Latency-Driven Fog Cooperation Approachin Fog Radio Access NetworksTe-Chuan Chiu , Student Member, IEEE, Ai-Chun Pang , Senior Member, IEEE,Wei-Ho Chung , Member, IEEE, and Junshan Zhang , Fellow, IEEEAbstract—Fog computing, evolves from the cloud and migrates the computing to the edge, is a promising solution to meet theincreasing demand for ultra-low latency services in wireless networks. Via the forward-looking perspective, we advocate aFog Radio Access NetworkðF-RANÞ model, which leverages the existing infrastructure such as small cells with limited computingpower, to achieve the ultra-low latency by joint edge computing and near-range communications across multiple Fog groups. Weformulate the low latency design as an NP-hard optimization problem, which demonstrates the tradeoff between communication andcomputing in the time domain. Due to each F-RAN node’s potential as each user’s master F-RAN node with 1) different self computingpower; and 2) different cooperative power of assisted F-RAN nodes, we first tackle globally optimized master F-RAN node selection foreach user and propose a latency-driven cooperative Fog algorithm with dynamic programming solution for simultaneous selection ofthe F-RAN nodes to serve proper heterogeneous Fog resource allocation for multi-Fog groups. Considering the limited heterogeneousFog resources shared among all users, we propose the one-for-all strategy for every user putting him/herself into others’ shoesand reaching a “win-win” outcome. The numerical results show that the low latency services can be accomplished by F-RAN vialatency-driven Fog cooperation approach.Index Terms—Fifth-generation (5G) cellular networks, fog computing, ultra-low latency, latency-driven, cooperative task computing,heterogeneous resource allocation, fog cooperationÇ1 INTRODUCTIONRECENTLY next generation cellular system is urgently arrived by the 5G wireless technology chasing for the2020, which proposes to satisfy the requirements of massivemachine-type communications, enhanced mobile broadband,ultra-reliable and low latency communications. Specifically,many applications (such as augmented/virtual reality andvehicle automation) are demanding in terms of high bandwidth and low latency. These applications require large computations to realize object tracking, content analytics andintelligent decision for better accuracy, performance, and userexperiences. Cloud computing traditionally can embrace plenteous computing resources for handling complex tasks, butone significant challenge therein is to achieve the ultra-lowlatency due to possible bulky network delay in traversing thetime-sensitive data traffics through the Internet backbone .To tackle these challenges, a new paradigm, called Fogcomputing, is emerging. It is a brand-new concept by extending cloud computing to the edge of the network so thatultra-low latency can be achieved at the edge . In fact,there have recent attempts on Fog computing by dedicatedacademic/industry projects and standardization activities,e.g., Cloudlet , Mobile edge computing , FP7 EuropeanProject (TROPIC) , and OpenFog Consortium . In ourrecent work , , we have proposed the Fog Radio AccessNetwork (F-RAN), which leverages the resources of thecurrent infrastructures in the radio access network (RAN),such as small cells, to promptly react to low latency requestsfrom mobile devices. In the F-RAN, those F-RAN nodessupport wireless connectivity as well as application serviceprovisioning, which invents a conceivable new businessmodel for telecommunication operators to collaborate withapplication/service providers.There are different studies in the Fog system , ,, , , , , , , , , . Li et al. and Shi et al.  gave an early stage survey on the edgeand Fog computing which opens a whole new researcharea. Ottenwalder et al. designed a placement and migration scheme to ensure end-to-end latency and release thenetwork overhead by earlier migration strategy in a cloudand Fog coexisting environment . Sardellitti et al. proposed a computation offloading algorithm to reduce theoverall users’ energy consumption by migrating the workloads to the remote powerful cloud server . Deng et al.leveraged the cooperation between the cloud and Fog, andT.-C. Chiu is with the Department of Computer Science and InformationEngineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.E-mail: [email protected]A.-C. Pang is with the Graduate Institute of Networking and Multimedia,Department of Computer Science and Information Engineering, NationalTaiwan University, Taipei, Taiwan 10617, R.O.C, and also with theResearch Center for Information Technology Innovation (CITI), AcademiaSinica, Taipei, Taiwan 11529, R.O.C. E-mail: [email protected]W.-H. Chung is with the Department of Electrical Engineering, NationalTsing Hua University, Hsinchu, Taiwan 300, R.O.C.E-mail: [email protected]J. Zhang is with the School of Electrical, Computer and EnergyEngineering, Arizona State University, Tempe, AZ 85281.E-mail: [email protected]Manuscript received 14 Dec. 2017; revised 28 May 2018; accepted 13 July2018. Date of publication 20 July 2018; date of current version 9 Oct. 2019.(Corresponding author: Ai-Chun Pang.)For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TSC.2018.2858253698 IEEE TRANSACTIONS ON SERVICES COMPUTING, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 20191939-1374 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See ht_tp://www.ieee.org/publications_standards/publications/rights/index.html for more information.Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.solved the workload allocation problem to decrease thepower consumption of the cloud server . Intharawijitret al. tried to minimize the blocking probability ratio amongall requested workloads in the entire system by deciding feasible selection policies of assisting Fog nodes . Nishioet al. also advocated a framework for various resources considering all possible factors such as CPUs, communicationbandwidth, and storage from the perspective of “time” .Huang et al. formulated resource allocation problems in aMECO system as a convex optimization problem to reduceweighted sum mobile energy consumption . Kuehn et al.focus on green radio unit selection with the leverage of cacheenabled F-RAN for minimizing total power consumption ofthe network . Sanchez et al. modeled the service allocationproblem as multidimensional knapsack problem in the Fogto-Cloud environment for optimal service allocation concerning delay, energy consumption, and workload . Le et al.considered joint computation offloading and resource allocation problem among mobile edge cloud and mobile users byD2D technology for minimizing weighted energy consumption . Park et al. proposed a novel superposition codingapproach to enhance delivery rate concerning fronthualcapacity and per-eRRH power constraints . However, theabove-related studies are substantially different from ourwork without considering 1) F-RAN dedicated scenario withcurrent cellular infrastructures 2) ultra-low latency application with extensive computation requirement 3) Fog cooperation problem tacking new tradeoff between computing andcommunication in the time domain.In this paper, we advocate a multi-Fog F-RAN framework,where the computing and communication resources amongall Fog are naturally heterogeneous, making it a great challenging to quantify the tradeoff therein. To fulfill the ultra-lowlatency in such a scenario, we propose to consider the framework where multiple F-RAN nodes jointly perform distributedcomputing after receiving the assigned computing tasks fromtheir belonging coordinator, called master F-RAN node, whichcoordinates with each assisted F-RAN node wirelessly andforms as a single Fog. This architecture targets a teamwork scenario so that there is a joint computing task where every cooperative F-RAN node is responsible for a sub-task. In this way,each master F-RAN node should wisely decide which F-RANnode to be selected considering the limited computing powerand communication resources for each F-RAN node. Specifically, more cooperative F-RAN nodes provide higher computing power and hence reduce total computing latency.However, each cooperative F-RAN node gains fewer radioresources from its belonging master F-RAN node and totalcommunication latency will increase consequently. Therefore,one primary goal of cooperative task computing is how tostrike a good balance between computing power and communication resources, contributing to total service latency.This paper targets multi-Fog scenario to serve multipleusers by multiple master F-RAN nodes simultaneously,which requires global view master F-RAN node selection andheterogeneous Fog resource allocation among all users. Ourcontributions are as follows. First, the latency-driven Fogcooperation problem is first cast as an optimization problem,and an optimal algorithm based on dynamic programming,namely, Fog-DP, is proposed and proved for the cooperativetask computing in the special case of single-Fog with a singleuser served by a single master F-RAN node. Second, wedesign a heuristic algorithm, CoFog, which combines the FogDP approach with “one-for-all” concept to provide an approximate solution regarding master F-RAN node selection, heterogeneous Fog resource allocation and cooperative taskcomputing in the general case of multi-Fog with multipleusers. In the multi-user CoFog algorithm, the global-view optimized master F-RAN node is decided for each user with bothconsideration of computing power and cooperative power underload-balance