Showing papers by "Ravi R. Mazumdar published in 2000"

A game theoretic framework for bandwidth allocation and pricing in broadband networks

Abstract: In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in high-speed networks. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto optimal from the point of view of the whole system, but are also consistent with the fairness axioms of game theory. We first consider the centralized problem and then show that this procedure can be decentralized so that greedy optimization by users yields the system optimal bandwidth allocations. We propose a distributed algorithm for implementing the optimal and fair bandwidth allocation and provide conditions for its convergence. The paper concludes with the pricing of elastic connections based on users' bandwidth requirements and users' budget. We show that the above bargaining framework can be used to characterize a rate allocation and a pricing policy which takes into account users' budget in a fair way and such that the total network revenue is maximized.

Cell loss asymptotics in buffers fed by heterogeneous long-tailed sources

Abstract: In this paper we consider a generalization of the so-called M/G//spl infin/ model where M types of long-tailed sessions enter a buffer. The instantaneous rates of the sessions are functions of the occupancy of an M/G//spl infin/ system with long-tailed G distributions. In particular we assume that a session of type i transmits r/sub i/ cells per unit time and lasts for a random time r with long-tailed distribution given by P(/spl tau/>x)/spl sim//spl alpha//sub i/x(-(1+/spl beta//sub i/)) where /spl beta//sub i/>0. We derive the mean cell loss asymptotics for large buffer size as well as the complementary distribution of the buffer occupancy exceeding a high level. When specialized to the homogeneous case we show that recent results on large buffer asymptotics, which have been shown under more restrictive assumptions, hold more generally. In the heterogeneous case, we show that the asymptotics are not necessarily governed by the sources with the smallest /spl beta//sub i/ but also depend on the rates r/sub i/ and it is the ratio of /spl beta//sub i/ to r/sub i/ which is important. Finally it is a simple observation that light-tailed (exponential tails for example) sources have no influence on the asymptotics except that they contribute to reducing the capacity available to heavy-tailed sources by their mean load.

Loss asymptotics in large buffers fed by heterogeneous long-tailed sources

Abstract: This paper presents the large-buffer asymptotics for a multiplexer which serves N types of heterogeneous sessions which have long-tailed session lengths. Specifically, the model considered is that sessions of type i ∈ {1,…,N} arrive as a Poisson process with rate λ i . Each type of session (independently) remains active for a random duration, say τ i , where P(τ i > x) ~ α i x -(1 + β i ) for positive numbers α i and β i . While active, a session transmits at a rate r i . Under the assumption that the average load ρ = ∑ N i=1 r i λ i E[τ i ] < C, where C denotes the server capacity, we show that both the tail distribution of the stationary buffer content and the loss asymptotics in finite buffers of size z behave approximately as z -κ J 0 , where κ J 0 depends not only on the β i but also on the transmission rates r i ; it is the ratio of β i to r i which determines κ J 0 . When specialized to the homogeneous case, i.e., when r i =r and β i = β for all i, the result coincides with results reported in the literature which have been shown under more restrictive hypotheses. Finally, it is a simple observation that light-tailed sessions only have the effect of reducing the available capacity for long-tailed sessions, but do not contribute otherwise to the definition of κ J 0 .

Distributed algorithms for fair bandwidth allocation to elastic services in broadband networks

Abstract: The Nash arbitration scheme from cooperative game theory provides a natural framework to address the allocation of available bandwidth in network links which is network (Pareto) optimal and satisfies precise notions of fairness. In this paper we propose two distributed bandwidth allocation schemes that allocate available bandwidths to elastic sources according to the Nash arbitration scheme. We prove convergence to the desired allocations for both algorithms. Finally we show how such a scheme can be implemented in a real network.