Analysis of a Geo/G/1 Queueing System with a Generalized N-Policy and Setup-Closedown Times

Abstract: We analyze a discrete-time single-server queueing system whose arrival stream is a Bernoulli process and service times are generally distributed. An extension of the N -policy is considered: the server remains idle till the queue length becomes 1 i ≥ with probability i θ . After the idle (vacation) period, the server needs a random amount of startup time before serving. Moreover, after the system is empty in a departure epoch, the service station employs a random time to close down the system, although the shutdown is interrupted and the service is resumed immediately without setup if an arrival takes place during such a period. By using the supplementary variable technique, we obtain the queue and system length distributions as well as some performance measures. We also find out the distributions and mean values of the different periods in a cycle and the waiting time. Finally, a cost model and several numerical results are presented.