Adaptive Multiservice Resource Allocation Algorithm With Wireless Network Virtualization

Wireless network virtualization (WNV) is emerging as a new paradigm to provide high speed communications and it is identified as one of the key enabling technologies to bring fifth-generation (5G) networks into fruition. With network slicing, physical networks are partitioned into multiple virtual networks to serve different types of service while satisfying their specific requirements. In this study, we present an adaptive spectrum control scheme for the WNV technology. Particularly, we develop a two-tier resource allocation algorithm to utilize a multi-service wireless network. In order to increase flexibility and independence among different network slices, our proposed approach is decoupled into two level bargaining games. These games are designed to solve the inter and intra slice resource allocation problems while ensuring traffic services with multiple requirements. Using four different bargaining solutions, we provide considerable benefits when network agents successfully cooperate and maintain an optimal performance balance. Simulation results and analyses are provided to reveal the effectiveness of our proposed approach compared with existing WNV based spectrum control protocols. Finally, we address some challenges and identify research areas for future studies.


I. INTRODUCTION
With the explosive growth of demands for a variety of communication services, wireless traffic has experienced explosive growth in recent years. Based on market predictions, mobile data traffic will keep growing at an astonishing compound annual growth rate of 47 percent toward 2030. Moreover, the average year-on-year subscriber growths of 5%-15% are expected to continue well into the next decade. At the same time, user expectation on service quality also continues to increase, regardless of their location or network load conditions. In response to this traffic explosion, a number of technical studies aim at breaking the capacity bottleneck by densification. To promote network capacity, we can increase the deployment density of low-power small base stations; it is ultra-dense small cell network (UDNs). Recently, The associate editor coordinating the review of this manuscript and approving it for publication was Barbara Masini . 5G network systems are expected to provide aggressively reuse spectrum through the UDN infrastructure [1], [2].
Throughout the 5G network's standardization, network densification has been the main driving force of cellular technology in the years to come, with the full integration of small cell technique in their specifications, and the commercial deployment of small cell products. However, it is important to realize that these new UDNs are fundamentally different from the traditional cellular networks, and thus UDNs cannot be deployed and operated in the same way as in the last 25 years. Therefore, UDNs are creating new and significant challenges for network system operators, and becoming increasingly complex with network planning and optimization techniques. For example, the scarce wireless spectrum resource and the network load imbalance in UDNs are the main challenges. Moreover, the operating and capital expenses are high because of the dense deployment of small base stations [1]- [3]. VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Owing to these problems, network sharing mechanism is promising for future networks. It allows to share the infrastructure and wireless spectrum resource among wireless end users. In addition, the decoupling of services and infrastructures is necessary in order to meet more service demands. This approach can convert the service mode from physical to virtual entities while reducing expenses. Otherwise, it is difficult to bring in new technologies or adjust the existing technologies because of the complex composition of infrastructure providers (InPs). Therefore, virtualization for UDNs has been considered as a promising technology in 5G network era. By virtualization, the physical infrastructure and resources of UDNs can be completely abstracted, pooled, and integrated into many virtual resources, which then can be effectively shared to increase network capacity [2].
As a promising network sharing framework, wireless network virtualization (WNV) allows diverse services and applications to coexist on the common network infrastructure. Simply, the WNV technique can be interpreted as decoupling and sharing. Specifically, it is the process of combining hardware, software resources and network functionality to enable resource sharing and to decouple the infrastructure from the services it provides. With the WNV, physical resources, such as infrastructure, wireless spectrum, backhaul and fronthaul, of a base station (BS) owned by an InP are abstracted into isolated virtual resources, called slices. As wireless services providers, mobile virtual network operators (MVNOs) do not own their wireless network infrastructures and network resources; they transparently share the slices, and virtually owns the entire BS resources. Several benefits can be achieved through the WNV technology. First, the resource utilization can be improved through statistical multiplexing. Second, the deployment and operation expenses can be reduced through sharing. Third, service providers can enrich their services through virtualization [4], [5].

