A stochastic car-following model in the framework of Kerner’s three-phase traffic theory

Abstract

The relationship between the mechanisms of traffic congestion and stochasticity remains a critical issue that requires further investigation. This paper aims to reveal the stochastic characteristics of driving behavior to explore the intrinsic mechanisms of traffic flow instability and capture the dynamic features of congestion patterns, further enhancing the reproduction of the effects of stochasticity on traffic oscillations. Based on this, a Multi-Factor Stochastic Traffic Flow Model (MSTF) is proposed from a microscopic perspective, incorporating conditions such as safe speed, movable distance, desired distance, and stochastic slow-down probability. Simulation results show that the model can reproduce all traffic flow patterns under various boundary conditions, including Local Synchronous Pattern (LSP), Widening Synchronous Pattern (WSP), Moving Synchronous Pattern (MSP), Dissolving General Pattern (DGP), and General Pattern (GP). Moreover, when in a critical state, the model accurately reproduces traffic flow metastable state, spatio-temporal patterns, and phase transitions. Calibration and validation results indicate that the model effectively simulates the actual phenomenon of spacing fluctuations between following vehicles (with a minimum RMSPE of less than 0.05) and accurately reproduces the concave growth pattern of speed oscillations in car-following platoons. The research outcomes further highlight, both theoretically and numerically, the influence of stochastic factors on traffic flow stability. These findings provide valuable insights for the development of stochastic car-following models capable of accurately reproducing observed traffic congestion patterns.