On Maxima of Stationary Delay in the \({M/G/2}\) Systems

The paper investigates a two-server system with a Poisson input, in which the service times on the servers have a Pareto distribution with the parameter \(\alpha>1\) . Using known asymptotics for the distribution of stationary waiting time, the distribution of the maximum stationary delay is obtained for two cases: \(\rho<1\) and \(1<\rho<2\) . Estimates of the extremal index of stationary waiting time were obtained in numerical experiments based on regenerative simulation.