Mean value analysis for polling systems in heavy traffic

R.D. Mei, van der, E.M.M. Winands

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

In this paper we present a new approach to derive heavy-traffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general service-time and switch-over time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closed-from expressions for the expected asymptotic delay; the expressions were derived earlier in [31], but in a different way. Moreover, the MVA-based approach enables us to derive closed-form expressions for the heavy-traffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavy-traffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.
Original languageEnglish
Title of host publicationProceedings First International Conference on Performance Evaluation Methodologies and Tools (ValueTools, Pisa, Italy, October 11-13, 2006)
EditorsL. Lenzini, R. Cruz
Place of PublicationNew York NY, USA
PublisherAssociation for Computing Machinery, Inc
ISBN (Print)1-59593-504-5
Publication statusPublished - 2006

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