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A note on M/G/1 vacation systems with waiting time limits

Published online by Cambridge University Press:  01 July 2016

T. Takine  and
T. Hasegawa
T. Takine*
Affiliation:
Kyoto University
T. Hasegawa*
Affiliation:
Kyoto University
*
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
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Abstract

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We consider two variants of M/G/1 queues with exhaustive service and multiple vacations; (1) customers cannot wait for their services longer than an interval of length T, and (2) customers cannot stay in the system longer than an interval of length T. We show that the probability distribution functions of the waiting times for the two systems are given in terms of those for the corresponding M/G/1 vacation systems without any residence-time limits.

Keywords

STEADY STATE DISTRIBUTIONACTUAL WAITING TIMEVIRTUAL WAITING TIMEUP- AND DOWNCROSSINGS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 513 - 518
Copyright
Copyright © Applied Probability Trust 1990 

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