 
Summary: DISCRETE AND CONTINUOUS Website: www.aimSciences.org
DYNAMICAL SYSTEMS
Supplement 2009 pp. 790799
A HYPERBOLIC RELAXATION MODEL FOR PRODUCT FLOW
IN COMPLEX PRODUCTION NETWORKS
Ali Unver, Christian Ringhofer and Dieter Armbruster
Department of Mathematics and Statistics
Arizona State University, Tempe, AZ 852871804, USA
Abstract. This paper presents a continuum  traffic flow like  model for the
flow of products through complex production networks, based on statistical
information obtained from extensive observations of the system. The resulting
model consists of a system of hyperbolic conservation laws, which, in a relax
ation limit, exhibit the correct diffusive properties given by the variance of the
observed data.
1. Introduction. We present a continuum  traffic flow like  model for the evo
lution of a large number of parts through a complex production system. The basic
idea of traffic flow like models for production systems is to model the evolution of
parts as moving on a virtual 'road', introducing an artificial spatial variable, namely
the stage of the production process. So, the raw part enters the system at stage
x = 0 and the finished part leaves the system at stage x = 1. In the work presented
