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Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle

E. G. Coffman, Jr., A. A. Puhalskii and M. I. Reiman
The Annals of Applied Probability
Vol. 5, No. 3 (Aug., 1995), pp. 681-719
Stable URL: http://www.jstor.org/stable/2245120
Page Count: 39
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Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle
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Abstract

In polling systems, M ≥ 2 queues are visited by a single server in cyclic order. These systems model such diverse applications as token-ring communication networks and cyclic production systems. We study polling systems with exhaustive service and zero switchover (walk) times. Under standard heavy-traffic assumptions and scalings, the total unfinished work converges to a one-dimensional reflected Brownian motion, whereas the workloads of individual queues change at a rate that becomes infinite in the limit. Although it is impossible to obtain a multidimensional limit process in the usual sense, we obtain an "averaging principle" for the individual workloads. To illustrate the use of this principle, we calculate a heavy-traffic estimate of waiting times.

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