Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T14:59:11.783Z Has data issue: false hasContentIssue false
  • English
  • Français

A limit theorem for priority queues in heavy traffic

Published online by Cambridge University Press:  14 July 2016

J. Michael Harrison
J. Michael Harrison*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

A single server, two priority queueing system is studied under the heavy traffic condition where the system traffic intensity is either at or near its critical value. An approximation is developed for the transient distribution of the low priority customers' virtual waiting time process. This result is stated formally as a limit theorem involving a sequence of systems whose traffic intensities approach the critical value.

Keywords

DIFFUSION APPROXIMATIONHEAVY TRAFFICPRIORITY QUEUEVIRTUAL WAITING TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 907 - 912
Copyright
Copyright © Applied Probability Trust 1973 

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] Benes, V. (1963) General Stochastic Processes in the Theory of Queues. Addison-Wesley, Reading, Mass.Google Scholar
[2] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[3] Borovkov, A. (1965) Some limit theorems in the theory of mass service, II. Theor. Probability Appl. 10, 375–400.Google Scholar
[4] Harrison, J. M. (1973) The heavy traffic approximation for single server queues in series. J. Appl. Prob. 10, 613–629.Google Scholar
[5] Hooke, J. A. (1969) Some limit theorems for priority queues. Technical Report No. 91, Dept, of Operations Research, Cornell University.Google Scholar
[6] Hooke, J. A. (1970) On some limit theorems for the GI/G/1 queue. J. Appl. Prob. 7, 634640.Google Scholar
[7] Iglehart, D. L. and Whitt, W. (1970) Multiple channel queues in heavy traffic. I. Adv. Appl. Prob. 2, 150–177.Google Scholar
[8] Iglehart, D. L. and Whitt, W. (1970) Multiple channel queues in heavy traffic. II: networks, sequences and batches. Adv. Appl. Prob. 2, 355–369.Google Scholar
[9] Kingman, J. F. C. (1961) The single server queue in heavy traffic. Proc. Camb. Phil. Soc. 48, 277–289.Google Scholar
[10] Kyprianou, E. (1971) The virtual waiting time of the GI/G/1 queue in heavy traffic. Adv. Appl. Prob. 3, 249–268.Google Scholar
[11] Prohorov, Yu. V. (1956) Convergence of random processes and limit theorems in probability theory. Theor. Probability Appl. 1, 157–214.Google Scholar
[12] Prohorov, Yu. V. (1963) Transient phenomena in processes of mass service. (In Russian) Litovsk. Mar. Sb. 3, 199–205.Google Scholar
[13] Skorokhod, A. V. (1965) Studies in the Theory of Random Processes. Addison-Wesley, Reading, Mass.Google Scholar
[14] Whitt, W. (1968) Weak convergence theorems for queues in heavy traffic. Technical Report No. 2, Dept. of Operations Research, Stanford University.Google Scholar
[15] Whitt, W. (1971) Weak convergence theorems for priority queues: preemptive-resume discipline. J. Appl. Prob. 8, 74–94.Google Scholar
[16] Whitt, W. (1971) A heavy traffic functional limit theorem for priority queues. Technical Report, Department of Administrative Sciences, Yale University.Google Scholar
[17] Wolff, R. W. (1970) Work conserving priorities. J. Appl. Prob. 7, 327–337.Google Scholar