Finite Capacity Queuing System with Vacations and Server Breakdowns

This paper deals with finite capacity single server queuing system with vacations. Vacation starts at rate nu if the system is empty. Also the server takes another vacation if upon his arrival to the system, finds the system empty. Customers arrive in the system in Poisson fashion at rate lamda0 during vacation, faster rate lamdaf during active service and slower rate lamdas during the breakdown. Customers are served exponentially with the rate mu. Server breakdowns at rate b and it immediately repaired exponentially with the rate r. We derive the explicit formulas for queue length distribution, average queue length, average number of customers in the system and average waiting time for a customer in  queue and in the system. Numerical illustrations have been cited to show the model proposed is practically sound.