Modeling and simulation of multilane traffic flow

Helbing, Dirk; Greiner, Andreas · 1997 · OpenAlex-citations

DOI: 10.1103/physreve.55.5498

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Summary

This paper addresses the need for realistic macroscopic models of multi-lane traffic flow, specifically focusing on simulating bottleneck situations. Previous macroscopic models often treated multi-lane roads as single lanes with higher capacity or relied on phenomenological approaches that assumed velocity equilibrium with density. These simplifications fail to capture disequilibria between neighboring lanes, such as density oscillations and stop-and-go waves, which significantly reduce freeway capacity. To resolve this, the authors derive a consistent macroscopic multi-lane model from a gas-kinetic (Boltzmann-like) microscopic approach. This derivation explicitly accounts for acceleration, deceleration, velocity fluctuations, overtaking, and lane-changing maneuvers, correcting deficiencies in earlier models like those by Payne or Michalopoulos. The methodology begins with a Boltzmann-like kinetic equation describing the phase-space density of vehicles, incorporating terms for vehicle motion, acceleration toward desired velocities, and interactions. The authors define interaction rates for same-lane deceleration and overtaking probabilities, as well as waiting times for lane-changing maneuvers, which vary based on regional traffic regulations (e.g., European autobahns vs. American freeways). By integrating these kinetic equations, they derive macroscopic moment equations for vehicle densities and average velocities on each lane. These fluid-dynamic equations include terms for traffic pressure and equilibrium velocities, capturing the mutual influences between lanes. For efficient computer simulations, the authors further derive a reduced model by eliminating velocity equations through time-averaging over oscillation periods. This results in coupled Burgers equations that describe coarse-grained traffic dynamics on a slow time scale, dependent only on densities and their spatial gradients. The study demonstrates the application of this reduced model through computer simulations of a two-lane autobahn. The simulations utilize empirical velocity-density and pressure relations derived from data on the Dutch highway A9. Lane-changing rates are modeled as proportional to the density of obstructing vehicles and the available space on adjacent lanes. The results show that the model successfully simulates difficult bottleneck situations, capturing the complex dynamics of multi-lane traffic without requiring computationally expensive microscopic simulations. The significance of this work lies in providing a theoretically sound, macroscopic framework for multi-lane traffic that bridges microscopic behavior and macroscopic flow. By systematically deriving equations from a gas-kinetic foundation, the model offers corrections to previous phenomenological approaches and enables efficient simulation of large freeway systems. This allows for better analysis of traffic instabilities, bottleneck formation, and the effects of lane-changing behaviors, contributing to improved traffic management and infrastructure planning.

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• traffic density