The phenomenon that pedestrians walk outside the crosswalk during green and flashing green is defined as overflow violation, and it is an illegal but common phenomenon in China. Few safety countermeasures can be applied to restrict it. At signalized intersections, one safety issue is the conflicts between turning vehicles and pedestrians. Large variations in overflow pedestrian trajectories lead to widely distributed conflict points. This paper puts forward a model to estimate spatial variations of overflow pedestrian trajectories. By video tracking, only trajectories of overflow violation pedestrians are collected. After analysis, crosswalk geometry, destination, previous passing position, and densities are determined as significant factors of trajectories variations. To simplify modeling process of trajectories variations, this paper assumes that individual trajectory is roughly represented by three feature points on the trajectory. Three feature points are defined as three crossing positions at three cross-sections. Furthermore, Weibull distribution is applied to estimate the spatial distribution of violation pedestrian crossing positions at three cross-sections; then, the spatial distributions of overflow violation pedestrians’ trajectories are gained by connecting crossing positions at three cross-sections. Finally, the validation result suggests that the established models are capable of explaining well the spatial maneuver of overflow violation pedestrians’ trajectories variations.
Vehicles are restricted to traveling within designated lanes, but pedestrian lateral positions in crosswalk are not confined which results in autonomous pedestrian trajectories. The importance of research on pedestrian behaviors has been well recognized in both the safety field and capacity assessments of road facilities. At signalized intersections in China, overflow violation represents the phenomenon that pedestrians choose to walk outside the crosswalk by taking the shortest path to their destinations. Qu et al. [
Conflict between turning vehicles and pedestrians.
Conflict between turning vehicles and law-abiding pedestrians
Conflict between turning vehicles and overflow violation pedestrians
Turner and Penn [
Nagel et al. [
In terms of multivariate equations, different multivariate equations were used to model pedestrian trajectories. A nonparametric pedestrian motion model based on Gaussian process regression was presented by Ellis et al. [
In summary, although many related studies on pedestrian behaviors were made, not enough attention is paid to pedestrian overflow violation at signalized crosswalk. By using video-processing technology to obtain observed pedestrian trajectories spatiotemporal data, this paper aims to investigate influencing factors of overflow violation pedestrian trajectories variations. For this, a model presenting the variations of overflow violation pedestrian trajectories for different crosswalk geometries is proposed. Spatial distributions of overflow violation pedestrian trajectories are analyzed considering different geometries and distances to the destinations. Variation of overflow violation pedestrian trajectories is modeled to design the position and length of safety barrier, so pedestrian trajectory (not a full path, just samples) is simplified to be represented by three points on pedestrian trajectory. Three points are defined as overflow violation pedestrians’ crossing positions at near-side, middle-side, and far-side cross-sections.
For the sake of analyzing the significance of various influencing factors on the overflow violation pedestrian trajectories, a series of overflow violation pedestrian trajectories data was collected by using video-processing technology at seven signalized crosswalks with different geometric characteristics and traffic environment. All these sites are located in Changchun City, China. The parameters in Table
Geometric characteristics of study sites and observation date.
Objective crosswalk | Hongqi Street | Tongzhi Street | Xian Road | Chongqing Road | |||
---|---|---|---|---|---|---|---|
East | North | East | North | East | South | West | |
Observation time (p.m) | 1:00–3:00 (2 days) | 1:00–3:00 (2 days) | 1:30–3:30 (2 days) | 1:30–3:30 (2 days) | 1:00–3:00 (2 days) | 1:00–3:00 (2 days) | 1:00–3:00 (2 days) |
Crosswalk width/m | 8 | 6 | 7 | 6 | 10 | 4 | 8 |
Crosswalk length/m | 43 | 23 | 27 | 18 | 44 | 15 | 40 |
Distance to destination/m | 130 | 260 | 90 | 42 | 82 | 30 | 45 |
Intersection angle/deg | 90 | 90 | 90 | 90 | 90 | 90 | 90 |
Sample size of overflow pedestrians | 205 | 136 | 172 | 117 | 160 | 160 | 162 |
Sample size of all pedestrians | 734 | 591 | 542 | 468 | 669 | 800 | 623 |
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Total | 4427 |
Schematic diagram of coordinates transformation (figure redrawn from Figure
The survey sites have significantly different crosswalk widths, lengths, distances to destinations, and pedestrian volumes. Such a wide range of differences is necessary to rationally study the variations in overflow violation pedestrian trajectories. Besides, all survey sites are located near the commercial centers, and there are bus station, business owners, and shopping malls around them. The software based on video image processing system is applied to extract pedestrian spatiotemporal data. On the basis of pedestrian spatiotemporal data, pedestrian trajectories are acquired. There are sufficient trajectories data to enable a thorough analysis of pedestrian overflow violation. The observation date and crosswalk geometries are shown in Table
Overflow violation pedestrian trajectories including the crossing positions at different moments are extracted from video data by using method developed by Jiang et al. [
Pedestrians modify their trajectories according to traffic environment and interactions with other pedestrians. They tend to choose the shortest path to destinations. In summary, pedestrian trajectories are determined by the perception of traffic environment and occasional elements. According to spatial-temporal database collected by the video, analyzing pedestrian crossing positions at different moments is thought to the best mean to obtain pedestrian trajectories. Because a mountain of work should be done to deal with the data, so it is harder to estimate the inner characteristics of pedestrian trajectories. Studies indicate that pedestrians will not change their current directions unless they meet other pedestrians. Pedestrian crossing positions at near-, middle-, and far-side cross-section determine pedestrian trajectory. The purpose of modeling overflow pedestrian trajectories variation is to serve to the optimization of pedestrian facilities, so pedestrian trajectory determined by three characteristic points is acceptable. As shown in Figure
Definition of the influencing factors on pedestrian trajectory.
