Online ISSN: 2515-8260

BERNOULLI SERVICE SCHEDULES AND MULTIPLE ADAPTIVE VACATIONS FOR BULK ARRIVAL AND GENERAL SERVICE QUEUE WITH CONTROL POLICY ON DEMAND FOR RE-SERVICE

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P. PRABHAKARAN1 , S. SEKAR

Abstract

The Bernoulli service schedule and re-service policy in queueing theory has been always a new and hot research field. ABulk queueing system with Poisson arrival rate λ and the general service random variable is considered here. In this paper, the server implements the notion of a binomial vacation schedule. In this policy, if there is no customer at a service completion epoch then the server takes multiple vacations. The number of vacations follows a binomial distribution with parameter????, otherwise the server gives service with probability 1−????if any new customers arrive in the queue. At the completion of an essential service, the batch of customers may request for a re-service with probability????. However, the re-service is rendered only when the number of customer waiting in the queue is less than one. If no request for reservice after an essential service and no customers in the queue, then the server avail a vacation of a random length with probability (1− ????). When the server returns from vacation and if there is no customer in the queue then he avails another vacation and so on until the server finds single customers in the queue. After completing of an essential service and the number of customers in the queue becomes one then the server will continue the service with general service rule.

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