The Annals of Applied Probability

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

E. G. Coffman, A. A. Puhalskii, and M. I. Reiman

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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.

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Ann. Appl. Probab. Volume 5, Number 3 (1995), 681-719.

First available in Project Euclid: 19 April 2007

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Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F17: Functional limit theorems; invariance principles 90B22: Queues and service [See also 60K25, 68M20]

Polling systems cyclic servers diffusion approximations heavy-traffic limits


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.

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