A kinematic wave theory of lane-changing traffic flow

Jin, Wen‐Long · 2010 · OpenAlex-citations

DOI: 10.1016/j.trb.2009.12.014

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Summary

This paper addresses the disruption of traffic flow and increased accident risks caused by frequent lane changes in highway merging, diverging, and weaving areas. While traditional macroscopic models like the Lighthill-Whitham-Richards (LWR) model effectively describe longitudinal vehicle interactions, they fail to capture the lateral interactions inherent in lane-changing behavior. The author proposes a simple kinematic wave model to quantify the bottleneck effects of lane-changing traffic on aggregate roadway dynamics. The motivation is to provide an intuitive, system-level description of how systematic lane changes impact overall traffic capacity and flow, filling a gap left by complex microscopic models and existing macroscopic studies that lack a unified framework for aggregate analysis. The methodology introduces a new variable, lane-changing intensity $\epsilon(x, t)$, to represent the lateral interaction where a vehicle affects traffic on both its current and target lanes. This leads to a modified effective density $\bar{\rho} = \rho(1 + \epsilon)$ and a revised fundamental diagram where speed is a function of this effective density. The paper derives the intensity variable for uniform traffic conditions, showing it depends on the number of lane changes, maneuver duration, and traffic density. For location-dependent intensity, the model is analyzed as a system of hyperbolic conservation laws. The author employs a supply-demand method for numerical solutions and analyzes the Riemann problem to understand traffic dynamics. The theoretical framework is calibrated using NGSIM vehicle trajectory data from a weaving section to establish a relationship between lane-changing intensity and traffic density. The results demonstrate that lane-changing traffic significantly reduces overall throughput. With a constant lane-changing intensity of $\epsilon = 0.1$, the model predicts a capacity reduction of approximately 9.1%, consistent with empirical observations of bottleneck effects. The modified fundamental diagram shows that lateral interactions are negligible in sparse traffic but cause substantial speed and flow reductions in congested conditions. Furthermore, the analysis of density-dependent intensity reveals that a sharp increase in lane-changing frequency at critical densities can produce a "reverse-$\lambda$" shaped fundamental diagram, explaining the phenomenon of capacity drop. The kinematic wave analysis confirms that the system behaves as a nonlinear resonant system, allowing for the unique solution of traffic states across discontinuities in lane-changing intensity. The significance of this work lies in providing a tractable macroscopic framework for evaluating the aggregate impacts of lane-changing behavior. By linking lane-changing intensity to road geometry, location, and traffic conditions, the model offers a tool for analyzing bottleneck formation in weaving sections. The findings suggest that systematic lane changes are a primary contributor to capacity drops and traffic instability. This modeling approach supports the development of lane management strategies, such as ramp metering, designed to mitigate the disruptive effects of lane changes and improve traffic flow efficiency in complex highway environments.

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Topics

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• traffic density
• lane changing