The Annals of Mathematical Statistics

On Pre-Emptive Resume Priority Queues

Peter D. Welch

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177703559

Digital Object Identifier
doi:10.1214/aoms/1177703559

Mathematical Reviews number (MathSciNet)
MR161386

Zentralblatt MATH identifier
0123.35702

JSTOR
links.jstor.org

Citation

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


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