On a spatiotemporally discrete urban traffic model

In order to control urban traffic with model-based control methods, a proper traffic model is very important. This traffic control model needs to have enough descriptive power to reproduce relevant traffic phenomena, and it also has to be fast enough to be used in practice. Consequently, macroscopic urban traffic flow models are usually applied as control models. In this study, a macroscopic spatiotemporally discrete urban traffic model with a variable sampling time interval is proposed for model-based control strategies. By selecting proper sampling time intervals and sampling space distances, it allows us to balance modelling accuracy and computational complexity of the spatiotemporally discrete model. In addition, an urban traffic Courant-Friedrichs-Lewy (CFL) condition is deduced for spatiotemporally discrete urban traffic models, which is a sufficient condition to guarantee the discrete model to bear enough descriptive modelling power to reproduce necessary traffic phenomena. The model is analysed and evaluated based on the model requirements for control purposes. The simulation results are compared for the situations where the CFL condition is violated and not violated.