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  • WSC19_LM

    Accepted author manuscript, 840 KB, PDF document

    Embargo ends: 16/12/19

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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A Spline-based Method for Modelling and Generating a Nonhomogeneous Poisson Process

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paper

Publication date3/06/2019
Host publicationProceedings of the 2019 Winter Simulation Conference
PublisherIEEE Press
Number of pages12
Original languageEnglish

Publication series

NameProceedings of the 2019 Winter Simulation Conference
PublisherIEEE Press


This paper presents a spline-based input modelling method for inferring the intensity function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations. A simple method for generating arrivals from the resulting intensity function is also presented. Splines are a natural choice for modelling intensity functions as they are smooth by construction, and highly flexible. Although flexibility is an advantage in terms of reducing the bias with respect to the true intensity function, it can lead to overfitting. Our method is therefore based on maximising the penalised NHPP log-likelihood, where the penalty is a measure of rapid changes in the spline-based representation. An empirical comparison of the spline-based method against two recently developed input modelling techniques is presented, along with an illustration of the method given arrivals from a real-world accident and emergency (A&E) department.