Nonparametric Estimation of Service Time Characteristics in Infinite-Server Queues with Nonstationary Poisson Input

Alexander Goldenshluger, David T. Koops

Research output: Contribution to journalArticlepeer-review

Abstract

This paper provides a mathematical framework for estimation of the service time distribution and expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process in the case of partial information, where only the numbers 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 provide some insight in the practical performance.
Original languageEnglish
Pages (from-to)183-207
Number of pages25
JournalStochastic Systems
Volume9
Issue number3
DOIs
StatePublished - 2019

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