Pilar Moreno. A $Geo/G/1/\infty$ queueing system under multiple vacations and setup-closedown times

Abstract. This paper concerns a $Geo/G/1/\infty$ queueing system under multiple vacations and setup-closedown times. When all the customers are served in the system exhaustively, the server is deactivated by a closedown time. After a shutdown time with arrivals, the server begins the service of the customers (is reactivated) without setup; however, after a shutdown time without arrivals, the server operates under a multiple vacation policy (the server takes another vacation whenever it returns from a vacation and there are not customers waiting in the system). After a vacation time with arrivals, the server requires a startup time (is reactivated) before providing the service until the system is empty. By applying the supplementary variable technique, the joint generating function of the server state and the system length together with the main performance measures are derived. We also study the length of the different busy periods of the server. The stationary distributions of the time spent waiting in the queue and in the system under the FCFS discipline are analysed too. Finally, a cost model with some numerical results is presented.