Advances in Applied Probability

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

A. A. Puhalskii and M. I. Reiman

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We consider a multiserver queue in the heavy-traffic regime introduced and studied by Halfin and Whitt [7] 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.

Article information

Adv. in Appl. Probab. Volume 32, Number 2 (2000), 564-595.

First available in Project Euclid: 12 February 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F17: Functional limit theorems; invariance principles 90B22: Queues and service [See also 60K25, 68M20]

Call centers multiserver queues priority queues heavy traffic diffusion approximation weak convergence


Puhalskii, A. A.; Reiman, M. I. The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. in Appl. Probab. 32 (2000), no. 2, 564--595. doi:10.1239/aap/1013540179.

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