Bridging Scales in Multi-Lane Traffic Flow: Modeling, Stability, and Simulation
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In this talk, we delve into the modeling and analysis of vehicular traffic dynamics on multi-lane roads, aiming to connect individual driver behavior with emergent macroscopic flow patterns. We present a hybrid microscopic model that extends the classical Bando-Follow-the-Leader approach by incorporating discrete lane-changing events. This extension captures the dual nature of traffic evolution: smooth longitudinal interactions and abrupt lateral shifts. From this enriched microscopic framework, we systematically derive novel first- and second-order macroscopic models that account for lane-changing effects in a principled way, avoiding heuristic transition rules. The first-order model generalizes the Lighthill–Whitham–Richards (LWR) theory by including source terms derived from microscopic lane-switching propensities. The second-order model, inspired by the Aw–Rascle–Zhang (ARZ) formulation, introduces balance laws for both momentum and inter-lane transfer, yielding a more detailed depiction of velocity dynamics. We examine steady-state configurations and carry out a linear stability analysis to identify conditions under which perturbations grow or decay. To validate our theoretical insights, we propose numerical simulations using a Roe-type scheme capable of resolving contact discontinuities. These simulations reveal the rich variety of spatio-temporal patterns that arise in realistic multi-lane traffic settings. Overall, this multi-scale modeling framework provides a deeper understanding of traffic phenomena and opens avenues for more predictive and reliable traffic flow simulations.