strategy, and then the communication and computing resources for each user are pre-allocated by heterogeneous Fog resource allocation, and finally the single-user FogDP with “one-for-all” concept is applied to solve cooperativetask computing among all users based on the assigned heterogeneous Fog resources and the chosen master F-RAN node.Since the total service latency is decided by the bottleneck ofthe last user from the last Fog finishing his/her cooperativetask computing, every user should be considerate of eachother and seeks for a “win-win” solution as the strategy of“one-for-all”. Third, we conduct a series of experiments,based on realistic parameter settings, to evaluate the proposedalgorithm, in comparisons with four baseline approaches. Thesimulation results show that the proposed scheme can significantly reduce the total service latency of the cooperativetask computing operation and adequately deal with masterF-RAN node selection and heterogeneous Fog resource allocation while handling the tradeoff between communicationand computing in the time domain.The remainder of this paper is organized as follows.Section 2 presents the system model and the formal formulation of the optimization problem. In Section 3, we showthat the problem is NP-hard and propose an efficient algorithm for the special/general case with evaluated time complexity. Simulation results and useful insights are discussedin Section 4. Section 5 concludes this work.2 SYSTEM MODEL AND PROBLEM FORMULATIONFOR LATENCY MINIMIZATION2.1 System ModelWe consider a scenario with densely deployed F-RANnodes to serve ultra-low latency and computing-intensiveservices, e.g., Augmented Reality (AR). Since a singleF-RAN node evolving from the current small cell only hasthe limited computing power and often requires a longertime to complete extensive computing tasks, one potentialsolution is to execute the tasks via distributed computing bymultiple F-RAN nodes. With this motivation, we propose toutilize multiple F-RAN nodes to accelerate joint data processing and transmission for the ultra-low temporal latency.In the scenario of multiple cooperative Fog groups asshown in Fig. 1, the target users first send their data to his/her responsible F-RAN node, also known as his/her masterF-RAN node which coordinates with other F-RAN nodes bymmWave communication technology  (mmWave ownssufficient dedicated bandwidth only for F-RAN node signaling usage and the associated cost is assumed negligible inthis paper). Since the closet F-RAN node may not be thebest choice as the master F-RAN node for two reasons:1) the closest F-RAN node owns limited computing andcommunication resources such that adopting load-balancingCHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 699Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.strategy can be a better choice for achieving ultra-low latencyservice by the different group of Fog; 2) the possible assistedset of F-RAN nodes for each master F-RAN node with itsbelonging coverage area is totally different which contributesto diverse results of cooperative task computing in terms ofservice latency. Therefore, in this paper we will further tacklehow to select a global-view optimized master F-RAN node foreach user in forming different cooperative Fog groups forminimizing total service latency in Fog Radio Access Networks. The chosen master F-RAN node decides whichF-RAN node to be selected for service provision and assignstheir processing data/computing tasks. Upon the task completion on all F-RAN nodes, each master F-RAN node collects,unifies, and sends back the outcomes to the target users.Finally, the target users execute the applications in their enddevice with ultra-low latency. Compared with the input datasize for each F-RAN node, the output data size is smaller andits transmit time can be omitted. Consequently, our first priority is to deal with the most time-consuming part for allcomputing-intensive and dividable tasks being distributivelyconducted among multiple cooperative Fog groups. Specifically, total data are split into different fragments and aretransmitted from those chosen master F-RAN nodes to different selected F-RAN nodes through wireless transmissions.Thus the total service latency consists of the two main parts:the communication delay and the computing delay.In this paper, the design goal is to pursue ultra-low service latency in completing the cooperative task computingamong different cooperative Fog groups for multiple users,including the transmission delay from different chosen master F-RAN node to each associated F-RAN node and thecomputing delay for each associated F-RAN node. Due tothe distributed architecture, the total service latency ofcooperative task computing for a single user is dominatedby the longest service time in the last F-RAN node to complete its assigned computing task. Besides, all of chosenmaster F-RAN nodes should deal with their responsibleusers’ service requests simultaneously, and the total servicelatency of cooperative task computing for multiple users isdominated by the longest service time of the final userto complete his/her service by multiple F-RAN nodesfrom the final cooperative Fog group. Since each F-RANnode may join different user’s cooperative task computingat the same time, we propose a conceptual unit, i.e.,“computing resource unit”, to quantify each F-RAN node’scomputing power such that each F-RAN node can decideamounts of efforts dedicated to different users, i.e., thecomputing resource allocation.Therefore, each master F-RAN node needs to recruit thesuitable combination of F-RAN nodes with consideration ofall possible radio resource allocation, processing data distribution, computing resource allocation and computing taskassignment. In fact, there exists a tradeoff between communication and computing delay. To pursue the min-max totalservice latency of the Fog cooperation approach amongmultiple users is an interesting and non-trivial challenge interms of master F-RAN node selection, heterogeneous Fogresource allocation and cooperative task computing, whichis the major focus of this paper. The system model underconsideration is formulated as follows.2.2 Problem FormulationIn this paper, we study Fog cooperation approach in terms ofmaster F-RAN node selection, joint heterogeneous Fogresource allocation and cooperative task computing for ultralow latency service provision in Fog Radio Access Networks.The objective is to minimize the total service latency amongmultiple users via offloading dividable computing tasks tomultiple F-RAN nodes from different Fog while meeting thedata requirements of each user and the availability constraintsin communication/computing resources of each F-RANnode. For brevity, we omit “8” wherever no confusion arises.In a network, the set of users in the service area coveredby the set of multiple F-RAN nodes F is denoted as N. Eachuser n first sends his/her latency service request to his/herresponsible serving F-RAN node which is his/her masterF-RAN node f^ and we consider there are many chosen master F-RAN nodes existing in this work. Then, the user nsends its processing data, represented as Dn, which is to betransformed into total dividable computing tasks (e.g., unitas per CPU instruction), denoted as Cn, and to be executedby multiple F-RAN nodes. In the viewpoint of each masterF-RAN node f^, the set of F-RAN nodes in its coverage areais denoted as F ^f (including master F-RAN node f^ itself) andmaster F-RAN node f^ has at most df^ radio resource blocks.When master F-RAN node f^ is associated with F-RAN nodef, it always adopts the achievable highest-rate modulationcoding scheme that F-RAN node f can receive, dependingon the signal-to-noise ratio; thus, a radio resource blockfrom master F-RAN node f^ can provide data rate gff ^ forF-RAN node f. As for F-RAN node f, its total computingpower is measured by a total number of computingresource units, represented as uf , whose computing abilityrf represents the number of instructions per second per single computing unit uf .For cooperative task computing of each user n, we willfirst decide whether F-RAN node f^ will be chosen as his/hermaster F-RAN node via an indicator function Inf^, i.e., onebeing selected and zero being not selected as the masterF-RAN node of user n. Next, the chosen master F-RAN nodef^ continuously decides which F-RAN node f to be selectedor not selected via an indicator function Inff ^ , i.e., one beingselected and zero being not selected by master F-RAN nodef^ for serving user n. Besides, master F-RAN node f^ alsodecides 1) the number of radio resource blocks dn^ff allocatedto each associated F-RAN node f and the amount of delivered processing data Dn^ff for F-RAN node f; 2) the number ofcomputing resource units un ff ^ from each joined F-RAN nodef allocated to each user n and the number of assignedFig. 