# Empirical Analysis and Modeling of Stop-Line Crossing Time and Speed at Signalized Intersections

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## Abstract

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## 1. Introduction

## 2. Past Research

## 3. Data Preparation

#### 3.1. Site Descriptions

#### 3.2. Data Collection and Reduction

## 4. Statistical Characteristics of Stop-Line Crossing Behavior

#### 4.1. Statistical Characteristics of Stop-Line Crossing Time

_{FG}) for the FGC pattern at the rural intersections was the highest, followed by those of the YC pattern, the STOP pattern, and the RLR pattern. Moreover, the mean speed of the RLR pattern was remarkably lower (i.e., about 17%) than those of the other patterns. At a lower speed level, the RLR drivers were supposed to have longer average time to make a stop as compared with those FGC and YC drivers, but they eventually chose to cross. The fact implies that most of the RLRs observed at the rural intersections might be intentional or due to drivers’ decision errors, not because of drivers’ incapability of making a stop. This finding is particularly interesting as it infers that the RLR enforcement cameras are probably less influential at the rural intersections. The differences in the means of V

_{FG}among the four patterns were comparably small at the urban intersections. The mean V

_{FG}of the STOP pattern was approximately 10% lower than those of other patterns, which is rational since the stopping probability of drivers generally increases with the reduced approaching speed.

_{FG}), it was found that the mean of D

_{FG}rose substantially (almost tripled) from the FGC pattern to the STOP pattern for both types of intersections. It reveals that the stopping probability of drivers is strongly associated with the D

_{FG}. Meanwhile, D

_{FG}can be a good explanatory variable for predicting the probabilities of YC and RLR as well.

#### 4.2. Statistical Characteristics of Stop-Line Crossing Speed

## 5. Prediction of Stop-Line Crossing Time and Speed

#### 5.1. Prediction of Stop-Line Crossing Time

_{FG}), and distance to the stop-line at the onset of FG (D

_{FG}). With respect to the IT, the intersections with a size larger than 50 m and with a cycle length greater than 150 s were classified as the large intersections in this study (i.e., Cao’an Road and Jiasongbei Road, Cao’an Road and Xiangjiang Road, and Siping Road andDalian Road listed in Table 1); the rest of the intersections were classified as the small intersections (i.e., Cao’an Road and Caofeng Road and Rende Road and Jipu Road as listed in Table 1). The details of the selected independent variables are explained below.

- VT = Vehicle Type, binary variable, 1 = Truck and 0 = Passenger Car;
- AT = Area Type, binary variable, 1 = Urban Area and 0 = Rural Area;
- IT = Intersection Type, binary variable, 1 = Large Intersection and 0 = Small Intersection;
- V
_{FG}= Speed at the onset of FG (km/h), continuous variable; - D
_{FG}= Distance to the stop-line at the onset of FG (m), continuous variable.

^{2}(i.e., 0.551) and the Hit-ratio (i.e., 87.6%). Based on the estimated model coefficients, the occurring probabilities of the FGC, YC, and RLR patterns against the STOP pattern can then be calculated by Equations (1)–(3) shown below. These equations can then be used to predict the ratios of various stop-line crossing patterns for a particular vehicle at a particular intersection.

_{FG}) and distance to the stop-line at the onset of FG (D

_{FG}) affected the occurring probabilities of the FGC and YC patterns at a significance level of 0.01. The former variable (V

_{FG}) had a positive effect and the latter variable (D

_{FG}) had a negative effect, i.e., the probabilities of the FGC and YC patterns against the STOP pattern increased as the V

_{FG}increased and the D

_{FG}decreased. In addition, the variable of AT positively contributed to the ratio of the YC pattern to the STOP pattern at the significance level of 0.05. It implies that drivers are more likely to choose crossing during the Y interval than taking a stop at the urban intersections, which is consistent with the previous findings presented in Table 2.

#### 5.2. Prediction of Stop-Line Crossing Speed

_{FG}, and D

_{FG}. A preliminary analysis showed that the variable of IT was an insignificant factor that influences the stop-line crossing speed. Thus, it was excluded from the model development. The estimated coefficients of the final model are summarized in Table 4, with a total sample size of 802 and a regression R

^{2}of 0.579. Based on the estimated model coefficients, the stop-line crossing speed can then be formulated by Equation (4) shown below.

