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Restricted Admissibility of Batches into an M/G/1 Type Bulk Queue with Modified Bernoulli Schedule Server Vacations

Published online by Cambridge University Press:  15 November 2002

Kailash C. Madan  and
Walid Abu–Dayyeh
Kailash C. Madan
Affiliation:
Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan; kailashmadan@hotmail.com.
Walid Abu–Dayyeh
Affiliation:
Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan; abudayyeh_walid@hotmail.com.
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Abstract

We investigate the steady state behavior of an M/G/1 queue with modified Bernoulli schedule server vacations. Batches of variable size arrive at the system according to a compound Poisson process. However, all arriving batches are not allowed into the system. The restriction policy differs when the server is available in the system and when he is on vacation. We obtain in closed form, the steady state probability generating functions for the number of customers in the queue for various states of the server, the average number of customers as well as their average waiting time in the queue and the system. Many special cases of interest including complete admissibility, partial admissibility and no server vacations have been discusssed. Some known results are derived as particular cases of our model.

Keywords

Steady statecompound Poisson processBernoulli schedule server vacationsexponential vacation periodsrestricted admissibility of batches.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 113 - 125
Copyright
© EDP Sciences, SMAI, 2002

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