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A multiclass feedback queue in heavy traffic

Published online by Cambridge University Press:  01 July 2016

Martin I. Reiman
Martin I. Reiman*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
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Abstract

We consider a single station queueing system with several customer classes. Each customer class has its own arrival process. The total service requirement of each customer is divided into a (possibly) random number of service quanta, where the distribution of each quantum may depend on the customer's class and the other quanta of that customer. The service discipline is round-robin, with random quanta.

We prove a heavy traffic limit theorem for the above system which states that as the traffic intensity approaches unity, properly normalized sequences of queue length and sojourn time processes converge weakly to one-dimensional reflected Brownian motion.

Keywords

BROWNIAN MOTIONDIFFUSION APPROXIMATIONWEAK CONVERGENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 1 , March 1988 , pp. 179 - 207
Copyright
Copyright © Applied Probability Trust 1988 

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