A Spline-Based Method for Modelling and Generating A Nonhomogeneous Poisson Process

Lucy E. Morgan, Barry L. Nelson, Andrew C. Titman, David J. Worthington

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


This paper presents a spline-based input modelling method for inferring the intensity function of a non-homogeneous Poisson process (NHPP) given arrival-time observations. A simple method for generating arrivals from the resulting intensity function 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 (AE) department.

Original languageEnglish (US)
Title of host publication2019 Winter Simulation Conference, WSC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages12
ISBN (Electronic)9781728132839
StatePublished - Dec 2019
Externally publishedYes
Event2019 Winter Simulation Conference, WSC 2019 - National Harbor, United States
Duration: Dec 8 2019Dec 11 2019

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736


Conference2019 Winter Simulation Conference, WSC 2019
Country/TerritoryUnited States
CityNational Harbor

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Science Applications


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