# Effect of Five Driver’s Behavior Characteristics on Car-Following Safety

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Objectives and Contributions

## 3. DSM Model and Its Parameter Calibration

_{n}(t) is the nth vehicle’s acceleration; S

_{MnDH}and S

_{MnDL}are respectively the lower and upper limits of the DSM for the nth driver; α

_{1}and α

_{2}denote the sensitivity coefficients of acceleration and deceleration, respectively; τ is driver’s reaction time; τ

_{2}is the brake system’s reaction time, and its value sets 0.15 s for the car; V

_{n}(t) is the nth vehicle’s speed; $\Delta {X}_{n}(t)={X}_{n-1}(t)-{X}_{n}(t)$ denotes spacing headway; d

_{n}(t) is the nth vehicle’s deceleration; L

_{n−1}is the length of the n−1th vehicle.

_{1}is about 8.51 m/s

^{2}, the std. deviation of α

_{1}is about 5.301 m/s

^{2}, and that the mean of α

_{2}is about 14.14 m/s

^{2}and the std. deviation of α

_{2}is about 8.276 m/s

^{2}, and that the mean of S

_{MnDL}is 0.76, and the std. deviation of S

_{MnDL}is 0.125, and that the mean of S

_{MnDH}is 0.95, and the std. deviation of S

_{MnDH}is 0.045. The mean of driver’s reaction time τ is 0.65 s, and the std. deviation of τ is 0.297 s.

## 4. Results for the REC Mechanism Car-Following Process

_{0}and initiate braking at decelerations of a

_{n−1}and a

_{n}, respectively, as shown in Figure 2.

_{t}. It implies that driver’s sensitivity factor for acceleration/deceleration of the leading car affects deceleration of the following car. Furthermore, Equation (7) implies that S

_{MnDL}and S

_{MnDH}determine time headway in the car-following process. In the platoon, the deceleration of leading vehicle denotes a

_{1}considering individual DBCs when a stopping wave is introduced.

_{0}denotes the minimum safe stopping distance among two cars. The relative stopping distance between two cars varied from 1.07 m to 4.83 m, and its mean is 2.17 m [31].

_{min}is a maximum deceleration. As suggested by the Highway Capacity Manual, the deceleration of a car varied from 2 and 8 m/s

^{2}[36]. Thus, a

_{min}is set to be −8 m/s

^{2}in this study.

## 5. Sensitivity Analysis of Five DBCs on REC Risk

_{H}= 40 to numerically illustrate the influence of five DBC parameters on REC risk, as shown in Figure 3. In addition, the initial positions and speeds of 20 vehicles are showed as follows:

^{2}after 200 s until it is stopped. In addition, other following cars follow the leading car to decelerate until they are stopped. Other parameters of model are set as as τ

_{2}= 0.15 s, d

_{n}(t) = d

_{n−1}(t) = 7.35 m/s

^{2}, L

_{n}= 4.3 m, n = 1, 2, 3, …, N. Collision happening is to determine whether two successive vehicles collide or not at any moment in the car-following process according to REC conditions of Equation (10).

#### 5.1. Impact of Response Time

^{2}and ${\alpha}_{2}=14.14\pm 8.276$ m/s

^{2}, and the limits of the DSM ${S}_{M}{}_{nDL}^{}=0.73\pm 0.132$ and ${S}_{M}{}_{nDH}^{}=0.94\pm 0.056$. Ten drivers of the platoon are randomly arranged on a single lane.

#### 5.2. Impact of the Limits of the DSM

^{2}and ${\alpha}_{2}=14.14\pm 8.276$ m/s

^{2}, respectively. Driver’s reaction time is set as $\tau =0.65\pm 0.297$ s. In order to investigate the influence of S

_{MnDH}on the REC probability, the range of S

_{MnDH}is set as ${S}_{M}{}_{nDH}^{}\in \left[0.86,1\right]$ to ensure ${S}_{M}{}_{nDH}^{}\ge {S}_{M}{}_{nDL}^{}$, in which ${S}_{M}{}_{nDL}^{}=0.73\pm 0.13$. Moreover, the range of S

_{MnDL}is set as ${S}_{M}{}_{nDL}^{}\in \left[0.73,0.88\right]$ to ensure ${S}_{M}{}_{nDL}^{}\le {S}_{M}{}_{nDH}^{}$, in which ${S}_{M}{}_{nDH}^{}=0.94\pm 0.056$.

