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arXiv · 1006.5545

On customer flows in Jackson queuing networks

Sen Tan·Aihua Xia
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Abstract

Melamed's theorem states that for a Jackson queuing network, the equilibrium flow along a link follows Poisson distribution if and only if no customers can travel along the link more than once. Barbour \& 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 paper, we prove that the customer flow process is a Poisson cluster process and then establish a general approximate version of Melamed's theorem accommodating all possible cases of $0\le p<1$.

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Sen Tan, Aihua Xia. 2010-06-29. On customer flows in Jackson queuing networks. https://arxiv.org/abs/1006.5545

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