On the stability of reentrant manufacturing systems

Danielle Hanson, Dieter Armbruster and Tom Taylor
Department of Mathematics and
Center for Systems Science and Engineering Research
Arizona State University
Tempe, Arizona 85287-1804
tom.taylor@asu.edu

Keywords: re-entrant manufacturing systems, discrete event systems, queueing theory, dynamical systems, topological dynamics

Abstract:

This paper considers a discrete event model of reentrant manufacturing systems, forgoing the usual Poisson process/stochastic queuing theory set-up in favor of deterministic dynamical systems theory. On the more theoretical side, results obtained include a restrictive characterization of the class of dynamical systems arising in this context, and a detailed description of the variety of orbit behaviors which can arise in the case of two-machine reentrant systems. Contrary to a conjecture of Beaumarriage and Kempf, chaotic behavior does not occur