Title: A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy

Authors: Gautam Choudhury, Kailash C. Madan

Addresses: Division of Mathematical Sciences,Institute of Advanced Study in Science and Technology, Paschim Boragoan, Guwahati 781035 Assam, India. ' Department of Mathematical Sciences, Ahlia University, P.O. Box 10878, Manama, Kingdom of Bahrain

Abstract: We consider a batch arrival queue with a Bernoulli vacation bschedule, where, after completion of a service, the server either goes for a vacation of random length with probability θ(0 ≤ θ ≤ 1) or may continue to serve the next unit, if any, with probability (1−θ), under a Restricted Admissibility (RA) policy of arriving batches with a random Setup Time (SET). Unlike the usual batch arrival queueing system, the RA-policy differs during a busy period and a vacation period and hence all arriving batches are not allowed to join the system at all times. We derive the steady state queue size distributions at a random point of time as well as at a departure epoch. Also, we obtain some important performance measures of this model. Further, we demonstrate the existence of stochastic decomposition result for this type of model.

Keywords: M^x/G/1 queues; Bernoulli schedule; vacation time; random setup time; SET; restricted admissibility policy; queue size; operational research; batch arrivals; performance measures; queueing control.

DOI: 10.1504/IJOR.2007.011445

International Journal of Operational Research, 2007 Vol.2 No.1, pp.81 - 97

Published online: 30 Nov 2006 *

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