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Polling Systems in Heavy Traffic: A Bessel Process Limit

E. G. Coffman, Jr., A. A. Puhalskii and M. I. Reiman
Mathematics of Operations Research
Vol. 23, No. 2 (May, 1998), pp. 257-304
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690512
Page Count: 48
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Polling Systems in Heavy Traffic: A Bessel Process Limit
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Abstract

This paper studies the classical polling model under the exhaustive-service assumption; such models continue to be very useful in performance studies of computer/communication systems. The analysis here extends earlier work of the authors to the general case of nonzero switchover times. It shows that, under the standard heavy-traffic scaling, the total unfinished work in the system tends to a Bessel-type diffusion in the heavy-traffic limit. It verifies in addition that, with this change in the limiting unfinished-work process, the averaging principle established earlier by the authors carries over to the general model.

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