Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T12:11:33.707Z Has data issue: false hasContentIssue false
  • English
  • Français

On the work load process in a general preemptive resume priority queue

Published online by Cambridge University Press:  14 July 2016

R. Schassberger
R. Schassberger*
Affiliation:
University of Calgary, Alberta, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider the following queuing system: A sequence of customers arrive at a service unit in a recurrent stream. A customer is of priority k with probability πk, k = 1, …, n. A class i customer preempts service of class k, k > i. Interrupted service is resumed without loss or gain in service time. Service is FIFO within classes. Service times for class k are drawn from a general distribution function Bk(t).

Using the method of phases and a resolution technique from the theory of Markov processes we obtain Laplace transforms of various distributions.

Keywords

QUEUINGPREEMTIVE PRIORITIESWORK LOADBUSY PERIODSPHASE METHODRESOLUTION TECHNIQUE
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 588 - 603
Copyright
Copyright © Applied Probability Trust 1972 

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

[1] Chung, K. L. (1960) Markov Chains with Stationary Transition Probabilities. Springer, Berlin.Google Scholar
[2] Cohen, J. W. (1969) The Single Server Queue. North Holland, Amsterdam.Google Scholar
[3] Dynkin, E. B. (1965) Markov Processes I. Springer, Berlin.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol II. Wiley, New York.Google Scholar
[5] Henderson, W. (1969) GI/M/1 priority queue. Operat. Res. 17, 907–910.Google Scholar
[6] Hooke, J. (1969) Some limit theorems for priority queues. Technical Report No. 91. Department of Operations Research, Cornell University.Google Scholar
[7] Jaiswal, N. K. (1968) Priority Queues. Academic Press, New York.Google Scholar
[8] Jaiswal, N.K. and Thiruvengadam, K. (1962) Preemptive resume priority queue with Erlangian inputs. Indian J. Math. 4, 53–70.Google Scholar
[9] Kennedy, D. (1972) The continuity of the single server queue. J. Appl. Prob. 9, 370–381.Google Scholar
[10] Schassberger, R. (1970) On the waiting time in the queuing system G/G/1. Ann. Math. Statist. 41, 182–187.Google Scholar
[11] Whitt, W. (1970) Weak convergence theorems for priority queues: preemptive resume discipline. Technical Report, Yale University.Google Scholar
[12] Whitt, W. (1971) The continuity of queues. Technical Report, Yale University.Google Scholar
[13] Wolff, R. (1970) Work conserving priorities. J. Appl. Prob. 7, 327–337.Google Scholar