 Research
 Open Access
Fog radio access network system control scheme based on the embedded game model
 Sungwook Kim^{1}Email author
https://doi.org/10.1186/s1363801709009
© The Author(s). 2017
Received: 28 January 2017
Accepted: 7 June 2017
Published: 24 June 2017
Abstract
As a promising paradigm for the 5G wireless communication system, a new evolution of the cloud radio access networks has been proposed, named as fog radio access networks (FRANs). It is an advanced socially aware mobile networking architecture to provide a high spectral and energy efficiency while reducing backhaul burden. In particular, FRANs take full advantages of social information and edge computing to efficiently alleviate the endtoend latency. Based on the benefit of edge and cloud processing, key issues of FRAN technique are radio resource allocation, caching, and service admission control. In this paper, we develop a novel FRAN system control scheme based on the embedded game model. In the proposed scheme, spectrum allocation, cache placement, and service admission algorithms are jointly designed to maximize system efficiency. By developing a new embedded game methodology, our approach can capture the dynamics of FRAN system and effectively compromises the centralized optimality with decentralized distribution intelligence for the faster and less complex decision making process. Through simulations, we compare the performance of our scheme to the existing studies and show how we can achieve a better performance under dynamic FRAN system environments.
Keywords
 Fog radio access network
 Service admission control
 Cache placement
 Embedded game model
 Radio resource allocation
1 Introduction
In the past decade, the evolution toward 5G is featured by the explosive growth of traffic in the wireless network, due to the exponentially increased number of user devices. Compared to the 4G communication system, the 5G system should bring billions of user devices into wireless networks to demand high bandwidth connections. Therefore, system capacity and energy efficiency should be improved to get the great success of 5G communications. Cloud radio access network (CRAN) is an emerging architecture for the 5G wireless system. A key advantage of CRAN is the possibility to perform cooperative transmissions across multiple edge nodes for the centralized cloud processing. However, the cloud processing comes at the cost of the potentially large delay entailed by fronthaul transmissions. It may become a major performance bottleneck of a CRAN system per critical indicators such as spectral efficiency and latency [1–3].
As an extension of CRAN paradigm, fog computing is a promising solution to the mission critical tasks involving quick decision making and fast response. It is a distributed paradigm that provides cloudlike services to the network edge nodes. Instead of using the remoted cloud center, the fogcomputing technique leverages computing resources at the edge of networks based on the decentralized transmission strategies. Therefore, it can help overcome the resource contention and increasing latency. Due to the effective coordination of geographically distributed edge nodes, the fogcomputing approach can meet the 5G application constraints, i.e., location awareness, low latency, and supports for mobility or geographical distribution of services. The most frequently referred use cases for the fogcomputing concept are related to the Internet of Things (IoT) [4, 5].
Taking full advantages of fog computing and CRANs, fog radio access networks (FRANs) have been proposed as an advanced socially aware mobile networking architecture in 5G systems. FRANs harness the benefits of, and the synergies between, fog computing and CRAN in order to accommodate the broad range of Quality of Service (QoS) requirements of 5G mobile broadband communications [2]. In the FRAN architecture, edge nodes may be endowed with caching capabilities to serve the local data requests of popular content with low latency. At the same time, a central cloud processor allocates radio and computational resources to each individual edge nodes while ensuring as much as various applications [6]. To maximize the FRAN system performance, application request scheduling, cache placement, and communication resource allocation should be jointly designed. However, it is an extremely challenging issue.
In the architecture of FRANs, multiple interest relevant system agents exist; they are the central cloud server (CS), edge nodes (ENs), and mobile users (MUs). The CS provides contents to download and allocates radio and communication resources to ENs. ENs, known as fogcomputingbased access points (FAPs), manage the allocated radio resource and admit MUs to provide application services. MUs wish to enjoy different QoS services from the FRAN system. Different system agents have their own benefits, but their benefits could conflict with each other, and each agent only cares about its own profit. Therefore, it is necessary to analyze the interactions among these conflicting system agents and design proper solutions. Although dozens of techniques have been proposed, a systematic study on the interactions among CS, FAPs, and MUs is still lacking [7].
Recently, game theory has been widely concerned and studied in solving conflict and cooperation in distributed optimization problems. As a branch of mathematics, it is suitable for analyzing the performance of multiagent systems. In game theory, a variety of interactive behaviors can be described by different payoff functions and the outcome of a game depends on the combinations of the decisions taken by each agent. Depending on the way the decisions are taken, it is possible to classify the games as cooperative or noncooperative games. Nowadays, game theory has been widely recognized as an important tool in many fields. In the last few years, it has attracted considerable attentions and has been investigated extensively in computer science and telecommunications [8]. This is one of the reasons why game theory is applied more and more intensively to cloud computing and network management fields.
However, the traditional game theoretic analysis should rely on the perfect information and idealistic behavior assumptions. Therefore, there is a quite general consensus to say that the predicted game solutions are useful but would be rarely observed in real world situations. Recently, specialized subbranches of game theory have been developed to encounter this problem. The main goal of this study is also to develop a new game paradigm. To design a practical game model for the FRAN system management, we adopt an online dynamic approach based on the interactive relationship among system agents. Our approach exploits a partial information on the game and obtains an effective solution under mild and practical assumptions. From the standpoint of algorithm designers, our approach can be dynamically implemented in the realworld FRAN environments.
