Resource Partitioning in Heterogeneous Networks Based on Bargaining Theory

This article presents some new, intuitive derivations of several results in the bargaining literature. These new derivations clarify the relationships among these results and allow them to be understood in a unified way. These results concern the way in which the risk posture of the bargainers affects the outcome of bargaining as predicted by Nash's (axiomatic) solution of a static bargaining model (Nash, 1950) and by the subgame perfect equilibrium of the infinite horizon sequential bargaining game analyzed by Rubinstein (1982). The analogous, experimentally testable predictions for finite horizon sequential bargaining games are also presented.

We analyze the problem of dividing a fixed amount of a single commodity between two players on the basis of the Nash bargaining solution (NBS). For one-shot negotiations, a cornerstone result of Roth (Axiomatic models of bargaining. Springer, Berlin, 1979) establishes that the more risk averse player will obtain less than half the total amount. In the present paper, we assume that the bargaining procedure occurs over several rounds. In each round, an increasing share of the total amount is negotiated over in accordance with the NBS, the disagreement point being determined by the outcome of the previous round. In line with Roth’s result, the final amount received by the more risk averse player is still bounded by half the total amount. As a new feature, however, this player does not lose from bargaining for more rounds if his opponent exhibits non-increasing absolute risk aversion. What is more, both players’ risk profiles become essentially irrelevant if successive bargaining takes place over sufficiently small commodity increments. Each player then gets approximately half of the commodity.

We consider a distributed reactive power compensation problem in a distribution network in which users locally generate reactive power using distributed generation units to contribute to the local voltage control. We model and analyze the interaction between one electric utility company and multiple users by using the Nash bargaining theory. On one hand, users determine the amount of active and reactive power generation for their distributed generation units. On the other hand, the electric utility company offers reimbursement for each user based on the amount of reactive power dispatched by that user. We first quantify the benefit for the electric utility company and users in the reactive power compensation problem. Then we derive the optimal solution for the active and reactive power generation, as well as reimbursement for each user under two different bargaining protocols, namely sequential bargaining and concurrent bargaining. Numerical results show that both the electric utility company and users benefit from the proposed decentralized reactive power compensation mechanism, and the overall system efficiency is improved.

Divide the Dollar and Conquer More: Sequential Bargaining and Risk Aversion

In this paper, a fair user association scheme is proposed for heterogeneous networks (HetNets), where the user association optimization is formulated as a Nash bargaining problem. The optimization objective is to maximize the sum of rate related utility, under users' minimal rate constrains, while considering user fairness and load balance between cells in different tiers. Nash bargaining solution and coalition are adopted to solve this optimization problem. Firstly, a two-player bargaining scheme is developed for two base stations (BSs) to bargain user association. Then this two-player scheme is extended to a multi-player bargaining scheme with the aid of Hungarian algorithm that optimally groups BSs into pairs. Simulation results show that the proposed scheme can effectively offload users from macrocells, improve user fairness, and also achieve comparable sum rate to the scheme that maximizes the sum rate without considering user fairness.

The article was dedicated to the application of cooperative games tools to the particular bargaining problem. The bargaining is about tariffrates between two countries. Analysis was performed on the framework of simple market model with perfect competition within countries and bilateral monopoly relation between them. There were two bargaining schemes applied in order to calculate cooperative solutions. First was Nash bargaining solution, the second was Kalai and Smorodinsky proposition. Both methods successfully indicated cooperative solutions. Application of chosen bargaining schemes brought the conclusion that outcome of the indications of cooperative solutions strongly depends on the nature of explored economic model. The examination of influence parameters' changes proved that worsening the situation of the subject led to the decrease of its benefit in every case. In one case it also caused the decrease of benefit of the other party. (original abstract)

As a prevailing concept in 5G, virtualization provides efficient coordination among multiple radio access technologies (RATs) and enables multiple service providers (SPs) to share different RATs’ infrastructure. This paper proposes a generic framework for virtualizing heterogeneous wireless network with different RATs. A novel “VMAC” (virtualized medium access control) concept is introduced to converge different RAT protocols and perform inter-RAT resource allocation. To suit the proposed framework, a virtualization based resource allocation scheme is devised. We formulate the problem as a mixed combinatorial optimization, which jointly considers network access and rate allocation. First, to solve the network access problem, “adaptability ratio” is developed to model the fact that different RATs possess different adaptability to different services. And a Grey Relational Analysis (GRA) method is adopted to calculate the adaptability ratio. Second, services are modeled as players, bargaining for RAT resources in a Nash bargaining game. And a closed-form Nash bargaining solution (NBS) is derived. Combining adaptability ratio with NBS, a novel resource allocation algorithm is devised. Through simulation, the superiority and feasibility of the proposed algorithm are validated.

