M/G/1Repairable Queueing System With Warm Standby Failure And Delayed Repair

An M/G/1repairable queueing system with warm standby and delayed repair is studied in this thesis. The service station is of different failure rate and repair rate during idle period and busy period. While the service station is in the course of "generalized busy period" it is subject to breakdowns (we call this the one type failure), While the service station is in the system idle period it is subject to breakdowns (we call this the two type failure). Employing the standard results in the total probability decomposition technique, Laplace transform and renewal reward process. Reliability index of system is derived. Then, N-threshold entering-control policy is introduced in this thesis. In other words, at most N(≥1) customers are allowed to enter into the system during warm standby failure period. The transient queue-length distribution and the steady-state queue-length distribution is obtained at any time t. At the same time, some special cases are discussed. Finally, the total long-run expected average cost per unit time for system is developed, and the optimal threshold N*is determined by numerically examples.