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On Pre-Emptive Resume Priority Queues
Peter D. Welch
The Annals of Mathematical Statistics
Vol. 35, No. 2 (Jun., 1964), pp. 600-612
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2238513
Page Count: 13
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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.
The Annals of Mathematical Statistics © 1964 Institute of Mathematical Statistics