofapplication services over future network systems not onlyrequire different QoE but also need different network controlstrategies. Based on different application characteristics, wedynamically select the most adaptable bargaining solution toaddress the task offloading problem. In the proposed scheme,the basic concepts of TABS and GLBS are adopted to distrib-ute the computation amount of each application task.Computation-intensive but delay-tolerant applications canbe ultimately executed without offloading services. Therefore,it is reasonable that the task offloading bargaining solution ismeasured based on the reference point as a starting point;GLBS is suitable for these services. For time-sensitive anddelay-constrained applications, it is worthless if we cannotmeet the time deadlines of applications. Therefore, it is appro-priate that the task offloading bargaining solution is measuredbased on the disagreement point as a starting point; TABS isappropriate for these services. By a sophisticated combinationof these two bargaining solutions, our cooperative game-basedapproach approximates a well-balanced performance amongconflicting requirements. The primary steps of the proposedscheme are described as follows, and they are described bythe following Figure 3:

Step 1. Control parameters and system factors are deter-mined by the simulation scenario in Section 4 and Table 1.

Step 2. At each time period, individual mobile devicesD gen-erate application tasks; different kinds of applications areequally generated.

Step 3. If a computation-intensive applicationA is generated,the GLBS is used to process the task offloading service.According to (1), (3), (9)-(12), and (13), the computationamount ΓA of an application task is effectively distributedto D, CL , and ℂ.

Step 4. If a time-sensitive applicationA is generated, TABS isused to process the task offloading service. According to (2),

(4)–(7), and (8), the computation amount ΓA of an applica-tion task is dynamically distributed to D, CL , and ℂ.

Step 5. Based on the interactive process, the current com-putation loads of a device, a cloudlet, and cloud server,i.e., βD

C , βCLC , and βℂ

C , respectively, are monitored in areal-time online manner. This information is used to cal-culate utility functions of each game players.

Step 6. The system is constantly self-monitoring the currentnetwork situation. If a new task offloading service isrequested, it can retrigger a new bargaining process; the sys-tem proceeds to Step 3 for the next game iteration.

4. Performance Evaluation

4.1. Simulation Setup. In this section, we evaluate the perfor-mance of our proposed protocol and compare it with that ofthe JRCRA [15], HFCCO [16], FCOWA [17] schemes. Toensure a fair comparison, the following assumptions and sys-tem scenario are used:

(i) The simulated hierarchical network system consistsof 10 cloudlets (m = 10) and 100 mobile devices(n = 100).

(ii) In the offered application load situation, the arrivalprocess for new application requests is the rate ofthe Poisson process (ρ). The offered range is variedfrom 0 to 3.0

(iii) Mobile devices are distributed randomly over thenetwork coverage area, and we assume the absenceof physical obstacles in the experiments

(iv) For mobile device, cloudlet, and cloud computationcapacities, i.e.,PD,PCL , andPℂ, we assume theirCPU computing powers. They are 5GHz, 100GHz,and 1000GHz per second, respectively

(v) Each mobile device selects its corresponding cloud-let at the closest distance for the task offloadingservice

(vi) We assume that 10% ofPD,PCL , and Pℂ may beconsumed to sustain the basic operations of amobile device, a cloudlet, and a cloud server

(vii) Computation-intensive applications and time-sensitive applications are equally generated

(viii) To reduce the computation complexity, the com-putation amount is specified in terms of the basiccomputation unit, i.e.,m, where onem is the min-imum computation capacity (e.g., 100MHz) for theoffloading service. Therefore, for practical imple-mentations, the computation amount distributionis negotiated discretely by the size of one m

(ix) The hierarchical network system performancemeasures obtained on the basis of 100 simulation


Start

Control factors n, m, 𝛽, 𝜓, 𝜑, 𝜔, 𝜉, m, 𝜎, are determined by Table 1

At each time period, individual mobiledevices generate application tasks

The GLBS is used toprocess the task

offloading service

According to (1), (3),(9)–(12), and (13), thecomputation amount

of task is offloaded

The TABS is used toprocess the task

offloading service

Using (4), utilityfunctions for a smart

device, a cloudlet,and cloud server are

calculated

According to (2), (4)–(7), and (8), the

computation amountof task is offloaded

Based on the interactive process, the 𝛽CD,𝛽C

CL, and 𝛽CC values are monitored in a real-time online manner

If a generated applicationis a computation-intensive

task?

