Stochastic LWR model with heterogeneous vehicles: Theory and application for autonomous vehicles

The introduction of autonomous vehicles (AV) will increase the vehicle heterogeneity on our roads. It is claimed that these vehicles will be able to achieve lower spacings for the same speed than human driven ones. Therefore, a good understanding of the influence of heterogeneous driver behavior on macroscopic traffic flow characteristics is crucial. This paper presents a stochastic Lighthill-Whitham Richards model by introducing heterogeneous, i.e., vehicle dependent, jam densities. The model is solved in Lagrangian coordinates, and the nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow, both through simulations and analytically. The results show that both static and dynamic macroscopic characteristics of the model, such as average speed, capacity drop and flow rate evolution at a bottleneck, are consistent with the deterministic version with an equivalent jam density, which is the harmonic mean of the distribution. Establishing the theoretical way to average the parameters will allow us to develop some control strategies for connected AV in a mixed environment to control the platoon behavior and drive traffic flow to the desired state. In this line, this paper discusses the relation between the desired AV characteristics and the market penetration rate to maximize the flow rate at bottlenecks by reducing the capacity drop effects. This further motivates future research on the technology development for AVs.