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On queues in discrete regenerative environments, with application to the second of two queues in series

Published online by Cambridge University Press:  01 July 2016

K. Balagopal
K. Balagopal*
Affiliation:
Indian Statistical Institute, New Delhi
*
∗Postal address: Statistical Quality Control and Operations Research Unit, Indian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi 110 029, India.
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Abstract

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn, n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model.

In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.

Keywords

DISCRETE-PARAMETER REGENERATIVE PROCESSESIDLE TIMEWAITING TIMEDEPARTURESSERIES QUEUESSTRONG LIMIT AND CENTRAL LIMIT THEOREMSLIGHT TRAFFIC AND HEAVY TRAFFIC LIMIT THEOREMS
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 4 , December 1979 , pp. 851 - 869
Copyright
Copyright © Applied Probability Trust 1979 

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