Title: Optimal management policy for a single and bulk service queue under Bernoulli vacation schedules

Authors: Lotfi Tadj, Chafik Abid

Addresses: Department of Management and e-Business, School of Business Administration, American University in Dubai, P.O. Box 28282, Dubai, UAE. ' Department of Management and e-Business, School of Business Administration, American University in Dubai, P.O. Box 28282, Dubai, UAE

Abstract: This paper generalises the single server queue with single and bulk service characterised by the bilevel service discipline introduced by Baburaj (1999). In this system if the size (n) is not more than r, then the server takes a single customer for service according to FCFS rule and if the size is more than r then he serves min{n,R} (R > r) units in a batch according to FCFS rule. While Baburaj assumes exponential service times we consider general service time distributions. We also consider that the server implements a Bernoulli vacation schedule, so that a vacation is taken with some positive probability when a service is completed. The first objective is to derive the probability generating function of the number of customers in the system at a service completion epoch and at an arbitrary instant of time, as well as the performance characteristics of the system. The second objective is to develop an optimal management policy through a quick search algorithm.

Keywords: queueing; single service queues; batch service queues; Markov chain; semi-regenerative techniques; Bernoulli schedules; vacation schedules; optimal policy.

DOI: 10.1504/IJADS.2009.027931

International Journal of Applied Decision Sciences, 2009 Vol.2 No.3, pp.262 - 274

Available online: 20 Aug 2009 *

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