In this paper, the (M/G/1): (FCFS/∞/∞) queueing system at steady state is considered. Firstly, the
nonparametric estimates of positive skewed density functions of service time are derived; and the
most important statistical properties of these estimates are stated. Also a simulation study to
evaluate the accuracy of these estimates is presented. Secondly, the above nonparametric
estimates are combined with Kendall's probability distribution of the customer's number in the
system to obtain the nonparametric distribution of the (M/G/1): (FCFS/∞/∞) queueing system.
Thirdly, the performance measures of the nonparametric model are derived. Finally, a numerical
example is introduced to illustrate the above estimates and the derivation of the nonparametric
model.