Time-Varying Distributed Delays and Their Use in Aggregative Models of Large Systems

The distributed delay has found widespread application in the modeling of aggregative processes involving the flow of entities with random transit times through a given process. In most of these applications it is assumed that the mean entity transit time is fixed. There are, however, a number of important applications in aggregative economic, physical, social, and biological systems in which the mean entity transit time is time varying. A time-varying distributed delay model is developed along with a Fortran subroutine for its simulation as part of a larger system model. Examples illustrate applications of this time-varying distributed delay model to aggregative biological and economic processes.