On the choice of an auxiliary function in the M/G/∞M/G/∞ estimation

The use of auxiliary functions in nonparametric inference for the M/G/∞M/G/∞ queueing model is considered. Estimation of the service time distribution G is challenging when only limited information about the busy/idle cycle is available. It is shown, using diagnostic plots of estimators, that a standard auxiliary function aimed at providing numerical stability fails in that regard but that a reliable auxiliary function can be constructed. The improvement made by the alternative auxiliary function is demonstrated.