Polling Models With and Without Switchover Times

S. C. Borst and O. J. Boxma
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S. C. Borst: CWI, Amsterdam, The Netherlands
O. J. Boxma: CWI, Amsterdam, The Netherlands

Operations Research, 1997, vol. 45, issue 4, 536-543

Abstract: We consider two different single-server cyclic polling models: (i) a model with zero switchover times, and (ii) a model with nonzero switchover times, in which the server keeps cycling when the system is empty. For both models we relate the steady-state queue length distribution at a queue to the queue length distributions at server visit beginning and visit completion instants at that queue; as a by-product we obtain a short proof of the Fuhrmann-Cooper decomposition. For the large class of polling systems that allow a multitype branching process interpretation, we expose a strong relation between the queue length, as well as waiting-time, distributions in the two models. The results enable a very efficient numerical computation of the waiting-time moments under different switchover time scenarios.

Keywords: queues; cyclic; influence of switchover times on queue lengths and waiting times; probability; stochastic model applications; queue length and waiting time distribution in polling models (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (7)

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