DAAD-PPP Great Britain: Robust simulation of networks with random switching

Project Description

Robust simulation methods are necessary tools to study physical models, in particular when these arise from industrial applications. In this project, we consider coupled systems of ordinary and partial differential equations and allow for uncertainty in real-life systems by including random switching and small noise sources into the mathematical modelling. The main field of application we will focus on are manufacturing networks, however, similar models may arise in networks of traffic flow, gas transport and neuroscience. The starting point for a hierarchy of models are networks, where the flow of products or traffic is described by continuous-time differential equations and failures of parts of the network are modelled by randomly switching between different subsets of differential equations. In further stages of the models we will also consider load dependent failure rates and small noise in the production process. For the resulting complex systems, we intend to develop and analyse appropriate and efficient numerical methods for large-scale simulation in this joint project.

Key words: production networks, random breakdowns, numerical simulation


Project Partners:

Dr. Evelyn Buckwar (Heriot-Watt University, Edinburgh, Scotland)
Dr. Thorsten Sickenberger (Heriot-Watt Universit, Edinburgh, Scotland)
Dr. Simone Göttliich (TU Kaiserslautern, Germany)

Funding: DAAD within the project "PPP Great Britain - ARC 2009"; travel expenses for two years

Duration: 07/2009 - 06/2011

Relevant Publications

  • S. Göttlich, S. Martin, T. Sickenberger - Production networks with stochastic machinery default - Progress in Industrial Mathematics at ECMI 2010, pp. 247-253, 2012.
  • S. Göttlich, S. Martin, T. Sickenberger - Time-continuous production networks with random breakdowns - Networks and Heterogeneous Media (NHM), Vol. 6(4), pp. 695-714, 2011.