N Policy For Repairable Bulk Arrival Queueing Model With Setup, Second Multi Optional Service Facility Under Restricted Number Of Server Vacations

摘要

This paper analyses a repairable batch arrival queueing model with a second multi optional service(SOS) channel under N policy in which the server takes restricted number of multiple vacations during his idle period.The server leaves the system for vacation as soon as the system empties and after returning from vacation if the server finds N or more customers in the system then he immediately starts the setup work. Otherwise he repeats his vacation until he finally finds at least N customers or returns to the system after taking L vacations.ie At the end of Lth vacation if the server finds less than N customers he joins the system and stays idle until the queue length reaches at least N to start the setup work. After the completion of setup work, busy period initiates.The server may undergo unpredictable breakdowns during the service and sent for repair immediately.As soon as the repair is completed, the server returns to the customer whose service was interrupted. The system size distribution at a random epoch and mean system length are calculated and the corresponding results for the classical single and multiple vacation models are obtained as special case.