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HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Published online by Cambridge University Press:  27 June 2014

M.A.A. Boon  and
E.M.M. Winands
M.A.A. Boon
Affiliation:
Eurandom and Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands E-mail: marko@win.tue.nl
E.M.M. Winands
Affiliation:
University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Science Park 904, 1098 XH Amsterdam, The Netherlands E-mail: e.m.m.winands@uva.nl
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Abstract

In this paper, we study a two-queue polling model with zero switchover times and k-limited service (serve at most ki customers during one visit period to queue i, i=1, 2) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-k2 distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 4 , October 2014 , pp. 451 - 471
Copyright
Copyright © Cambridge University Press 2014 

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