Optimal management policy for a single and bulk service queue under Bernoulli vacation schedules Online publication date: Thu, 20-Aug-2009
by Lotfi Tadj, Chafik Abid
International Journal of Applied Decision Sciences (IJADS), Vol. 2, No. 3, 2009
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.
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