Analyses of lattice hydrodynamic area occupancy model for heterogeneous disorder traffic

In developing countries, traffic not only consists of a wide range of vehicles, including automobiles, trucks, buses, motorbikes, etc. but is also disordered. Controlling and managing increasingly complex transport networks depend heavily on modeling the mechanics of mixed (heterogeneous) traffic. In heterogeneous disordered traffic, every vehicle has its size and speed, and even they are different from each other in the case of occupying the area on the road, so these can affect the overall movement of vehicular flow. Therefore, a new lattice model is designed by considering the area occupancy of different vehicles in a heterogeneous disorder traffic system with a variable proportion of slow-moving to fast-moving automobiles. In addition, stability analysis is done to investigate the ability of a heterogeneous traffic model. The mixed traffic phase diagrams show a link between traffic stability and the fraction of vehicles. Moreover, a reduction perturbation approach is used to explore the behavior of the disordered traffic, and the mKdV equation is achieved near the critical point. Furthermore, numerical simulations are performed to verify the consistency of theoretical analysis. Results portray that a higher fraction of small vehicles is beneficial for stabilizing the traffic flow.