Definition of crosswalk geometry
Definition of crossing position
Definition of density detection areas
As shown in Figure
In previous work, three crosswalks were used to prove the central tendency of overflow pedestrians’ trajectories [
Overflow violation pedestrian trajectories variation.
(
(
The overflow pedestrian trajectory is illustrated in Figure
Figure
Pedestrian crossing position distributions at every cross-section.
Near-side
Middle-side
Far-side
Average crossing position is defined as the average value of all overflow violation pedestrians crossing positions at every cross-section in the same green light.
Hongqi Street east crosswalk is taken as an example to illustrate the influence of average crossing position at previous cross-section on the average crossing position at current cross-section. Linear relationship is adopted to describe the relationship between previous average crossing position and the current average crossing position. Adjusted
Current average crossing position versus previous average crossing position.
According to adjusted
The same method is applied at other study sites. The minimum adjusted
As shown in Figure
Relationship between crosswalk width and average crossing position.
Similar to the relationship between crosswalk width and average crossing position, Figure
Relationship between crosswalk length and average crossing position.
Through regression analysis,
Pedestrian density versus average crossing position.
The same method is applied to analyzing the relationship between pedestrian density and average crossing position at other study sites. The minimum adjusted
It is clear that pedestrians prefer to choose larger crossing position to shorten the distance between his/her current position and destination, which is validated in Figure
Relationship between distance and average crossing position.
Pedestrian trajectories are curved by connecting three crossing positions at three cross-sections. So, we should model the crossing positions distributions at three cross-sections, and then trajectory variation of crosswalk overflow violation pedestrians is acquired. Walck [
Before modeling pedestrian crossing positions distributions, two assumptions are made.
(
(
At near-side cross-section, the function is shown in (
At middle-side cross-section, the function is shown in (
At far-side cross-section, the function is shown in (
The purpose of trajectory variation model is to illustrate pedestrian overflow violation motion and finally put forward countermeasure to confine pedestrian overflow violation.
Four steps are needed to obtain overflow violation pedestrian trajectories variation at crosswalk. Firstly, pedestrian crossing positions distribution at near-side cross-section are calculated according to established equations (
Model validation is conducted to confirm whether established model can well represent overflow pedestrian trajectories variation at signalized crosswalk. By comparing observed pedestrian trajectories variation and estimated results, validation is conducted at Hongqi Street east crosswalk based on pedestrian crossing positions distributions at three cross-sections.
Hongqi Street east crosswalk is selected as the validation site, because it has longer crosswalk length, width, pedestrian volumes, and attraction point. The crosswalk geometry is shown in Table
As shown in Figure
Comparison of observed and estimated pedestrian trajectories variation.
By comparing the probability and cumulative probability of observed and estimated crossing positions at three cross-sections, it is obvious that the distributions of estimated crossing positions agree with observed ones better at the near- and middle-side cross-sections than that at far-side cross-section. It is due to the fact that pedestrians have more choices at far-side cross-section when pedestrians walk outside the crosswalk; in addition, turning vehicles have more influences on pedestrian motion, and pedestrian movements are more stochastic. It means that estimated pedestrian trajectories variation agrees with the observed pedestrian trajectories variation well.
