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It is a dangerous behaviour for pedestrians and nonmotorized vehicles to cross intersections without waiting when they arrive at intersections during the red-light period. This paper investigates three typical signalized major-major intersections in the center of Beijing, by collecting and analyzing 1368 samples of pedestrians and nonmotorized vehicles. A random parameter logit model (RPLM) is established, with immediate red-light running (IRLR) behaviour as the dependent variable. The results show that the number of people waiting upon arrival, number of people crossing upon arrival, traffic mode, motor vehicle phase upon arrival, and speed change upon arrival have significant effects on IRLR behaviour. Accordingly, we suggest enforcing education administration on cyclists to reduce cyclists’ IRLR behaviour. Thus, people’s red-light running (RLR) behaviour will further decrease with fewer cyclists’ IRLR behaviour.

Walking is an essential mode of transportation for citizens in all areas. Due to their convenience, low carbon, and environmental friendliness, traditional bicycles and electric ones are two important modes of transportation. In recent years, with the development of shared bicycles in China, the users number had reached 18,860,000 by the end of 2016. As efficient regulation and supervision are inadequate, however, illegal and unsafe behaviours are prevailing for all three modes of transportation. Consequently, the rate of traffic accidents related to the modes has been harrowingly high. In 2014, 15110 pedestrians and 11448 cyclists (in this paper, nonmotorized vehicles and cyclists are used to refer to bicycles and electric bicycles and their riders, respectively) died in traffic accidents in China, representing 25.82% and 19.56% of the total deaths, respectively [

In 2014, 34,065 pedestrians and 46,314 cyclists were injured in traffic accidents in China, representing 16.08% and 21.86%, respectively [

Accordingly, the safety of pedestrians and nonmotorized vehicles at signalized intersections has attracted the increasing attention of researchers. To improve the safety level of signalized intersections in the city, there is a need to further analyze and summarize the RLR behaviour of pedestrians and cyclists and then propose suggestions on management and control strategy.

The RLR behaviour has been categorized by some scholars in the previous studies. Basically, there are three kinds of classification:

The rest of the paper is organized as follows. Section

Researchers have conducted a substantial number of studies to reduce the occurrence of RLR behaviour, analyzing the factors of pedestrians and cyclists’ RLR behaviour using different statistic models based on data from different sources. The most common data source is field observational video, combined with questionnaires. It has been proved that logit regression model is an effective method to handle these problems.

Johnson et al. [

Wu et al. [

Using questionnaire data, Johnson et al. [

Zhang et al. [

Considering there are few researches on the RLR behaviour of pedestrians, Yang et al. [

Except for the researches mentioned above, logistic regression method is widely used for analyzing the red-light violations of pedestrians and bicyclists in a lot of other previous studies [

The above researches provided many achievements on how factors affect the RLR behaviour of pedestrians and cyclists so that administrators can make more scientific decisions based on them. However, because of the inherent variability in the site conditions and other influential factors of specific intersections, there is likely a considerable amount of unobserved heterogeneity-variability that cannot be explained by the measurable data. Those previous studies failed to take the effects of unobserved heterogeneity into account [

In the light of these two defects discussed above, there are some researchers who have improved their studies by using the approach of RPLM when investigating the effect of the factors on dependent variables in other traffic research areas. Anastaspopoulos et al. [

The field observational data were obtained by continuous recording using video camera in Beijing, China. This method of data gaining has been widely used in studies on RLR behaviour at intersections in the urban area [

Four criteria were used to select the signalized intersections for continuous recording in this study. First, the type of intersection selected is the typical major-major intersection type in the urban area, which have four characters:

Three signalized major-major intersections in the central city of Beijing were selected based on the above criteria: Zhongguancun East Rd.-Zhichun Rd., Zhongguancun South Rd.-Weigongcun Rd., and Zhongguancun East Rd.-North Third Ring West Rd. To ensure that the data is more representative, this research only chooses one direction for shooting for each intersection. The chosen directions were westward, eastward, and eastward for Zhongguancun East Rd.-Zhichun Rd., Zhongguancun South Rd.-Weigongcun Rd., and Zhongguancun East Rd.-North Third Ring West Rd., respectively. The main characteristics and traffic light phase plans of the three selected intersections are listed in Table

Characteristics of the three observed intersections.

