Exponential martingales and Wald's formulas for two-queue networks-Reference-Cited by-同舟云学术

Exponential martingales and Wald's formulas for two-queue networks

Published:1986-09 Issue:3 Volume:23 Page:812-819
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Baccelli François

Abstract

An exponential martingale is defined for a class of random walks in the positive quarter lattice which are associated with a wide variety of Markovian two-queue networks. Balance formulas generalizing Wald's exponential identity are derived from the regularity of several types of hitting times with respect to this martingale. In a queuing context, these formulas can be interpreted as functional relations of practical interest between the number of customers at certain epochs and the utilization of the queues up to these epochs.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference11 articles.

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2. Classification of two-dimensional positive random walks and almost linear semimartingales;Malyshev;Soviet Math. Dokl.,1972

3. Baccelli F. and Makowski A. M. (1985) Exponential martingales for M/G/1 queues in random environment. Presented at the Atlanta ORSA/TIMS Joint National Meeting, Atlanta.

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