Generation of non-homogenous poisson processes by thinning : programming considerations and comparison with competing algorithms.

Abstract

In this thesis we study several computer implementations of the thinning algorithm, a new method for generating non-homogeneous Poisson processes. The method, developed by Professor P.A.W. Lewis, Naval Postgraduate School, Monterey, California, and G.S. Shedler, IBM Research Laboratory, San Jose, California, is valid for Poisson processes with any given intensity function. The basic thinning algorithm is modified to exploit several refinements which reduce computer execution time by approximately one-third. The basic and modified thinning programs are compared with a previous algorithm of Lewis and Shedler, the Poisson decomposition and gap-statistics algorithm, which is easily implemented for Poisson processes with intensity functions of the form exp (aQ+a, t+a^t 2 ). The thinning programs are competitive in both execution time and computer memory requirements. One program implementation generates the events in a Poisson process one at a time; another program implements the algorithmic refinements which improve efficiency.