Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-16T11:10:38.486Z Has data issue: false hasContentIssue false
  • English
  • Français

Expected number of departures in M/M/1 and G/G/1 queues

Published online by Cambridge University Press:  01 July 2016

Hydar Ali
Hydar Ali*
Affiliation:
The University of the West Indies
*
∗Postal address: Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad.
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.

For an initially empty M/M/1 queue, it is shown that the transform of the expectation of the number of departures in the interval (0, t] is invariant under an interchange of arrival and service rates. However, in the GI/G/1 queue with an initial single customer, the corresponding transform does not have this symmetric property.

Keywords

TRANSFORM: EXPECTATIONDEPARTURE PROCESS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 770 - 772
Copyright
Copyright © Applied Probability Trust 1990 

References

Ali, H. (1970) Two results in the theory of queues. J. Appl. Prob 7, 219–226.CrossRefGoogle Scholar
Boxma, O. J. (1984) The joint arrival and departure process for the M/M/1 queue. Statistica Neerlandica 38, 199–208 CrossRefGoogle 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
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar