Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T07:23:40.912Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Cobham, A. (1954) Priority assignment in waiting line problems. Operat. Res. 2, 70–76.Google Scholar
Cohen, J. W. (1956) Certain delay problems for a full availability trunk group loaded by two traffic sources. Communication News 16, 105–113.Google Scholar
Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
Cohen, J. W. (1982) On the M/G/2 queueing model. Stoch. Proc. Appl. 12, 231–248.Google Scholar
Cohen, J. W. and Boxma, O. J. (1983) Boundary Value Problems in Queueing System Analysis. North-Holland, Amsterdam.Google Scholar
Davis, R. H. (1966) Waiting-time distribution of a multi-server, priority queuing system. Operat. Res. 14, 133–136.Google Scholar
De Smit, J. H. A. (1983) The queue GI/M/s with customers of different types or the queue GI/Hm/s . Adv. Appl. Prob. 15, 392–419.CrossRefGoogle Scholar
Gunning, R. C. and Rossi, H. (1965) Analytic Functions of Several Complex Variables. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Kella, O. and Yechiali, U. (1985) Waiting times in the non-preemptive priority M/M/c queue. Stoch. Models 1, 257–262.Google Scholar
Kleinrock, L. (1976) Queueing Systems, Volume II: Computer Applications. Wiley, New York.Google Scholar
Little, J. D. C. (1961) A proof for the queueing formula L = ?W. Operat. Res. 9, 383–387.CrossRefGoogle Scholar
Mitrani, I. and King, P. J. B. (1981) Multiprocessor systems with preemptive priorities. Performance Evaluation 1, 118–125.CrossRefGoogle Scholar
Sennott, L. I. (1985) Tests for the nonergodicity of multidimensional Markov chains. Operat. Res. 33, 161–167.CrossRefGoogle Scholar