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SIMULATION
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Numerical Methods for Realizing Nonstationary Poisson Processes with Piecewise-Constant Instantaneous-Rate Functions

Steven Harrod

Department of Quantitative Analysis and Operations Management University of Cincinnati P.O. Box 210130 Cincinnati, OH 45221-0130, harrodss{at}email.uc.edu

W. David Kelton

Department of Quantitative Analysis and Operations Management University of Cincinnati P.O. Box 210130 Cincinnati, OH 45221-0130

Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. The authors review the risks of ignoring nonstationarity in Poisson processes and demonstrate three algorithms for generation of Poisson processes with piecewise-constant instantaneous rate functions, a capability that has been implemented in commercial simulation software. They test these algorithms in C programs and make comparisons of accuracy, speed, and variability across disparate rate functions and microprocessor architectures. Choice of optimal algorithm could not be predicted without knowledge of microprocessor architecture.

Key Words: Nonstationary Poisson process • nonhomogeneous Poisson process • simulation • realization generation • Poisson process realization

SIMULATION, Vol. 82, No. 3, 147-157 (2006)
DOI: 10.1177/0037549706065514
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