Yes No

Using (9)–(11), utilityfunctions for a smart

device, a cloudlet, andcloud server are

calculated

The system is constantly self-monitoringthe current network situation

Figure 3: Flowchart of the proposed algorithm.

Table 1: System parameters used in the simulation experiments.

(a)

Parameter Value Description

n, m 100, 10 Total number of mobile devices and fog nodes

PD , PCL , Pℂ 5, 100, 1000GHz/s The computation capacities of D, CL , and ℂ, respectively

ψD , ψCL , ψℂ 1.5, 1.75, 2 Coefficient QoE parameters of D, CL , and ℂ, respectively

φD , φCL , φℂ 0.2, 0.5, 1 Control factors to decide the reference point value rD,CL ,ℂ S, xð ÞωAD , ω

ACL , ω

Aℂ 125, 75, 50msec Computation delay factors of D, CL , and ℂ, respectively

ξDCL , ξDℂ 100, 200msec Communication delay factors of CL and ℂ, respectively

m 100MHz Basic computation unit for computation offloading service

σ 1 second The system’s basic time-unit for the task offloading service

(b)

Application type Application task Computation amount (ΓAk ) Time deadline (ΤAk )

Computation-intensive applications

Ak ∈ I 300GHz N/A

Ak ∈ II 400GHz N/A

Ak ∈ III 500GHz N/A

Time-sensitive applications

Ak ∈ IV 250GHz 5 seconds

Ak ∈V 450GHz 10 seconds

Ak ∈VI 900GHz 15 seconds


runs are plotted as functions of the Poisson pro-cess (ρ)

To demonstrate the validity of our proposed method, wemeasured the task delay-out probability, normalizedthroughput of edge devices, and fairness of edge devices fortheir payoffs. Table 1 shows the control parameters and sys-tem factors used in the simulation. These parameters and fac-tors have their own characteristics.

5. Results and Discussion

In Figure 4, we evaluate the task delay-out probability underfour methods. As a criterion of QoE assessment, the taskdelay-out probability is a measurement of howmany applica-tion tasks fail to meet their time delay constraints. It is a keyperformance evaluation factor in the future network opera-

tion. The fail ratio of all schemes is increasing with theincrease of the task request rate. It is reasonable since thehigher task requests lead to the system resource exhaustion,thus making the task delay-out probability increases. How-ever, we observe that there is a considerable performanceexcellence in the proposed scheme. Our bargaining-basedapproach can fair-efficiently share the future network systemresource to improve the service quality. Therefore, we canmaintain the stable performance superiority under differentapplication load intensities.

Normalized throughput of edge devices, which is dis-played in Figure 5, represents the resource efficiency of thehierarchical network system. This is another main criterionon the performance evaluation. As can be observed, the per-formance trend of all schemes is similar. Typically, a highersystem throughput can increase the network capacity; it ismore profitable for the system operator. In the proposedscheme, each smart device adaptively offloads its tasks tothe fog node and cloud server based on a proper bargainingsolution. Especially, we explore the reciprocal combinationof the GLBS and TABS methods to balance contradictoryrequirements. Under dynamic network system environ-ments, the possible advantages of our approach includeadaptability, flexibility, and responsiveness to current net-work system conditions. Therefore, we can effectively man-age the three-layer hierarchical network system resourcewhile satisfying desirable features, which are defined asaxioms of a selected bargaining solution. Due to this reason,we can actually distribute the system resource to increase thethroughput of mobile edge devices than the existing JRCRA,HFCCO, and FCOWA schemes.

