The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well.
"Nonparametric estimation of the service time distribution in the M/G/∞ queue." Adv. in Appl. Probab. 48 (4) 1117 - 1138, December 2016.