Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T13:48:34.955Z Has data issue: false hasContentIssue false
  • English
  • Français

A single server tandem queue

Published online by Cambridge University Press:  14 July 2016

Sreekantan S. Nair
Sreekantan S. Nair*
Affiliation:
Purdue University, Lafayette, Indiana
Get access Rights & Permissions [Opens in a new window]

Abstract

Avi-Itzhak, Maxwell and Miller (1965) studied a queueing model with a single server serving two service units with alternating priority. Their model explored the possibility of having the alternating priority model treated in this paper with a single server serving alternately between two service units in tandem.

Here we study the distribution of busy period, virtual waiting time and queue length and their limiting behavior.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 1 , March 1971 , pp. 95 - 109
Copyright
Copyright © Applied Probability Trust 1971 

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] Avi-Itzhak, B., Maxwell, W. L. and Miller, L. W. (1965) Queueing with alternating priorities. Operat. Res. 13, 306–318.Google Scholar
[2] Nair, S. S. (1969a) Tandem queues with alternating priorities (Abstract). Ann. Math. Statist. 40, 183.Google Scholar
[3] Nair, S. S. (1969b) On certain priority queues. Purdue Univ. Dept. of Stat. Mimeo Series 214.Google Scholar
[4] Nair, S. S. (1970) A modified exponential series. To appear in Simon Stevin (October issue).Google Scholar
[5] Nelson, R. T. (1968) Dual-resource constrained series service systems. Operat. Res. 16, 324–341.CrossRefGoogle Scholar
[6] Neuts, M. F. (1968) Two queues in series with a finite intermediate waiting room. J. Appl. Prob. 5, 123–142.Google Scholar
[7] Neuts, M. F. and Yadin, M. (1968) The transient behavior of the queue with alternating priorities, with special reference to the waiting times. Purdue Univ. Dept. of Stat. Mimeo Series 136.Google Scholar
[8] Pyke, R. (1961) Markov renewal processes: definitions and preliminary properties. Ann. Math. Statist. 32, 1231–1242.CrossRefGoogle Scholar
[9] Smith, W. L. (1955) Regenerative stochastic processes. J. R. Statist. Soc. A 232, 6–31.Google Scholar
[10] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[11] Welch, P. D. (1965) On the busy period of a facility which serves customers of several types. J. R. Statist. Soc. B 27, 361–370.Google Scholar
[12] Zygmund, A. (1951) A remark on characteristic functions. Proc. Second Berkeley Symp. on Math. Statist. and Prob. 369–372.Google Scholar