Several Types of Convergence Rates of the MG1 Queueing System

Abstract EN

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 ε0 and s0 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.

And we give the parameters ε1 and s1 of the rate of convergence and the decay of the stationary tail, respectively, for the subgeometric rate r(n)=exp(sn1/(1+α)), s>0, α>0.