Explicit Solution for Stationary Queue Length Distribution of Geo/T-IPH/1 Queue

In this paper we study a discrete-time Geo/T-IPH/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 (QBD) process with countably many phases. Using operator-geometric solution method, we first give the expression of the joint stationary distribution. Then we obtain the explicit stationary queue length distribution of the queue we considered. Finally, a numerical example is also presented to illustrate the computational procedure.