Some Remarks on Stability and Robustness of Production Networks Based on Fluid Models

Abstract

The dynamics of complex, large-scale production networks present an important issue not only for the management of such networks but also for scientific research. This problem is usually investigated either by numerical simulations or by mathematical analysis of the associated queueing model. One major property of stable production networks is the robustness of these networks with respect to perturbations of the arrival process of jobs from outside. Given a generic structure of the considered network with several production locations, different products and re-entrant material flows the determination of robustness is non trivial. In this paper we use a fluid model approach to analyse the robustness of queueing networks. First conditions for stability of a fluid network are introduced. These conditions allow to assess the dynamic behavior of the production network. Second the obtained results are investigated with the help of a simulation of the fluid and queueing network. Simulations of a test case scenario accompany the results of the theoretical analysis.