Integrating Stochastic Properties into Traffic Flow Modeling: A Stimulus-Response Approach

• 1Konate N’Golo

  English

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• Mark Kimathi

  English

  Author

Highway traffic congestion, characterized by its inherent instability, has been extensively studied using
deterministic models, providing valuable insights. However, these models often overlook the stochastic nature of
driver behavior, a key factor that significantly impacts traffic flow. Recognizing this, a car-following model with
discretionary lane changes to analyze their effect on traffic dynamics was introduced. While the mathematical results
were sound, the use of the Optimal Velocity Model (OVM) led to unrealistic outcomes in certain situations, such as
heavy traffic jams, due to its oversimplification. To address these limitations, a car- following model incorporating
human behavior through the Cox-Ingersoll- Ross (CIR) process, demonstrating that traffic instability arises from
the stochastic characteristics of traffic flow was proposed. However, traffic instability can be triggered by various
factors, including high lane-change rates, incivility, queue properties, and accidents. In this study, we propose an
enhanced model that integrates stochastic elements into traffic flow dynamics, while retaining the key stimulus-
response mechanisms. Using the Intelligent Driver Model (IDM) and incorporating the Langevin equation with
stochastic behavior modeled through the Ornstein-Uhlenbeck process, we aim to provide a more realistic
representation of traffic flow. The model is calibrated using the NGSIM dataset and compared with existing
approaches, to evaluate its effectiveness in capturing real-world traffic phenomena. Our results highlight the
significant impact of perturbations, such as moving bottlenecks, on traffic oscillations.

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