General bulk service queueing system with N-policy, multiplevacations, setup time and server breakdown without interruption

摘要

In this paper, we have considered an M~X /G(a,b)/1 queueing system with server breakdown without interruption, multiple vacations, setup times and N-policy. After a batch of service, if the size of the queue is ζ.(< a), then the server immediately takes a vacation. Upon returns from a vacation, if the queue is less than N, then the server takes another vacation. This process continues until the server finds atleast N customers in the queue. After a vacation, if the server finds at least N customers waiting for service, then the server needs a setup time to start the service. After a batch of service, if the amount of waiting customers in the queue is ζ (≥ a) , then the server serves a batch of min (ζ,b) customers, where b≥a. We derived the probability generating function of queue length at arbitrary time epoch. Further, we obtained some important performance measures.