Hongqi Street east crosswalk is selected as the validation site. Sensitivity analysis enables us to understand variation of established models with the change of five variables. Sensitivities of previous average crossing position, crosswalk width and length, pedestrian density, and distance are analyzed. Other variables values are shown in Table
Variables values for sensitivity analysis.
Variable | Value | Cross-section |
---|---|---|
Previous average crossing position | 6.72 [m] | Middle-side |
Pedestrian density | 0.33 [ped/m2] |
Sensitivity analysis of previous average crossing position is conducted under conditions that average crossing positions at near-side are set to be a set of values, such as 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, and 10 m. The computation results are shown in Figure
The sensitivity of previous average passing position.
In a similar way, crosswalk widths are set as 4 m, 5 m, 6 m, 7 m, and 8 m, and other variables are set as shown in Tables
The sensitivity of crosswalk width.
Similar to the sensitivity of crosswalk width, crosswalk lengths are set as 20 m, 25 m, 30 m, 35 m, 40 m, 45 m, and 50 m, as shown in Figure
The sensitivity of crosswalk length.
Because subject pedestrians meet opposite pedestrians at middle-side cross-section, so pedestrian density is the density of bidirectional pedestrian which is set to be 0 ped/m2, 0.15 ped/m2, 0.30 ped/m2, 0.45 ped/m2, and 0.6 ped/m2 for analyzing. From Figure
The sensitivity of pedestrian density.
Distances between crosswalks and destinations are set as 50 m, 100 m, 150 m, and 200 m, and the middle cross-section is selected for analyzing. As shown in Figure
The sensitivity of distance between crosswalk and destination.
At those intersections where traffic attractive points exist, pedestrians overflow violation is a common behavior. In previous work, countermeasures were put forward to restrict overflow violations [
Overflow violation pedestrian trajectories variation has central tendency. Considering this characteristic, countermeasure is suggested to alleviate the overflow violation, as shown in Figure
Countermeasure for overflow violation (figure redrawn from Figure
Taking Hongqi Street east crosswalk as an example, we set safety barrier with different length, and the frequencies of overflow violation were recorded. Besides, we estimated the frequencies of overflow violation based on the overflow violation pedestrian trajectories variation model when safety barrier length takes different value. Safety barrier is adopted to prevent the overflow violation from occurring, and the observed frequency of overflow violation and estimated frequency of overflow violation are compared, and the comparison results are shown in Figure
Frequency of the overflow violation after setting countermeasure.
When the safety barrier length is 12.5 meters, the observed and estimated frequencies of overflow reduce to 50%, and half of overflow pedestrians no longer walk outside the crosswalk. And then, the observed and estimated frequencies of overflow reduce to 5% when the safety barrier lengths are 17 meters and 15 meters, respectively. When the safety barrier length goes on increasing to 19 meters and 17 meters, the overflow almost no longer occurs according to both observed data and estimated data.
It is clear that most of overflow pedestrians could be confined to walking on the crosswalk when the safety barrier length reaches a certain value, which suggests that the countermeasure is effective. The largest length of safety barrier can be estimated according to proposed overflow violation pedestrian trajectories variation model. With the safety barrier length increasing, more and more overflow pedestrians are limited to walking on the crosswalk.
In the previous work, the overflow characteristics were analyzed, and the central tendency of overflow pedestrians’ trajectories was proved [
After analyzing the influences of previous average crossing position, crosswalk geometry, distance, and pedestrian density on pedestrian current crossing position, Weibull distribution is selected to model the distributions of pedestrian crossing positions at three cross-sections. Based on the distributions of pedestrian crossing positions, overflow violation pedestrian trajectories variation is obtained, but one other thing to note is that we only get the contour of pedestrian trajectories rather than real and detailed pedestrian trajectories. The established overflow violation pedestrian trajectories variation model is unfit for describing the detailed pedestrian motion and the interactions with other road users, but the model can be used as to design pedestrian safety facility. Based on proposed model, countermeasures for overflow violation are suggested to alleviate overflow violation. It is found that most of overflow pedestrians could be confined to walking on the crosswalk when the safety barrier length reaches certain value, which suggests that the countermeasure is effective. The largest length of safety barrier can be estimated according to overflow violation pedestrian trajectories variation calculated by the proposed model. Furthermore, the proposed model gives guidance on how to prohibit pedestrians overflow violation in China.
However, several limitations of the established model should not be ignored. The influences of turning vehicles and phase are not considered. For example, pedestrians tend to choose a larger crossing position at the end of the green light at near-side cross-section. That is our future research.
The authors declare that they have no conflicts of interest.
This research is funded by the National Natural Science Foundation of China (nos. 51278520 and 51278220).