Several Types of Convergence Rates of the M/G/1 Queueing System

We study the workload process of the M/G/1 queueing system. Firstly, we give the explicit criteria for the geometric rate of convergence and the geometric decay of stationary tail. And the parameters ε 0 and s 0 for the geometric rate of convergence and the geometric decay of the stationary tail are obtained, respectively. Then, we give the explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases. Andwe give the parameters ε 1 and s 1 of the rate of convergence and the decay of the stationary tail, respectively, for the subgeometric rate r(n) = exp(sn), s > 0, α > 0.