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.

We study the problem of simulating a class of nonstationary spatio-temporal Poisson processes. The Poisson intensity function is non-stationary and piecewise linear in both the time dimension and the spatial location dimensions. We propose an exact simulation algorithm based on the inversion method. This simulation algorithm adopts three advantages. First, the entire procedure involves only closed-form computation with no need for numerical integration or numerical inversion of any function. Each step in the algorithm only requires exact arithmetic operations. Second, the proposed algorithm is sample efficient, especially compared to the thinning method when the maximum intensity value is much larger than the minimum intensity value. Third, the algorithm generates arrivals sequentially, one at a time in ascending order, so that they can be conveniently fed into real-time or online decision-making tools.

Computer Performance Modeling Handbook

Simulation Methods for Reliability and Availability of Complex Systems discusses the use of computer simulation-based techniques and algorithms to determine reliability and availability (R and A) levels in complex systems. The book: shares theoretical or applied models and decision support systems that make use of simulation to estimate and to improve system R and A levels, forecasts emerging technologies and trends in the use of computer simulation for R and A and proposes hybrid approaches to the development of efficient methodologies designed to solve R and A-related problems in real-life systems. Dealing with practical issues, Simulation Methods for Reliability and Availability of Complex Systems is designed to support managers and system engineers in the improvement of R and A, as well as providing a thorough exploration of the techniques and algorithms available for researchers, and for advanced undergraduate and postgraduate students.

A method is presented of simulating a class of nonstationary Gaussian random processes by passing a Gaussian white noise through a system introducing desirable nonstationarity at some phase of simulation. The method might have wide applications in stochastic mechanics such as in analysis of aircraft structures subjected to severe, random aerodynamic loading and in earthquake engineering. The relation between the proposed nonstationary Gaussian process and the filtered Poisson process is discussed in detail. Examples show that, if the convolution integrals, involved in general in the expressions for the output of the system and also for the output of the structure, can be avoided by particular choice of the impulse response functions of the system and the structure, then a set of numerical simulations of the nonstationary process and the structural response can be performed on an IBM 7090 within a period of approximately 30 sec. (Author).