This thesis explores the analysis, periodicity, and scalable modelling of Max-Min-Plus-Scaling systems, a versatile approach to modelling Discrete Event systems. Unlike traditional continuous-time or discrete-time systems that evolve through differential or difference equations, DE systems progress through discrete events. MMPS systems rely only on maximisation, minimisation, addition, and scaling, making them highly suitable for modelling processes with synchronisation and/or competition such as energy delivery, transportation, and manufacturing.
The work is divided into three main segments. First, a new Mixed-Integer Linear Program ming based method is developed for analysing growth rates and fixed points of general implicit MMPS systems. This extends an existing MILP formulation for homogeneous and non-expansive explicit MMPS systems, introducing adaptations for general implicit cases.
A dedicated preprocessing step and search strategy are introduced, resulting in an analysis method that significantly reduces computational requirements. Secondly, the dynamical and stability behaviour of periodic MMPS systems with periods greater than one is examined.
A new canonical form is proposed, enabling the use of existing analysis tools on periodic systems, along with a method for determining the stability of periodic orbits. Thirdly, a modelling framework for transportation systems is introduced, featuring a connectable, node based toolbox and an algorithm that transforms high-level system descriptions into sets of equations.
All developed methods, theories, and tools are demonstrated on a real-world 4-node transportation system. The results confirm the efficiency of the new MILP approach, reveal periodic behaviour and stable periodic orbits, and highlight fixed points, all within the proposed transportation network framework.