Macroscopic simulation of widely scattered synchronized traffic states

Treiber, Martin; Helbing, Dirk · 1999 · OpenAlex-citations

DOI: 10.1088/0305-4470/32/1/003

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Summary

This paper addresses the discrepancy between theoretical macroscopic traffic models and empirical observations regarding congested traffic states. While free traffic follows a unique one-dimensional flow-density relationship, empirical data for congested traffic exhibits a wide scattering of data points across a two-dimensional region, a phenomenon termed "synchronized traffic." Previous macroscopic models, such as the gas-kinetic-based traffic (GKT) model, successfully described the hysteretic phase transition to synchronized states but failed to reproduce this wide scattering when assuming a homogeneous vehicle population. The authors demonstrate that this scattering can be accurately simulated within a macroscopic framework by accounting for traffic heterogeneity, specifically the mixture of cars and trucks. The study employs the GKT model, which describes the evolution of vehicle density and average velocity through continuity and momentum equations incorporating transport, pressure, and relaxation terms. To simulate mixed traffic, the authors distinguish between two vehicle types: cars and trucks, each characterized by distinct parameters for desired velocity, time headway, and maximum density. For instance, cars are assigned a desired velocity of 112 km/h and a time headway of 1.0 s, while trucks are assigned 90 km/h and 5.0 s. The model uses time-dependent "effective" parameters calculated as weighted averages of these vehicle-specific sets, where the weights are determined by the empirically measured proportion of trucks at any given time. This approach introduces stochasticity into the macroscopic equations via boundary conditions rather than assuming microscopic interactions. The simulations were validated against empirical data from a section of the Dutch highway A9, utilizing one-minute aggregated measurements of velocity, flow, and truck proportions. The results show that the model accurately reproduces the transition from free to congested traffic and the subsequent hysteretic behavior. Crucially, the simulation replicates the wide scattering of flow-density data in the congested regime, matching the empirical distribution observed at various detector cross-sections. The authors find that the scattering in low-density regimes is primarily driven by variations in desired velocity, whereas the significant scattering in congested traffic is caused by large variations in time headway due to the changing truck fraction. The significance of this work lies in demonstrating that macroscopic models can capture complex, scattered traffic phenomena without resorting to computationally intensive microscopic simulations. By incorporating vehicle heterogeneity through time-varying effective parameters, the model provides a realistic description of synchronized traffic states. The findings imply that analyzing the proportion of trucks is essential for understanding dynamical phenomena in empirical traffic data. Furthermore, the study suggests that the GKT model combined with heterogeneous parameter weighting serves as a prototype for introducing empirically justified stochasticity into macroscopic traffic equations.

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• traffic density