Motivated by the above discussion, we propose a novel FRAN control scheme based on the methodology of game theory. In this study, we design a new game model, called embedded game, to effectively solve the conflict problem among FRAN system agents. From the realistic point of view, we need not the complete knowledge of the system information. Instead, our game procedure imitates the interactive sequential game process while ensuring the system practicality. To summarize, the major contribution of this study is to provide a new gamebased FRAN control algorithm. Main features of our proposed game model are as follows: (i) the adjustable dynamics considering the current FRAN system environment, (ii) an interactive online process based on the embedded game model, (iii) a cooperative control manner with the nested noncooperative approach, (iv) the joint design to obtain synergistic and complementary features, and (v) a practicality under realistic system operation scenarios. Especially, the important novelty of our proposed scheme is obtained from the key principle of embedded game approach, which can better capture the reality of FRAN operations. To the best of our knowledge, very little research has been done, and there is still few published work to discuss the joint FRAN control algorithms.
This article is organized as follows. In the next section, we review some related schemes and their problems. In Section 3, we define the embedded game model considered in this paper and explain in detail the proposed FRAN control scheme. In particular, this section provides fresh insights into the benefits and design of developed control algorithms. For convenience, the main steps of the proposed scheme are also listed in Section 3. Section 4 reports the simulation results and performance analysis. Lastly, we give our conclusion in Section 5. Open issues and challenges are also discussed in Section V.
2 Related work
Over the years, a lot of stateoftheart research work on the radio access network control problem has been conducted. In [9], K. Sundaresan et al. proposed a scalable, lightweight scheme for realizing the full potential of CRAN systems. For small cells, this scheme determined configurations that maximized the traffic demand while simultaneously optimizing the compute resource usage in the baseband processing unit pool. Briefly, the developed scheme in [9] adopted a twostep approach: (i) the firststep determined the optimal combination of configurations; it needed to support the traffic demand from a set of small cells, and (ii) the second step consolidated the configurations to further reduce the compute resource usage [9].
The article [10] provided a brief overview of the infrastructure and logic structure of CRAN systems. In addition, a new coordinated user scheduling algorithm and parallel optimum precoding algorithm were specifically designed based on the concept of a service cloud and a threelayer logical structure. This approach utilized extensive computation resources to improve the CRAN system performance. Compared to traditional CRAN algorithms, the developed scheme in [10] matched well with the CRAN architecture while managing interference efficiently and accelerating the cooperation processing in parallel.
Q. Vien et al. [11–13] proposed a nonorthogonal multiple accessbased power allocation scheme for CRAN systems. In this scheme, base stations were allocated with different power levels depending on their distances to the cloud, and the optimal number of BSs in CRAN systems was found to achieve an improved performance. Specifically, a successive interference cancellation mechanism was designed at the cloud to lay multiple base stations over each other in the power domain. Taking into account the constraints of the total available power and the cloudedge throughput requirement, this approach has shown to support a higher number of base stations when compared to the existing scheme [11–13].
The paper [14] surveyed heterogeneous CRAN research achievements and challenges, and provided a summary of recent advancements in the computing convergence of heterogeneous wireless networks. In particular, the system architecture, performance analysis, cloudcomputingbased cooperative processing, networking techniques, key largescale cooperative processing and networking techniques, including cloudcomputingbased coordinated multipoint transmission, cooperative radio resource management, and selforganizing networks have been briefly summarized. Furthermore, potential challenges and open issues in heterogeneous CRANs have been discussed as well [14].
In [15], Sengupta et al. provided a latencycentric analysis of the degrees of freedom of an FRAN by accounting for the total content delivery delay across the fronthaul and wireless segments of the network. The main goal of the analysis was the identification of optimal caching, fronthaul, and edge transmission policies. In this study, authors detailed a general model and a novel performance metric, referred to as Normalized Delivery Time (NDT), which captured the worstcase delivery latency with respect to an ideal interferencefree system. Finally, they revealed optimal cachingfronthaul transmission policies as a function of the system resources [15].
Azimi, et al. [16] considered an online caching setup, in which the set of popular files was timevarying and both cache replenishment and content delivery could take place in each time slot. They developed online caching and delivery schemes based on both reactive and proactive caching principles, and bounds on the corresponding achievable longterm NDTs were derived. In particular, a lower bound on the achievable longterm NDT was obtained. Using this bound, the performance loss caused by the variations in the set of popular files in terms of delivery latency was quantified by comparing the NDTs achievable under offline and online caching. Finally, numerical results were provided in which the performance of reactive and proactive online caching schemes were compared with offline caching [16].
The Traffic Balancing and Dynamic Clustering (TBDC) scheme investigated the joint design of multicast beamforming, dynamic clustering, and backhaul traffic balancing [17]. To minimize the power consumption for higher energy efficiency, the TBDC scheme designed the beamforming vectors and clustering pattern in the downlink of FRAN. This approach balanced the backhaul traffic according to individual backhaul capacities, guaranteed the QoS of each user, and minimized the power consumption. Especially, the TBDC scheme dynamically excluded a radio unit from a cluster when it contributed comparatively less to the corresponding multicast group. If a radio unit contributed comparatively more to the corresponding multicast group, it would be involved in a cluster in order to guarantee the required QoS [17].
The Cloud Structure with Edge Caching (CSEC) scheme presented an informationtheoretic model of FRANs [6]. This scheme aimed at providing a latencycentric understanding of the degrees of freedom in the FRAN network by accounting for the available limited resources in terms of fronthaul capacity, cache storage sizes, as well as power and bandwidth on the wireless channel. In addition, a new performance measure was introduced; it captured the worstcase latency incurred over the fronthaul. Finally, the CSEC scheme characterized the tradeoff between the fronthaul and caching resources of the system while revealing optimal cachingfronthaul transmission policies [6].