A. RESEARCH MOTIVATIONS
Even though the WNV technology has many advantages as a new control framework, there is still a major challenge, such as a designing of resource allocation process. In WNV, resource allocation means the problem of how to slice the physical resources for virtual networks to accommodate the dynamic demands of multiple MVNOs. This resource allocation problem is more challenging if network agents are selfinterested. When each agent acts selfishly, it is very hard to achieve a desirable social efficiency. In this study, our main goal is to design a novel WNV resource allocation scheme, i) to boost network capacity, ii) to improve spectrum resource utilization, iii) to promote quality of service, and iv) to strike a performance balance. However, it is a complex and difficult work to satisfy these requirements. To overcome these challenges, a drastic change in control paradigm is required [1], [5].
In this study, we design a new spectrum control scheme with the WNV technology in the UDNs. Under a dynamically changing 5G network environment, it should provide inter and intra slice customization through efficient resource allocation. The major challenge of our proposed scheme is to coordinate the different MVNOs while ensuring good global properties. To the best of our knowledge, it is a hot research topic, but has not been well investigated. In our proposed scheme, autonomous, distributed, and intelligent MVNOs coordinately make rational and strategic decisions based on novel solution concepts. This scenario may fall into cooperative game theory. Cooperative game theory offers an effective model of cooperation between rational game players. The critical issue of cooperative games is how to distribute surplus outcome among all players. Therefore, various distribution solutions have been introduced by embodying different criteria [6].

B. TECHNICAL CONCEPTS
In cooperative game theory, bargaining solutions strive to understand the interplay between efficiency and fairness. Usually, bargaining solutions can be categorized into two different generalizations; one is proportional solution, and the other is Nash solution. For surplus sharing and rationing problems, proportional solution corresponds to the basic idea of Kalai-Smorodinsky solution. Depending on the kind of properties, Nash solution corresponds to the standard Nash bargaining idea. Under the assumption of unlimited liability, the proportional solution preserves the self-duality nature of equal losses solution for rationing problems and the equalgains solution for surplus sharing problems, whereas the Nash solution preserves the idea of egalitarian allocations; it is defined by equal weighted net gains or losses from the entitlements point [7].
Usually, MVNOs may be concerned with the proportion of their claims that is satisfied, or with the total amount they get. In order to relate both perspectives, proportional bargaining solution is considered as a standard solution and the most widely used idea. The main reason is the fact that a proportional solution allows individuals to compare the treatment afforded to each one, in terms of the proportion of the claim that is honored. Therefore, from the viewpoint of relative fairness, the obtained amount per unit of individual claim is the same for all. As an interesting interpretation of proportionality in a conflicting claims problem, the egalitarian bargaining solution corresponds with the proportional rule, whereas when considering different reference points the Nash solution provides different loss rules in conflicting claims problems [8].
Since the 2000s, many research papers have taken a game theoretic approach to bankruptcy problems in terms of adequately generalized properties. They interpret the bankruptcy problem as the feasible set of a bargaining problem as introduced by J. Nash. This situation may be viewed as a theory of consensus, because it is often assumed that a Restricted Truncated Proportional Solution (RTPS). Based on the bargaining game theory, these solutions derive new axiomatic characterizations, which concern changes in the claims. To implement the WKSBS, CPS, TPS and RTPS, individual utility is normalized in such a way that allocating nothing corresponds to a utility level of zero. Therefore, it is convenient to consider the zero vector as a natural benchmark for allocations instead of an exogenous disagreement point as within bargaining problems. The WKSBS, CPS, TPS and RTPS satisfy a number of appealing properties from the point of view of cooperative game theory [9], [14].

