This paper provides a mathematical framework for estimation of the service time distribution and the expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process, in the case of partial information, where only the number of busy servers are observed over time. The problem is reduced to a statistical deconvolution problem, which is solved by using Laplace transform techniques and kernels for regularization. Upper bounds on the mean squared error of the proposed estimators are derived. Some concrete simulation experiments are performed to illustrate how the method can be applied and to provide some insight in the practical performance.
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