The Joint Optimization of Cloud and Edge (JOCE) scheme introduced the joint design of cloud and edge processing for the downlink of FRAN [3]. To design the delivery phase for an arbitrary prefetching strategy, transfer modes can be categorized into two classes: hardtransfer mode and softtransfer mode. In the hardtransfer mode, noncached files are communicated over the fronthaul links to a subset of access points. Therefore, this approach transfers hard information of subfiles that were not cached. In the softtransfer mode, the fronthaul links are used to convey quantized baseband signals as in a cloud RAN. Therefore, this approach transfers a quantized version of the precoded signals for the missing files in line with the CRAN paradigm. In the JOCE scheme, a novel superposition coding approach was proposed that was based on the hybrid use of the fronthaul links in both hardtransfer and softtransfer modes. The problem of maximizing the delivery rate was tackled under fronthaul capacity and per enhanced remote radio head power constraints. This study was concluded that the JOCE scheme based on the superposition coding provided a more effective way and could have the potential to strictly outperform both conventional softtransfer and hardtransfer modes [3].
2.1 Comparison and main contributions
Some earlier studies [9–16] have attracted considerable attention while introducing unique challenges in handling the cloud radio control problems. Even though these existing schemes dynamically control the cloud radio access network for the efficient system management, there are some difficulties to compare performance between these work with our proposed scheme. The scheme in [9] was developed only for small cells, i.e., houses, based on the partially centralized CRAN model. The studies in [11–13] strongly concentrated on the nonorthogonal multiple access method to improve the spectral efficiency. Therefore, these studies were specially focused on the wireless downlink control problems in CRAN systems. The papers [10, 14] surveyed various CRAN research achievements and challenges and discussed issues of system architectures, spectral and energy efficiency performance, and promising key techniques. However, these surveys only covered research fields of traditional cloud radio access methods. In particular, the earlier studies [9–14] did not concern the issue of fogcomputing paradigm. Therefore, they did not provide cloudlike services to the network edge nodes.
The studies [15, 16] considered the edge processing in FRANs and specially investigated fundamental information theoretic limits. However, these schemes relied upon the cacheaided fog network paradigm while causing the extra cost to implement control mechanisms. This architectureoriented approach was inappropriate to fairly compare performance under general FRAN system operations. The schemes in [3, 6, 17] have attracted considerable attention while introducing unique challenges in handling the edge cloud control problems. In this paper, we demonstrate through extensive simulation and analysis that our proposed scheme significantly outperforms these existing TBDC, CSEC, JOCE schemes.
The specific difference between the proposed scheme and the existing schemes in [3, 6, 9–17] is the decision making procedure; we designed a new embedded game model for the FRAN system. Based on the stepbystep interactive mechanism, the proposed scheme jointly develops spectrum allocation algorithm and service admission algorithm; they are interlocked and serially correlated to capture the dynamics of FRAN systems. Therefore, our approach is suitable in dynamically changing FRAN environments and provides a wellbalanced system performance than existing schemes, which were designed as onesided protocols.
3 Embedded game model for FRAN control algorithms
 A.
Embedded game model for FRAN systems
In the CRAN architecture, all control functions and application storage are centralized at the CS, which requires a lot of MUs to transmit and exchange their data fast enough through the fronthaul link. To overcome this CRAN’s disadvantage with the fronthaul constraints, much attention has been paid to mobile fog computing and the edge cloud. The design of a fogcomputing platform has been introduced to deliver largescale latencysensitive applications. To implement the fogcomputing architecture, traditional edge nodes are evolved to the fogcomputingbased access point (FAP) by being equipped with a certain caching, cooperative radio resource, and computation power capability [2, 18].
The main difference between the CRAN and the FCRAN is that centralized storage cloud and control cloud functions are distributed to individual FAPs. Usually, FAPs are used to forward and process the received data, and interface to the CS through the fronthaul links. To avoid all traffic being loaded directly to the centralized CS, some local traffic should be delivered from the caching located in FAPs. Therefore, each FAP integrates not only the front radio spectrum but also the locally distributed cached contents and computation capacity. This approach can save the spectral usage of constrained fronthauls while decreasing the transmission delay. In conclusion, the main characteristics of FRAN include ubiquity, decentralized management, and cooperation [2, 18]. The general architecture of a FRAN system is shown in Fig. 1.During the FRAN system operations, system agents, i.e., CS, FAPs, MUs, should make decisions individually by considering the mutualinteraction relationship. Under the dynamic FRAN environments, system agents try to maximize their own profits in a competitive or cooperative manner. In this study, we develop a new game model, called embedded game, for the FRAN system. According to the decision making method, the embedded game procedure can be divided two phases. At the first phase, the CS and FAPs play a superordinated game; the CS distribute the available spectrum resource to each FAP by using a cooperative manner. At the second phase, FAPs and MUs play subordinated games. By employing a noncooperative manner, an individual FAP selectively admits its corresponding MUs to provide different application services. Taken as a whole, multiple subordinated games are nested in the superordinated game.
Formally, we define the embedded game model \( \mathbb{G}=\left\{{\mathbb{G}}^{super},{\mathbb{G}}_{i,1\le i\le n}^{sub}\right\} \) where \( {\mathbb{G}}^{super} \) is a superordinated game to formulate interactions between CS and FAPs, and \( {\mathbb{G}}_i^{sub} \) is a subordinated game to formulate interactions between the ith FAP and its corresponding MUs. Firstly, the \( {\mathbb{G}}^{super} \) can be defined as \( {\mathbb{G}}^{super}=\left\{\mathbb{N},{\mathcal{R}}_{CS},{\boldsymbol{S}}_{CS}^{\mathcal{R}},{U}_{i,1\le i\le n}, T\right\} \) at each time period t of gameplay.
\( \mathbb{N} \) is the finite set of \( {\mathbb{G}}^{super} \) game players \( \mathbb{N}=\left\{\mathrm{CS}, F{AP}_1, F{AP}_2\dots F{AP}_n\right\} \) where the total n + 1 number of \( {\mathbb{G}}^{super} \) players; one CS and n FAPs.