Figure 6 depicts the fairness among edge devices. Fairnessis a prominent issue for the operation of traffic intensive net-works, and it is analogous to the social welfare for theresource allocation problem. Especially, under heavy applica-tion load environments, fairness is a highly desirable prop-erty for different edge devices. To characterize the fairnessnotion, we follow Jain’s fairness index [25], which has been

0 0.5 1 1.5 2 2.5 30

0.10.20.30.40.50.60.70.80.9

1

Offered application load (task request rate)

Task

del

ay-o

ut p

roba

bilit

y

The proposed schemeThe JRCRA schemeThe HFCCO schemeThe FCOWA scheme

Figure 4: Task delay-out probability.

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5


Nor

mal

ized

thro

ughp

ut o

f edg

e dev

ices


Figure 5: Normalized throughput of edge devices.

0.5 1 1.5 2 2.5 30

0.5

1

1.5


Fairn

ess o

f edg

e dev

ices

for t

heir

payo

ffs


Figure 6: Fairness of edge devices for their payoffs.


frequently used to measure the fairness in network manage-ment. In the proposed scheme, we adopt the basic idea ofTABS and GLBS, and share the system resource fairly whilesatisfying their fair-oriented axioms. Therefore, in our pro-posed scheme, the actual outcome is fairly dealt out amongindividual edge devices. As shown in Figure 6, the profit-sharing fairness in our approach is distinctly better comparedto the existing schemes, which are designed as lopsided andone-way methods and do not effectively consider the fairnessissue.

The simulation results shown in Figures 4–6 demonstratethat the proposed scheme can attain an appropriate perfor-mance balance. In contrast, the JRCRA [15], HFCCO [16],and FCOWA [17] schemes cannot offer this outcome underwidely different network application request situations.

6. Summary and Conclusions

In this paper, we investigate the application task offloadingproblem based on the edge, fog, and cloud computing para-digms. According to the 3-tier network hierarchy, i.e., mobiledevice-cloudlet-cloud infrastructure, the task offloadingproblem is formulated and addressed by using the coopera-tive bargaining game concept. Especially, we practically applythe TABS and GLBS methods to effectively offload the com-putation amount of each application task. By jointly consid-ering the computation intensity and delay sensitivity, weadaptively select the most suitable bargaining method in anintelligent manner. For the evolution of the future networkapplication services, our bargaining-game-based approachis attractive and appropriate to operate the real-world net-work system. The performance evaluations are presented toillustrate the effectiveness of the proposed scheme and dem-onstrate the superior performance over the existing JRCRA,HFCCO, and FCOWA schemes.

In the future, we would like to consider privacy issuessuch as the differential privacy during the task offloadingoperation. Further, we will investigate the mobile devicemobility to excellently adapt the dynamic network environ-ments. In that case, the required information exchange andcommunication overhead need to be carefully investigated.In addition, we will extend the scenario from one cloudletfog node to multiple cloudlets fog nodes when an individualapplication task is offloaded. For this future work, interfer-ence management, control overhead and load balancing willbe considered.

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request.

Conflicts of Interest

The author, Sungwook Kim, declares that there are no com-peting interests regarding the publication of this paper.

Authors’ Contributions

The author, Sungwook Kim, is the sole contributor to thisresearch work.

Acknowledgments

This research was supported by the MSIT (Ministry ofScience and ICT), Korea, under the ITRC (InformationTechnology Research Center) support program (IITP-2020-2018-0-01799) supervised by the IITP (Institute forInformation and Communications Technology Planningand Evaluation), and was supported by the Basic ScienceResearch Program through the National Research Founda-tion of Korea (NRF) funded by the Ministry of Education(NRF-2018R1D1A1A09081759).

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