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. Keywords: Polling systems, cyclic servers, diffusion approximations, heavy-traffic limits. June 21, 1995 The research of this author was supported in part under contract with AT&T Bell Laboratories, and in part under a grant from the I...

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