1. Scenario of ultra-low latency service with Fog cooperation.700 IEEE TRANSACTIONS ON SERVICES COMPUTING, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 2019Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.computing tasks Cn^ff for F-RAN node f; 3) the number ofcomputing resource units un f^f^ from master F-RAN node f^itself allocated to each user n and the number of assigned computing tasks Cn^ff^ for master F-RAN nodef^itself. The out put for a set of F-RAN nodes in the associated states needs tobe a feasible solution which meets the following constraints.2.2.1 Communication Resource FeasibilityFor each master F-RAN node f^, the sum of allocated radioresource blocks for all of cooperating F-RAN nodes to serveall of users cannot exceed the total available radio resourceblocks, i.e.,X8n2NX8f2F ^f I Iff n^ dn ff ^ df^; 8f: ^ n^f (1)2.2.2 Computing Resource FeasibilityFor each cooperating F-RAN node f, the sum of allocatedcomputing resource units for all of serving users by all ofpossible master F-RAN nodes cannot exceed the total available computing resource units, i.e.,X8n2NX ^8f2FIn^f Iff n^ un ff ^ uf; 8f: (2)2.2.3 Processing Data AssuranceFor all of the F-RAN nodes involved in the cooperative taskcomputing of user n by master F-RAN node f^, the sum ofreceived processing data should be more than total originalprocessing data, i.e.,X ^8f2FX8f2F ^fIn^f Iff n^ Dn ff ^ Dn; 8n: (3)2.2.4 Computing Tasks AssuranceFor all of the F-RAN nodes involved in the cooperative taskcomputing of user n by master F-RAN node f^, the sum ofassigned computing tasks should be more than total original computing tasks, i.e.,X ^8f2FX8f2F ^fIn^f Iff n^ Cff n^ Cn; 8n: (4)2.2.5 Unique Master F-RAN Node AssociationFor each user n served in the cooperative task computing,everyone can only associate with single F-RAN node ashis/her master F-RAN node in each service time, i.e.,X ^8f2FIn^f ¼ 1; 8n: (5)Constraints (3), (4) ensure that cooperative multipleF-RAN nodes receive sufficient data information to complete all required computing tasks.2.2.6 The Latency-Driven Fog Cooperation ProblemInput Instance. Among the set of users N, let the user n transmit processing data Dn (which is transformed into total Cncomputing tasks) to a potential master F-RAN node f^ whichhas d ^f radio resource blocks. Consider the set of F-RANnode F in which each F-RAN node f has uf computingresource units (with computing rate rf), and master F-RANnode f^ can provide data rate gff ^ in a radio resource blockfor F-RAN node f when the F-RAN node f is associatedwith master F-RAN node f^ and the highest modulationcoding scheme is adopted.Objective. Our objective is to pursue the min-max of thetotal service latency via finding a global-view optimized master F-RAN node f^ and a feasible set of F-RAN nodes Ff^ foreach user n, (i.e., In^f ¼ 1 or 0, 8f^ 2 F; 8n 2 N, and Iff n^ ¼ 1 or0, 8f 2 Ff^; 8n 2 N), the number of allocated radio resource blocks dn^ff, the amount of delivered processing data D, the n ff ^ number of allocated computing resource units un ff ^ and thenumber of assigned computing tasks Cn^ff of each associatedF-RAN node f for cooperative task computing of user n inthe network. We state our objective function formally as minmax8n2N;8f^2F;8f2F ^In^ff fð1 In^f Þ Dn ff ^dnff ^ gff ^þCn^ ffun^ff rf !;subject to constraints (1) to (5), whereð1In^fÞDn^ffðÞ shows ifmaster F-RAN node f^ joining the cooperative task computing of user n (i.e., In^f ¼ 1 and Ifn^f^ ¼ 1), it only takes computing delay (i.e.,Cnf^f^ðÞ ) without consuming any communicationdelay (i.e.,0Dnf^f^ðÞ ). Besides, Iff n^ ðÞ indicates the servicelatency for selected F-RAN node f serving user n. Thenmin max8f^2F;8f2F ^fðÞ represents total service latency for theset of cooperating F-RAN nodes Ff^ serving user n (whenthe last F-RAN node f finishes the cooperative task computing), and finally min max8n2N;8f^2F;8f2F ^fðÞ accounts for totalservice latency for the set of users N (when the last user ncompletes his/her cooperative task computing among multiple F-RAN nodes from the last Fog). Table 1 summarizes thenotations of all used variables in the problem formulation.3 LATENCY-DRIVEN FOG COOPERATIONAPPROACHIn this section, we consider the latency-driven Fog cooperation problem. In Section 3.1, we show NP-hardness of theproblem. For simplicity, in Section 3.2, we consider a specialcase of single-Fog with only a single user served by a singlemaster F-RAN node in cooperative task computing andpropose a polynomial-time optimal algorithm based ondynamic-programming to minimize total service latency bymultiple F-RAN nodes for a single user. Then, in Section 3.3,we present an efficient and effective algorithm, which relieson the algorithm presented in Section 3.2, for the generalcase of multi-Fog with multiple users and deal with Fogcooperation problem in terms of 1) master F-RAN nodeselection; 2) joint heterogeneous Fog resource allocation; and3) cooperative task computing to minimize total servicelatency among all users.gðr; c; fÞ¼0; if c ¼ 0;tf^r;c; else if r ¼ 0 or f ¼ 0;minr^2½1;r;c^2½1;cðmaxðgðr r; ^ otherwise.c c; f ^ 1Þ; tf r; ^ c^Þ; gðr; c; f 1ÞÞ;8>>>:(6)CHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 701Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.3.1 Problem HardnessIn this subsection, we show target problem NP-hardness byits subproblem (only with a single master F-RAN node)reduction from the partition problem known to beNP-complete .Theorem 1. The latency-driven Fog cooperation problem isNP-hard.(Refer to Appendix A, which can be found on theComputer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TSC.2018.2858253 for the proof). 188.8.131.52Special CaseA Polynomial Time Optimal Algorithm Next, we consider a special case of the target problem whenthere is a single user with a single master F-RAN nodeserved by cooperative task computing of multiple F-RANnodes. Since there is only one user, the target user n canleverage all the available radio resource blocks from thechosen master F-RAN node f^ (i.e., P8f2F ^fInff ^ dn ff ^ ¼ df^)and computing resource units for each F-RAN node (i.e.,un^ff ¼ uf; 8f), and the problem is thus feasible for the set ofF-RAN nodes in cooperative task computing of the targetuser. In other words, an algorithm is optimal if it can derivethe minimum service latency provided by multiple F-RANnodes for the target user. For the problem formulation ofthe single user with a single master F-RAN node version,we omit “n” and “f^” wherever its meaning is clear from thecontext (e.g., D; C; If; df; Df; uf; Cf).For this single-user case (with a single master F-RANnode), we propose an optimal algorithm with polynomialtime property based on dynamic-programming, namedcooperative task computing for single Fog with DynamicProgramming (Fog-DP) algorithm. It determines whichF-RAN nodes should be selected to serve the target user,the number of allocated radio resource blocks, the amountof delivered processing data, and the number of assignedcomputing tasks. Besides, the master F-RAN node can alsocontribute itself to cooperative task computing without consuming any extra radio resource block while occupying itscomputing resource units. The proposed algorithm is basedon the recursive formula given in Equation (6). Let gðr; c; fÞbe the minimum service latency achieved by the first fF-RAN nodes, where F-RAN node f can be allocated withany number of radio resource blocks within total available rradio resource blocks and can execute any possible numberof computing tasks within total required c computing tasks.There exist three possible cases in Equation (6).1) If c = 0, gðr; c; fÞ is set as 0. That is, total servicelatency is zero because there is no any computingtask to be executed.2) If r = 0 or f = 0, then gðr; c; fÞ is set as tf r;c ^ . That is, service can only be provided by master F-RAN node f^itself because either there are no available radioresource blocks or there are no joined F-RAN nodesto do cooperative task computing.3) Otherwise, F-RAN node f is either dedicated or notdedicated to joining cooperative task computing. 1)If it is dedicated to executing computing tasks c^ forthe target user with allocated radio resource blocks r^and it will consume tfr; ^ c^ (i.e., r^Dgff þ ufc^rf) servicelatency for its working part. Then, the remainingavailable radio resource blocks, i.e., r r^, can beused for the first f 1 F-RAN nodes, each of whichcan be responsible for the remaining required computing tasks, i.e., c c^, and the first f 1 F-RANnodes will consume gðr r; c ^ c; f ^ 1Þ servicelatency for completing the remaining working part.In this case, the total service latency will choose thebigger one (maxðgðr r; c ^ c; f ^ 1Þ; tf r; ^ c^Þ) as the totalservice complete time. Since there are many combinations for the allocated resource block (r^ 2 ½1; r) andassigned computing tasks (c^ 2 ½1; c) for F-RAN node f,the formula will try every possible cases and recordthem as one of candidate solutions. 