Intersection | Zhongguancun East Rd. - Zhichun Rd. | Zhongguancun East Rd.- North third ring West Rd. | Zhongguancun South Rd. - Weigongcun Rd. |
---|---|---|---|

Intersection type | 4-leg | 4-leg | 4-leg |

Observed approaches | Zhongguancun East Rd.(North) | Zhongguancun East Rd.(North) | Zhongguancun South Rd.(South) |

Crossing approaches | Zhichun Rd. | North third ring West Rd. | Weigongcun Rd. |

Cycle length(s) | 119 | 130 | 135 |

Number of motor vehicle lanes on the crossing streets in both directions | 4(enter)+4(exit) | 5(enter)+3(exit) | 5(enter)+5(exit) |

Crossing distance (m) | 40 | 38.5 | 44 |

Area types | Urban | Urban | Urban |

Separate signal for cyclists and pedestrians | No | No | No |

Pedestrian signal type | Flashing | Flashing | Flashing |

The traffic light phase plan of motor vehicles, pedestrians, and cyclists at three observed intersections.

There are two criteria adopted to select the sites of cameras in this study:

The intersection layout, camera locations, and camera shooting directions at Zhongguancun East Rd.-Zhichun Rd. intersection.

The dates of video shooting were weekdays in July 2014. The time periods of video shooting were 9:00~11:00 am and 14:00~16:00 pm to ensure the behaviour of pedestrians and cyclists was unaffected by traffic congestion. The weather was clear to ensure the behaviour of pedestrians and cyclists was unaffected by the inclement factors such as rain. Figure

Photographs from Cameras 1, 2, and 3 at Zhongguancun East Rd.-Zhichun Rd. intersection.

It is a challenge to extract pedestrian and cyclist attributes from videos. To ensure the validity of these data, the following efforts were made:

The video cameras were well hidden behind roadside fixed objects such as trees or telegraph poles to avoid being seen by the individuals and consequently causing a change in crossing behaviours.

Three synchronized high-resolution video cameras were used to collect data of road users crossing behaviours. To make sure the whole crossing process can be recorded clearly, Camera 1 and Camera 3 were positioned on the opposite side of crosswalk to shoot the same road user group. Camera 2 was placed on the vertical direction with Camera 1 and Camera 3 as supplement.

Since the road users arrive one by one, we can distinctly see and identify the road user attributes (e.g., hairstyle/dress preference/gender) and bicycle attribute (ordinary bike/electric bike).

The data extraction process was performed by two researchers (Yanting Liu and Wencheng Wang) who have received training on the requirements of extraction and judgement of road user attributes. Yanting Liu was in charge of those videos recorded by Camera 1 whose shooting direction was the same as the road users’ heading direction. Wencheng Wang was in charge of those videos recorded by Camera 2 whose shooting direction was opposite to the road users’ heading direction. Two researchers identified road users’ attributes separately, and then their records were matched. If the information of the same road user matched successfully, this information was accepted as the final dataset. If the same road user has different record or judgement, the third researcher (Xiaobao Yang) makes the final decision to decide which one was closer to the truth by combining Cameras 1, 2, and 3.

The first researcher judged road users’ age by their dress preference, hairstyle, and gesture, while the second researcher judged that by road users’ countenance.

The researchers marked on the screen to make it easier to identify the speed of the pedestrians, bicycles, and electric bicycles.

Since batteries provided a key clue to isolating electric bicycles from ordinary ones, identification of bicycle type was thought to be less of a problem. Furthermore, the stopping cyclists at red lights that were observed not to propel their bicycles by pedaling (i.e., instead, by using the throttle) were identified as the users of electric bicycles [

The main research object is the behaviour of pedestrians and cyclists who infringe the red light. Thus, only the pedestrians and cyclists who arrive at the intersection at the red phase were taken as samples. When the pedestrians and cyclists arrive at the intersection, if the signal is green, these persons’ behaviour was not coded to analyze because they have no probability of running the red light. When the pedestrians and cyclists arrive at the intersection at a red light, they have to make decision on whether to wait with some behaviours as the decision basis. To ensure the observation is clear and accurate, only those samples whose direction is the same as the video shooting direction were selected with left-turn road users neglected.