C. MAIN CONTRIBUTIONS
According to the main concept of proportional bargaining solutions, we develop a novel spectrum control scheme with the WNV technology. In the UDN platform, each individual MVNO fair-efficiently share the limited spectrum resource of each BS by considering the current traffic conditions. For the inter-MVNO slice allocation process, the inter-slice customization is operated based on the idea of WKSBS. For the intra-MVNO slice allocation process, the intra-slice customization is implemented according to the ideas of CPS, TPS and RTPS. These solutions work together toward an appropriately balanced system performance. Our interactive joint game approach provides the most proper combination of different bargaining solutions while ensuring good global properties. In detail, the major contributions of this study are as follows: • This study considers the spectrum control problem in the WNV platform. During the interactive cooperative game paradigm, the control decisions for the resource allocation problems are made in an effective online fashion based on the different proportional bargaining solutions.
• At first-tier, multiple MVNOs fair-efficiently shares the BS's spectrum resource. To effectively coordinate MVNOs, we adopt the main characteristics of the WKSBS, and the inter-MVNO slice allocation process is dynamically operated based on the current conditions of MVNOs.
• At second-tier, each individual MVNO allocates its allocated spectrum resource for its corresponding devices. The CPS, TPS and RTPS solutions are used to implement intra-MVNO slice allocation processes by considering the heterogeneity of different traffic types.
• Under our two-tier bargaining procedure, we explore the interaction of WKSBS, CPS, TPS and RTPS while leveraging the synergistic features. The main novelty of our approach lies in the reciprocal combination of four different proportional bargaining solutions.
• We evaluate the performance of the proposed scheme via extensive experiments in a simulated environment. Our experimental results reveal that the proposed joint-bargaining approach can achieve a higher UDN system performance compared with the existing WNV based spectrum control protocols.

II. RELATED WORK
So far, there have been many types of research about WNV resource allocation problems in the academic community. L. Wang et al. propose the Hierarchical Game based Resource Management (HGRM) scheme for virtualized UDNs [2]. They formulate the virtual resource allocation problem as a hierarchical game and obtain the closed-form spectrum control solution. In the HGRM scheme, a two-layer architecture is presented to map the resource allocation problem from physical to virtual networks. And then, a hierarchical game is adapted to address matching interactions between resource providers and requests in the proposed two-layer architecture. To promote spectrum resource efficiency, a new low-complexity distributed customer-first algorithm is implemented, and the existence and uniqueness of equilibrium are analyzed for the HGRM scheme. Finally, simulation results confirm the effectiveness of the HGRM scheme in improving network performance while reducing the user access-reject probability [2]. The Multi-scale Virtualized Resource Allocation (MVRA) scheme is designed for the WNV platform, which is developed as a two time-scale hierarchical algorithm to reduce the complexity [4]. For the increasing independence among heterogeneous users, the InP virtualizes spectrum resources into three different types in large time period. At the begin of each small time slot, MVNOs assign their sub-channels to different users to maximize the total utility. To balance the tradeoff between the network stability and the system performance, the spectrum control problem is formulated as a mixed integer optimization problem. To tackle this problem, the MVRA scheme is implemented as a two-step process consisting of a heuristic sub-channel assignment method and a fast barrier method. By using Lyapunov drift-plus-penalty function, the original optimization problem is transformed into a Lyapunov optimization problem. Even though this approach does not fully consider the fairness among users, simulation results show the effectiveness of the MVRA scheme [4].
In [10], the Multi-service Hierarchical Resource Allocation (MHRA) scheme is developed with the WNV technology. Based on the three generic scenarios in 5G networks, the MHRA scheme is a two-dimension time scale resource allocation algorithm in the WNV platform. In order to increase flexibility while reducing the task complexity, the resource allocation problem is decoupled into two time scales: large time period for inter-MVNO resource allocation and small time slot for intra-MVNO resource scheduling. In the inter-MVNO resource process, the spectrum resource is virtualized to support services with multiple service requirements. Due to the different optimization objectives, it can be set up as a multi-objective optimization problem, which is solved by using the weighted Tchebycheff approach. In the intra-MVNO resource process, the allocated virtual resource is managed in every transmission time interval for a better VOLUME 10, 2022 performance. This process can be transformed into a delayaware optimization problem, which is solved by using a distributed heuristic algorithm. Finally, the simulation results validate that the MHRA scheme has a good performance close to the optimal solution with a lower complexity [10].
The HGRM, MVRA and MHRA schemes have introduced unique challenges to efficiently solve the virtualized spectrum control problem. Recently, they have attracted considerable attention because of their various advantages. Although a number of researches on spectrum control problems in virtualized networks have been done, bargaining game based approach is still at the beginning level. To the best of our knowledge, we are the first to propose a two-tier bargaining model for the UDN spectrum control problem by applying the concept of virtualization. Compared to the existing HGRM, MVRA and MHRA schemes [2], [4], [10], we demonstrate that the proposed scheme achieves a better UDN system performance with the WNV technology.

