Extending Particle Hopping Models for road traffic with Timed Automata

Abstract

Particle Hopping Models (PHM) are discrete models employed to mimic vehicular traffic, protein transport mechanisms, granular flows and other extended dynamic systems. Despite their simplistic exclusion principle, PHM correctly reproduce many macroscopic phenomena. Currently, positions of simulated entities in a PHM are updated at distinct moments by random selection, sequential iteration or in parallel. We advance these techniques by developing two time-continuous PHM for traffic applications on one-dimensional lattices and two-dimensional chequerboard topologies. By employing Timed Automata (TA) to formulate temporal boundaries and guide the movement process, driver behaviour can be finely adjusted. Both models are equipped with several stochastic components which influence critical densities and transition progressions. The proposed models can emulate almost all discrete update schemes at the level of individual movements and reproduce all major macroscopic free-flow to jamming progressions.