The Annals of Mathematical Statistics

On Pre-Emptive Resume Priority Queues

Peter D. Welch

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The following queueing problem is considered. Customers arrive at a service facility at $r$ priority levels. At each priority level the input process is Poisson and these processes are mutually independent. The service times have an arbitrary distribution function which depends upon the priority level. A single server serves under a pre-emptive resume discipline. Results are obtained which characterize the transient and asymptotic distribution of the queue sizes and the waiting times. The analysis proceeds through reductions of the processes of interest to corresponding processes in a simple generalization of an M/G/1 queue.

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Ann. Math. Statist., Volume 35, Number 2 (1964), 600-612.

First available in Project Euclid: 27 April 2007

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Welch, Peter D. On Pre-Emptive Resume Priority Queues. Ann. Math. Statist. 35 (1964), no. 2, 600--612. doi:10.1214/aoms/1177703559.

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