_{MnDH}. However, the REC probability of vehicles has no obvious reduction when S

_{MnDH}is increased to a certain value (S

_{MnDH}≥ 0.96) in our case study. Likewise, the REC probability of vehicles decreases with the increasing of S

_{MnDL}as shown in Figure 5b. However, the REC risk has more sensitivity to S

_{MnDL}. The REC accidents will not happen when S

_{MnDL}≥ 0.85 in our case study. Results imply that the stopping waves gradually weaken with the increasing of the S

_{MnDL}or S

_{MnDH}. Thus, a large upper (or lower) limit of the DSM can reduce the REC risk. Adjusting the limits of the DSM of the driver can improve traffic safety in the car-following process.

#### 5.3. Impact of Acceleration and Deceleration Preference Coefficients

^{2}, in which the deceleration preference coefficient ${\alpha}_{2}=14.14\pm 8.276$ m/s

^{2}. However, the range of deceleration preference coefficient is set as ${\alpha}_{2}\in \left[9,30\right]$ m/s

^{2}, in which the acceleration preference coefficient ${\alpha}_{1}=8.51\pm 5.301$ m/s

^{2}.

_{2}> 18 m/s

^{2}) in our case study. Results show that a large deceleration preference (or a small acceleration preference) can reduce the REC risk, and that the stopping waves gradually weaken with increasing of the deceleration preference and decreasing of the acceleration preference. Therefore, the car-following safety can improve if the driver can maintain the smaller acceleration preference and the larger deceleration preference for drivers.

## 6. Numerical Experiment and Discussion

_{n}(0) denotes the nth vehicle’s initial position; V

_{n}(0) is the nth vehicle’s initial speed; ${\dot{V}}_{n}(0)$ is the nth vehicle’s initial acceleration; and ${\xi}_{1}(\tilde{t})$ denotes a small acceleration disturbances of the leading car after $\tilde{t}$, and its distribution function obeys $5\times {10}^{-2}\times U(-1,1)$.

^{3}kinds of combinations based on driving behavior parameters. The vector ${\Omega}_{i}=\left(\tau ,{\alpha}_{1},{\alpha}_{2},S{M}_{nDH},S{M}_{nDL}\right),i=1,2,\cdots M$ is used to represent DBCs. In this study, in order to analyze the impact of heterogeneity DBCs on REC risk, we choose four kinds of combinations of DBCs parameters without the loss of generality as follows:

- Case 1: ℂ
_{1}of 50% and ℂ_{2}of 50%; - Case 2: ℂ
_{3}of 50% and ℂ_{4}of 50%; - Case 3: ℂ
_{1}of 90%, ℂ_{2}of 4%, ℂ_{3}of 2% and ℂ_{4}of 4%; - Case 4: ℂ
_{1}of 70%, ℂ_{2}of 26%, ℂ_{3}of 2% and ℂ_{4}of 2%; - Case 5: ℂ
_{1}of 30%, ℂ_{2}of 50%, ℂ_{3}of 10% and ℂ_{4}of 10%; - Case 6: ℂ
_{1}of 10%, ℂ_{2}of 20%, ℂ_{3}of 40% and ℂ_{4}of 30%; - Case 7: ℂ
_{1}of 10%, ℂ_{2}of 10%, ℂ_{3}of 46% and ℂ_{4}of 34%; - Case 8: ℂ
_{1}of 6%, ℂ_{2}of 6%, ℂ_{3}of 50% and ℂ_{4}of 38%;

_{3}and Ω

_{4}. Here, Ω

_{3}and Ω

_{4}can be claimed as unstable drivers, and Ω

_{1}and Ω

_{2}can be claimed as stable drivers. Therefore, it implies that the shock wave occurs, and the RECs happen when Ω

_{3}and Ω

_{4}increase in the platoon as shown in the cases 3–4 of Figure 7a–d. Otherwise, decreasing the proportions of Ω

_{3}and Ω

_{4}, the shock waves gradually weakened, and REC will not occur as shown in cases 1–2 of Figure 7a–d.

