M/G/1 Repairable Queueing System With Warm Standby Failure And Control Policy

In this paper, we consider an M/G/1 repairable queueing system with warm standby failure and control policy. In Chapter 1, "N -threshold entering-control policy" is introduced into the M/G/1 repairable queueing system with warm standby failure and delayed repair. Under such a policy, at most N(?1) customers are allowed to enter into the system during warm standby failure period. By using the total probability decomposition technique and the Laplace transform, we discuss some reliability indices of the service station, such as the probability distribution of the first failure time, the unavailability, the expected failure number during a given time interval (0, t] and the probability that the service station is waiting for being repaired in the warm standby failure. Furthermore, we obtain the expressions of these reliability indices under the steady state. In Chapter 2, we consider the M/G/1 repairable queueing system with Min(N, D) -policy and warm standby failure. The transient queue-length distribution and the steady-state queue-length distribution is studied at any time t. Meanwhile,some system reliability indices are discussed. Finally, we numerically determined the optimal control policy(N*, D*) under a constructed cost model.