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POLLING SYSTEMS WITH TWO-PHASE GATED SERVICE

HEAVY TRAFFIC RESULTS FOR THE WAITING TIME DISTRIBUTION

Published online by Cambridge University Press:  25 September 2008

R. D. van der Mei  and
J. A. C. Resing
R. D. van der Mei
Affiliation:
Centre for Mathematics and Computer Science, Department of Probability and Stochastic Networks, Amsterdam, Netherlands and Faculty of Sciences, Vrije Universiteit, Department of Mathematics, Amsterdam, Netherlands E-mail: mei@cwi.nl
J. A. C. Resing
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands E-mail: resing@win.tue.nl
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Abstract

We study an asymmetric cyclic polling system with Poisson arrivals, general service-time and switch-over time distributions, and so-called two-phase gated service at each queue, an interleaving scheme that aims to enforce some level of “fairness” among the different customer classes. For this model, we use the classical theory of multitype branching processes to derive closed-form expressions for the Laplace–Stieltjes transform of the waiting-time distributions when the load tends to 1, in a general parameter setting and under proper heavy-traffic scalings. This result is strikingly simple and provides new insights in the behavior of two-phase polling systems. In particular, the result provides insight in the waiting-time performance and the trade-off between efficiency and fairness of two-phase gated polling compared to the classical one-phase gated service policy.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 4 , October 2008 , pp. 623 - 651
Copyright
Copyright © Cambridge University Press 2008

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