An M~X/(G_1 G_2)/1 repeated service queue with N-policy and setup time subject to server's breakdown and delayed repair

摘要

This article deals with the N-policy with setup time of an unreliable M-X/G/1 queue provides two types of general heterogeneous service under optional repeated service and delayed repair. The server is turned off each time as soon as the system becomes empty and waits until the queue size becomes exactly. As soon as exactly () customers accumulate in the system, the server has to undertake a set up period before starting the busy period. The steady state queue size distributions by considering both elapsed and remaining times as well as various system characteristics has been derived for this model.