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August, 1995 Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle
E. G. Coffman Jr., A. A. Puhalskii, M. I. Reiman
Ann. Appl. Probab. 5(3): 681-719 (August, 1995). DOI: 10.1214/aoap/1177004701

Abstract

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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E. G. Coffman Jr.. A. A. Puhalskii. M. I. Reiman. "Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle." Ann. Appl. Probab. 5 (3) 681 - 719, August, 1995. https://doi.org/10.1214/aoap/1177004701

Information

Published: August, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0842.60088
MathSciNet: MR1359825
Digital Object Identifier: 10.1214/aoap/1177004701

Subjects:
Primary: 60K25
Secondary: 60F17 , 90B22

Keywords: cyclic servers , diffusion approximations , heavy-traffic limits , polling systems

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 3 • August, 1995
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