Mixed traffic flow of human-driven vehicles and connected autonomous vehicles: String stability and fundamental diagram

Lijing Ma; Shiru Qu; Jie Ren; Xiangzhou Zhang; Lijing Ma; Shiru Qu; Jie Ren; Xiangzhou Zhang

doi:10.3934/mbe.2023107

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 2280-2295. doi: 10.3934/mbe.2023107

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Research article

Mixed traffic flow of human-driven vehicles and connected autonomous vehicles: String stability and fundamental diagram

School of Automation, Northwestern Polytechnical University, Xi'an 710072, China

Academic Editor: Hamidreza Namazi

Received: 08 September 2022 Revised: 12 November 2022 Accepted: 13 November 2022 Published: 17 November 2022

The introduction of connected autonomous vehicles (CAVs) gives rise to mixed traffic flow on the roadway, and the coexistence of human-driven vehicles (HVs) and CAVs may last for several decades. CAVs are expected to improve the efficiency of mixed traffic flow. In this paper, the car-following behavior of HVs is modeled by the intelligent driver model (IDM) based on actual trajectory data. The cooperative adaptive cruise control (CACC) model from the PATH laboratory is adopted for the car-following model of CAVs. The string stability of mixed traffic flow is analyzed for different market penetration rates of CAVs, showing that CAVs can effectively prevent stop-and-go waves from forming and propagating. In addition, the fundamental diagram is obtained from the equilibrium state, and the flow-density chart indicates that CAVs can improve the capacity of mixed traffic flow. Furthermore, the periodic boundary condition is designed for numerical simulation according to the infinite length platoon assumption in the analytical approach. The simulation results are consistent with the analytical solutions, suggesting the validity of the string stability and fundamental diagram analysis of mixed traffic flow.
- connected autonomous vehicle,
- human-driven vehicle,
- car-following,
- mixed traffic flow,
- heterogeneous traffic flow,
- string stability,
- fundamental diagram
Citation: Lijing Ma, Shiru Qu, Jie Ren, Xiangzhou Zhang. Mixed traffic flow of human-driven vehicles and connected autonomous vehicles: String stability and fundamental diagram[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 2280-2295. doi: 10.3934/mbe.2023107

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Abstract

The introduction of connected autonomous vehicles (CAVs) gives rise to mixed traffic flow on the roadway, and the coexistence of human-driven vehicles (HVs) and CAVs may last for several decades. CAVs are expected to improve the efficiency of mixed traffic flow. In this paper, the car-following behavior of HVs is modeled by the intelligent driver model (IDM) based on actual trajectory data. The cooperative adaptive cruise control (CACC) model from the PATH laboratory is adopted for the car-following model of CAVs. The string stability of mixed traffic flow is analyzed for different market penetration rates of CAVs, showing that CAVs can effectively prevent stop-and-go waves from forming and propagating. In addition, the fundamental diagram is obtained from the equilibrium state, and the flow-density chart indicates that CAVs can improve the capacity of mixed traffic flow. Furthermore, the periodic boundary condition is designed for numerical simulation according to the infinite length platoon assumption in the analytical approach. The simulation results are consistent with the analytical solutions, suggesting the validity of the string stability and fundamental diagram analysis of mixed traffic flow.

References

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