Research on replacement model for M/G/1 queuing system with repairable service station of ' not as good as new'

The optimal replacement policy for the M/G/1 queuing system of ' not as good as new' with repairable service station is studied. Assuming that the service station after repair is ' not as good as new' and the life distribution obeys the exponential one, by using geometric process and renewal process. We have taken the number N of the customer that have been serviced at the service station and the long-run expected benefit of the system in unity time as its replacement policy and the objective function respectively, then the objective (unction has achieved its maximum with choosing the optimal replacement policy N . The explicit expressions of long-run expected benefit of system in unity time are derived in this paper and finally its result is discussed also.