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The multiclass GI/PH/N queue in the Halfin-Whitt regime

Part of: Limit theorems Special processes Operations research and management science

Published online by Cambridge University Press:  19 February 2016

A. A. Puhalskii  and
M. I. Reiman
A. A. Puhalskii*
Affiliation:
University of Colorado
M. I. Reiman*
Affiliation:
Lucent Technologies
*
∗ Postal address: Department of Mathematics, University of Colorado at Denver, Denver, CO 80217, USA, and Institute for Problems in Information Transmission, Moscow.
∗∗ Postal address: Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, USA.
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Abstract

We consider a multiserver queue in the heavy-traffic regime introduced and studied by Halfin and Whitt who investigated the case of a single customer class with exponentially distributed service times. Our purpose is to extend their analysis to a system with multiple customer classes, priorities, and phase-type service distributions. We prove a weak convergence limit theorem showing that a properly defined and normalized queue length process converges to a particular K-dimensional diffusion process, where K is the number of phases in the service time distribution. We also show that a properly normalized waiting time process converges to a simple functional of the limit diffusion for the queue length.

Keywords

Call centersmultiserver queuespriority queuesheavy trafficdiffusion approximationweak convergence

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60F17: Functional limit theorems; invariance principles 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 564 - 595
Copyright
Copyright © Applied Probability Trust 2000 

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