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

TL;DR

This paper develops a nonparametric method to estimate service time distributions in infinite-server queues with nonstationary Poisson arrivals, using partial observations and Laplace transform techniques.

Contribution

It introduces a novel nonparametric estimation framework for service times in nonstationary queueing systems with partial data, employing deconvolution and regularization methods.

Findings

Derived upper bounds on mean squared error of estimators

Demonstrated the method's effectiveness through simulation experiments

Provided practical insights into estimation performance

Abstract

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.