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On the equivalence of flows in networks of queues

Published online by Cambridge University Press:  14 July 2016

J. Walrand
J. Walrand*
Affiliation:
Cornell University
*
∗Present address: Department of Electrical Engineering and Computer Sciences, Cory Hall, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

Consider a network of queues in equilibrium. When are the flows observed on two given links of that network equivalent, i.e., when do they have the same law?

The verification of the equivalence of two such point processes is first reduced to an algebraic problem by a technique based on the filtering theory.

This method is then used to show that the arrival and departure processes at an M/M/1 node in a Jackson network are not always equivalent, thereby contradicting a conjecture made in [8]. An example where that equivalence holds is also given; it provides new results on the time reversibility of some familiar processes.

Keywords

M/M/1 QUEUENON-LINEAR FILTERINGREVERSIBILITYBIRTH AND DEATH PROCESSESPOINT PROCESSES
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 195 - 203
Copyright
Copyright © Applied Probability Trust 1982 

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References

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