The video data should be converted to data applicable to the statistical package. Before analysing in the statistical package, all needed information and variables are coded into an EXCEL by a certain set of rules. In total, variables including basic information, behaviours, and environment conditions when arriving and behaviour and environment conditions when awaiting are coded and defined. The detailed contents are shown in Table

Definitions of variables coded.

Variables | Descriptions |
---|---|

| |

Gender | Male, 0; Female, 1 |

Age | Estimated age group: young (<30), 1; middle-aged (30-50), 2; elderly (>50), 3 |

Mode of transportation | Pedestrian, 1; bicycle, 2; electric bicycle, 3 |

Direction | The direction which the people come from when the people arrives at the intersection: left, 1; right, 2; back, 3 |

| |

| |

Arrival phase | The phase of motor vehicles: the left-turn light of the approach whose direction is same as the direction of observation group is green (close left turn), 1; the go straight light of the approach whose direction is vertical to the direction of observation group is green, 2; the left-turn light of the approach whose direction is vertical to the direction of observation group is green (far left turn), 3 |

Speed change upon arrival | The people’s speed change when the people arrive at the intersection: slower, 1; faster, 2; unchanged, 3 |

Cross traffic volume^{∗} | Average volume crossing motor vehicles per lane per minute during the red-light phase of pedestrians and cyclists when the people arrive at the intersection (rank from small to large): low (0-25%), 1; medium (26%-75%), 2; high (76%-100%), 3 |

No. of people waiting upon arrival | The number of other pedestrians who are waiting for the green light when the people arrive at the intersection |

No. of people crossing upon arrival | The number of other pedestrians who are crossing against the red light when the people arrive at the intersection |

IRLR behaviour | Whether to run the red light immediately when the people arrive at the intersection: no, 0; yes, 1 |

RLR behaviour | Whether to run the red light: no, 0; yes, 1 |

The concepts of close left turn and far left turn are shown in Figure

Illustration of the concepts of close left turn and far left turn.

This paper studied IRLR behaviour of pedestrians and cyclists crossing the street immediately after arrival at a signalized intersection by the method of RPLM.

The logistic regression is used to identify fitting, defensible models that describe the relationship between a binary dependent variable and explanatory variables [

In this study,_{n}(_{n} is a vector of the observable characteristics (covariates) that may have an effect on the IRLR behaviour for observation

As mentioned above, the logit model is suitable for many applications. However, it also has limitations, which may result in erroneous parameter estimates if the basic assumptions are not satisfied. The RPLM addresses several weaknesses of the traditional logit model by allowing parameter values to vary across observations [

As presented in articles of McFadden and Train [_{n} is the propensity function that determines the probability of observation_{n} is assumed to be extreme value Type I distributed [

As discussed above, the RPLM assumes the vector of estimable parameter_{n} is more than 2. Therefore, it should be solved by the simulation algorithm.

Since there is no prior knowledge for random parameters, all parameters are assumed random and then evaluate their estimated standard deviations according to

Since it is almost impossible to interpret the effect of a variable only based on the direct observation of the parameters, marginal effects should also be computed. The marginal effect can offer an overview of the effect caused by a one-unit variation in an explanatory variable on the probabilities of IRLR behaviour [_{k} is continuous variable, the marginal effect of_{k} is_{k} is an indicator variable, when its value changes from zero to one, marginal effect is denoted as

In total, 1368 samples were collected. The samples of pedestrians, bicycle riders, and electric bicycles riders are 503, 339, and 526, respectively. The proportion of sample who run the red light immediately is 19.3% (264). It can be seen from Table

Descriptive statistic and proportions of observation value with different attribute.

Mode of transportation | Total | |||
---|---|---|---|---|

Pedestrian | Bicycle | Electric bicycle | ||

| ||||

| ||||

Female | 15% | 20% | 18% | 17% |

Male | 18% | 15% | 25% | 20% |

| ||||

Young | 13% | 9% | 20% | 15% |

Middle-aged | 18% | 23% | 27% | 24% |

Elderly | 30% | 15% | 17% | 21% |

| ||||

| ||||

RLR^{∗} | 48% | 47% | 63% | 54% |

IRLR | 17% | 17% | 24% | 19% |

| ||||

| ||||

Min | Max | Mean | Std. Dev | |

No. of people waiting upon arrival | 0 | 35 | 5.9 | 6.201 |

No. of people crossing upon arrival | 0 | 21 | 1.14 | 2.339 |

^{∗}Including IRLR.