2) In contrast, ifF-RAN node f is not dedicated to providing cooperativetask computing, the target user will seek for the firstf 1 F-RAN nodes’ assistance such that the wholecomputing tasks c are assigned to the first f 1 F-RANnodes with total available r radio resource blocks, andthe total service latency will consume gðr; c; f 1Þ as itscomplete time. Finally, the algorithm will choose all possible candidate solutions from 1) and 2), and the smallerone will be the final service latency with the best strategy of radio and computing resource allocation.Algorithm 1, represented as Fog-DP, conducts thedynamic-programming in Equation (6). First, the algorithmTABLE 1Summary of NotationsSymbol DescriptionN The set of usersF The set of F-RAN nodesF ^f The set of cooperating F-RAN nodes in thecoverage of master F-RAN node f^Dn The amount of total processing data of user nCn The number of total computing tasks of user nd ^f The number of total radio resource blocks ofmaster F-RAN node f^gff ^ The data rate per radio resource block for F-RANnode f received from master F-RAN node f^ withhighest modulation-coding schemeuf The number of total computing resource units ofF-RAN node frf The computing rate per computing resource unitof F-RAN node fInf^ An indicator function, which is 1 if F-RAN node f^is chosen as the mster F-RAN node of user n, and0 otherwiseInff ^ An indicator function, which is 1 if F-RAN node fis chosen for serving user n by master F-RANnode f^, and 0 otherwisednff ^ The number of radio resource blocks allocated toF-RAN node f for delivering processing data ofuser n by master F-RAN node f^Dnff ^ The amount of delivered processing data of usern for F-RAN node f by master F-RAN node f^unff ^ The number of computing resource units fromF-RAN node f allocated to user n in cooperativetask computing by master F-RAN node f^Cnff ^ The number of assigned computing tasks of usern for F-RAN node f by master F-RAN node f^702 IEEE TRANSACTIONS ON SERVICES COMPUTING, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 2019Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.initializes all possible variables to zero. Then, a 3-dimensionaltable g½ is created, each entry of which stores the solutionderived by gðr; c; fÞ. The Procedure FILL-TABLE() simplyfills in the corresponding table g½ according to Equation (6).Upon the completion of the table, Procedure BACK-TRACE()is invoked to select the feasible set of F-RAN nodes withthe allocated radio resource blocks, delivered processingdata and assigned computing tasks such that the total servicelatency of the target user is minimized by back tracing thetable, after which the algorithm returns the solutionIf; Df; df; and Cf.Algorithm 1. Fog-DPInput: F; D; C; d; gf; uf; rfOutput: If; df; Df; Cf1: If 0; df 0; Df 0; Cf 0; 8f2: FILL-TABLE (d; C; F)3: BACK-TRACE (d; C; F)4: return If, df, Df, and Cf; 8fProcedure FILL-TABLE() takes d; C; F as inputs and fills intable entry g½r; c; f based on Equation (6) (Lines 4-9). Thecomputation of a table entry may refer to some other entries,and thus the table entries are computed sequentially, i.e.,from c = 0 to C first; then from f = 0 to F; and finally from r =0 to d.Procedure1. FILL-TABLE(d; C; F)1: for r 0 to d do 2:3:4:5:6:7:for f 0 to F dofor c 0 to C doif c = 0 theng½r; c; f 0else if r = 0 or f = 0 theng½r; c; f tf r;c ^ 8:9:elseg½r; c; f minr^2½1;r;c^2½1;cðmaxðg½r r; c ^ c; f ^ 1;tfr; ^ c^Þ; g½r; c; f 1Þend ifend forend for10:11:12: 13: end forProcedure BACK-TRACE() also takes d; C; F as inputs,and selects a feasible set of F-RAN nodes F (i.e., If ¼ 1; 8f),with allocated radio resource blocks df and assigned processing data/computing tasks (Df; Cf) to pursue the lowerservice latency for the target user by back tracing table g½.We begin with the last entry (i.e., g½d; C; F) by setting threeindexes r; c and f as d; C and F respectively (Lines 1-3). During Procedure FILL-TABLE(), g½r; c; f is set as 1) tf r;c ^ or 2)the minimum among g½r; c; f 1 and maxðg½r r; c ^ c; ^f 1; tf r; ^ c^Þ. We discuss the following two cases. In the firstcase, if there is no available radio resource blocks or noother possible assisted F-RAN node for master F-RAN nodef^ delivering processing tasks to join cooperative task computing (i.e., r ¼ 0 or f ¼ 0), the master F-RAN node can onlyprovide task computing by itself with assigned computingtasks c and record the remaining available radio resourceblocks r. Therefore, If is set as 1, df is set as r, Cf is set as c,and we also set f as 1 as terminal condition (Lines 5-7).Procedure 2. BACK-TRACE(d; C; F)1: r d2: c C3: f F4: while f >¼ 0 do 5:6:7:8:9:10:11:12:13:14:if f ¼ 0 or r ¼ 0 thenIf 1; df r; Cf cf 1else if g½r; c; f ¼ g½r; c; f 1 thenIf; df; Df; Cf; 0f f 1elsefor r^ 1 to r dofor c^ 1 to c doif g½r; c; f ¼ maxðg½r r; c ^ c; f ^ 1; tf r; ^ c^Þ thenIf 1; df r^; Df ^ D; Cf c^15: Cc 16:17:18:19:20:21:22:r r r^c c c^f f 1end ifend forend forend if 23: end whileIn the second case if the minimum is the first term asg½r; c; f 1, then radio resource blocks r and computingtasks c are not allocated for/assigned to the F-RAN node f.That is, the first f 1 F-RAN nodes will be responsible forcooperative task computing of the target user with totalavailable radio resource blocks. Hence, f is updated tof 1 and other output variables are updated (i.e., If; df;Df; Cf are set as 0) (Lines 8-10). If the minimum is the second term as maxðg½r r; c ^ c; f ^ 1; tf r; ^ c^Þ, then F-RAN nodef is to be selected with allocated radio resource blocks r^ andassigned computing tasks c^ among all possible combinationsof radio and computing resource allocation (Lines 12-13).Therefore, If is set as 1, df is set as r^, Df is set as Cc^ D (whichmeans computing tasks are transformed into processingdata), Cf is set as c^, and the three indexes are updated to theircorresponding values (Lines 14-18). Then, we start with theentry indexed by the updated r, c, and f, and repeat the aboveprocess until all the F-RAN nodes have been examined.3.2.2 The Properties of Algorithm 1Theorem 2. The time complexity of Algorithm 1 is Oðjdj2jCj2jFjÞ.Proof. Due to the sequential computing order, the timecomplexity of the Algorithm 1 is a function of the numberof table entries and the time required for obtaining eachentry. The 3-dimensional table is composed of jdjjCjjFjtable entries. Moreover, the value of each entry g½ refersto at most jdjjCj other entries and requires OðjdjjCjÞ complexity. Within a single round of operation, a derivedentry value will not be changed. Therefore the table canbe completed in Oðjdj2jCj2jFjÞ. Besides, constructing thecorresponding allocation via back tracing the table evaluates at most jCjjFj other entries, and each evaluationrequires at most OðjdjjCjÞ complexity. Thus, the time complexity of Algorithm 1 is Oðjdj2jCj2jFjÞ, which is apseudo-polynomial time function of the total computingtasks requirement C of the target user. t uCHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 703Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.Theorem 3. Algorithm 1 yields the minimum service latency fora single user in cooperative task computing.Proof. We prove this theorem via two-dimensional mathematical induction on the indexes r and c. At inductionbasis, c = 0, there is no any computing tasks and no needfor cooperative task computing. Thus, the minimum service latency is 0, i.e., gðr; 0; fÞ ¼ 0; 8r; f: For induction, suppose gð0; c 1; fÞ; 8f; sustains for some positive integer c.We intend to show that the formula gð0; c; fÞ; 8f; also sustains. When r ¼ 0; there is no any available radio resourceblocks for the master F-RAN node to deliver processingdata to other cooperating F-RAN node and the masterF-RAN node can only provide ultra-low latency service byitself. Thus, the minimum service latency is tf 0^;c (i.e.,gð0; c; fÞ ¼ tf 0^;c; 8c; f), the theorem is correct when r ¼ 0:Next, we consider the case when r ¼ 1. For induction,we suppose that the formula gð0; c 1; fÞ; 8f; sustains forsome positive integer c. We intend to show that the formula gð1; c; fÞ; 8f; also sustains. If the available numberof radio resource block is only one, the minimum servicelatency can be achieved by one of cooperative F-RANnodes and the master F-RAN node handling total computing tasks. By the induction hypothesis and the claimproved to hold when r = 0, the minimum service latencygð1; c; fÞ ¼ minc^2½1;cðmaxðgð0; c c; f ^ 1Þ; tf 1;c^Þ; gð1; c; f 1ÞÞ ¼minc^2½1;cðmaxðtf 0^;cc^; tf 1;c^Þ; gð1; c; f 1ÞÞ: In case of the firstf 1 F-RAN nodes, for an arbitrary node assigned topart of computing tasks but without any available radioresource blocks, only the master F-RAN node itself cando task computing and will consume total service latencyas t^f0;cc^ (i.e., gð0; c c; f ^ 1Þ ¼ tf 0^;cc^; 8c; f). Therefore,the total computing tasks are possibly assigned to 1) thetarget F-RAN node f with c^ tasks, one allocated radioresource block and the master F-RAN node f^ with c c^tasks or 2) to the first f 1 F-RAN nodes with oneallocated radio resource block. That is, the minimum service latency is the smaller one of the two values, i.e.,minc^2½1;cðmaxðtf 0^;cc^; tf 1;c^Þ; gð1; c; f 1ÞÞ: Thus, the claimsustains when r = 1. The validity of the theorem withr 2 can be proved to hold, via the similar procedure.Finally, we conclude that the formula gðr; c; fÞ; 8r; c; f; holds correctly.t u184.108.40.206The General CaseAlgorithm Description In this section, we propose an efficient algorithm, namedlatency-driven cooperative Fog (CoFog) algorithm, to solvethe general case of cooperative task computing among multiple users. Since there are multiple users to be served, eachuser will jointly utilize the available radio resource blocksfrom each chosen master F-RAN node and computingresource units from each cooperating F-RAN node. Theproblem thus includes three subproblems 1) master F-RANnode selection 2) heterogeneous Fog resource allocation and 3)cooperative task computing to pursue minimizing total servicelatency among all users.In the first part of master F-RAN node selection problem,we propose a Master F-RAN Node Selection Mechanism() toefficiently and wisely select an optimized master F-RANnode for each user from each possible F-RAN node in a distributed way. Considering each master F-RAN node candidate can contribute to cooperative task computing of eachuser in terms of 1) total computing power from how manyavailable computing resource units it has and each computing resource unit’s computing capability. 