Bilateral Distributed Delays and Their Use in Modeling Classes of Distributed Parameter Processes

Abstract

A bilateral distributed delay model is developed which is useful in modeling a number of reversible processes with or without losses. It is shown that as k, the number of stages in the delay process, becomes large the solution of the distributed delay model approaches that of a first-order partial differential equation with a number of important applications in modeling distributed parameter flow processes in the real world. It is also shown that with smaller k values the distributed delay model introduces z-axis diffusion which can be useful in modeling some flow-plus-diffusion processes. This paper is concluded with an illustrative application of the bilateral distributed delay.