Multiclass first-order traffic model using stochastic fundamental diagrams

The first-order continuum traffic model has been extensively studied in the state-of-the-art of traffic flow theory due to its simplicity and capability to represent many real traffic problems, such as a shock-wave formation. Furthermore, recent extension of the first-order model to multiclass traffic dynamics has revealed some interesting non-linear traffic phenomena such as hysteresis and capacity drop. However, most of the existing first-order continuum models do not display the widely scattered flow-density relationship. We argue in this article that the widely scattered flow-density relationship might be caused by the random variations in driving behaviour. It is shown that both of the hysteresis transitions and the wide scattering can be reproduced by a multiclass first-order model with a stochastic setting in the model parameters. The simulation results support our findings and are in good agreement with the real data.