The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 5, Number 3 (1995), 681-719.
Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle
In polling systems, $M \geq 2$ 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.
Ann. Appl. Probab. Volume 5, Number 3 (1995), 681-719.
First available in Project Euclid: 19 April 2007
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Coffman, E. G.; Puhalskii, A. A.; Reiman, M. I. Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle. Ann. Appl. Probab. 5 (1995), no. 3, 681--719. doi:10.1214/aoap/1177004701. http://projecteuclid.org/euclid.aoap/1177004701.