A two-phase queueing system with threshold

Abstract

We consider a single-server, two-phase queueing system with N-policy. Customers arrive at the system according to a Poisson process and receive a batch service in the first phase followed by individual services in the second phase. When the server completes second phase services, if the system becomes empty, it is turned off. After an idle period, when the queue length reaches N (threshold), the server is turned on and begins to serve customers. We obtain the system size distribution and show that the system size decomposes into three random variables. The system sojourn time is provided. The mean queue waiting is also obtained by heuristic interpretation. Finally we derive a condition under which the optimal operating policy is achieved.