The total spectrum resources of CS is ℛ_{ CS }, which would be distributed to n FAPs.

\( {\boldsymbol{S}}_{CS}^{\mathrm{\mathcal{R}}} \) = {δ _{1}, δ _{2},…. δ _{ n }} is the sets of CS’s strategies for the spectrum resource allocation. δ _{ t } in \( {\boldsymbol{S}}_{CS}^{\mathrm{\mathcal{R}}} \) is the allocated spectrum amount for the F ‐ AP_{ t,1 ≤ i ≤ n }.

The U _{ t, 1 ≤ i ≤ n } is the payoff received by the F ‐ AP_{ t }. It is estimated as the obtained outcome minus the cost from the spectrum resource allocation.

The T is a time period. The \( {\mathbb{G}}^{\mathrm{super}} \) is repeated t ∈ T < ∞ time periods with imperfect information.
Secondly, the \( {\mathbb{G}}_i^{\mathrm{sub}} \) is the ith subordinated game, and it can be defined as \( {\mathbb{G}}_i^{\mathrm{sub}}=\Big\{{\mathbb{M}}_i,{\mathrm{\Re}}_i,{\boldsymbol{S}}_{F A{P}_i}^{\delta i},{\boldsymbol{S}}_{F A{P}_i}^{{\mathcal{C}}^i},{\boldsymbol{S}}_{F A{P}_i}^{\sigma^i}, \) \( {\mathcal{U}}_{j,1\le j\le m}^i, T\Big\} \) at each time period t of gameplay.
\( {\mathbb{M}}_i \) is the finite set of \( {\mathbb{G}}_i^{\mathrm{sub}} \) game players \( {\mathbb{M}}_i \) = {F ‐ AP_{ i }, \( {\mathrm{MU}}_1^i \),…, \( {\mathrm{MU}}_m^i \)} where \( {\mathrm{MU}}_{j,1\le j\le m}^i \) is the jth MU in the area covered by the F ‐ AP_{ i }.

The set of F ‐ AP_{ i }’s resources is ℜ_{ i } = {δ _{ i }, \( {\mathcal{C}}_i \), σ _{ i }} where δ _{ i }, \( {\mathcal{C}}_i \), σ _{ i } are the allocated spectrum resource, the computation capacity, and the placed cache files in the F ‐ AP_{ i }, respectively.

\( {\boldsymbol{S}}_{F A{P}_i}^{\delta_i} \), \( {\boldsymbol{S}}_{F A{P}_i}^{{\mathcal{C}}_i} \) and \( {\boldsymbol{S}}_{F A{P}_i}^{\sigma_i} \) are the sets of F ‐ AP_{ i }’s strategies for the spectrum allocation for MUs, the computation capacity assignment for MUs, and cache placement in the F ‐ AP_{ i }, respectively.

The \( {\mathcal{U}}_{j,1\le j\le m}^i \) is the \( {\mathrm{MU}}_j^i \)’s payoff received by the F ‐ AP_{ i }.

The T is a time period. The \( {\mathbb{G}}_i^{\mathrm{sub}} \) is repeated t ∈ T < ∞ time periods with imperfect information.
Table 1 lists the notations used in this paper.Table 1Parameters used in the proposed algorithm
Notations
Explanation
CS
Cloud server
FAPs
Fogcomputingbased access points
MUs
Mobile users
ENs
Edge nodes
ℕ
The finite set of superordinated game players
ℛ_{ CS }
The total spectrum resources of CS
δ _{ i }
The allocated spectrum amount for the F ‐ AP_{ i }
δ _{ i }(t − Δt)
The δ _{ i } value at the time period [t − Δt].
U _{ i }(Δt)
The payoff received by the F ‐ AP_{ i } during the recent Δt time period
\( {\mathbb{M}}_{\mathrm{i}} \)
The finite set of subordinated game players
ℜ_{ i }
The set of F ‐ AP_{ i }‘s resources
C _{ i }
The computation capacity in the F ‐ AP_{ i }
σ _{ i }
The placed cache files in the F ‐ AP_{ i }
\( {\mathrm{U}}_{\mathrm{j}}^{\mathrm{i}} \)
The \( {\mathrm{MU}}_{\mathrm{j}}^{\mathrm{i}} \) ‘s payoff received by the F ‐ AP_{ i }
β
The parameter weighs the past experience by considering a trust decay over time
ϕ
The parameter specifies the impact of past experience
T _{ i } (t)
At time t, the F ‐ AP_{ i }‘s trust assessment
\( {\mathrm{F}}_{\mathrm{KSBS}}^{\mathrm{t}} \)
KSBS at time t
d = (d _{1}, .. d _{n})
Disagreement point when players cannot reach an agreement
\( {\upomega}_{\mathrm{i}}^{\mathrm{t}} \)
The player F ‐ AP_{ i }‘s bargaining power at time t
ℝ^{n}
A jointly feasible utility solution set
τ
Factor to characterize the file popularity
\( \mathbb{M}= \) {ℳ_{1}.. ℳ_{ L }}
A multimedia file set consists of L popular multimedia files
\( \mathcal{Q}=\left[{\mathrm{\mathcal{M}}}_1,\dots, {\mathrm{\mathcal{M}}}_{\mathrm{L}}\right] \)
Vector to represent the popularity distribution among \( \mathbb{M} \)
\( \mathbb{I}={\left[0,1\right]}^{\mathrm{n}\times \mathrm{L}} \)
A twodimensional matrix to indicate the caching placement
\( {\mathcal{Z}}_{\mathrm{i}}^{\mathrm{l}} \)
The revenue from the lth file caching in the F ‐ AP_{ i },
\( {\mathrm{\mathfrak{C}}}_{\mathrm{i}}^{\mathrm{l}} \)
The cost from the lth file caching in the F ‐ AP_{ i },
\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)
New service request of \( {\mathrm{MU}}_{\mathrm{j}}^{\mathrm{i}} \)
Min_S(\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \))
The minimum spectrum requirement of \( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)
Min_C(\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \))
The minimum computation requirement of \( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)
χ ^{ i }
The currently using spectrum amount in the F ‐ AP_{ i }
y ^{ i }
The currently using computation amount in the F ‐ AP_{ i }
\( {\mathfrak{X}}^{\mathrm{i}} \)
The current fronthaul transmission rate
\( {\mathfrak{M}}^{\mathrm{i}} \)
The maximum fronthaul transmission rate

