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Some Duality Results in the Theory of Queues

Published online by Cambridge University Press:  14 July 2016

Irwin Greenberg
Irwin Greenberg*
Affiliation:
Technische Hogeschool Delft, Netherlands, and New York University, Bronx, N. Y.
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Abstract

When the interarrival and service time distributions of a queue are interchanged a new queue is obtained which can be considered as the dual of the original. Another dual system, a dam, can also be associated with the original queue. Events defined for the original system can be transformed into events defined for the duals and conversely, and hence, probabilities obtained for one system can be extended to the others. In this paper several duality relations are derived, with particular emphasis on results pertaining to a single busy period. Examples are given, most of which refer to the M/G/1 – G/M/l queues.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 99 - 121
Copyright
Copyright © Applied Probability Trust 

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