III. THE SPECTRUM CONTROL SCHEME WITH WNV TECHNOLOGY
In this section, we first introduce the UDN system infrastructure, and explain the main ideas of the WKSBS, CPS, TPS and RTPS. Subsequently, our joint interactive bargaining model is formulated for the spectrum control process in the WNV platform. Finally, we explain the main steps of our proposed spectrum control algorithm.
A. The UDN system infrastructure with WNV As illustrated in Fig. 1, we consider a UDN infrastructure with an InP including multiple BSs and wireless resources. B = {B 1 , B 2 , . . . , B n } is the set of BSs, and B i ∈ B has its own spectrum resource, i.e., M B i . The B i provides its service to a set N B i of IoT devices, which are covered by the B i . Then, N = B i ∈B N B i represents the total number of IoT devices in the multi-cell UDN system. We assume that individual IoT devices generate three different type services such as primary services (PSs), secondary services (SSs) and tertiary services (TSs). The PSs are latency-sensitive services like as self-driving and drone control, which need low-latency QoS requirements. The SSs are characterized by high data rate like as high definition videos and virtual reality with high transmission data rates. For connection density like as smart city and smart home, the TSs need a large number of local and temporary transmissions with no strict QoS requirements in capacity, latency, and reliability. The InP virtualizes each BS's spectrum resource into three slices, i.e., S P , S S and S T , and assigns them for PSs, SSs, and TSs, respectively. In each BS, three MVNOs, i.e., M P , M S and M T , are installed to share and operate the virtualized S P , S S and S T , respectively [4], [10].
In our proposed scheme, we design a two-tier spectrum control process for UDNs. Without a loss of generality, we consider the B i ∈ B as an example.
and assigns these slices for its corresponding traffic services. For the B i , our proposed scheme consists of two tiers. At the first tier, the inter-slice spectrum allocation problem is formulated as the game G B i . In this game, the M P , M S and M T work together to solve the matching problem of slice demands and physical spectrum resource M B i in the B i . At the second tier, the intra-slice scheduling problem for each type service is modeled as three games such as For these games, the M P , M S and M T work independently in a distributed fashion. Based on service types, they schedule their assigned S P , S S and S T slices to their corresponding PSs, SSs, and TSs, respectively. Under dynamically changing traffic environments, a fixed spectrum allocation and scheduling approach cannot effectively adapt to current UDN conditions. Therefore, the M P , M S and M T must be dynamically adjustable. To satisfy this goal, we design a joint interactive bargaining game (G) in a coordination manner; G is subdivided into two-tier subgames; And, different bargaining solutions are adopted to effectively solve each bargaining games. Formally, we define game . . , t c , t c+1 , . . .} denotes time, which is represented by a sequence of time steps.

