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A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times

Published online by Cambridge University Press:  14 July 2016

Bharat T. Doshi
Bharat T. Doshi*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: AT&T Bell Laboratories, Holmdel, H04K428, NJ 07733, USA.
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Abstract

In this note we prove some stochastic decomposition results for variations of the GI/G/1 queue. Our main model is a GI/G/1 queue in which the server, when it becomes idle, goes on a vacation for a random length of time. On return from vacation, if it finds customers waiting, then it starts serving the first customer in the queue. Otherwise it takes another vacation and so on. Under fairly general conditions the waiting time of an arbitrary customer, in steady state, is distributed as the sum of two independent random variables: one corresponding to the waiting time without vacations and the other to the stationary forward recurrence time of the vacation. This extends the decomposition result of Gelenbe and Iasnogorodski [5]. We use sample path arguments, which are also used to prove stochastic decomposition in a GI/G/1 queue with set-up time.

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 419 - 428
Copyright
Copyright © Applied Probability Trust 1985 

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