_{FG}and D

_{FG}were positive and those of VT, AT, and CP were negative. The results support that the greater the approaching speed and the distance to the stop-line are, the higher the stop-line crossing speed is. Furthermore, stop-line crossing speed tends to be significantly higher for rural intersections, passenger cars, and the FGC pattern. These findings are easy to understand if considering the site conditions presented in Table 1.

## 6. Conclusions

- Compared with the rural intersections, the urban intersections had a higher ratio of stop-line crossings during the Y interval and an approximately 0.7 s longer stop-line crossing time which is defined as the elapsed time after the onset of FG.
- Not only approaching speed and distance to the stop-line at the onset of FG, but also area type, imposed a significant influence on the ratios of the FGC and YC patterns to the STOP pattern. Area type also positively contributed to the ratio of the YC pattern to the STOP pattern; in addition, the ratio of RLR to STOP was higher at the large intersections with a long cycle length.
- The larger the approaching speed and the distance to the stop-line were, the higher the stop-line crossing speed was. Stop-line crossing speed was also significantly higher for the rural intersections, the passenger cars, and the FGC pattern.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Observed vehicle trajectories at the study intersections; (

**a**) Rural intersections (speed limit: 80 km/h); (

**b**) Urban intersections (speed limit: 50 km/h).

**Figure 4.**Boxplots of the stop-line crossing speeds for the FGC (crossing during the flashing green interval), YC (crossings during the yellow interval) and RLR (red-light-running) patterns.

Intersections | Cao’an Road & Jiasongbei Road | Cao’an Road & Xiangjiang Road | Cao’an Road & Caofeng Road | Siping Road & Dalian Road | Rende Road & Jipu Road |
---|---|---|---|---|---|

Area Type | Rural Area | Urban Area | |||

Speed Limit | 80 km/h | 50 km/h | |||

Approaches | EB | EB | WB/EB | EB | NB |

Lane Configuration | L-T-T-T-R | L-T-T-T-R | L-T-T-T-TR | L-L-T-TR | L-TR |

Intersection Size | 72 m | 72 m | 48 m | 64 m | 40 m |

Cycle Length | 161 s | 160 s | 104 s | 200 s | 86 s |

Number of Phases | 4 | 4 | 3 | 4 | 2 |

Green Time | 38 s | 45 s | 45 s | 77 s | 45 s |

Flashing Green Time | 3 s | 3 s | 3 s | 3 s | 3 s |

Yellow Time | 3 s | 3 s | 3 s | 3 s | 3 s |

All-Red Time | 1 s | 1 s | 1 s | 2 s | 1 s |

Observation Time Periods | 12 AM Peak Hours and 6 PM Off-Peak Hours | 4 AM Peak Hours and 4 PM Off-Peak Hours | 8 AM Peak Hours | 8 PM Peak Hours | 2 AM Peak Hours and 8 PM Off-Peak Hours |

First-to-Go Vehicles (Passenger Cars/Trucks) | 201 (156/45) | 153 (119/34) | 165 (115/50) | 177 (127/50) | 112 (103/9) |

Last-to-Stop Vehicle (Passenger Cars/Trucks) | 156 (111/45) | 101 (77/24) | 272 (175/97) | 75 (68/7) | 53 (37/16) |

FGC (Passenger Cars/Trucks) | 111 (85/26) | 62 (49/13) | 58 (35/23) | 91 (63/28) | 40 (38/2) |

YC (Passenger Cars/Trucks) | 83 (65/18) | 82 (64/18) | 104 (78/26) | 84 (63/21) | 63 (58/5) |

RLR (Passenger Cars/Trucks) | 7 (6/1) | 9 (6/3) | 3 (2/1) | 2 (1/1) | 9 (7/2) |

**Table 2.**Descriptive statistics of distances to the stop-line and speeds at the onset of FG for various stop-line crossing patterns.

Intersection Area Types | Variables | Statistical Parameters | Stop-Line Crossing Patterns | |||
---|---|---|---|---|---|---|

FGC | YC | RLR | STOP | |||

Rural Intersections (Speed Limit: 80 km/h) | D_{FG}, m | Mean | 35.0 | 72.0 | 92.1 | 104.8 |

