TY - JOUR ID - 71945 TI - Finite Capacity Queuing System with Vacations and Server Breakdowns JO - International Journal of Engineering JA - IJE LA - en SN - 1025-2495 AU - Basnet, Ritu AU - Ghimire, Ram AD - mathematics, Kathmandu University AD - Mathematics, Kathmadu University Y1 - 2011 PY - 2011 VL - 24 IS - 4 SP - 387 EP - 394 KW - Keywords Multiple–vacation KW - Server breakdowns KW - Repair KW - Generating Functions KW - Average queue length DO - N2 - 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. UR - https://www.ije.ir/article_71945.html L1 - https://www.ije.ir/article_71945_4624b57ef8749b8baaa6f7a63cf65628.pdf ER -