Polling systems and multitype branching processes

Polling systems and multitype branching processes

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Article ID: iaor19941196
Country: Netherlands
Volume: 13
Issue: 4
Start Page Number: 409
End Page Number: 426
Publication Date: Jul 1993
Journal: Queueing Systems
Authors:
Keywords: branching process
Abstract:

The joint queue length process in polling systems with and without switchover times is studied. If the service discipline in each queue satisfies a certain property it is shown that the joint queue length process at polling instants of a fixed queue is a multitype branching process (MTBP) with immigration. In the case of polling models with switchover times, it turns out that the paper is dealing with an MTBP with immigration in each state, whereas in the case of polling models without switchover times it is dealing with an MTBP with immigration in state zero. The theory of MTBPs leads to expressions for the generating function of the joint queue length process at polling instants. Sufficient conditions for ergodicity and moment calculations are also given.

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