## 7. Conclusions

_{MnDL}and S

_{MnDH}to describe driving risk preference; α

_{1}and α

_{2}to describe the acceleration and deceleration sensitivity; and τ to describe driver’s responsiveness. Therefore, the risk preference, sensitivity, and responsiveness affect car-following safety.

_{MnDL}or S

_{MnDH}can reduce the REC risk, and that the traffic safety can improve if the driver can maintain the smaller acceleration sensitivity and the larger deceleration sensitivity. Because these parameters can portray DBCs, each parameter divided into three types of DBCs to further discuss the impact of different DBCs on the REC risk. Through the numerical experiments, if the vehicle platoon has stable and unstable DBCs, then the proportion of drivers with different DBCs plays an important role in the car-following safety. Once the traffic flow is in an unstable state, the shock waves gradually enhanced, and REC will occur. Moreover, REC probability patterns also imply that different DBCs with an inappropriate proportion would lead to shock waves, thereby increasing REC risk. A potential strategy of the adjustment of the proportions of the unstable DBCs can improve car-following safety.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Varying of REC probability with the limits of the DSM, (

**a**) upper limit of the DSM; (

**b**) lower limit of the DSM.

**Figure 6.**Varying of REC probability with the acceleration and deceleration preference coefficients, (

**a**) acceleration preference coefficient; (

**b**) deceleration preference coefficient.

**Figure 7.**Gap patterns of all vehicles with DBCs at: (

**a**) t = 300 s; (

**b**) t = 500 s; (

**c**) t = 800 s; (

**d**) t = 1000 s.

Parameters | Mean | Std. Deviation | Median | Minimum | Maximum |
---|---|---|---|---|---|

α_{1} | 8.51 | 5.301 | 6.52 | 3.79 | 29.91 |

α_{2} | 14.14 | 8.276 | 12.18 | 3.01 | 30.00 |

S_{MnDL} | 0.73 | 0.132 | 0.75 | 0.50 | 0.98 |

S_{MnDH} | 0.94 | 0.056 | 0.94 | 0.76 | 1 |

τ | 0.65 | 0.297 | 0.48 | 0.30 | 1.60 |

Parameters | DBCs | Observation | Mean | Std. Deviation | Median |
---|---|---|---|---|---|

α_{1} | Insensitive | 18 | 5.92 | 0.909 | 5.60 |

α_{2} | 5.57 | 1.173 | 5.28 | ||

α_{1} | Moderate | 24 | 7.27 | 2.350 | 6.27 |

α_{2} | 13.59 | 5.418 | 12.18 | ||

α_{1} | Sensitive | 18 | 12.56 | 7.668 | 10.24 |

α_{2} | 23.09 | 4.489 | 23.64 | ||

S_{MnDL} | Risk-averse | 12 | 0.53 | 0.035 | 0.52 |

S_{MnDH} | 0.91 | 0.075 | 0.93 | ||

S_{MnDL} | Risk-neutral | 23 | 0.70 | 0.053 | 0.71 |

S_{MnDH} | 0.94 | 0.053 | 0.95 | ||

S_{MnDL} | Risk-prone | 25 | 0.86 | 0.049 | 0.84 |

S_{MnDH} | 0.95 | 0.048 | 0.96 | ||

τ | Responsive | 30 | 0.42 | 0.068 | 0.4 |

Moderate | 18 | 0.71 | 0.076 | 0.7 | |

Unresponsive | 12 | 1.13 | 0.227 | 1.1 |

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**MDPI and ACS Style**

Zhang, J.; Yang, C.; Zhang, J.; Ji, H.
Effect of Five Driver’s Behavior Characteristics on Car-Following Safety. *Int. J. Environ. Res. Public Health* **2023**, *20*, 76.
https://doi.org/10.3390/ijerph20010076

**AMA Style**

Zhang J, Yang C, Zhang J, Ji H.
Effect of Five Driver’s Behavior Characteristics on Car-Following Safety. *International Journal of Environmental Research and Public Health*. 2023; 20(1):76.
https://doi.org/10.3390/ijerph20010076

**Chicago/Turabian Style**

Zhang, Junjie, Can Yang, Jun Zhang, and Haojie Ji.
2023. "Effect of Five Driver’s Behavior Characteristics on Car-Following Safety" *International Journal of Environmental Research and Public Health* 20, no. 1: 76.
https://doi.org/10.3390/ijerph20010076