Heavy-traffic analysis of k-limited polling systems

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

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

5 Citaties (Scopus)
9 Downloads (Pure)

Uittreksel

In this paper, we study a two-queue polling model with zero switchover 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-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-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 traffic.
Originele taal-2Engels
Pagina's (van-tot)451-471
Aantal pagina's21
TijdschriftProbability in the Engineering and Informational Sciences
Volume28
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 2014

Vingerafdruk

Polling Systems
Traffic Analysis
Perturbation techniques
Heavy Traffic
Queue
Queue Length Distribution
Vacation
Customers
Polling
Perturbation Technique
Queue Length
Singular Perturbation
Heavy traffic
Joint Distribution
Siméon Denis Poisson
Scaling
Zero

Citeer dit

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Heavy-traffic analysis of k-limited polling systems. / Boon, M.A.A.; Winands, E.M.M.

In: Probability in the Engineering and Informational Sciences, Vol. 28, Nr. 4, 2014, blz. 451-471.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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