Finite Capacity Queueing System With Vacations and Server Breakdowns

Abstract this paper deals with finite capacity single server queuing system with vacations. vacation starts at rate ν 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 λ during vacation, faster rate λ during active service and slower rate λ≥0 during the breakdown. customers are served exponentially with the rate µ . server breakdowns at rate b and it is 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 that the proposed model is practically sound.