In addition, both the proportion of RLR behaviour and the proportion of IRLR behaviour for different transportation modes are different. The proportion of the RLR behaviour of electric bicycle riders (63%) is obviously greater than that of pedestrians (48%) and bicycle riders (47%). The proportion of IRLR behaviour of electric bicycle riders (24%) is obviously greater than that of pedestrians and bicycle riders (both are 17%). The proportions of IRLR behaviour for different transportation modes are similar when only accounting for the samples who have the RLR behaviour.

The results of comparison between RPLM and the fixed parameter logit model (FPLM) are shown in Table

Summary of random and fixed parameter logit models estimation results for IRLR behaviour.

RPLM | FPLM | |||
---|---|---|---|---|

Coefficient | z | Coefficient | z | |

Intercept | 1.739^{∗∗∗} | 5.3 | -0.492 | -0.23 |

No. of people waiting upon arrival | -0.946^{∗∗∗} | -9.79 | -0.121^{∗∗∗} | -6.31 |

| 0.893^{∗∗∗} | 10.04 | ||

No. of people crossing upon arrival | 1.054^{∗∗∗} | 9.02 | 0.219^{∗∗∗} | 5.85 |

| 3.064^{∗∗∗} | 9.91 | ||

| ||||

| ||||

Pedestrian VS. Electric bicycle | -2.629^{∗∗∗} | -6.9 | -0.759^{∗∗∗} | -4.04 |

| 3.995^{∗∗∗} | 8.08 | ||

Bicycle VS. Electric bicycle | -0.327 | -0.327 | -1.63 | |

| 2.005^{∗∗∗} | |||

| ||||

| ||||

Arriv_phs_1 | -1.908^{∗∗∗} | -5.67 | -0.586^{∗∗} | -2.44 |

| 0.275 | 1.12 | ||

Arriv_phs_2 | -3.754^{∗∗∗} | -8.84 | -1.833^{∗∗∗} | -8.25 |

| 2.19^{∗∗∗} | 6.41 | ||

| ||||

| ||||

Slower VS. Unchanged | -1.295^{∗∗∗} | -4.56 | -0.402^{∗∗} | -2.1 |

| 0.517 | 1.57 | ||

Faster VS. Unchanged | 11.359^{∗∗∗} | 6.51 | 3.641^{∗∗∗} | 4.97 |

| 2.501 | 1.3 | ||

Sample size | 1368 | 1368 | ||

| -522.5 | -521.152 | ||

| -496.72 | -671.030 | ||

AIC | 1015.3 | 1060.3 |

^{∗∗} Significant at 0.95 level of confidence.

^{∗∗∗} Significant at 0.99 level of confidence.

When the coefficient is positive, IRLR behaviour occurrence takes a higher probability with the rising value of the variable. When the corresponding

Table

Goodness-of-fit measures for the random and fixed parameter logit models.

RPLM | FPLM | |
---|---|---|

Number of parameters | 8 | 7 |

| -522.5 | -521.152 |

| -496.72 | -671.03 |

^{2} = -2[ | 348.62 | |

Degrees of freedom | 1 | |

Critical ^{2} | 7.88(0.995 level of confidence) | |

Number of observations | 1368 | 1368 |

Interpreting the effects of the explanatory variables would be difficult because the coefficient of more than one variable passed the test of normal distribution. Thus, the marginal effect of these variables is also estimated. The change of the probability of the IRLR behaviour when a variable’s value from 0 changes into 1 was calculated to reveal the marginal effect of these variables.

