The $M/G/\infty$ estimation problem revisited

Abstract

The subject of this paper is the $M/G/\infty$ estimation problem: the goal is to estimate the service time distribution $G$ of the $M/G/\infty$ queue from the arrival–departure observations without identification of customers. We develop estimators of $G$ and derive exact non-asymptotic expressions for their mean squared errors. The problem of estimating the service time expectation is addressed as well. We present some numerical results on comparison of different estimators of the service time distribution.