Duality and other results for M/G/1 and GI/M/1 queues, via a new ballot theorem

Duality and other results for M/G/1 and GI/M/1 queues, via a new ballot theorem

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Article ID: iaor19881268
Country: United States
Volume: 14
Issue: 2
Start Page Number: 281
End Page Number: 293
Publication Date: May 1989
Journal: Mathematics of Operations Research
Authors: ,
Abstract:

The authors generalize the classical ballot theorem and use it to obtain direct probabilistic derivations of some well-known and some new results relating to busy and idle periods and waiting times in M/G/1 and GI/M/1 queues. In particular, they uncover a duality relation between the joint distribution of several variables associated with the busy cycle in M/G/1 and the corresponding joint distribution in GI/M/1. In contrast with the classical derivations of queueing theory, the present arguments avoid the use of transforms, and thereby provide insight and term-by-term ‘explanations’ for the remarkable forms of some of these results.

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