A Multi-commodity Lighthill-Whitham-Richards Model of Lane-changing Traffic Flow

Abstract

Systematic lane changes can seriously deteriorate traffic safety and efficiency inside lane-drop, merge, and other bottleneck areas. In our previous studies (Jin, 2010a,b), a phenomenological model of lane-changing traffic flow was proposed, calibrated, and analyzed based on the concept of lane-changing intensity. In this study, we further consider weaving and non-weaving vehicles as two commodities and develop a multi-commodity, behavioral Lighthill-Whitham- Richards (LWR) model of lane-changing traffic flow. Based on a macroscopic model of lane-changing behaviors, we derive a fundamental diagram with parameters determined by car-following and lane-changing characteristics as well as road geometry and traffic composition. In particular, we calibrate and validate fundamental diagrams corresponding to a triangular car-following fundamental diagram with NGSIM data. We introduce an entropy condition for the multi-commodity LWR model and solve the Riemann problem inside a homogeneous lane-changing area. From the Riemann solutions, we derive a flux function in terms of traffic demand and supply. Then we apply the model to study lane-changing traffic dynamics inside a lane-drop area and show that the smoothing effect of HOV lanes is consistent with observations in existing studies. The new theory of lane-changing traffic flow can be readily incorporated into Cell Transmission Model, and this study could lead to better strategies for mitigating bottleneck effects of lane-changing traffic flow.