 B.
Solution concept for the superordinated game
In the superordinated game, game players are CS and FAPs, and they are rational to reach a winwin situation. In many situations, each rational agent is able to improve its objectives without preventing others from improving their objectives. Therefore, they are more prone to coordinate and willing to play cooperative games [19]. Usually, solution concepts are different in different games. For the CS and FAP interactions, the Kalai and Smorodinsky Bargaining Solution (KSBS) is an interesting solution concept. Like as the wellknown Nash Bargaining Solution (NBS), the KSBS also provides a fair and optimal solution in a cooperative manner. In addition, the KSBS can be used when the feasible payoff set is not convex. It is the main advantage of KSBS over the NBS. Due to this appealing property, the KSBS approach has been practically implemented to solve realworld problems [8].
In order to show the effectiveness of the KSBS, it is necessary to evaluate each player’s credibility. In this paper, we obtain the KSBS based on the FAPs’ trustworthiness. This information can be inferred implicitly from the FAPs’ outcome records. Therefore, we can enhance the effectiveness of KSBS while restricting the socially uncooperative FAPs. At time t, the F ‐ AP_{ i }’s trust assessment \( \left({\mathcal{T}}_{\mathrm{i}}\left(\mathrm{t}\right)\right) \) for the spectrum allocation process is denoted by$$ {\mathcal{T}}_i(t)=\left\{\left(1\beta \right)\times {\mathcal{T}}_i\left( t\varDelta t\right)\right\}+\left\{\beta \times \left(\raisebox{1ex}{$\left(\frac{U_i\left(\varDelta t\right)}{{\displaystyle {\sum}_{j=1}^n}{U}_j\left(\varDelta t\right)}\right)$}\!\left/ \!\raisebox{1ex}{$\left(\frac{\delta_i\left( t\varDelta t\right)}{{\mathrm{\mathcal{R}}}_{CS}}\right)$}\right.\right)\right\} $$(1)$$ \mathrm{s}.\mathrm{t}.,\upbeta =\raisebox{1ex}{$\left(\phi \times {\mathcal{T}}_{\mathrm{i}}\left(\mathrm{t}\Delta \mathrm{t}\right)\right)$}\!\left/ \!\raisebox{1ex}{$\left(1+\left\{\phi \times {\mathcal{T}}_{\mathrm{i}}\left(\mathrm{t}\Delta \mathrm{t}\right)\right\}\right)$}\right.\;\mathrm{and}\;\phi \ge 0 $$where U _{ i }(Δt) is the throughput of the F ‐ AP_{ i } during the recent Δt time period, and δ _{ i }(t − Δt) is the δ _{ i } value at the time period [t − Δt]. The parameter β is used to weigh the past experience by considering a trust decay over time. In addition, we introduce another parameter ϕ to specify the impact of past experience on \( {\mathcal{T}}_{\mathrm{i}}\left(\mathrm{t}\Delta \mathrm{t}\right) \) _{.} Essentially, the contribution of current information increases proportionally as ϕ increases. In this case, we can effectively adapt to the currently changing conditions while improving resiliency against credibility fluctuations [20]. In Eq. 1, the first term means the \( {\mathcal{T}}_{\mathrm{i}} \) value of the previous time period, and the second term represents the change ratio of δ _{ i } to U _{ i } at the current time period. In the point view of CS, \( {\mathcal{T}}_{\mathrm{i}}\left(\mathrm{t}\right) \) is a weighted average of these two terms.
Under the dynamic FRAN environment, we assume that FAPs request individually their spectrum resources to the CS at each time period. To adaptively respond to the current FRAN system conditions, the sequential KSBS bargaining approach gets the different KSBS at each time period. It can adapt the timely dynamic FRAN situations. At time t, the timed KSBS (\( {\mathfrak{F}}_{\mathrm{KSBS}}^{\mathrm{t}} \)) for the spectrum resource problem is mathematically defined as;$$ \begin{array}{l}\kern7.08em {\mathfrak{F}}_{KSBS}^t\left({\boldsymbol{S}}_{cs}^{\mathrm{\mathcal{R}}}\right)=\left\{{\delta}_1(t),{\delta}_2(t),\dots {\delta}_n(t)\right\}=\\ {}\\ {}\left(\frac{\;\mathbf{sup}\left\{{U}_1^t\left({\delta}_1(t)\right)\right\}{d}_1}{\omega_1^t\times \left({\mathbb{O}}_1^t{d}_1\right)}=\dots =\frac{\mathbf{sup}\left\{{U}_i^t\left({\delta}_i(t)\right)\right\}{d}_i}{\omega_i^t\times \left({\mathbb{O}}_i^t{d}_i\right)}=\dots =\frac{\mathbf{sup}\left\{{U}_n^t\left({\delta}_n(t)\right)\right\}{d}_n}{\omega_n^t\times \left({\mathbb{O}}_n^t{d}_n\right)}\right)\\ {}\\ {}\kern1.2em s. t.,, = \kern0.5em {\mathbb{O}}_i^t=\mathbf{max}\ \left\{{U}_i^t\left({\delta}_i(t)\right)\ \Big\ {U}_i^t\left({\delta}_i(t)\right)\in {\mathrm{\mathbb{R}}}^{\mathrm{n}}\right\},\kern0.49em {\omega}_i^t\kern0.49em =\raisebox{1ex}{${\mathcal{T}}_i(t)$}\!\left/ \!\raisebox{1ex}{${\displaystyle {\sum}_{j=1}^n}{\mathcal{T}}_j(t)$}\right.\\ {}\\ {}\kern1em \mathrm{and}\kern1em \mathbf{sup}\left\{{U}_i^t\left({\delta}_i(t)\right)\right\}=\mathbf{sup}\left\{{U}_i^t\left({\delta}_i(t)\right):\left\{\left({U}_1^t\left({\delta}_1(t)\right),\dots, {U}_n^t\left({\delta}_n(t)\right)\right)\right\}\subset {\mathrm{\mathbb{R}}}^{\mathrm{n}}\right\}\end{array} $$(2)where \( {\mathrm{U}}_{\mathrm{i}}^{\mathrm{t}}\left({\updelta}_{\mathrm{i}}\left(\mathrm{t}\right)\right) \) is the F ‐ AP_{ i }’s payoff with the strategy δ _{ i } during the recent time period (Δt). ℝ^{n} is a jointly feasible utility solution set, and a disagreement point (d) is an action vector d = (d _{1}, .. d _{ n }) ∈ ℝ^{n} that is expected to be the result if players, i.e., FAPs, cannot reach an agreement (i.e., zero in the system). \( {\upomega}_{\mathrm{i}}^{\mathrm{t}} \) (0 < \( {\upomega}_{\mathrm{i}}^{\mathrm{t}} \) < 1) is the player F ‐ AP_{ i }’s bargaining power at time t, which is the relative ability to exert influence over other players. \( {\mathbb{O}}_{\mathrm{i}}^{\mathrm{t}} \) is the ideal point of player F ‐ AP_{ i } at time t. Therefore, players choose the best outcome subject to the condition that their proportional part of the excess over the disagreement is relative to the proportion of the excess of their ideal gains. Geometrically, the \( {\mathfrak{F}}_{\mathrm{KSBS}}^{\mathrm{t}}\left({\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}}\right) \) is the intersection point between the bargaining set \( {\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}} \) and the line, which is drawn from the disagreement point (d) to the best utilities, i.e., the ideal gains, of players. Simply, we can think that the KSBS is the maximal point which maintains the ratios of gains [21]. Therefore, \( {\mathfrak{F}}_{\mathrm{KSBS}}^{\mathrm{t}}\left({\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}}\right) \) = {δ _{1}(t), δ _{2}(t), … δ _{ n }(t)} = {\( \sup \left\{{\mathrm{U}}_1^{\mathrm{t}}\left({\updelta}_1\left(\mathrm{t}\right)\right)\right\} \), \( \sup \left\{{\mathrm{U}}_2^{\mathrm{t}}\left({\updelta}_2\left(\mathrm{t}\right)\right)\right\} \), …, \( \sup \left\{{\mathrm{U}}_{\mathrm{n}}^{\mathrm{t}}\left({\updelta}_{\mathrm{n}}\left(\mathrm{t}\right)\right)\right\} \)} is a joint strategy, which is taken by the CS at time t.
