Heavy-traffic analysis of k-limited polling systems

M.A.A. Boon, E.M.M. Winands

Onderzoeksoutput: Boek/rapportRapportAcademic

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Samenvatting

In this paper we study a two-queue polling model with zero switch-over times and k-limited service (serve at most k_i 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-traf¿c 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-k_2 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 traf¿c.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's21
StatusGepubliceerd - 2013

Publicatie series

NaamReport Eurandom
Volume2013002
ISSN van geprinte versie1389-2355

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  • Citeer dit

    Boon, M. A. A., & Winands, E. M. M. (2013). Heavy-traffic analysis of k-limited polling systems. (Report Eurandom; Vol. 2013002). Eurandom.