B. BARGAINING SOLUTIONS FOR COOPERATIVE GAME MODELS
The cooperative game theory will serve as a very convenient template for the theory of bargaining with claims. In 1950, J. Nash proposed Nash bargaining solution based on axioms pertaining to changes in the feasible set. In the Nash traditional bargaining model, the outcome of a negotiation is a function only of the bargaining set and the disagreement point. It has been noted by a number of literatures that other aspects of the environment influence the outcome of the bargain. Recently, the focus has shifted to the proportional bargaining solution. This approach can be fruitfully adapted to develop the basic idea of Kalai-Smorodinsky solution; the utility gains at the compromise are proportional to what they would be at the ideal point, the point whose ith coordinate is the maximal utility the player i could obtain in the part of bargaining set [11].
To characterize the basic concepts of proportional bargaining solutions, we preliminarily define some mathematical expressions. The nonempty and finite set N = {1, . . . , n} will denote the game player set. R (R + , R ++ ) denote the set of all (non-negative, positive) real numbers and let R n R n + , R n ++ be the n-fold Cartesian product of R (R + , R ++ ). Vector inequalities in R n are denoted by ≥, >, . For any x, y ∈ R N + , x ≤ y denotes x i ≤ y i for all i ∈ N , and x < y denotes x i < y i for all i ∈ N . The zero-vector x ∈ R N + with x i = 0 for all i ∈ N is denoted by 0 N . E ⊆ R N + is the set of attainable utility allocations where E = x ∈ R N + |∃ y∈E : y ≥ x . Elements of E are assumed to be normalized such that allocating nothing to a player corresponds to zero utility. Let c be the vector of claims of N on E where c ∈ R N + with c <x for all x ∈ E. The claim vector c represents the individual utility claims on the resource. With the limited resource amount M ∈ R + , a bargaining problem is denoted by (N , E, c) where E = x ∈ R N + | i∈N x i ≤ M , c ∈E and E = {0 N } . Let (N , E, c) ∈ n and a solution is a function f : n → R n that associates a unique point of E, f (N , E, c), called the solution outcome of (N , E, c) [12].
For any t ∈ R ++ , the set (t · E) ⊆R N + is defined by (t · E) = {t · x| x ∈ E}. Note that u t·E = t · u E for all t ∈ R ++ . For any set of payoff allocations E ⊆ R n ++ , u E is the vector of utopia values; it is given by The following solution definitions are WKSBS, CPS, TPS and RTPS [12], [13].
Definition 2: The CPS for all (N , E, c) ∈ n is CPS (N , E, c), which is the maximal point of E on the segment connecting d = {0 N } and c. To express it as a mathematical formula type,  [13].
is the set of positive claimants.

