Stability Analysis of Continuous Stochastic Linear Model

Jun Du, Bin Jia and Shiteng Zheng
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Jun Du: Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China
Bin Jia: Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China
Shiteng Zheng: Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China

Sustainability, 2022, vol. 14, issue 5, 1-13

Abstract: Many scholars have conducted research on the traffic oscillations and reproduced the growth pattern by establishing stochastic models and simulations. However, the growth pattern of oscillations caused by uncertainty have not been thoroughly studied. Recently, a frequency domain stability analysis method was proposed to analyze the discrete stochastic model. This paper extends this analysis to a continuous situation based on frequency domain tools (e.g., Laplace transform) by introducing a continuous bandlimited white noise. The analytical expression for the evolution of speed standard deviation has been derived. Our study of a homogeneous case reveals an interesting phenomenon: when | G ( ω ) | ∞ < 1 , the speed variance will converge to a constant value, which only depends on the self-disturbance of vehicles. The simulation results verified that the continuous models and corresponding discrete model tend to be consistent when the discrete time step tends to the infinitesimal. Overall, this paper makes up for the deficiency of previous studies on continuous oscillations in car-following theory and can potentially be used to develop new control strategies to help dampen traffic oscillations.

Keywords: car-following; traffic oscillations; stochastic analysis (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2022
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