Numerical Computations and Tail Asymptotics for Stationary Indices of a Discrete-time Queue

This paper considers numerical computations and tail asymptotics for stationary queue length and sojourn time distribution of the Geo/T-IPH/1 queue, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death chain with countably many states. By analysis of probability generating functions, recursive formulas for queue length and sojourn time, and factorial moments of queue length and sojourn time are given. Moreover, a complete characterization of the regions of system parameters for exact tail asymptotic characterizations for such indices is also given, and the results show that there are three types of exact tail asymptotics for the indices in different regions.