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Stochastic Monotonicities in Jackson Queueing Networks

Published online by Cambridge University Press:  27 July 2009

Torgny Lindvall
Torgny Lindvall
Affiliation:
Department of Mathematics, University of Göteborg, 41296 Göteborg, Sweden
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Abstract

When starting from 0, a standard M/M/k queueing process has a second-order stochastic monotonicity property of a strong kind: its increments are stochastically decreasing (the SDI property). A first attempt to generalize this to the Jackson queueing network fails. This gives us reason to reexamine the underlying theory for stochastic monotonicity of Markov processes starting from a zero-point, in order to find a condition on a function of a Jackson network process to have the SDI property. It turns out that the total number of customers at time t has the desired property, if the network is idle at time O. We use couplings in our analysis; they are also of value in the comparison of two networks with different parameters.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 1 , January 1997 , pp. 1 - 9
Copyright
Copyright © Cambridge University Press 1997

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References

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