In nondeterministic settings, \( {\mathfrak{F}}_{\mathrm{KSBS}}^{\mathrm{t}}\left({\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}}\right) \) is a selection function to define a specific spectrum allocation strategy for every FAPs. Due to the main feature of KSBS, the increasing of bargaining set size in a direction favorable to a specific FAP always benefits that FAP. Therefore, in our superordinated game, selfinterested FAP can be satisfied during the FRAN system operations. To practically obtain the \( {\mathfrak{F}}_{\mathrm{KSBS}}^{\mathrm{t}}\left({\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}}\right) \) in Eq. 2, we can rethink the KSBS as a weighted maxmin solution like as$$ \begin{array}{l}{\mathfrak{F}}_{KSBS}^t\left({\boldsymbol{S}}_{cs}^{\mathrm{\mathcal{R}}}\right)=\left\{{\delta}_1(t),{\delta}_2(t),\dots {\delta}_n(t)\right\}=\\ {}\\ {}\kern3.24em = arg\underset{\left\{{\delta}_1(t),{\delta}_2(t),\dots {\delta}_n(t)\right\}}{max}\left\{\underset{\delta_{i,1\le i\le n}(t)}{min}\left(\frac{\mathbf{sup}\left\{{U}_i^t\left({\delta}_i(t)\right)\right\}{d}_i}{\omega_i^t\times \left({\mathbb{O}}_i^t{d}_i\right)}\right)\right\}\end{array} $$(3)  C.
Solution concept for the subordinated games
Edge processing is a key emerging trend in the FRAN system. It refers to the localization of computing, communication, and storage resources at the FAPs. In the FRAN architecture, FAPs are connected to the CS through fronthaul links. Under this centralized structure, the performance of FRANs is clearly constrained by the fronthaul link capacity; it incurs a high burden on fronthaul links. Therefore, a prerequisite requirement for the centralized CS processing is the high bandwidth and low latency fronthaul interconnections. However, during the operation of FRAN system, unexpected growth of service requests may create a traffic congestion. It has a significant impact on the FRAN performance. To overcome the disadvantages of FRAN architecture imposed by the fronthaul constraints, new techniques have been introduced with the aim of reducing the delivery latency by limiting the need to communicate between the CS and MUs [6].
Currently, there are evidences that MUs’ downloading of ondemand multimedia data is the major reason for the data avalanche over FRAN; numerous repetitive requests on the same data lead to redundant transmissions. Usually, multimedia data are located in the CS and far away from MUs. To ensure an excellent QoS provisioning, an efficient solution is to locally store these frequently accessed data into the cache memory of FAPs while reducing the transmission latency; it is known as caching. This approach can effectively mitigate the unnecessary fronthaul overhead caused by MUs’ repetitive service requests. Therefore, CS, FAPs and MUs are all the beneficiaries from the local caching mechanism [22].
In the subordinated game, an efficient caching mechanism is designed by carefully considering the relations and interactions among CS, FAPs and MUs. This approach can relive the heavy traffic load at fronthaul links, and also decrease the request latency; it results in better QoS [6]. A practical caching mechanism is coupled with the data placement. In our FRAN architecture, we assume that a multimedia file set \( \mathbb{M} \) = {ℳ_{1},…, ℳ_{ L }} consists of L popular multimedia files in the CS, and files in \( \mathbb{M} \) can be possibly cached in each FAP. The popularity distribution among \( \mathbb{M} \) is represented by a vector \( \mathcal{Q} \) = [g _{1},…, g _{ L }]. Generally, the vector \( \mathcal{Q} \) can be modeled by a Zipf distribution [22];$$ {g}_l=\raisebox{1ex}{$\left(\frac{1}{l^{\tau}}\right)$}\!\left/ \!\raisebox{1ex}{$\left({\displaystyle {\sum}_{f=1}^L}\frac{1}{f^{\tau}}\right)$}\right., s. t.,1\le l\le L\kern0.24em and\;\tau >0 $$(4)where the τ factor characterizes the file popularity. In this study, we assume that MUs in each FAP area request independently the lth file ℳ_{ l,1 ≤ l ≤} _{ L }. Therefore, the τ value is different for each FAP. According to (4), ℳ_{1} (or ℳ_{ L }) has the highest (or lowest) popularity. The CS intends to rent a frequencyaccessing fraction of \( \mathbb{M} \) for caching to maximize the FRAN system performance. In this study, we can denote the caching placement strategy as a twodimensional matrix \( \mathbb{I}={\left[0,1\right]}^{\mathrm{n}\times \mathrm{L}} \) consisting of binary entries where 1 is indicating the caching placement in a FAP, and 0 is not. \( \mathbb{I} \) is defined as$$ \mathbb{I}\triangleq \left[\begin{array}{ccc}\hfill {I}_1^1\hfill & \hfill \cdots \hfill & \hfill {I}_1^L\hfill \\ {}\hfill \vdots \hfill & \hfill \ddots \hfill & \hfill \vdots \hfill \\ {}\hfill {I}_n^1\hfill & \hfill \cdots \hfill & \hfill {I}_n^L\hfill \end{array}\right]\in {\left[0,1\right]}^{n\times L} $$(5)where \( {\mathrm{I}}_{\mathrm{i}}^{\mathrm{l}}=1 \) means that the file ℳ_{ l } is cached at the F ‐ AP_{ i } and \( {\mathrm{I}}_{\mathrm{i}}^{\mathrm{l}}=0 \) means the opposite. For the F ‐ AP_{ i }, the profit (\( {\mathrm{\Re}}_{\mathrm{i}}^{\mathrm{c}} \)) gained from the local caching mechanism can be defined as follows;$$ {\mathrm{\Re}}_i^c={\displaystyle \sum_{l=1}^L}\left({g}_l^i\times {\mathrm{\mathcal{L}}}^i\times {\mathcal{Z}}_l^i\times {I}_i^l\right){\displaystyle \sum_{l=1}^L}\left({\mathrm{\mathfrak{C}}}_l^i\times {I}_i^l\right),\mathrm{s}.\mathrm{t}.,{g}_l^i\in {\mathcal{Q}}^i $$(6)where \( {\mathcal{Q}}^{\mathrm{i}} \) is the vector \( \mathcal{Q} \) of F ‐ AP_{ i } and ℒ^{ i } is the total number of service requests on average. \( {\mathcal{Z}}_{\mathrm{i}}^{\mathrm{l}} \) and \( {\mathrm{\mathfrak{C}}}_{\mathrm{i}}^{\mathrm{l}} \) is the revenue and cost from the lth file caching in the F ‐ AP_{ i }, respectively. From the viewpoint of F ‐ AP_{ i }, the fraction [\( {\mathrm{I}}_{\mathrm{i}}^1\dots {\mathrm{I}}_{\mathrm{i}}^{\mathrm{L}} \)] of \( \mathbb{I} \) (\( {\mathcal{Q}}^{\mathrm{i}} \)) needs to be optimized for maximizing the \( {\mathrm{\Re}}_{\mathrm{i}}^{\mathrm{c}} \).
Based on the current caching placement, Service Admission Control (SAC) algorithm should be developed to make admission decisions to maximize the spectrum efficiency while maintaining a desirable overhead level. Especially, when the requested services are heavy, that is, the sum of the requested resource amount exceeds the currently available system capacity, the SAC algorithm comes into act whether to accept a new service request or not. Based on the acceptance condition, such as the current caching status and resource capacity, the SAC problem can be formulated as a joint optimization problem. In this problem, we take into account the maximization of spectrum efficiency while minimizing the fronthaul overhead.
