Convergence of synchronous and asynchronous greedy algorithms in a multiclass telecommunications environment

Zhang, Z.; Douligeris, Christos

doi:10.1109/26.156630

Cited by 54 publications

(40 citation statements)

References 10 publications

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“…Consequently, this constraint may be treated as absent, resulting in an unconstrained game, that was shown to have a unique Nash equilibrium. Convergence of synchronous and asynchronous implementations of the algorithm to the unique equilibrium point was examined in Zhang and Douligeris [1992]. The greedy algorithm for a "store-andforward" network of ./M/l queues was studied in Bovopoulos and Lazar [1988].…”

mentioning

confidence: 99%

On the existence of equilibria in noncooperative optimal flow control

Korilis

Lazar

1995

J. ACM

121

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Abstract. The existence of Nash equilibria in noncooperative flow control in a general productform network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average time-delay. Previous attempts to study existence of equilibria for this flow control model were not successful, partly because the time-delay constraints couple the strategy spaces of the individual users in a way that does not allow the application of standard equilibrmm existence theorems from the game theory literature.To overcome this difficulty, a more general approach to study the existence of Nash equilibria for decentralized control schemes is introduced. This approach is based on directly proving the existence of a fixed point of the best reply correspondence of the underlying game. For the investigated flow control model, the best reply correspondence is shown to be a function, implicitly defined by means of K interdependent linear programs. Employing an appropriate definition for continuity of the set of optimal solutions of parametrized linear programs, it is shown that, under appropriate conditions, the best reply function is continuous. Brouwer's theorem implies, then, that the best reply function has a fixed point.

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mentioning

confidence: 99%

On the existence of equilibria in noncooperative optimal flow control

Korilis

Lazar

1995

J. ACM

121

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“…What is valuable to highlight is that this convergence is proved in a more general case with respect with those available in literature (e.g. Zhang and Douligeris 1992, Orda et al 1993, Altman et al 2002.…”

Section: Comparison With Related Workmentioning

confidence: 94%

“…In Zhang and Douligeris (1992) the problem of convergence of the greedy algorithms is analysed by referring to the flow control problem in networks where the users adopt power as utility function (the non-concave nature of the power function does not allow the application of the results obtained in Li and Bas°ar (1987)); the authors explicitly prove that, in this flow control context, synchronous (Gauss-Siedel) greedy algorithms are always convergent to NEP; moreover, for the same scenario, they define the necessary and sufficient conditions such that also asynchronous (Jacobi) greedy algorithms converge to the equilibrium point.…”

Section: Stability Considerationsmentioning

confidence: 96%

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Routing and dynamic resource assignment joint game: a non-cooperative model for QoS routing

Conforto¹,

Priscoli²

2004

International Journal of Control

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In this paper we present an innovative game theoretic non-cooperative model for the quality of service (QoS) routing in communication networks implementing a differentiated service model for the QoS support. The proposed model allows us to solve a joint problem of non-cooperative QoS routing and dynamic capacity allocation over a network of parallel links. This problem is solved by playing a Nash game taking place among players belonging to two categories: (i) the category of individual users, whose objectives are to ship their macroflows from the source node to the destination node, by suitably splitting them over the parallel links, and (ii) the category of capacity players, whose task is to partition and to assign to the classes of traffic upon which the macroflows are mapped, the dynamic portion of capacity over each link. One of the main innovative aspects of our model is that the allocation of the dynamic portion of capacity to each class of traffic over each link is realised during the actual operation of the network, i.e. in conjunction with the QoS routing. Extensive simulation results validate the proposed model, show some of its interesting properties and highlight the remarkable performance enhancements that it achieves with respect to the other results present in the literature

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“…The power criterion has been widely used [20]- [22], [29]- [35]. Although we found some criticism of this criterion in [36], we also found many arguments for using it [32], [35]. We shall add to it another interpretation of this criterion as follows.…”

Section: B Noncooperative Flow Control With Power Criterionmentioning

confidence: 97%

Inefficient Noncooperation in Networking Games of Common-Pool Resources

Kameda

Altman

2008

IEEE J. Select. Areas Commun.

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Abstract-We study in this paper a noncooperative approach for sharing resources of a common pool among users, wherein each user strives to maximize its own utility. The optimality notion is then a Nash equilibrium. First, we present a general framework of systems wherein a Nash equilibrium is Pareto inefficient, which are similar to the 'tragedy of the commons' in economics. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks where each user decides its throughput to optimize its own utility. As such a utility, we first consider the power which is defined as the throughput divided by the expected end-to-end packet delay, and then consider another utility of additive costs. For both utilities, we establish the non-efficiency of the Nash equilibria.

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Convergence of synchronous and asynchronous greedy algorithms in a multiclass telecommunications environment

Cited by 54 publications

References 10 publications

On the existence of equilibria in noncooperative optimal flow control

On the existence of equilibria in noncooperative optimal flow control

Routing and dynamic resource assignment joint game: a non-cooperative model for QoS routing

Inefficient Noncooperation in Networking Games of Common-Pool Resources

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