Modelling and generating nonhomogeneous poisson processes using a spline function
Lucy E. Morgan · Winter Simulation Conference · 2018
Approaches to modelling nonhomogeneous Poisson processes (NHPPs) commonly use piecewise representations of the rate function. In reality, real-world rate functions are unlikely to take a piecewise form and therefore bias is introduced. We propose a spline function representation using a large number of knots. The resulting function, being both smooth and highly flexible, is able to take on a wide variety of functional shapes reducing the bias between it and the true process. Due to the added flexibility we control overfitting, and thus variability, by adding a penalty to the NHPP log-likelihood. Our approach optimizes the spline coefficient and penalty parameter combination by minimizing a modified AIC score. Our approach also leads to a simple method for arrival generation from the resulting spline function.