Dynamic operating policy for the controllable queue with two removable unreliable servers

In this paper, we investigate an infinity capacity M/M/2 queueing system under a dynamic operating policy. In the system, there are two identical removable servers. Initially, these two servers are turned off. Once the number of customers in the system reaches the first/second start-up threshold, the first/second server is turned on. Similarly, once the number of customers in the system reduces to the second/first shut-down threshold, the second/first server will be turned off. When these two servers provide services to the customer, they are assumed to be unreliable and so may break down. If a server fails, it is immediately sent to the maintenance department. The probability-generating technique and matrix-geometric method are employed to obtain the steady-state results. The equilibrium condition of the system is explicitly developed. We further develop matrix-form expressions for various system characteristics. Finally, an optimization analysis is performed.