Fairness in network optimal flow control: optimality of product forms

Mazumdar, Ravi R.; Mason, L.; Douligeris, Christos

doi:10.1109/26.87140

Cited by 201 publications

(123 citation statements)

References 10 publications

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“…These and other schemes are discussed by Blackorby et al (2002), Gaertner (2009), and Yaari and Bar-Hillel (1984). Proportional fairness objectives for communication networks are closely related to the Nash bargaining solution and are discussed by Kelly et al (1999) and Mazumdar et al (1991), among others. The efficiency cost of proportional and maximin fairness objectives is studied by Bertsimas et al (to appear).…”

Section: Introductionmentioning

confidence: 99%

Combining Equity and Utilitarianism in a Mathematical Programming Model

Hooker

Williams

2012

Management Science

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Revised 18 November 2011 AbstractWe discuss the problem of combining the conflicting objectives of equity and utilitarianism, for social policy making, in a single mathematical programming model. The definition of equity we use is the Rawlsian one of maximising the minimum utility over individuals or classes of individuals. However, when the disparity of utility becomes too great, the objective becomes progressively utilitarian. Such a model is particularly applicable to health provision but to other areas as well. Building a mixed integer/linear programming (MILP) formulation of the problem raises technical issues, as the objective function is nonconvex and the hypograph is not MILP representable in its initial form. We present a succinct formulation and show that it is "sharp" in the sense that its linear programming relaxation describes the convex hull of the feasible set (before extra resource allocation or policy constraints are added). We apply the formulation to a health care planning problem and show that instances of realistic size are easily solved by standard MILP software.

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Section: Introductionmentioning

confidence: 99%

Combining Equity and Utilitarianism in a Mathematical Programming Model

Hooker

Williams

2012

Management Science

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“…Such approach was first presented for packet-switched data networks by Mazumdar et al [15]. The concept of Nash bargaining solution is used by Yaiche et al [16] to derive a price-based resource allocation scheme that can be applied to the available bit rate service in ATM networks.…”

Section: Related Workmentioning

confidence: 99%

A Nash Bargaining Solution for Cooperative Network Formation Games

et al. 2011

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Abstract. The Network Formation problem has received increasing attention in recent years. Previous works have addressed this problem considering almost exclusively networks designed by selfish users, which can be consistently suboptimal. This paper addresses the network formation issue using cooperative game theory, which permits to study ways to enforce and sustain cooperation among agents. Both the Nash bargaining solution and the Shapley value are widely applicable concepts for solving these games. However, we show that the Shapley value presents three main drawbacks in this context: (1) it is non-trivial to define meaningful characteristic functions for the cooperative network formation game, (2) it can determine for some players cost allocations that are even higher than those at the Nash Equilibrium (i.e., if players refuse to cooperate), and (3) it is computationally very cumbersome. For this reason, we solve the cooperative network formation game using the Nash bargaining solution (NBS) concept. More specifically, we extend the NBS approach to the case of multiple players and give an explicit expression for users' cost allocations. Furthermore, we compare the NBS to the Shapley value and the Nash equilibrium solution, showing its advantages and appealing properties in terms of cost allocation to users and computation time to get the solution. Numerical results demonstrate that the proposed Nash bargaining solution approach permits to allocate costs fairly to users in a reasonable computation time, thus representing a very effective framework for the design of efficient and stable networks.

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“…It may cause the waste of resources since it does not consider the characteristics of the users and the devices. The NBS is the well-known solution in game theory that can be implemented to assign limited capacity, control the flow on the network, or design the network structure [13]- [16]. Although the proportional fairness policies were also implemented successfully in other works [17], [18], they have not considered the dynamic bandwidth exchanges among collaborative devices and the resulting impact on the multimedia quality for various content-aware and delaysensitive applications.…”

Section: Game Theoretic Resource Allocationmentioning

confidence: 99%

“…The optimality conditions of both solutions and differences between the quantitative proportional fairness of the NBS and the qualitative proportional fairness of the KSBS for multimedia services are analyzed in [3]. The KSBS allows choosing a proportional fair solution among the Nash equilibrium if it preserves four axioms: Pareto optimality, symmetry, independence from linear transformation, and individual monotonicity [13].…”

Section: Bargaining Gamementioning

confidence: 99%

Multimedia Service Discrimination Based on Fair Resource Allocation Using Bargaining Solutions

Shin¹

2012

ETRI J

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We deal with a resource allocation problem for multimedia service discrimination in wireless networks. We assume that a service provider allocates network resources to users who can choose and access one of the discriminated services. To express the rational service selection of users, the utility function of users is devised to reflect both service quality and cost. Regarding the utility function of a service provider, total profit and efficiency of resource usage have been considered. The proposed service discrimination framework is composed of two game models. An outer model is a repeated Stackelberg game between a service provider and a user group, while an inner model is a service selection game among users, which is solved by adopting the Kalai-Smorodinsky bargaining solution. Through simulation experiments, we compare the proposed framework with existing resource allocation methods according to user cost sensitivity. The proposed framework performed better than existing frameworks in terms of total profit and fairness.

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Fairness in network optimal flow control: optimality of product forms

Cited by 201 publications

References 10 publications

Combining Equity and Utilitarianism in a Mathematical Programming Model

Combining Equity and Utilitarianism in a Mathematical Programming Model

A Nash Bargaining Solution for Cooperative Network Formation Games

Multimedia Service Discrimination Based on Fair Resource Allocation Using Bargaining Solutions

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