Standard Deviation | 15.3 | 20.4 | 22.6 | 37.2 | ||

Min | 3.2 | 6.3 | 49.8 | 23.1 | ||

Max | 98.1 | 125.6 | 132.9 | 217.7 | ||

# (%) | 322 (27.2%) | 314 (26.5%) | 21 (1.8%) | 529 (44.6%) | ||

V_{FG}, km/h | Mean | 63.4 | 61.8 | 50.4 | 59.3 | |

Standard Deviation | 15.1 | 17.6 | 23.9 | 18.9 | ||

Min | 5.6 | 19.4 | 20.9 | 16.7 | ||

Max | 115.0 | 106.2 | 99.3 | 118.9 | ||

# (%) | 322 (27.2%) | 314 (26.5%) | 21 (1.8%) | 529 (44.6%) | ||

Urban Intersections (Speed Limit: 50 km/h) | D_{FG}, m | Mean | 28.8 | 52.6 | 80.2 | 95.8 |

Standard Deviation | 14.0 | 15.0 | 16.2 | 26.9 | ||

Min | 7.5 | 20.9 | 53.2 | 39.8 | ||

Max | 82.8 | 93.6 | 97.6 | 163.2 | ||

# (%) | 42 (15.4%) | 93 (34.1%) | 10 (3.7%) | 128 (46.9%) | ||

V_{FG}, km/h | Mean | 45.9 | 45.5 | 44.4 | 39.2 | |

Standard Deviation | 10.3 | 10.4 | 7.6 | 8.7 | ||

Min | 15.6 | 15.5 | 27.7 | 16.4 | ||

Max | 63.1 | 68.0 | 53.3 | 64.5 | ||

# (%) | 42 (15.4%) | 93 (34.1%) | 10 (3.7%) | 128 (46.9%) |

Variables | FGC | YC | RLR | |||
---|---|---|---|---|---|---|

B | Sig. | B | Sig. | B | Sig. | |

Constant | 2.454 *** | 0.001 | 1.156 *** | 0.003 | −3.226 *** | 0.001 |

Vehicle Type, $VT$ | −0.181 | 0.638 | −0.088 | 0.656 | 0.271 | 0.524 |

Area Type, $AT$ | −0.196 | 0.654 | 0.528 ** | 0.020 | 0.563 | 0.200 |

Intersection Type, $IT$ | 0.300 | 0.364 | 0.097 | 0.568 | 1.267 * | 0.008 |

Speed at the Onset of FG (km/h), V_{FG} | 0.256 *** | <0.001 | 0.080 *** | <0.001 | 0.002 | 0.865 |

Distance to the Stop-Line at the Onset of FG (m), D_{FG} | −0.316 *** | <0.001 | −0.078 *** | <0.001 | −0.011 | 0.135 |

Summary Statistics | Number of observations: 1459 veh; Log-likelihood at constant: 3335.696; Log-likelihood at convergence: 1497.164; McFadden R ^{2}: 0.551;Hit Ratio: 87.6%. |

**Table 4.**Multiple linear regression (MLR) model estimation results for the prediction of stop-line crossing speed.

Variables | B | Standard Error | t | Sig. |
---|---|---|---|---|

Constant | 41.749 *** | 2.102 | 19.863 | 0.000 |

Vehicle Type, $VT$ | −4.407 *** | 0.845 | −5.215 | 0.000 |

Area Type, $AT$ | −12.247 *** | 1.02 | −12.009 | 0.000 |

Distance to the Stop-Line at the Onset of FG (m), D_{FG} | 0.212 *** | 0.024 | 8.798 | 0.000 |

Speed at the Onset of FG (km/h), V_{FG} | 0.336 *** | 0.028 | 12.152 | 0.000 |

Stop-Line Crossing Patterns, $CP$ | −5.925 *** | 1.044 | −5.673 | 0.000 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Tang, K.; Wang, F.; Yao, J.; Sun, J. Empirical Analysis and Modeling of Stop-Line Crossing Time and Speed at Signalized Intersections. *Int. J. Environ. Res. Public Health* **2017**, *14*, 9.
https://doi.org/10.3390/ijerph14010009

**AMA Style**

Tang K, Wang F, Yao J, Sun J. Empirical Analysis and Modeling of Stop-Line Crossing Time and Speed at Signalized Intersections. *International Journal of Environmental Research and Public Health*. 2017; 14(1):9.
https://doi.org/10.3390/ijerph14010009

**Chicago/Turabian Style**

Tang, Keshuang, Fen Wang, Jiarong Yao, and Jian Sun. 2017. "Empirical Analysis and Modeling of Stop-Line Crossing Time and Speed at Signalized Intersections" *International Journal of Environmental Research and Public Health* 14, no. 1: 9.
https://doi.org/10.3390/ijerph14010009