Repairable MX/G(M/M)/1 queueing system with two service speeds

A batch arrival queueing system with two service speeds on the basis of repairable M/G(M/M)/1 queueing system with changeable service speed is considered, and a repairable MX/G(M/M)/1 queueing system with two service speeds is derived. In this batch arrival queueing system the server can provide two service speeds: if the number of the batch customers in the systems is more than N, which is preset in the beginning, the server provides service for the customers with higher speed 2 until there is no customer in the system; if the number of the batch customers in the system is less than or equal to N, the server provides service for the customers with the lower speed 1. By the method of supplementary variable the state transition-rate diagram, the system of equations, the queue length and some reliability indexes are derived.