To enhance the performance and the coverage area of the next‐generation heterogeneous wireless networks (HetNets), smaller cells such as femtocells are deployed. A reasonable resource allocation strategy is crucial for the operation of such systems. In this work, the Nash bargaining solution (NBS), Kalai–Smorodinsky bargaining solution (KSBS), and a proposed bargaining solution, which is the combination of NBS and KSBS, are studied to ensure the efficiency and fairness in the transmission rate allocation among femtocells. The mentioned bargaining solutions are optimised subject to the rate constraints due to the Han–Kobayashi (HK) rate splitting scheme, and a maximum tolerable interference caused by femtocell base stations (FBSs) at the macrocell user equipment. Two methods are used to address the bargaining solutions' optimisations. First, the conventional optimisation‐based method is used for the situations where the channel gains are known, then a reinforcement learning‐based algorithm for a real environment is proposed without being aware of the channel gains. To accelerate the speed of the learning process and to initialise the values of quality functions, the hotbooting technique is used. The bargaining solutions are compared by fairness and efficiency criteria in both methods. Numerical simulations show that the proposed reinforcement learning‐based algorithm achieves the same performance derived from the conventional optimisation method. First, this paper studies the two well‐known Nash and Kalai–Smorodinsky bargaining solutions as the good tools to establish fairness in rate allocation problem among femtocells in a HetNet. Then a new bargaining solution is proposed as the combination of the two bargaining solutions. The fairness and the efficiency of the allocated rates to femtocells as the output of optimisation problems of bargaining solutions are compared via Jain index criterion (as the fairness metric) and inverse price of anarchy criterion (as the efficiency metric). Moreover, the femtocell base stations are allowed to use Han–Kobayashi signalling scheme to send their signals in private and common messages which results in the best‐known achievable rate region. Two methods are used to solve the optimisation problems: the conventional optimisation method and the reinforcement learning‐based method (to formulate a real‐world model with the unknown channel gains). It is shown that the proposed bargaining solution (in both methods) results in fairer rates than Nash and Kalai–Smorodinsky bargaining solutions while all of them are efficient.

To fully utilize the resources of heterogeneous cellular networks (HCNs), an effective approach that offloads users to the underloaded small cells from overloaded macrocells is widely advocated. However, this operation often leads to a bad result that the offloaded users achieve lower signal-to-interference-plus-noise-ratio (SINR) than these users in macrocells. Thus, some appropriate interference avoidance techniques should be adopted to partially alleviate the SINR degradation. For this, we consider the resource (frequency) partitioning that turns off some fraction of such resources in a macrocell. Naturally, an optimal offloading strategy should be closely coupled with resource partitioning, and in turn the optimal partition decides the offloading performance. In this paper, we propose a distributed association strategy with joint offloading and resource partitioning for HCNs. We reveal that load balancing, by itself, is insufficient, and additional resource partitioning is required to improve system performance. Meanwhile, we also show that, compared with the best power association and range extension association, the proposed scheme provides better association performance.

To realize collaborative transmission in wireless overlay access networks, the question of rate allocation arises as how to divide the traffic flow among heterogeneous networks. Different networks role as game players and they try to transmit the traffic flow by a cooperative method. Power costs and transmission capabilities in heterogeneous networks are different according to terminal position, network load etc, so the grand coalition is not always beneficial and the coalition structure should be adjusted in time. With the power cost introduced in the utility function, the rate allocation is formulated in a coalition formation game framework in the paper. The stable coalition structure is formed with the merge-and-split rule, then the utility is distributed to different players and the transmission rates in different networks are determined. Such a process continues until the end of the traffic transmission. The theoretical and experimental results are presented to validate our proposed method. Compared with the Nash Bargaining Solution and the Shapley value, the coalition structure can be adjusted with the terminal position through the new scheme and then the highest coalition utility can be obtained with low power cost. Moreover, the proposed method turns to be the bargaining game framework if the power cost is not considered.

