Programming combined discrete-continuous simulation models for performance

Continuous state variables in combined discrete-continuous simulation models (combined models) commonly represent physical quantities, such as fluid levels or temperatures, that are governed by physical laws, and these laws are expressed as differential equations of state. The combined simulation modeling program commonly integrates the differential equations numerically, in step with its computations that describe the evolution of the discrete events. In addition to the pitfalls familiar to numerical integration, special hazards due to the interacting discrete events may confront the analyst seeking high performance in a complex model. This paper first discusses, in the context of discrete event modeling packages, some requirements for obtaining accuracy and speed in the numerical integration of the continuous variables in combined models, and second, it describes approaches that can be used to meet those requirements in selected commercial modeling packages.