In the proposed scheme, we set out to obtain fundamental insights into the SAC problem by means of a game theoretic approach. Therefore, the subordinated game is designed to formulate the interactions of the FAP and MUs while investigating the system dynamics with imperfect information. To implement our subordinated game, we adopt the concept of dictator game, which is a game in experimental economics, similar to the ultimatum game, first developed by D. Kahneman et al. [23]. In the dictator game, one player, called the proposer, distributes his resource, and the other players, called the responders, simply accept the decision, which is made by the proposer. As one of decision theory, the dictator game is treated as an exceptional noncooperative game or a multiagent system game that has a partnerfeature and involves a tradeoff between self and otherutility. Based on its simplicity, the dictator game can capture an essential characteristic of the repeated interaction situation [8].
In the proposed subordinated game model, each FAP is the proposer and MUs are the responders. They interact with each other and repeatedly work together toward an appropriate FRAN performance. To effectively make SAC decisions, the proposer considers the current system conditions such as the available spectrum amount, the current caching placement and fronthaul overhead status. By a sophisticated combination of these conflicting condition factors, the proposer attempts to approximate a temporary optimal SAC decision. The SAC decision procedure is shown in Fig. 2.According to the SAC procedure, each F ‐ AP_{ i } can maintain the finest SAC solution while avoiding the heavy computational complexity or overheads. For the subordinated game, we propose a new solution concept, Temporal Equilibrium (TE). In the proposed scheme, all MUs follow compulsorily the decision of FAPs, and the outcome profile of our SAC process constitutes the TE, which is the current service status.$$ T E={\overrightarrow{\mathbf{\mathcal{T}}\mathbf{\mathcal{E}}}}_i\Big\left({\boldsymbol{\mu}}_i{\displaystyle \cup }{\boldsymbol{\psi}}_i\right)\to \left({\Theta}_{j,1\le j\le m}^i\in \left({\boldsymbol{\mu}}_i{\displaystyle \cup }{\boldsymbol{\psi}}_i\right)\right){\displaystyle \cup }{\overrightarrow{\mathbf{\mathcal{T}}\mathbf{\mathcal{E}}}}_i=\left\{\begin{array}{c}\hfill {\Theta}_j^i\in {\boldsymbol{\mu}}_i, if\;{\Theta}_j^i\; is\; accepted\hfill \\ {}\hfill \hfill \\ {}\hfill {\Theta}_j^i\in {\boldsymbol{\psi}}_i, otherwise\kern0.72em \hfill \end{array}\right. $$(7)where \( \overrightarrow{\mathcal{T}\mathrm{\mathcal{E}}} \) is the set of MUs in the F ‐ AP_{ i } and μ _{ i }, ψ _{ i } are the MUs’ set of accepted or rejected by the F ‐ AP_{ i }, respectively. Therefore, TE is the status quo of dictator game.
 D.
The main steps of proposed FRAN control algorithm
For 5G wireless communications, the FRAN architecture is a promising paradigm to provide high spectrum efficiency and improved QoS. The core idea of FRAN is to take full advantages of distributed edge processing, cooperative spectrum allocation, and reduced communication latency [24–26]. However, it is questionable whether existing FRAN control schemes are adequate in dynamically changing FRAN environments. In this study, we have studied the joint design of spectrum allocation and SAC decision in an FRAN architecture. Focusing on the practical assumption, we develop a new embedded game model while investigating the benefits and challenges of FRAN control mechanisms. In our embedded game approach, the superordinated game for spectrum allocations and the subordinated game for SAC decisions are interlocked and serially correlated. The subordinated game depends on the outcome of the superordinated game, and the result of subordinated games is the input back to the superordinated game process. Structurally, the multiple subordinated games are nested in the superordinated game, and they are linked based on the stepbystep interactive feedback process. It may be the only realistic approach to solve complex and dynamically changing FRAN control problems. Usually, the traditional optimal and centric algorithms have exponential time complexity. However, the proposed distributed control method has only polynomial time complexity. The main steps of the proposed FRAN control algorithm are given next (see Fig. 3). Step 1:
At the initial time, the spectrum resource allocation \( {\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}} \) = {δ _{1}, δ _{2},…. δ _{ n }} and trustworthiness (\( \mathcal{T} \)) for FAPs are equally distributed. This starting guess guarantees that each FAP enjoys the same benefit at the beginning of the game.
 Step 2: Control parameters are given from the simulation scenario (refer to Table 2). To fairly compare with the existing schemes, the system parameters are carefully selected in our simulation model.Table 2
System parameters used in the simulation experiments
Application type
Computation offloading
Computation requirement
Minimum spectrum requirement
Maximum spectrum requirement
I
Y
300 MHz/s
128 kbps
128 kbps
II
N
N/A
256 kbps
768 kbps
III
Y
600 MHz/s
384 kbps
640 kbps
IV
N
N/A
512 kbps
1.28 Mbps
Parameter
Value
Description
n
10
The number of FAPs
ℛ_{ CS }
200 Mbps
The total spectrum resources of CS
\( \mathcal{C} \)
5 GHz
The FAP’s computation capacity
ϕ
0.2
A factor to specify the impact of recent experience
Δt
1 s
The time interval to monitor the FRAN system
\( \mathcal{Z} \)
5 / one bps
The revenue from the caching per one bps
ℭ
1 / one bps
The cost from the caching per one bps
τ
[0.1–0.9]
A factor to characterize the file popularity: randomly selected for FAP
L
10
The popular multimedia files in the CS for caching
\( \mathfrak{M} \)
30 Mbps
The maximum fronthaul transmission rate
ϵ
0.95
A control factor to consider the fronthaul congestion
 Step 3:
By taking into account the current FRAN situations, our superordinated and subordinated games are executed in parallel.
 Step 4:
The trustworthiness (\( \mathcal{T} \)) for each FAP is modified periodically by using (1).
 Step 5:
At each superordinated game period, \( {\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}} \) = {δ _{1}, δ _{2},…. δ _{ n }} is dynamically adjusted according to the timed KSBS manner. According to (2), the \( {\mathfrak{F}}_{\mathrm{KSBS}}^{\mathrm{t}}\left({\mathrm{S}}_{\mathrm{cs}}^{\mathrm{\mathcal{R}}}\right) \) is obtained, and each δ value is decided for the next game period.
 Step 5:
At each subordinated game period, the caching placement in each FAP occurs while maximizing the ℜ^{ c } according to Eqs. 4, 5 and 6.
 Step 7:
In a distributed manner, each FAP makes MUs’ admission decisions based on the service admission procedure of Fig. 2, and the TE is obtained using (7).
 Step 8:
The superordinated and subordinated games are interlocked and serially correlated. Based on the assigned δ value, each FAP performs its subordinated game, and the result of each subordinated game is the input back to the superordinated game.
 Step 9:
Based on the interactive feedback mechanism, the dynamics of embedded game can cause cascade interactions of game players and players can make their decisions to quickly find the most profitable solution.
 Step 10:
Under widely diverse FRAN environments, the CS and FAPs are selfmonitoring constantly for the next embedded game process; proceed to step 3.
 Step 1:
4 Performance evaluation