In heterogeneous networks (HetNets), mobile users are proactively offloaded to small cells by association bias. To alleviate the signal-to-interference-plus-noise-ratio (SINR) degradation to offloaded users, resource partitioning and transmit power reduction are proposed in Long Term Evolution-Advanced (LTE-A), which is known as enhanced inter-cell interference coordination (eICIC). In this paper, we develop a tractable framework for performance analysis of eICIC with joint cell association, resource partitioning, and transmit power reduction by using stochastic geometry. We derive the downlink coverage probability of the network. Numerical results are provided and we give some valuable insights and guidelines for eICIC in cochannel HetNets.

The exiting DEA methods generally consider energy consumption as input indicator. It is reasonable from the perspective of economy or energy conservation. But from the perspective of environment or clean energy utilization, a region using more energy to generate lower pollutants is considered to be more efficient. Thus, energy consumption should be regarded as output indicator. If we consider the two perspectives at the same time, it will be difficult to judge energy consumption as input indicator or output indicator. To solve this problem, we incorporate Nash bargaining game (NBG) into DEA model to estimate the economic efficiency, environmental efficiency and united efficiency for China's 30 provinces during 2000-2011. It is found that the economic efficiency, environmental efficiency and united efficiency during 2000-2011 in China present distinct stage characteristics. The results obtained by employing the Mann and Whitney rank sum test imply that three efficiency measures among east area, central area and west area of China have significant heterogeneity, and the differences of provinces on the three performance measures are significant. On the basis of clear understanding about performance difference among provinces of China, it will contribute to realizing the win-win strategy as regard to the economy and environment on the whole by carrying out targeted economic and environmental policies for different regions.

Several interference mitigation strategies can be used in LTE networks to meet the consumers' increasing need for faster data speeds. Dynamic Spectrum Allocation (DSA), which maintains spectrum in a converged radio system and distributes it across all participating radio terminals, is one of the most promising solutions. However, the fundamental obstacle to achieving increased network capacities is increased inter-cell interference. The aim of this paper is to analyse the effectiveness of a newly proposed DSA technique by comparing its bit error rate (BER) and throughput (TP) with a typical uplink LTE configuration. To maximise throughput in a heterogeneous network, the suggested DSA technique utilises the Nash Bargaining Solution (NBS) scheme, a cooperative game theory that could correlate with the bit error rate. The software tool GNU Radio, which offers signal-processing blocks to develop softwaredefined radios and signal-processing systems, was used to create the setups. After the simulations were performed, the BER values were recorded and compared, while the TP values were established and computed appropriately. According to the results, the uplink (UL-LTE) architecture with DSA has an improved TP and a lower BER value. As a result, spectral efficiency can also be improved.

: In RM 23, a proof was given that the nucleolus is continuous as a function of the characteristic function. This proof is not correct; the author, at least, does not know how to complete it. In the paper a correct proof for this fact is given. The proof is based on an alternative definition of the nucleolus, which is of some interest in its own right. (Author)

In heterogeneous network (HetNet), the combined cell range extension (CRE) and enhanced inter-cell interference coordination (elCIC) proposed by 3GPP is considered as the most effective user association scheme. However, this scheme requires strict frame synchronization between macrocells and small cells. In this paper, we propose a Nash bargaining solution (NBS) based user association scheme which does not require such synchronization between cells in different tiers. The proposed scheme formulates user association optimization problem as a Nash bargaining problem. The objective is to maximize the sum data rate related utility of all users in the overall system while guaranteeing user's minimal data rate and considering the user fairness. The simulation results show the proposed scheme can achieve higher sum rate of all users and better user fairness compared with the combined CRE and elCIC based user association scheme. Moreover, the proposed scheme has low computational complexity by applying Hungarian algorithm.