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On customer flows in jackson queueing networks

Published online by Cambridge University Press:  01 July 2016

Sen Tan*
Affiliation:
University of Melbourne
Aihua Xia*
Affiliation:
University of Melbourne
*
Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3052, Australia.
Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3052, Australia.
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Abstract

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Melamed's theorem states that, for a Jackson queueing network, the equilibrium flow along a link follows a Poisson distribution if and only if no customers can travel along the link more than once. Barbour and Brown (1996) considered the Poisson approximate version of Melamed's theorem by allowing the customers a small probability p of travelling along the link more than once. In this note, we prove that the customer flow process is a Poisson cluster process and then establish a general approximate version of Melamed's theorem that accommodates all possible cases of 0 ≤ p < 1.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2010 

References

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