Deterministic microscopic three-phase traffic flow models

Kerner, Boris S.; Klenov, Sergey L. · 2006 · OpenAlex-citations

DOI: 10.1088/0305-4470/39/8/002

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Summary

This paper introduces two deterministic microscopic traffic flow models—the Acceleration Time Delay (ATD) model and the Speed Adaptation (SA) model—developed within the framework of Kerner’s three-phase traffic theory. The research addresses a critical limitation in existing traffic flow models, particularly those based on the fundamental diagram approach, which fail to explain the empirical observation that traffic breakdown at bottlenecks involves a first-order phase transition from free flow to synchronized flow (F→S), rather than directly to wide moving jams (F→J). While stochastic models had previously been developed to simulate these transitions, deterministic models capable of reproducing the F→S→J sequence were absent. The authors aim to fill this gap by creating deterministic frameworks that incorporate realistic driver behaviors, such as time delays and speed adaptation, to simulate congested patterns consistent with empirical data. The ATD model explicitly incorporates driver time delays in acceleration and deceleration, varying these delays based on the local traffic phase (free flow, synchronized flow, or wide moving jam). It assumes that synchronized flow steady states occupy a two-dimensional region in the flow–density plane, bounded by safe speed limits and synchronization gaps. The model uses differential equations to describe vehicle acceleration, accounting for effects like driver over-acceleration in free flow and over-deceleration in synchronized flow. The SA model, in contrast, simplifies the steady states of synchronized flow to a one-dimensional curve, focusing on vehicle speed adaptation to preceding vehicles under specific driving conditions. Both models are tested using numerical simulations on a road with an on-ramp bottleneck, employing specific parameters for sensitivities, time delays, and safety conditions derived from empirical observations. The results demonstrate that both the ATD and SA models successfully reproduce the spatiotemporal features of congested traffic observed in real-world data. Specifically, both models exhibit the F→S→J transition sequence, where congestion onset at a bottleneck is triggered by a transition from free flow to synchronized flow, and wide moving jams emerge spontaneously only within synchronized flow. The ATD model captures additional empirical features, such as the "pinch effect" in synchronized flow, where drivers reduce space gaps at lower speeds. The study also compares these deterministic models with earlier stochastic models and fundamental diagram-based models, highlighting that the latter incorrectly predict F→J transitions as the primary mechanism for congestion onset. The significance of this work lies in providing a deterministic theoretical foundation for three-phase traffic theory, validating that complex traffic phenomena like synchronized flow and moving jams can be modeled without relying on stochastic fluctuations. By successfully simulating the F→S→J transition, the paper challenges the validity of traditional fundamental diagram approaches and offers more realistic tools for understanding and potentially managing traffic congestion. The findings support the hypothesis that driver behavioral responses, particularly time delays and speed adaptation strategies, are sufficient to explain the phase transitions governing freeway traffic breakdown.

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• mental model of traffic