Showing papers by "Ravi R. Mazumdar published in 1991"

Fairness in network optimal flow control: optimality of product forms

Abstract: Consideration is given to the problem of optimal flow control in a multiclass telecommunications environment where each user (or class) desires to optimize its performance while being fair to the other users (classes). The Nash (1950) arbitration scheme from game theory is shown to be a suitable candidate for a fair, optimal operation point in the sense that it satisfies certain axioms of fairness and is pareto optimal. This strategy can be realized by defining the product of individuals user performance objectives as the network optimization criterion. This provides the rationale for considering the product of user powers, as has been suggested in the literature. For delay constrained traffic, the constrained optimization problem of maximizing the product of user throughputs subject to the constraints leads to a Nash arbitration point. It is shown that these points are unique in throughput space, and the authors also obtain some convexity properties for power and delays with respect to throughputs in a Jackson network. >

On rate conservation for non-stationary processes

Abstract: This paper extends the rate conservation principle to cadlag processes whose jumps form a non-stationary point process with a time-dependent intensity. It is shown that this is a direct consequence of path integration and the strong law of large numbers for local martingales. When specialized to mean rates a non-stationary version of Miyazawa's result is obtained which is recovered in the stationary case. Some applications of the result are also given.

Efficient flow control in a multiclass telecommunications environment

Abstract: Efficient (Pareto optimal) flow control in a multiclass telecommunications environment is analysed. Several classes of users compete for the resources provided by an exponential server, using power as their performance criterion. The neces- sary and sufficient conditions that the throughputs of the different classes have to satisfy are present- ed. Relations with definitions of global per- formance measures are analysed. Several algorithms that converge to efficient points are considered.

Fairness in Network Optimal Control: Optimality of Product Flow Forms

Abstract: In this paper we consider the problem of optimal flow control in a multiclass telecommunications environment where each user (or class) desires to optimize its performance while being fair to the other users (classes). The Nash arbitration scheme from game theory is shown to be a suitable candidate for a fair, optimal operation point in the sense that it satisfies certain axioms of fairness and is pareto optimal. This strategy can be realized by defining the product of individual user performance objectives as the network optimization criterion. This provides the rationale for considering the product of user powers as has been suggested in the literature. For delay constrained traffic, the constrained optimization problem of maximizing the product of user throughputs subject to the constraints leads to a Nash arbitration point. It is shown that these points are unique in throughput space and we also obtain some convexity properties for power and delays with respect to throughputs in a Jackson network.

A white noise version of the Girsanov theorem

Abstract: Let M be a nonlinear transformation on a separable Hilbert space with range in H. Let mu denote a standard Gauss measure on H. It is shown that, under suitable conditions on M, there exists an exponential transformation L (completely characterized by M) on H such that d eta =Ld mu defines a finitely additive or cylindrical probability measure on H under which (I-M)(.) is white noise. This is the white noise version of the Girsanov theorem. The nonlinear filtering model is considered, and the Radon-Nikodym derivative of the cylindrical measure induced by the observation process on H is interpreted, showing that it has a pathwise characterization in terms of the nonlinear filter map. It is then shown that if the signal process is the solution to a nonlinear differential equation with a white noise input, then the innovation process is white noise under the cylindrical measure induced by the observation process and the innovations process is related to the observation process by a continuous, causally invertible map. >

Direct modeling of white noise in stochastic systems

Abstract: In this paper we explain the line of development that led to a direct modeling of white noise in stochastic systems. This is followed by the mathematical theory of finitely additive white noise and some recent results on modeling the state process with white noise input. Likelihood ratio plays a central role throughout this paper.