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A result in queueing theory

Published online by Cambridge University Press:  17 April 2009

A. Ghosal
A. Ghosal
Affiliation:
Council of Scientific and Industrial Research, Rafi Marg, New Delhi, India.
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Abstract

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In a single-server queueing system, subject to the queue discipline ‘First come first served’, the equilibrium distribution function of the waiting time of a server depends on the distribution of the random variable (u) which is the difference between the service time and the inter-arrival time. If in two queueing systems u's are equivalent in distribution, the waiting times are also equivalent in distribution (known result). It has been shown in this note that equivalence in waiting time distributions does not necessarily imply equivalence in distributions of u's. The proof is heuristic. This result has useful practical implications.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 125 - 129
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Ghosal, A., Some aspects of queueing and storage systems (Lecture Notes in Operations Research and Mathematical Systems, 23. Springer-Verlag, Berlin, Heidelberg, New York, 1970).CrossRefGoogle Scholar
[2]Ghosal, A., “Isomorphic queues”, Bull. Austral. Math. Soc. 17 (1977), 275–289.CrossRefGoogle Scholar
[3]Lindley, D.V., “The theory of queues with a single server”, Proc. Cambridge Philos. Soc. 48 (1952), 277–289.CrossRefGoogle Scholar
[4]Smith, Walter M., ‘On the distribution of queueing times”, Proc. Cambridge Philos. Soc. 49 (1953), 449–461.CrossRefGoogle Scholar