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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

Information

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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