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Volume 13,     Number 1,     Spring 2005

 

ANALYSIS OF BULK QUEUE WITH REPAIR
OF SERVICE STATION AND SETUP TIME
R. ARUMUGANATHAN AND T. JUDETH MALLIGA

Abstract. In this paper a Mx/G(a, b)/1 queueing system with multiple vacations and repair of service station on request by a leaving batch of customers and setup time is considered. Arrivals come in batches according to a Poisson Process with batch size X where X is a random variable. After finishing a service either with repair with probability π or without repair with probability (1 - π), if the server finds the queue length is less than a, the server leaves for a vacation of random length. When he returns, if the queue length is less than a the server leaves for another vacation and so on, until, he finds at least a customers in the queue. Upon return from vacation, if the server finds at least a customers waiting for service, the server requires a setup time S to start the service and serves a batch of size (a, b) customers with ba. Probability generating function of the steady state queue size at an arbitrary time is obtained using supplementary variable technique. Expected length of the queue, the busy period, the idle period and a Cost model with numerical results are presented.

 

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© 2005, Canadian Applied Mathematics Quarterly (CAMQ)