2) total cooperativepower from its possible assisted set of F-RAN nodes whosetotal available computing power and communication capability between the master F-RAN node candidate and theassisted F-RAN node, we should carefully evaluate bothtwo main factors for each master F-RAN node candidateand also make a global view decision for minimizing totalservice latency for all of users.Next, in the second part of heterogeneous Fog resourceallocation problem, each chosen master F-RAN node willmake a centralized decision as a Fog group leader to serveeach user with dedicated cooperation of multiple F-RANnodes. In the beginning, each master F-RAN node directlyallocates communication resources to each user based on his/her weight of processing data such that every user roughlyconsumes the same communication delay. However, the sameconcept may not be applicable for computing resource allocation since each F-RAN node may not actually serve every userin the distributed computing architecture. Compared withprior reserving communication resources for each user fromeach F-RAN node, it is better to leverage dynamic computingresource allocation in determining each user’s available computing resources from each cooperating F-RAN node.Finally, in the third part of cooperative task computingproblem, each master F-RAN node will rely on thedynamic-programming algorithm presented in Section 3.2to derive a feasible set of F-RAN nodes that minimize totalservice latency for all users with cooperative task computing of different Fog cooperation in a distributed way. Then,based on the Algorithm 1, Fog-DP, we propose “one-for-all”concept such that each user will select the suitable set ofcooperating F-RAN nodes while taking others’ penalty intoconsideration. Since dynamic computing resource allocationshould instantly update available computing resources foreach user in the same F-RAN node’s serving group as a newuser joining, the cooperative task computing of such newuser without “one-for-all” concept must result in additionallatency increasing for those original users. We note that thetotal service latency is decided by the bottleneck of the longest time period for the last user completing his/her cooperative task computing. Every user should compromise witheach other and seeks for a “win-win” solution as the strategyof “one-for-all”. Therefore, our proposed solution will jointlydeal with master F-RAN node selection, heterogeneous Fogresource allocation and cooperative task computing to minimize total service latency among all users. Finally, for serving each user every chosen master F-RAN node (i.e.,Inf^ ¼ 1; 8n; f^) will decide which F-RAN node to be selected(i.e., In^ff ¼ 1; 8n; f; f ^ ), the suitable number of radio resource blocks dn^ff, the amount of delivered processing data D, the n ff ^ actual number of computing resource units un ff ^ and thenumber of assigned computing tasks Cn^ff.Algorithm 2, represented as CoFog, starts with the initialization of parameters. In Line 1, all of the output parametershIn^f ; Iff n^ ; dn ff ^ ; Dn ff ^ ; un ff ^ ; Cff n^ i with two additional parameters704 IEEE TRANSACTIONS ON SERVICES COMPUTING, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 2019Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.hdn^f; Nfi are initialized as zero. The parameter dn f^ accounts forthe allocated number of radio resource blocks from master !F-RAN node f^ to each user n while the set Nf represents theset of users choosing F-RAN node f as their master F-RANnode or are served by F-RAN node f for cooperative taskcomputing. Then, we sort the set of users N based on his/herprocessing data value Dn from the largest to the smallest inLine 2. For each user, we first decide his/her global-view optimized master F-RAN node by triggering Master F-RAN NodeSelection Mechanism() and tackle heterogeneous Fog resourceallocation following his/her cooperative task computing(Lines 3-26). In Master F-RAN Node Selection Mechanism(), wechose a global-view optimized master F-RAN node for eachuser based on both consideration of computing power andcooperative power among all master F-RAN node candidatesin Line 3. In the second part of heterogeneous Fog resourceallocation for each user n^ (Lines 4-13), the number of allocated radio resource blocks from master F-RAN node f^ is inproportion to the ratio of user n^’s processing data value (Dn^)to the sum of all serving users’ processing data value(P8n2N ^fDn). Specifically, this will let master F-RAN node f^balance all serving users’ radio resources and approximatelyachieve the same communication latency. On the other hand,since each possible assisted F-RAN node under coverage ofmaster F-RAN node f^would not serve every user for cooperative task computing, the number of allocated computingresource units from each F-RAN node f to user n^ onlydepends on those actually serving users (Nf), which is inproportion to the ratio of user n^’s computing tasks value(Cn^) to the sum of all serving users’ computing tasks value(P8n2Nf Cn þ ð1 Ifn^ÞCn^ i.e., when f ¼ f; ^ n^ is already inthe set N ^f). That is, we instantly update the current availablecomputing resources for each F-RAN node to serve user n^and also let each F-RAN node balance all serving users’ computing resources according to the work loading. In the thirdpart of cooperative task computing for user n^ (Lines 14-26),we uses Algorithm 1 with input instance hFf^; Dn^; Cn^;dn^f^; gff ^ ; un ff ^^ ; rfi to derive a feasible set of F-RAN nodes (i.e.,In^ff ^ ¼ 1; 8f) with the number of allocated radio resourceblocks (dn^^ff), the amount of delivered processing data (Dn ff ^^ )and the number of assigned computing tasks (Cn^^ff) such thatthe total service latency of user n^ is minimized in Line 14. Infact, Fog-DP will apply one-for-all concept such that each tableentry would record not only user n^’s service latency but alsoother users’ additionally increased latency. For example, ifuser n^ chooses F-RAN node f for cooperative task computing, user n^ will jointly utilize computing resources of F-RANnode f. However, the other users already in serving usergroup Nf are forced to reduce their allocated computingresource units and this results in additional increasinglatency as the penalty. Therefore, the user n^ should need toconsider other users in his/her own decision of whetherchoosing F-RAN node f or not to achieve the minimizationof total service latency among all users. Since the feasible setof F-RAN nodes F ^f requested by master F-RAN node f^ foruser n^ is decided, we need to add user n^ into each cooperating F-RAN node f’s serving user group Nf (Lines 15-17).Besides, each user n already in the same serving user groupNf also needs to update their current available computingresource units un_ff with their belonging master F-RAN node f_(i.e., In_f ¼ 1) (Lines 18-20). On the other hand, for those FRAN node f, which does not join cooperative task computing of user n^ (i.e., In^^ff 6¼ 1; 8f) should release their computingresource units reserved previously for user n^ in Line 22.Finally, after all users finish their heterogeneous Fogresource allocation and cooperative task computing, thealgorithm returns the derived instances hIn^f ; Iff n^ ; dn ff ^ ; Dn ff ^ ;un^ff; Cff n^ i in Line 27. Based on the returned instances, eachmaster F-RAN node f^ can calculate for total service latencyamong their serving users and jointly respond the final service latency among all users.Algorithm 2. CoFogInput: N; F; Ff^; Dn; Cn; df^; gff ^ ; uf; rfOutput: In^f ; Iff n^ ; dn ff ^ ; Dn ff ^ ; un ff ^ ; Cff n^1: Inf^ 0; Iff n^ 0; dn ff ^ 0; Dn ff ^ 0;unff ^ 0; Cff ^ 0; dn f^ 0; Nf 0; 8n; f; f ^2: Sort N in a decreasing order by the value of Dn3: Mater F-RAN Node Selection Mechanism()4: for n^ 1 to N do5: for f 2 F do6: if In^f ¼ 1 then 7:8:9:f^ fend ifend for 10: d^Dn d ^fDn^ n^fP8n2N ^f11: for all f 2 Ff^ do12: un^^ ffCn^P8n2Nf Cnþð1Ifn^ÞCn^ uf 13: end for14: In^ff ^ ; dn ff ^^ ; Dn ff ^^ ; Cff n^^ ; 8f Algorithm 1 (n^)15: for all f 2 Ff^ do16: if In^ff ^ ¼ 1 then17: Nf ¼ Nf þ fn^g18: for all n 2 Nf; n 6¼ n^ do19: un_ff ICnCn uf; 8f_ fn_ P8n2Nf20: end for21: else22: un^ff ^ 023: end if24: end for25: n^ ¼ n^ þ 126: end for27: return Inf^; Iff n^ ; dn ff ^ ; Dn ff ^ ; un ff ^ ; Cff n^ ; 8n; f; f: ^Master F-RAN Node Selection Mechanism(). In theProcedure 1, our proposed solution tries to match the userwith the heaviest loading to its optimized master F-RANnode with the highest cooperative efficiency while considering global view optimized master F-RAN node selection withload-balance strategy for minimizing total service latencyamong all users. In Line 1, we set three additional parameters hF; ^ vf; Wfi and initialize them as F; 0; 0 respectively.The set F^ accounts for the set of total F-RAN node F and isdesigned for managing the list of all possible master F-RANnode candidates. The parameter vf and Wf represent cooperative power and cooperative ratio of F-RAN node f respectively. In fact, we evaluate each F-RAN node’s potential ascooperative ratio for being each user n’s master F-RAN nodeCHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 705Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.in two main parts: 1) each F-RAN node’s computing powerfrom its total available computing resource units and eachcomputing resource unit’s computing capability. 