Poisson Simulation—A Method for Generating Stochastic Variations in Continuous System Simulation

Abstract

In continuous systems simulation a model is built as a system of differential equations. An implicit assump tion is that the number of items is so large that the changes can then be regarded as continuous. How ever, many systems can be modeled by differential equations when the numbers involved are moderately large. Such systems show stochastic variations that can be described in terms of events per time unit. If the events happen one at a time, and if the number of events during the interval is independent of both the number of past events and the times these events oc curred, we have a Poisson process. The system's variations can be modeled by replacing the flow to or from a state during the integration step with a Pois son probability. This not only adds variations to the model, but can also reveal system properties not cov ered by continuous system simulation. Furthermore, the "intensity parameter" controlling the flow may vary over time without further problems.