Performance Bounds and Pathwise Stability for Generalized Vacation and Polling Systems

Eitan Altman, Serguei Foss, Eric Riehl and Shaler Stidham
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Eitan Altman: INRIA, Centre Sophia Antipolis, Sophia Antipolis Cedex, France
Serguei Foss: Institute of Mathematics, Novosibirsk, Russia
Eric Riehl: University of North Carolina, Chapel Hill, North Carolina
Shaler Stidham: University of North Carolina, Chapel Hill, North Carolina

Operations Research, 1998, vol. 46, issue 1, 137-148

Abstract: We consider a generalized vacation or polling system, modeled as an input-output process operating over successive “cycles,” in which the service mechanism can be in an “up” mode (processing) or “down” mode (e.g., vacation, walking). Our primary motivation is polling systems, in which there are several queues and the server moves cyclically between them providing some service in each. Our basic assumption is that the amount of work that leaves the system in a “cycle” is no less than the amount present at the beginning of the cycle. This includes the standard gated and exhaustive policies for polling systems in which a cycle begins whenever the server arrives at some prespecified queue. The input and output processes satisfy model-dependent conditions: pathwise bounds on the average rate and the burstiness (Cruz bounds); existence of long-run average rates; a pathwise generalized Law of the Iterated Logarithm; or exponentially or polynomially bounded tail probabilities of burstiness. In each model we show that these properties are inherited by performance measures such as the workload and output processes, and that the system is stable (in a model-dependent sense) if the input rate is smaller than the up-mode processing rate.

Keywords: Queues; polling and vacation systems; pathwise analysis; performance bounds; Communications; token-ring local area networks (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:46:y:1998:i:1:p:137-148

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