The simulated system consists of one CS, 10 FAPs and multiple MUs. The number of MUs (m) for each FAP is generated based on the process for new service requests.

The process for new service requests is Poisson with rate λ (services/s), and the range of offered service load was varied from 0 to 3.

There are four different service applications. They are randomly generated from MUs, and some of them are computation offloading tasks.

The durations of service applications are exponentially distributed.

The total spectrum resources of CS (ℛ_{ CS }) is 200 Mbps.

For each FAP, the computation capacity (\( \mathcal{C} \)) is 5 GHz, and the fronthaul link capacity is 30 Mbps.

The cache size in each FAP is the same as the file set \( \mathbb{M} \) in the CS.

System performance measures obtained on the basis of 100 simulation runs are plotted as functions of the service generation rate.

For simplicity, we assume the absence of physical obstacles in the experiments.
Performance measures obtained through simulation are the normalized FRAN throughput, spectrum efficiency, and fronthaul transmission delay. To facilitate the development and implementation of our simulator, Table 2 lists the system control parameters.
5 Conclusions
As a promising paradigm for the 5G communication system, the FRAN has been proposed as an advanced socially aware wireless networking architecture to provide the higher spectral efficiency while maximizing the system performance. In this study, we have studied joint design of cloud and edge processing in the FRAN system to solve the resource allocation and SAC problems. Based on the newly developed embedded game model, we have explored the feasibility of FRAN control decision process and the practicality for the realworld implementation. In our embedded game structure, the SAC algorithm is nested in the spectrum allocation algorithm to effectively control the conflict problem of FRAN system agents. Based on the interactive feedback mechanism, the proposed scheme has the potential to handle multiple targets without using more complex multitarget tracking algorithm. The extensive simulation result is very encouraging, showing that our embedded gamebased approach provides a more effective way to control the FRAN system than the other existing schemes. Open issues for the further research are the designs and validations of the original FRAN systems for big data mining, cognitive radio, softwaredefined network, and network security problems. The progress of trial tests and test bed development of FRANs can be anticipated to be promoted in the future, which makes FRANs’ commercial rollout as early as possible.
Declarations
Acknowledgements
This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (IITP20172014000636) supervised by the IITP (Institute for Information & communications Technology Promotion), and was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2015R1D1A1A01060835)
Author’s contribution
SK: is a sole author of this work and ES (i.e., participated in the design of the study and performed the statistical analysis).
Competing interests
The author, Sungwook Kim, declares that there is no competing interests regarding the publication of this paper.
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Authors’ Affiliations
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