The Queue Length of GI/G/1 Queueing System with Server Setup Times

This paper deals with the GI/G/1 queuing system with a random setup time. The server is turned off each time when the system becomes empty. At this point of time the idle period starts. As soon as a customer arrives, the setup of the service facility begins which is needed before starting each busy period. In this paper we study the transient distribution of queue length by applying the Markov skeleton process approach. We show that the transient distribution of queue length is the minimal nonnegative solution and also the unique bounded solution to a nonnegative linear equation.