C. THE PROPOSED SPECTRUM CONTROL SCHEME IN THE UDNs
In the UDN infrastructure, the InP virtualizes all base stations' spectrum resources with WNV technology. Each individual base station operate its two-tier game (G) in a distributed manner. In the viewpoint of B i ∈ B, we explain the procedure of G, which consists of In the G B i , three MVNOs, i.e., M P , M S and M T , are game players, who need S P , S S and S T slices to ensure their services. The utility payoff obtained by each MVNO depends on the current traffic flow and the amount of allocated slice. According to the satisfaction from MVNOs, the utility func- are derived as follows: where χ, σ , η are control parameters for U M P (·), ξ , ε, ζ are system adjustment factors for U M S (·), and γ , are control parameters for U M T (·). R B i P , R B i S , R B i T are the requested amount from the M P , M S , M T , respectively. To implement our spectrum allocation algorithm, we concern the different characteristics of PSs, SSs, and TSs. Therefore, we should treat asymmetrically the PSs, SSs, and TSs. Usually, one main feature of traditional bargaining solutions is Symmetry. However, assuming Symmetry is unreasonable for the first-tier spectrum allocation problem; imposing Symmetry can mean, assuming equality of bargaining skill among the PSs, SSs, and TSs. In order to mediate the particularity of different traffic services, we adopt the idea of WKSBS by relaxing Symmetry, and make the solution more flexible [14]. Therefore, the idea of WKSBS is adopted for the solution of G B i ; it is given by: where W M and U * M are the vectors of weights and utopia values for MVNOs, respectively. According to (2), the values of S B i P , S B i S and S B i T are obtained. Based on the result of G B i , the second-tier spectrum scheduling algorithm is operated. Independently, individual MVNOs schedule their slices for their corresponding devices. Using the S B i P , the G M P B i is designed to support multiple PSs. In the G M P B i , devices in the N P B i , i.e., D B i ,P j ∈ N P B i , are game players and the scheduled spectrum amount for the D B i ,P j , i.e., S B i ,P j , is his strategy. The utility function of D B i ,P j , i.e., U B i ,P j (·), is defined as follows: where α, δ, θ are control parameters for U B i ,P j (·). From the viewpoint of the M P , PSs should be operated monotonically due to the feature of latency sensitivity. Therefore, SSN, EM, D and IIA axioms are more desirable, hence we adopt the CPS for the solution of G M P B i . According to each service request, devices in the N P B i have their claims, which simply maximize their payoffs. With their claims, the S B i ,P j value is decided by using the concept of the CPS. For the G M P B i , the CPS is given by: . 51520 VOLUME 10, 2022 . According to (4), the S B i ,P j is obtained for where φ, β, ρ, ω are control parameters for U B i ,S k (·). Owning to the high data rate characterization, the M S focuses on the axioms of CC and PA. Therefore, we accept the concept of TPS for the G M S B i , and it is obtained as follows: where µ, τ are control parameters for U B i ,T k (·). To support TSs, we need a large number of temporary transmissions with no strict QoS requirement. Therefore, the M T strongly emphasizes the restricted truncated proportionality. Therefore, we use the approach of RTPS for the G M T B i , and it is given by: Devices in the N T B i have also their truncated claims ĉ T ,D l to ensure their TSs. With their truncated claims, the S B i ,T l value is decided by using the concept of the RTPS. For s.t.,

D. MAIN STEPS OF PROPOSED SPECTRUM CONTROL ALGORITHM
In this study, we have developed a new spectrum control scheme with wireless network virtualization. To design our proposed scheme, we formulate a novel joint bargaining game model in two-tier spectrum control processes. Especially, game players work together to make control decisions, and bargain with each other to get mutual advantages. By adopting the main concepts of WKSBS, CPS, TPS and RTPS, multiple IoT devices can share fair-efficiently the limited spectrum resources. Based on the interactive bargaining approach, different bargaining solutions are interdependent to strike the appropriate performance balance of UDN system platform. The main steps of the proposed spectrum control algorithm are as follows: Step 1: For our simulation model, the values of the system parameters and control factors are listed in Table 1, and the simulation scenario is presented in Section IV.
Step 2: Individual IoT devices generate application services such as PSs, SSs, and TSs. To support different traffic services, the M P , M S and M T operators work together at the first-tier process and work independently at the second-tier process.
Step 3: At the first-tier, the game G B i is operated to share the M B . By using (1), the players' utility functions are defined, and the concept of WKSBS is adopted for the G B i . Therefore, the values of S P , S S and S T slices are decided according to (2).
Step 4: At the second-tier, the games are operated in parallel to support the PSs, SSs, and TSs. Each game has its own game solution based on the different traffic service characteristics.
Step 5: In the G M P B i , the S P is scheduled for the devices in the N P B i . By using (3), the devices' utility functions are defined, and the concept of CPS is adopted for the G M P B i . Therefore, the S P distribution is executed according to (4).
Step 6: In the G M S B i , the S S is scheduled for the devices in the N S B i . By using (5), the devices' utility functions are defined, and the concept of TPS is adopted for the G M S B i . Therefore, the S S distribution is executed according to (6).
Step 7: In the G M T B i , the S T is scheduled for the devices in the N T B i . By using (7), the devices' utility functions are defined, and the concept of RTPS is adopted for the G M T B i . Therefore, the S T distribution is executed according to (8).
Step 8: The network operators and agents constantly self-monitor the current UDN situations, and proceed to Step 2 for the next spectrum control process.

