Statistical techniques for a numerical evaluation of the proximity of G/G/1 and G/M/1 queueing systems

We study the strong stability of a $G/M/1$ queueing system after perturbation of the service times. We are interested in the determination of the proximity error between the corresponding service time distributions of $G/G/1$ and $G/M/1$ systems, the approximation error on the stationary distributions, and confidence intervals for the difference between the corresponding characteristics of the quoted systems in the stationary state, when the general distribution of service times $G$ in the $G/G/1$ system is unknown and must be estimated by means of a nonparametric estimation method. We use the Student test to accept or reject the equality of the corresponding characteristics. The boundary effects are taken into account. Simulation studies are performed to support the results.