# A Car-Following Model for Mixed Traffic Flows in Intelligent Connected Vehicle Environment Considering Driver Response Characteristics

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## Abstract

**:**

## 1. Introduction

## 2. The Extended IDM

#### 2.1. Car-Following Model for RVs

#### 2.2. Car-Following Model for CAVs

- (1)
- RV followed by CAV

- (2)
- CAV followed by CAV

## 3. Linear Stability Analysis

#### 3.1. Stable Analysis of the Model

_{d}= 0, then Formula (26) will degenerate to the stability condition of the classical IDM model:

#### 3.2. Stability Analysis for Different Driver Types

#### 3.3. Stability Analysis of Homogeneous Traffic Flows of RV, ACC, and CACC Vehicles

#### 3.4. Stability Analysis of MTF with CAVs and RVs

## 4. Numerical Simulation Analysis and Results

#### 4.1. Microscopic Numerical Simulation

#### 4.1.1. Microscopic Numerical Analysis in the Vehicle Starting Scenario

#### 4.1.2. Microscopic Numerical Analysis in the Vehicle Braking Scenario

#### 4.2. Macroscopic Numerical Analysis

#### 4.2.1. Macroscopic Numerical Analysis in the Vehicle Starting Scenario

#### 4.2.2. Macroscopic Numerical Analysis in the Vehicle Braking Scenarios

^{2}that decreased in magnitude to 0 until coming to a complete stop. The remaining 20 test vehicles decelerated in response to the speed change of the leading vehicle by the extended IDM model. Finally, all vehicles came to a complete stop. Calculate and record the averages of the acceleration difference of the fleet at 0.1 s intervals, as shown in Figure 8.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The critical stability curves for different driver types with different reaction characteristics.

**Figure 2.**The critical stability curves for homogeneous traffic flows of RVs, ACC, and CACC vehicles.

**Figure 5.**The variations of vehicle acceleration over time with Car 5 being an RV (with each of four driver types) or an ACC or a CACC in the starting scenario.

**Figure 6.**The variations of vehicle acceleration over time with Car 5 being an RV (with each of four driver types) or an ACC or a CACC in the braking scenario.

**Figure 7.**The averages of acceleration differences of the fleet at distinct penetration rates and different distribution degrees of CAVs in the starting scenario.

**Figure 8.**The averages of acceleration differences of fleets at distinct penetration rates and different distribution degrees of CAVs in the braking scenario.

Driver Type | Characteristics of Car-Following Behavior | Response Characteristics |
---|---|---|

Type I | Low speed but a long headway | Less perceptive and highly responsive |

Type II | Highest speed and short headway | More perceptive and steadily responsive |

Type III | A medium level of speed and headway | Standard |

Type IV | Lowest speed and longest headway | Less perceptive and less responsive |

Driver Type | ${\mathit{\tau}}_{\mathit{n}}$ | ${\mathit{v}}_{0}$ |
---|---|---|

Type I | 1.1 | $11\mathrm{m}/\mathrm{s}$ |

Type II | 0.9 | $13\mathrm{m}/\mathrm{s}$ |

Type III | 1 | $12\mathrm{m}/\mathrm{s}$ |

Type IV | 1.2 | $10\mathrm{m}/\mathrm{s}$ |

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**MDPI and ACS Style**

Wang, Y.; Xu, R.; Zhang, K.
A Car-Following Model for Mixed Traffic Flows in Intelligent Connected Vehicle Environment Considering Driver Response Characteristics. *Sustainability* **2022**, *14*, 11010.
https://doi.org/10.3390/su141711010

**AMA Style**

Wang Y, Xu R, Zhang K.
A Car-Following Model for Mixed Traffic Flows in Intelligent Connected Vehicle Environment Considering Driver Response Characteristics. *Sustainability*. 2022; 14(17):11010.
https://doi.org/10.3390/su141711010

**Chicago/Turabian Style**

Wang, Yunze, Ranran Xu, and Ke Zhang.
2022. "A Car-Following Model for Mixed Traffic Flows in Intelligent Connected Vehicle Environment Considering Driver Response Characteristics" *Sustainability* 14, no. 17: 11010.
https://doi.org/10.3390/su141711010