IV. PERFORMANCE EVALUATION
In this section, the performance of our proposed algorithm is evaluated through simulations, and is compared with other existing protocols to confirm the superiority of our approach.
• The process for service request generation is Poisson with rate (services/s), and the range of the offered service load was varied from 0 to 3.0.
• Three type traffic services are assumed based on the different characteristics of services. Each type traffic has different applications according to the connection duration and spectrum requirements.
• The total spectrum capacity of each BS (M B ) is 100 Gbps.
• To reduce computational complexity, the amount of spectrum allocation is specified in terms of basic spectrum units (BSUs), where one BSU is the minimum amount (e.g., 2.5 Mbps in our system) of spectrum adjustment.  2).
• The system performance measures obtained based on 100 simulation runs are plotted as a function of the offered service request load.
• The performance measures obtained are the normalized payoff of device, system throughput, and fairness among devices in the UDN system.
• For simplicity, we assume the absence of physical obstacles in wireless communications.   is normalized for a fair comparison. This performance criterion is very important from the viewpoint of end users. It is strongly related to user's satisfaction and service quality. In Fig. 2, we can see the performance trend under different service request rates. Under low to heavy traffic load distributions, our joint-bargaining approach can effectively share limited BS spectrum resource. This can lead to a higher device payoff, resulting in a greater service satisfaction. This is a significant advantage for end users. Fig. 3 shows the system throughput of the UDN infrastructure for the different schemes. In our simulation model, the throughput is the ratio of the traffic service that is successfully completed to all the requested applications. Because the system throughput is strongly associated with the summation of the payoff of each device, the performance trend shown in Fig. 3 is very similar to the curves in Fig. 2. Under different service request intensities, our proposed scheme mediates different bargaining solution ideas to effectively handle the different type traffic services. Therefore, our approach is comparatively better than the existing protocols while adaptively responding to the current UDN system situations; this is what it has come to. Fig. 4 plots the fairness among devices in the UDN system. This fairness index represents how to share the limited spectrum resource in the viewpoint of social welfare. Our two-tier bargaining model effectively compromises the contrasting viewpoints of the M P , M S and M T operators, and provides the most proper combination of the different fair issues among different bargaining solutions. Therefore, under diversified traffic condition changes, our proposed scheme can maintain a higher fairness among devices while efficiently sharing the limited UDN spectrum resource.

V. SUMMARY AND CONCLUSION
Facing with the different type traffic coexisting scenario in the future network, wireless network virtualization will be utilized to slice and share the network resource among different service providers. In this study, we have presented a new UDN spectrum control algorithm, which is designed as a twe-tier bargaining game model. By jointly considering the WKSBS, CPS, TPS and RTPS, each individual MVNO work together at the first-tier and work independently at the secondtier. Based on different bargaining solutions, our interactive bargaining approach can strike an appropriate performance balance for the UDN system. To confirm the superiority of our approach, we conduct extensive simulations to compare our proposed scheme with existing state-of-the-art HGRM, MVRA and MHRA protocols. The numerical results demonstrate that we can improve the performance of the UDN system in terms of the system throughput, device's payoff and fairness.
In future work, we can extend our current study in multiple directions. One future direction is to explore the transmission strategy for vehicle network scenarios, and we will consider the congestion problem with traffic prediction techniques. Another potential direction for future research is to investigate the user location issue, which is strongly related to the user mobility. In addition, we will extend this work by incorporating multiple carrier aggregation techniques and developing a more sophisticated spectrum control scheme that can be applied when different carrier aggregations occur.

ACKNOWLEDGMENT
The author declares that there are no competing interests regarding the publication of this article. He is a sole author of this work and ES (i.e., participated in the design of the study and performed the statistical analysis).