Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T02:00:22.703Z Has data issue: false hasContentIssue false
  • English
  • Français

On the departure processes of M/M/1/N and GI/G/1/N queues

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Xiuli Chao
Xiuli Chao*
Affiliation:
New Jersey Institute of Technology
*
∗Postal address: Division of Industrial and Management Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this note is to point out the connection between the invariance property of M/M/1 and GI/G/1 queues (which has been reported in several papers) and the interchangeability and reversibility properties of tandem queues. This enables us to gain new insights for both problems and obtain stronger invariance results for M/M/1, GI/G/1, as well as loss systems M/M/1/N, GI/G/1/N and tandem systems.

Keywords

M/M/1GI/G/1DEPARTURE PROCESSESINTERCHANGEABILITYREVERSIBILITYTANDEM QUEUES

MSC classification

Primary: 60K25: Queueing theory
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 751 - 754
Copyright
Copyright © Applied Probability Trust 1992 

Footnotes

This research is partially supported by SBR, NJIT.

References

Ali, H. (1970) Two results in the theory of queues. J. Appl. Prob. 7, 219–226.CrossRefGoogle Scholar
Ali, H. (1990) Expected number of departures in M/M/1 and GI/G/1 queues. Adv. Appl. Prob. 22, 770–772.Google Scholar
Chao, X. and Pinedo, M. (1991) On reversibility of tandem queues with blocking. Naval Res. Logist. To appear.Google Scholar
Chao, X., Pinedo, M. and Sigman, K. (1989) On the interchangeability and stochastic ordering of exponential queues in tandem with blocking. Prob. Eng. Inf. Sci. 3, 223–236.Google Scholar
Greenberg, H. and Greenberg, I. (1966) The number served in a queue. Operat. Res. 14, 137–144.Google Scholar
Hubbard, J. R., Pegden, C. D. and Rosenshine, M. (1986) The departure process for the M/M/1 queue. J. Appl. Prob. 23, 249–255.Google Scholar
Muth, E. (1970) The reversibility property of production lines. Management Sci. 25, 152–158.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
Tembe, S. and Wolff, R. W. (1974) Optimal order of servers in tandem queues. Operat. Res. 22, 824–832.Google Scholar
Weber, R. R. (1979) The interchangeability of tandem queues in series. J. Appl. Prob. 16, 690–695.Google Scholar
Weber, R. R. (1992) The interchangeability of tandem queues with heterogeneous customers and dependent service times. Adv. Appl. Prob. 24, 727–737.Google Scholar