A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics
Hong-Sheng Qi(祁宏生)1,† and Yu-Yan Ying(应雨燕)2
1 College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China; 2 College of Polytechnic, Zhejiang University, Hangzhou 310015, China
Abstract The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models, especially the car-following (CF) models. These models of the movement of vehicles serve as the backbone of traffic flow analysis, simulation, autonomous vehicle development, etc. Two-dimensional (2D) vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics. Current microscopic models either neglect 2D noise, or overlook vehicle dynamics. The modeling capabilities, thus, are limited, so that stochastic lateral movement cannot be reproduced. The present research extends an intelligent driver model (IDM) by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model, with vehicle dynamics based on the stochastic differential equation (SDE) theory. Control inputs from the vehicle include the steer rate and longitudinal acceleration, both of which are developed based on an idea from a traditional intelligent driver model. The stochastic stability condition is analyzed on the basis of Lyapunov theory. Numerical analysis is used to assess the two cases: (i) when a vehicle accelerates from a standstill and (ii) when a platoon of vehicles follow a leader with a stop-and-go speed profile, the formation of congestion and subsequent dispersion are simulated. The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement. The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.
(Granular models of complex systems; traffic flow)
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2021YFE0194400), the National Natural Science Foundation of China (Grant Nos. 52272314 and 52131202), the Fund for Humanities and Social Science from the Ministry of Education of China (Grant No. 21YJCZH116), and the Public Welfare Scientific Research Project (Grant No. LGF22E080007).
Hong-Sheng Qi(祁宏生) and Yu-Yan Ying(应雨燕) A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics 2023 Chin. Phys. B 32 044501
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