Reliability Analysis of the MAP/M/c Queue with Server Breakdowns

We consider the MAP/M/c queue with markovian flow of breakdowns. There are K waiting positions for arrival customers in the system. The system we consider comprises c servers, of which one are has to work for the customers. The other servers is in the cold standby , repairing or waiting for repairing, only the working server can fails, and there is only one repairman. This model is quite general enough to cover most of the communication networks. The queue and main indexes reliability are also derived by a quasi-birth-and-death (QBD) process. Besides, we give numerical examples to illustrate the effect of the parameters on several performance measures.