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This paper provides a mathematical framework for estimation of the servicetime distribution and the expected service time of an infinite-server queueingsystem with a nonhomogeneous Poisson arrival process, in the case of partialinformation, where only the number of busy servers are observed over time. Theproblem is reduced to a statistical deconvolution problem, which is solved byusing Laplace transform techniques and kernels for regularization. Upper boundson the mean squared error of the proposed estimators are derived. Some concretesimulation experiments are performed to illustrate how the method can beapplied and to provide some insight in the practical performance.

Nonparametric estimation of service time characteristics in infinite-server queues with nonstationary Poisson input