M/G/1Repairable Oueueing System Under P-entering Discipline During Server Idle Period With N-policv And Set-up Times

This paper analyzes an M/G/1repairable queueing system withN--policy and set-up times where the customers enter the system with probabilityp (0p1)during server idle period. Once there is no customer in the system, theserver switch to idle state till the number of customers in the system reaches the valueof N. At this point, the server immediately from the idle state to the work state after arandom period starts to service customs. In the process of service time, the serverstation may break downs because of the aging effect and the accumulative wear. Thecustomer who is current being service should receive service again after the serverstation is repaired. By introducing the "idle time of system"、"server busy period" and"generalized service time ", using the total probability decomposition technique andthe Laplace transform、the Laplace-Stieltjes transform、Generating function tool, wediscuss our system from the queueing theory and the reliability theory. Meanwhile, therecursive expressions of the distribution and stochastic decomposition of the queuelength at a random point in equilibrium are obtained. Furthermore, the first failure timedistribution of service station、the steady-state unavailability and the expected failurenumber during (0, t]are also studied.