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Analysis of a non-preemptive priority multiserver queue

Published online by Cambridge University Press:  01 July 2016

H. R. Gail ,
S. L. Hantler  and
B. A. Taylor
H. R. Gail*
Affiliation:
IBM Thomas J. Watson Research Center
S. L. Hantler*
Affiliation:
IBM Thomas J. Watson Research Center
B. A. Taylor*
Affiliation:
University of Michigan
*
∗Postal address: IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA.
∗Postal address: IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA.
∗∗Postal address: Department of Mathematics, The University of Michigan, Ann Arbor, MI 48109, USA.
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Abstract

We consider a non-preemptive priority head of the line queueing system with multiple servers and two classes of customers. The arrival process for each class is Poisson, and the service times are exponentially distributed with different means. A Markovian state description consists of the number of customers of each class in service and in the queue. We solve a matrix equation to obtain the generating function of the equilibrium probability distribution by analyzing singularities of the equation coefficients, which are meromorphic matrices of two complex variables. We then obtain the mean waiting times for each class.

Keywords

ALGEBRAIC ELIMINATION THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 4 , December 1988 , pp. 852 - 879
Copyright
Copyright © Applied Probability Trust 1988 

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