2) eachF-RAN node’s cooperative power from all of the possibleassisted F-RAN nodes (under its coverage) whose computing power and communication capability between eachassisted F-RAN node and the target F-RAN node. Next, wedecide each user’s master F-RAN node from the largestprocessing data to the smallest one (Lines 2-14). For eachuser n, we calculate each master F-RAN node candidate’scooperative power and cooperative ratio respectively (Lines 3-6). In fact, we set the weight of computing power the same ascooperative power for each master F-RAN node candidate’scooperative ratio. Then, we choose each user n’s masterF-RAN node f^ with the highest cooperative ratio in the candidate list, updating its indicator value as 1 (i.e., In^f ¼ 1) andalso add user n into serving user group of master F-RANnode f^ (Lines 7-8). Besides, with global view and load-balancestrategy we remove this target F-RAN node from the masterF-RAN node candidate list and restore the candidate listuntil the list is already empty (Lines 9-12). We believe thisstep can efficiently shift the loading of following users tothe other candidates instead of overloading the same groupof F-RAN nodes with a higher cooperative ratio. Finally, theProcedure 1 finishes master F-RAN node selection for eachuser and returns to Algorithm 2.Procedure 1. Master F-RAN Node Selection Mechanism()1: F^ F; vf 0; Wf 02: for all n 1 to N do 3:4:5:6:7:for all f 2 Fn F^ dovf ðP8f_2Ff gff_ uf_ rf_Þ=jFfjWf ð1=2Þ uf rf þ ð1=2Þ vfend forf^ arg maxfWf; 8f 2 Fn F^ 8:9:10:11:12:13:I¼ 1; Nf^ ¼ Nf^ þ fngF^ ¼ F^ ff^gif F^ ¼ ? thenF^ Fend ifn ¼ n þ 1 nf^ 14: end for3.3.2 The Properties of Algorithm 2Theorem 4. The time complexity of Algorithm 2 is O(jdj2jCj2jFjjNj), where d ¼ maxn2Njdnj and C ¼ maxn2NjCnj.Proof. For each user n, Algorithm 1 is invoked once andtakes O(jdnj2jCnj2jFj) time to derive a feasible set of FRAN nodes for cooperative task computing, as analyzedin Theorem 2. Thus, it takes O(jdj2jCj2jFjjNj) time forcooperative task computing of all users, where d ¼maxn2Njdnj and C ¼ maxn2NjCnj. Besides, the Master FRAN Node Selection Mechanism() would decide each user’sglobal-view optimized master F-RAN node and take O(jF^jjNj) time, where F^ ¼ maxn2NjFnj (see Line 3). Next, theheterogeneous Fog resource allocation includes two parts:1) radio resource allocation of each user takes O(1) time (seeLine 10) and 2) computing resource allocation of each userbefore executing their cooperative task computing takes O(jFj) time (see Line 12). Thus, the total heterogeneous Fogresource allocation takes O(jFjjNj) time. Moreover, afterfinishing cooperative task computing of each user, we needto update each related user’s current computing resourceunits and takes O(jFjjNjjN^j) time, where N^ ¼ maxf2FjNfj(see Line 19). Therefore, the time complexity of Algorithm 2is bounded by the time complexity of cooperative task computing and takes O(jdj2jCj2jFjjNj), which also is a pseudopolynomial time function of the maximum computing tasksrequirement C among all users. t u4 PERFORMANCE EVALUATION4.1 Simulation SettingsIn this section we develop simulations to evaluate our proposed algorithm, abbreviated as CoFog (latency-drivencooperative Fog algorithm), and compare with fourapproaches including uniNode, preFog (preserved Fog),selFog (selfish Fog) and bigFog. The comparison baselineuniNode is set as leveraging the most powerful F-RANnodes to serve corresponding users’ computing task undertheir coverage. Because uniNode’s architecture is not able toexecute distributed computing, each powerful F-RAN nodewill conduct each user’s task sequentially. Thus, we takeuniNode as the performance lower bound in our problemand show the advantages of leveraging multiple F-RANnodes for cooperative task computing. For the remainingthree baselines with different Fog solutions in terms of heterogeneous Fog resource allocation and cooperative taskcomputing, their master F-RAN node selection policy is setto choose the closest F-RAN node as each user’s defaultmaster F-RAN node which can verify the efficiency of ourproposed master F-RAN selection solution. The preFogapproach for each chosen master F-RAN node is designedto preserve all radio and computing resources for their serving users according to their workloads in advance, whichcan avoid the resource starvation problem for those users atthe bottom of the serving list of each master F-RAN node.However, the side-effect is the utilization degradation of eachuser’s performance since most resources are not fully in usebut actually preserved by their belonging master F-RANnode and assisted F-RAN nodes in advance. As a result, thecomparison baseline preFog is selected to demonstrate theside-effect of reservation in distributed computing architecture. Next, the comparison baseline selFog for each masterF-RAN node, without using “one-for-all” concept, is chosento demonstrate the policy of only pursuing each user’s ownbest feasible set of F-RAN nodes, which may lead to worseside-effects. That is, other users may suffer the penalty ofadditional increasing latency due to the policy’s lack of anoverall consideration of minimizing total service latency forall users. Finally, the comparison baseline bigFog for eachmaster F-RAN node is designed to use “all-in-one” concept,with which we gather each master F-RAN node’s total servingusers into different virtual giants and let their service requestsmerge as different individual huge requests separately. Sinceeach virtual giant can leverage all radio and computingresources from all F-RAN nodes under his/her belongingmaster F-RAN node coverage now, the problem can be redefined as a special case problem mentioned in Section 3.2.Therefore, we can directly use Fog-DP to derive an optimal706 IEEE TRANSACTIONS ON SERVICES COMPUTING, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 2019Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.solution for different virtual giants and take bigFog as the performance upper bound in our problem. The performance metric was the total service latency of cooperative task computingincluding the communication delay (i.e., the time for eachchosen master F-RAN node to transmit processing data ofeach user to all joined F-RAN nodes) and computing delay(i.e., the time for all joined F-RAN nodes to conduct their computing tasks for each user) when the last user from the last Fogfinishes his/her cooperative task computing.For simulations, we adopted various practical configurations and used Augmented Reality as the representativeultra-low latency application . Our proposed solutionattempts to accelerate the AR tracking, i.e., the most computation-intensive component in AR , with cooperativetask computing among multiple F-RAN nodes. The parameters in the simulation model are based on the LTE standardfor a 20 MHz spectrum . The network consists of multiple users selecting his/her belonging master F-RAN nodewith an assisted set of F-RAN nodes for his/her cooperativetask computing (total number of F-RAN node is set as 40).Each F-RAN node is randomly located in the serving area(1000 1000 m2) as a possible cooperative F-RAN node at adistance within 100 meters  from their possible masterF-RAN node. The user first sends its AR request to his/herchosen master F-RAN node. The standard AR codec usesQCIF resolution 176 144 pixels ,  per frame, andthe data size of each frame ranges from 0.64 – 1 ratio of standard AR frame size, which will transform into the total computing tasks in the unit of CPU instructions. The ARtracking video frames are encoded by H.264 in gray scalewith 8 bits per pixel. Each master F-RAN node has at most100 radio resource blocks to communicate with otherF-RAN nodes and the number of F-RAN node candidatesdepends on the number of F-RAN nodes under its coverage.The path loss model is PLðdBÞ ¼ 35:2 þ 35log 10ðd1Þ, whered1 is in meters . The F-RAN node’s signal-to-noise ratio(SNR) is derived based on its distance to its assisting masterF-RAN node and the path loss model. Each F-RAN nodeuses the best feasible modulation-coding scheme accordingto Table 2 . Path loss, shadowing, and multi-path fadingare all conducted in our simulations. To obtain empirical computing capability of the different F-RAN node, we conductexperiments in ARToolkit  with Intel i7 Dual-core 2.5 GHzCPU, 8G RAM platform and analyze the computing capability by Valgrind . The results of the real computingthroughput range from 700-1700 million instructions/secondin different states of workloads. At the beginning, each chosenmaster F-RAN node associates with each F-RAN node via thebest feasible modulation-coding scheme within its reachableregion. The F-RAN node is set to possess distinct computingcapability in the above-mentioned range. The results areobtained by averaging over 5,000 independent runs.4.2 Total Service LatencyFig. 