Three-phase traffic theory and highway capacity

Kerner, Boris S. · 2003 · OpenAlex-citations

DOI: 10.1016/j.physa.2003.10.017

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Summary

This paper introduces and validates the three-phase traffic theory, a framework that challenges the traditional fundamental diagram approach to traffic flow modeling. The research addresses the complexity of highway traffic dynamics, specifically the probabilistic nature of traffic breakdown at bottlenecks and the formation of congested spatial-temporal patterns. The author argues that existing models, which assume a single curve of steady states in the flow-density plane, fail to accurately describe empirical observations of congested traffic. Instead, the paper proposes that traffic exists in three distinct phases: free flow, synchronized flow, and wide moving jams. The study combines empirical analysis of real-world traffic data from the A5 highway in Germany with theoretical modeling and numerical simulations. The empirical component utilizes detector data to analyze spatial-temporal features, distinguishing between synchronized flow (where vehicle speeds synchronize across lanes and the downstream front is fixed at a bottleneck) and wide moving jams (which propagate through traffic states while maintaining a constant downstream front velocity). The theoretical component presents a probabilistic theory of highway capacity, linking the transition from free flow to synchronized flow (F→S transition) to a first-order local phase transition. Additionally, the author employs a KKW cellular automata model to simulate congested patterns and validate the theory’s hypotheses regarding phase transitions and capacity drops. Key findings demonstrate that congested traffic is not a single state but comprises two qualitatively different phases. The paper identifies that moving jams do not emerge directly from free flow but rather from synchronized flow via a subsequent S→J transition. Empirical evidence shows that synchronized flow states cover a two-dimensional region in the flow-density plane, contradicting the fundamental diagram hypothesis of a single curve. The study highlights specific patterns such as the General Pattern (GP), where synchronized flow and wide moving jams coexist, and the Synchronized Flow Pattern (SP), where synchronized flow persists without jam formation. Furthermore, the analysis reveals a Z-shaped characteristic in the probability of passing and speed differences, explaining the hysteresis and overlapping states between free flow and synchronized flow. The significance of this work lies in its redefinition of highway capacity as a probabilistic phenomenon rather than a fixed value. By establishing that capacity drop is linked to the F→S transition, the theory provides a more accurate explanation for traffic breakdowns at bottlenecks. The distinction between synchronized flow and wide moving jams offers a refined understanding of stop-and-go phenomena, suggesting that narrow moving jams are part of synchronized flow rather than distinct jams. This framework improves the predictive capability of traffic models, particularly in explaining how congested patterns evolve and propagate across multiple bottlenecks, thereby offering a robust alternative to traditional traffic flow theories.

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• traffic density