MANTRAS · A Novel Mathematical Framework for the Modelling and the Analysis of Transportation Networks (MANTRAS)

Transportation networks are ubiquitous nowadays: people move over transit links (airspace, highway systems, networks of subways and railways), trade goods through industrial networks (logistics and production networks, manufacturing systems) and assets through financial networks (market and banking systems), support their lifestyle via distribution networks (power, energy, food and water distribution systems), and communicate and exchange knowledge through information networks (based on telephone lines, satellite stations, optical grids, cable and wireless internet, postal networks and the media). A reliable, resilient, secure, efficient, and effective operation of these networks is of paramount importance both when the systems are operated to the limits of their performance during critical situations, as well as under regular operating conditions. The quest for a quantitative understanding of these networks and their properties necessitates the development of descriptive formal models to represent, analyze, and control them. Discrete Event Systems (DES) and Stochastic Hybrid Systems (SHS) are general mathematical models that, while rather different in nature, by virtue of their structural properties and dynamical features are both particularly suitable at modelling transportation networks. This project has two original objectives. The first major goal is theoretical, and is aimed at the introduction of a formal mathematical framework that is capable of connecting between the theory of DES and that of SHS. The second objective deals with the applications of this novel formal model in the description, analysis, and control of classes of transportation networks (road traffic networks and railway systems). This innovative project is expected to yield theoretical results that will be foundational for further investigations, and to originate compelling and relevant practical outcomes of considerable industrial, economic, societal, and environmental impact.