Deformed q-statistics derived from position-dependent mass Schrödinger Eq

• Jesus Juan Peña Gil and

  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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