2 shows the impact of the number of users on the totalservice latency. As the total number of users increases, weevaluate the performance of our proposed scheme CoFogwith other baseline approaches. In this figure, the largertotal number of users leads to more challenging Fog cooperation problem in terms of 1) critical master F-RAN nodeselection for each user; 2) competitive heterogeneous Fogresource allocation for each master F-RAN node; and 3)more complicated cooperative task computing among multiple F-RAN nodes and their belonging master F-RAN nodefrom different Fog groups. However, our proposed schemeCoFog can effectively deal with the communication andcomputing tradeoff in the time domain and successfullyselect a proper Fog group including a global-view optimized master F-RAN node and a feasible set of F-RANnodes for each user at the cost of slightly increasing the totalservice latency. We have the following observations: (1) TheCoFog is lower bounded by uniNode (11x) which only usesone powerful master F-RAN node to execute whole computing tasks of all users without any cost of communicationdelay. The result shows that our proposal of leveragingmultiple F-RAN nodes is a possible solution to achieve theultra-low latency within 30 ms for AR tracking . (2) Onthe other hand, although CoFog does not perform as wellas the upper bound solution bigFog in the beginning part oftime evaluation, CoFog owns the marginal increasing slopethan bigFog does, and CoFog achieves lower total servicelatency than bigFog when the total number of users exceeds50 finally. The key reason behind this phenomenon is due tothe master F-RAN node selection strategy in our proposedsolution which can select a global-view optimized masterF-RAN node for each user and evenly distribute all users todifferent Fog groups composed of a master F-RAN nodeand a set of assisted F-RAN nodes. In fact, the best servicelatency of CoFog is about 18 ms under 80 users in comparison with bigFog taking 22 ms. Besides, the total programexecution time for CoFog is within 34 seconds while for bigFog it takes approximately 14 hours (1468x). Therefore, theCoFog is observed to be a feasible solution for the practicalFog cooperation approach. (3) CoFog reduces more servicelatency (4.5x) than preFog due to the fact that global viewmaster F-RAN node selection and dynamic computingresource allocation can avoid utility degradation problemwhile all serving users, regardless of locations and belonging Fog group, can be jointly considered, and the resourcestarvation can be avoided under the management of eachmaster F-RAN node with the increasing number of totalTABLE 2Modulation-Coding Schemes with Different SNRModulation Coding rate gf (kbps) SNR range (dB)QAM16 1/2 9.6 [9.6598,12.361)QAM16 3/4 14.4 [12.361,16.6996)QAM64 2/3 19.2 [16.6996,17.9629)QAM64 3/4 21.6 [17.9629,+1)Fig. 2. Impacts of number of users on total service latency.CHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 707Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.users. (4) CoFog with one-for-all concept effectively reduces35 percent service latency than selfFog and also demonstrates the rationale to take other user’ penalty into consideration for cooperative task computing, especially in themultiple cooperative Fog groups.4.3 Cooperative Fog GroupsFig. 3 shows the impact of the number of users on the totalnumber of cooperative Fog groups. Intuitively, the largertotal number of users leads to more number of cooperativeFog groups in terms of a master F-RAN node and a set ofassisted F-RAN nodes for cooperative task computing. However, CoFog with global view optimized master F-RAN nodeselection constantly selects 10 suitable F-RAN nodes as master F-RAN nodes and comprises 10 different cooperative Foggroups compared with other baselines owning more Foggroups with the increasing number of users. The reasonbehind this interesting observation is CoFog can achieveload-balanced goal among all cooperative Fog groups and further improve total service latency among all users in comparison with other baselines forming different cooperative Foggroups without a global view. To further demonstrate theoperation effects on individual Fog group, users, and F-RANnodes, we show the results of various performance metricsunder the scenario of 50 users in the following figures.4.4 Individual Operational MetricsThe individual conditions of each Fog group, user, andF-RAN node, as shown in Fig. 4, demonstrate the completeheterogeneous Fog resource distribution of our proposedscheme and other baseline approaches with five differentevaluation metrics: total serving number of users, total service latency, the percentage of allocated radio resources,total selected number of F-RAN nodes, and percentage ofassigned computing tasks.The first Fig. 3 shows the user distribution for each Foggroup to serve totally 50 users by CoFog and other baselines. Since our proposed master F-RAN node selection considers global view optimized strategy, CoFog merely chooses10 master F-RAN nodes to form as the 10 cooperative Foggroups while other baselines with the closest master F-RANnode selection policy actually comprise 16 cooperative Foggroups. Besides, each chosen master F-RAN node in ourproposed solution is evenly responsible for serving totalusers and achieves closely total service latency among different Fog groups. However, each selected master F-RANnode in other baselines do not consider load-balance strategywhich leads to the extremely different serving number ofusers in each cooperative Fog group (e.g., 4 Fog groups onlyserve 1 user while 1 Fog group serves up to 8 users). Therefore, we can verify the importance of our proposed globalview optimized master F-RAN node selection which contributes to a critical impact on the following heterogeneousFog resource allocation and cooperative task computing.Due to the fact that the total service latency among allusers is decided by the last user’s completion time fromhis/her belonging Fog group, the Fig. 4b shows total servicelatency of each user in the last finished Fog group with different approaches (e.g, CoFog owns the last Fog group serving totally 5 users; other baselines have the last Fog groupserving totally 8 users). Since total service latency of eachFog group is decided by the longest one among all users,our proposed scheme CoFog can intelligently select eachuser’s cooperating set of F-RAN nodes with one-for-all concept to achieve the win-win situation among all users. As wecan see, the index number of each user represents the service order in the user list. Since selFog only concerns the target user’s optimized feasible set of F-RAN nodes withoutconsidering others’ penalty, users in the front of user list(e.g., user 1,2,3,4) may suffer from other users’ side-effects(e.g., user 5,6,7,8) which leads to additional latency. Therefore, we can verify that the one-for-all rationale is beneficialfor cooperative task computing among multiple users.Next, as shown in Fig. 4c, most approaches will allocateindividual users with a different percentage of radio resources in proportion to its workloads except uniNode and bigFog. Because uniNode will sequentially serve each user bytheir powerful master F-RAN node without using any radioresources while bigFog will let each master F-RAN nodeserve their responsible users as different single virtual giantwith fully utilizing of all available radio resources, we onlyshow CoFog and other three baselines except uniNode inFig. 4c. In fact, CoFog follows the same radio resource allocation policy as preFog does but performs better cooperativetask computing than preFog. Therefore, we can concludethat dynamic computing resource allocation is an importantkey to perform effective cooperative task computing.Then, the metrics of interest include each user’s totalselected number of F-RAN nodes, as shown in Fig. 4d.Except for uniNode, which only has one powerful masterF-RAN node to serve sequentially, other approaches willleverage multiple F-RAN nodes for cooperative task computing. Specifically, bigFog will let each master F-RANnode demand all possible assisted F-RAN nodes to joinsince each virtual giant from different Fog groups operatesall huge tasks as a whole unit. In contrast, our proposedscheme CoFog utilizes 3 to 4 F-RAN nodes for each user’scooperative task computing and achieve the better goodperformance. Therefore, the CoFog is applicable to the infrastructure without much extra burden.Finally, the Fig. 4e shows the percentage of assignedcomputing tasks of each F-RAN nodes in differentapproaches. In fact, CoFog demonstrates the heaviest loading cooperative Fog group serving total 5 users with total 22F-RAN node candidates in cooperative task computingwhile other baselines show their heaviest loading cooperative Fog group serving total 8 users with total 28 F-RANnode candidates. As the F-RAN node with index 0 is set asthe master F-RAN node in the target Fog group, otherFig. 3. Impacts of number of users on total number of Fog groups.708 IEEE TRANSACTIONS ON SERVICES COMPUTING, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 2019Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.F-RAN nodes with different indexes are considered possibleassisted F-RAN node under the coverage of the target masterF-RAN node. We have observed that bigFog let the targetmaster F-RAN node leverage all F-RAN nodes for cooperative task computing while our proposed scheme CoFog follows the same trend of leveraging nearly all F-RAN nodes(81 percent). That is due to the fact that CoFog with one-for-allconcept will take others’ penalty into consideration, whichleads to a higher possibility of selecting many other F-RANnodes for better choices. Furthermore, the target masterF-RAN node is also responsible for a higher proportion ofcomputing tasks to release other F-RAN node’s work loadingand gives a positive feedback to entire cooperative task computing. Therefore, CoFog also demonstrates the property ofload-balancing among all F-RAN nodes and pursues the goalof minimizing total service latency for all users. In summary,Fig. 4 shows that global view master F-RAN node selectionwith load-balancing strategy and dynamic computing resourceallocation with one-for-all concept are crucial techniques in theFog cooperation approach among multiple users.4.5 Running Time and FeasibilityFig. 