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

Published online by Cambridge University Press:  14 July 2016

François Baccelli
François Baccelli*
Affiliation:
INRIA
*
∗Postal address: INRIA, Rocquencourt — BP 105, 78153 Le Chesnay Cedex, France.
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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.

Keywords

TWO-DIMENSIONAL RANDOM WALKSERGODICITYHITTING TIMESBUSY PERIOD
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 812 - 819
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This work was done when the author was visiting the Applied Probability Group, Bell Communications Research, Morristown, NJ, USA.

References

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