Numerical analysis of M/G/1 type queueing systems with phase type transition structure

A number of existing results describe the numerical calculation of the steady-state distribution of an M/G/1/ type Markov process. However, these numerical methods have difficulties when the forward transition structure has a long tail asymptotic. This paper proposes a numerical approximation that can account for the polynomial decay of the steady-state distribution over several orders of magnitude, where the other known methods fail. An important advantage of the proposed approximation is that it uses numerically stable techniques.