5 shows the impact of the number of users on the average overall simulation running time required by eachapproach per run. Since bigFog let each master F-RAN nodeserve their responsible users as different single virtual giantwhich accumulates total workloads into a highly timeconsuming cooperative task computing, its running timeincreases exponentially with the number of users, as shownin Fig. 5a. Therefore, bigFog as a performance upper boundis not a feasible solution in practice especially when the totalnumber of users exceeds 50 even with a lower performancecompared with our proposed CoFog approach. On the otherhand, four other approaches are shown in Fig. 5b. As weknow, uniNode only has one powerful master F-RAN nodeto sequentially serve each user per round, its running timeis smoothly increasing as the number of users increases. Incontrast, all the running time required by preFog, selFog,and CoFog decreases significantly as the scale grows. Thereason behind this interesting phenomenon is that we usedynamic-programming in the cooperative task computingFig. 4. Operational metrics for each Fog group, user and F-RAN node.CHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 709Authorized licensed use limited to: Macquarie University. Downloaded on October 06,2021 at 00:52:20 UTC from IEEE Xplore. Restrictions apply.for above three approaches. Although more users to beserved results in a more complicated cooperative task computing, the average number of allocated heterogeneous Fogresources for each user also reduces such that the runningtime for each user’s cooperative task computing can beshorter eventually. Even though CoFog needs to add additional running time for one-for-all concept implementation,the total running time reduces sharply and is close to selFogand preFog within 15 sec for serving total 80 users. Therefore, our proposed scheme CoFog is a scalable approachwith the increasing number of users.5 CONCLUSIONSIn this paper, we studied the latency-driven Fog cooperation problem in Fog Radio Access Networks. To enable FRAN for temporally low latency operations within limitedcomputing and communication resources, we introduce theconcept to leverage multiple F-RAN nodes which operateseparately on different parts of the computing tasks. In themulti-Fog scenario, this work deals with a more challengingmaster F-RAN node selection and heterogeneous Fogresource management for each user and ensures to achievelow total service latency. We first formulate the problem asan optimization problem which is shown to be NP-hardand then we propose a latency-driven cooperative Fog algorithm to select the joining F-RAN nodes and their globalview optimized master F-RAN node for each user request.Our proposed framework targets the joint consideration ofcommunication resource allocation and computing taskassignment, in the time domain. The simulations are conducted to show that our proposed master F-RAN nodeselection approach with load-balance strategy can evenlydistribute users to their belonging cooperative Fog groupbased on each master F-RAN node’s computing power andcooperative power jointly. Besides, each master F-RANnode of different cooperative Fog group via consideringone-for-all concept can significantly reduce the total servicelatency of the cooperative task computing and reach awin-win situation for each user. We have also observed thatleveraging dynamic-programming design approach canefficiently reduce total running time with the increasingnumber of users, which validates the feasibility and scalability of our proposed scheme. In the future work, our proposed Fog cooperation approach can further extend tosupport multiple types of ultra-low latency services andhandle more sophisticated virtual Fog pool in terms ofhierarchical and horizontal heterogeneous resource management for achieving minimum service latency with different types of ultra-low latency service groups.ACKNOWLEDGMENTSThis work was supported in part by Ministry of Science andTechnology under Grants 104-2221-E-007-147-MY3, 105-2221-E-002-144-MY3, 105-2221-E-007-144-MY3, 106-2221-E-002-035-MY2, 107-2923-E-002-006-MY3, 106-3114-8-002-002,107-3017-F-009-001 and Digital Economy AdvancementProject 106-2218-E-002-014-MY4, by National TaiwanUniversity under Grant NTU-CC-107L891903, by Ministryof Education Project “Center for Open Intelligent Connectivity” and Project “Center for mmWave Smart RadarSystems and Technologies”, and by Information and Communications Research Laboratories of the Industrial Technology Research Institute (ICL/ITRI).REFERENCES S. 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Yang, “Real-time scalable recognition and tracking based on the server-client model for mobile augmented reality,” in Proc. IEEE Int. Symp. VR Innovation, 2011, pp. 1–5. P. Li, H. Zhang, B. Zhao, and S. Rangarajan, “Scalable video multicast in multi-carrie wireless data systems,” in Proc. 17th IEEE Int.Conf. Netw. Protocols, 2009, pp. 141–150. ARtoolKit. 2016. [Online]. Available: http://artoolkit.sourceforge.net Valgrind. 2016. [Online]. Available: http://valgrind.org G. Klein and D. Murray, “Parallel tracking and mapping for smallAR workspaces,” in Proc. 6th IEEE ACM Int. Symp. MixedAugmented Reality, 2007, pp. 1–10.Te-Chuan Chiu received the BS degree in computer science from National Tsing Hua University,Hsinchu City, Taiwan, in 2010, and the MSdegree in Computer Science and InformationEngineering from National Taiwan University,Taipei, Taiwan, in 2012. He is currently workingtoward the PhD degree in Computer Science andInformation Engineering from Nanyang Technological University. He was a research scholar ofSchool of Electrical, Computer and Energy Engineering, Arizona State University from 2016 to2017. His research interests include 5G communications, fog/edge computing, and energy harvesting technology. He was awarded the 2018Member of the Phi Tau Phi Scholastic Honor Society of the Republic ofChina. He is a student member of the IEEE.Ai-Chun Pang received the BS, MS and PhDdegrees in Computer Science and InformationEngineering from National Chiao Tung University,Taiwan, in 1996, 1998 and 2002, respectively.She joined the Department of Computer Scienceand Information Engineering (CSIE), NationalTaiwan University (NTU), Taipei, Taiwan, in2002. She was the director of Graduate Instituteof Networking and Multimedia (INM), in 2013-2016, and is now a professor of CSIE and INM,NTU. She is also an adjunct professor of Graduate Institute of Communication Engineering, NTU, and an adjunctresearch fellow of Research Center for Information Technology Innovation, Academia Sinica, Taiwan. Her research interests include wirelessand multimedia networking, 5G communications, software defined networking, and fog/edge Computing. She is a senior member of the IEEE.Wei-Ho Chung received the BSc and MScdegrees in electrical engineering from theNational Taiwan University, Taipei, Taiwan, andthe PhD degree in electrical engineering from theUniversity of California, Los Angeles, in 2009.From 2002 to 2005, he was with ChungHwa Telecommunications Company. In 2008, he workedon CDMA systems at Qualcomm, Inc., SanDiego, CA. His research interests include communications, signal processing, and networks.He received the Ta-You Wu Memorial Awardfrom Ministry of Science and Technology in 2016, Best Paper Award inIEEE WCNC 2012, and Taiwan Merit Scholarship from 2005 to 2009.He has published more than 50 journal articles and more than 50 conference papers. Since January 2010, He had been an assistant researchfellow, and promoted to the rank of associate research fellow in January2014 in Academia Sinica. Since 2018, he holds the position of full professor and leads the Wireless Communications Lab at Electrical Engineering, National Tsing Hua University, Taiwan. He is a member of the IEEE.Junshan Zhang received the PhD degree fromthe School of ECE, Purdue University, in 2000.He joined the School of ECEE, Arizona State University, in August 2000, where he has been fultonchair professor since 2015. His research interestsfall in the general field of information networksand data science, including communication networks, Internet of Things (IoT), fog computing,social networks, smart grid. His current researchfocuses on fundamental problems in informationnetworks and data science, including fog computing and its applications in IoT and 5G, IoT data privacy/security, optimization/control of mobile social networks, cognitive radio networks,stochastic modeling and control for smart gridHe is recipient of the ONRYoung Investigator Award in 2005 and the NSF CAREER award in2003. He received the IEEE Wireless Communication Technical Committee Recognition Award in 2016. His papers have won a few awards,including the Kenneth C. Sevcik Outstanding Student Paper Award ofACM SIGMETRICS/IFIP Performance 2016, the Best Paper Runner-upAward of IEEE INFOCOM 2009 and IEEE INFOCOM 2014, and theBest Paper Award at IEEE ICC 2008 and ICC 2017. Building on hisresearch findings, he co-founded Smartiply Inc, a Fog Computingstartup company delivering boosted network connectivity and embeddedartificial intelligence. He was TPC co-chair for a number of major conferences in communication networks, including IEEE INFOCOM 2012 andACM MOBIHOC 2015. He was the general chair for ACM/IEEE SEC2017, WiOPT 2016, and IEEE Communication Theory Workshop 2007.He was a distinguished lecturer of the IEEE Communications Society.He was an associate editor for the IEEE Transactions on Wireless Communications, an editor for the Computer Network Journal, and an editorthe IEEE Wireless Communication Magazine. He is currently serving asan editor-at-large for the IEEE/ACM Transactions on Networking and aneditor for the IEEE Network Magazine. He is a fellow of the IEEE.CHIU ET AL.: LATENCY-DRIVEN FOG COOPERATION APPROACH IN FOG RADIO ACCESS NETWORKS 711Authorized licensed use limited to: Macquarie University. 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