Two algorithms for generating a non-homogeneous Poisson process with log-quadratic intensity function are implemented into computer programs and compared for relative speed, core storage requirements and fidelity. By simulating several cases of non-homogeneous Poisson processes with log-quadratic intensity functions it is shown that the Poisson-decomposition and gap statistic algorithm substantially reduces computation time from that required by an algorithm that uses a time-scale transformation of a homogeneous Poisson process. The experience gained from implementing the algorithm has led to several possibilities which are suggested for improving the efficiency of the Poisson-decomposition and gap statistic algorithm.

The nonhomogeneous Poisson process is a widely used model for a series of events (stochastic point process) in which the rate or intensity of occurrence of points varies, usually with time. The process has the characteristic properties that the number of points in any finite set of nonoverlapping intervals are mutually independent random varialbes, and that the number of points in any of these intervals has a Poisson distribution. This paper first discusses several general methods for simulation of the one-dimensional nonhomogeneous Poisson process. Then a particular and very efficient method for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the nonhomogeneous Poisson process to the gap statistics from a random number of exponential random variables with suitably chosen parameters. Finally, a simple and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is applicable for any given rate function and is based on controlled deletion of points in a Poisson process with a rate function that dominates the given rate function.

A simple and relatively efficient method for simulating one- dimensional and two-dimensional nonhomogeneous Poisson processes is presented. The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function. In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.

"Simulation is a technique of creating representations or models of real world systems or processes and conducting experiments to predict behavior of actual systems. Input modeling is a critical aspect of simulation modeling. Stochastic input models are used to model various aspects of the system under uncertainty including process times and interarrival times. This research focuses on input models for nonstationary arrival processes that can be represented as nonhomogeneous Poisson processes (NHPPs). In particular, a smooth flexible model for the mean-value function (or integrated rate function) of a general NHPP is estimated. To represent the mean-value function, the method utilizes a specially formulated polynomial that is constrained in least-squares estimation to be nondecreasing so the corresponding rate function is nonnegative and continuously differentiable. The degree of the polynomial is determined by applying a modified likelihood ratio test to a set of transformed arrival times resulting from a variance stabilizing transformation of the observed data. Given the degree of polynomial, final estimates of the polynomial coefficients are obtained from original arrival times using least-squares estimation. The method is extended to fit an NHPP model to multiple observed realizations of a process. In addition, the method is adapted to a multiresolution procedure that effectively models NHPPs with long term trend and cyclic behavior given multiple process realizations. An experimental performance evaluation is conducted to determine the capabilities and limitations of the NHPP fitting procedure for single and multiple realizations of test processes. The method is implemented in a Java-based programming environment along with a web interface that allows user to upload observed data, fit an NHPP, and generate realizations of the fitted NHPP for use in simulation experiments."--Abstract.

Simulation means driving a model of a system with suitable inputs and observing the corresponding outputs. It is widely applied in engineering, in business, and in the physical and social sciences. Simulation method ology araws on computer. science, statistics, and operations research and is now sufficiently developed and coherent to be called a discipline in its own right. A course in simulation is an essential part of any operations re search or computer science program. A large fraction of applied work in these fields involves simulation; the techniques of simulation, as tools, are as fundamental as those of linear programming or compiler construction, for example. Simulation sometimes appears deceptively easy, but perusal of this book will reveal unexpected depths. Many simulation studies are statistically defective and many simulation programs are inefficient. We hope that our book will help to remedy this situation. It is intended to teach how to simulate effectively. A simulation project has three crucial components, each of which must always be tackled: (1) data gathering, model building, and validation; (2) statistical design and estimation; (3) programming and implementation. Generation of random numbers (Chapters 5 and 6) pervades simulation, but unlike the three components above, random number generators need not be constructed from scratch for each project. Usually random number packages are available. That is one reason why the chapters on random numbers, which contain mainly reference material, follow the ch!lPters deal ing with experimental design and output analysis.