Modern Sediment Model of Traffic Flow

Yedilbayev, Bauyrzhan; Brener, Arnold; Shokanova, Akmaral; Boltayeva, Aigul · 2021 · Crossref

DOI: 10.2478/ttj-2021-0023

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Summary

This paper introduces a novel mathematical framework for modeling vehicular traffic flow, termed the "sediment model," which draws an analogy between traffic dynamics and particle sedimentation processes. The research is motivated by the limitations of existing macroscopic and microscopic traffic models, which often fail to adequately capture complex phenomena such as traffic hysteresis, spontaneous jam formation, and the impact of traffic lights. The authors aim to provide a unified conceptual explanation for these observed behaviors and to identify control parameters for optimal traffic management. The methodology combines qualitative analysis with numerical experiments. The core of the model relies on a logistic equation to describe the dependence of traffic rate on vehicle density, integrated with a continuity equation to account for conservation of vehicle numbers. The authors define three characteristic densities: optimal density for maximum speed, density near traffic lights, and jam density where motion stops. By solving the resulting partial differential equations using the Lagrange-Sharpe method, the model derives solutions in the form of solitary density waves. Additionally, the paper proposes a separate hypothesis for jam formation based on driver reaction times and maneuver radii, establishing a critical speed threshold below which motion becomes impossible. The results demonstrate that the sediment model qualitatively aligns with empirical data from highway observations, including Canadian highway datasets. The model successfully explains transport hysteresis, showing that reducing traffic density does not immediately restore flow due to the formation of wave fronts with specific phase velocities. It also provides a mathematical derivation for critical density, beyond which traffic intensity declines rapidly. Furthermore, the model offers a new explanation for traffic jams, positing that they occur when vehicle speed drops to a level where the required maneuver radius exceeds the available space, effectively halting movement. The significance of this work lies in its ability to unify the explanation of hysteresis and jam formation under a single conceptual framework, addressing gaps in previous theoretical approaches. The authors conclude that the model introduces new control parameters that can be utilized for designing road networks, optimizing traffic light regulations, and preventing jams. While the current study is conceptual and lacks full quantitative verification, it provides a foundation for future research to refine these parameters using extensive experimental data, potentially improving urban traffic efficiency and reducing environmental pollution.

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• traffic density