Analysis for stationary indices of discrete-time T-IPH/Geo/1 queue

In this paper, we study a T-IPH/Geo/1 queue model, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death process with countably many states. The queue model can be described by a quasi-birth-and-death process with countably phases. Using operator-geometric solution method, we first give the expression of the operator and the joint stationary distribution. Then we obtain the steady-state distributions for the number of customers in the system, and waiting time for an arbitrary customer.