No. of people waiting upon arrival, no. of people crossing upon arrival, mode of transportation, and arrival phase passed the test according to Table

The effect of no. of people waiting upon arrival on the IRLR behaviour is significantly negative (-0.946). The parameter is subjected to a normal distribution whose mean value is -0.946 and whose standard deviation is 0.893. Therefore, the parameters of 85.5% of samples are less than 0 while 14.5% of samples are greater than 0. This demonstrates that effect of no. of people waiting upon arrival on 85.5% of samples is negative, and the probability of the IRLR behaviour decreases. That effect on 14.5% of samples is positive, and the probability of the IRLR behaviour increases. The results of marginal effect indicated that the mean of the probability of the IRLR behaviour for each sample will decrease 0.3% when no. of people waiting upon arrival increases one unit. The result is consistent with the previous studies [

The effect of no. of people crossing upon arrival on the IRLR behaviour is significantly positive (1.054). The parameter follows a normal distribution whose mean value is 1.054 and whose standard deviation is 3.064. Therefore, the parameters of 63.3% of samples are greater than 0 while 36.7% of samples are less than 0. This demonstrates that effect of no. of people crossing upon arrival on 63.3% of samples is positive, and the probability of the IRLR behaviour increases. That effect on 36.7% of samples is negative, and the probability of the IRLR behaviour decreases. The difference of this variable among different individuals is greater than that of no. of people waiting upon arrival. The results of marginal effect indicated that the mean of the probability of the IRLR behaviour for each sample will increase 0.3% when no. of people crossing upon arrival increases one. These results are similar to previous research, in which the odds of the IRLR behaviour of bicycle riders and electric bicycle riders increase with increasing no. of people crossing upon arrival [

Together with the result above, this result indicates that IRLR behaviour is influenced by other road users’ behaviour. The more the road users crossing against red light are, the more likely the road users run the red light. This conformity tendency was confirmed in many previous studies on road users’ street-crossing behaviour [

The mode of transportation is a three-category variable. Two dummy variables are set by the model. The first dummy variable is expressed by pedestrians vs. electric bicycle riders with 0 denoting electric bicycle riders and 1 denoting pedestrians. The second dummy variable is expressed by bicycle riders vs. electric bicycle riders with 0 denoting electric bicycle riders and 1 denoting bicycle riders.

Only the first dummy variable has significantly decreasing effect (-2.629). The parameter follows a normal distribution and is estimated with a mean of -2.629 with a standard deviation of 3.995, which shows that 74.5% of this distribution is below zero and 25.5% is above zero. This implies that most pedestrians (74.5%) are less likely to have IRLR behaviour, and 25.5% of pedestrians have a higher probability of the IRLR behaviour. The results of marginal effect indicated that the mean of the probability of the IRLR behaviour for each sample will decrease 0.8% when the sample from an electric bicycle rider changes into a pedestrian. These results are confirmed by previous study [

The second dummy variable’s effect on the IRLR behaviour is not significant. The rate of the IRLR behaviour of bicycle riders is 17% and that rate of electric bicycle riders is 24%. Although the difference of the rate of the IRLR behaviour between bicycle riders and electric bicycle riders is 7%, these two rates are not significantly different. This may be due to the same operation environment the bicyclist and e-bicyclist have. For instance, bicycles and e-bikes are operated in the same lane with fixed width which is commonly separated from motor-vehicle lanes. This may be the reason why they are able to influence each other in the mixed traffic and show similar behaviours as a result [

In addition, bicycles and electric bicycles are classified as nonmotor vehicles according to the traffic law in China, which makes them subject to the same traffic rules; in turn, they have similar performances. These results are similar to previous researches [

Arrival phase is also a three-category variable. Two dummy variables are set by the model. The first dummy variable is expressed by close left turn vs. far left turn with 0 denoting far left turn and 1 denoting close left turn. The second dummy variable is expressed by straight vehicle in road vs. far left turn with 0 denoting far left turn and 1 denoting straight vehicle in road.

The first dummy variable has significantly decreasing effect (-1.908). The estimation of the standard deviation is 0.275. However, it did not pass the test, showing that the first dummy variable is a fixed variable. Therefore, the odds of IRLR during close left-turn phase is 14.8% (

The second dummy variable has significantly decreasing effect (-3.754). The parameter is found to be normally distributed with a mean of -3.754 and a standard deviation of 2.19, showing 95.6% of this distribution is below zero and 4.4% is above zero. This implies that, compared with far left-turn phase, most road users (95.6%) are less likely to have IRLR behaviour during straight phase. The results of marginal effect indicated that the mean of the probability of the IRLR behaviour for each sample will decrease 1.1% when the phase of motor vehicles changes from straight into far left turn.

The result is consistent with the previous study by Yang et al. [

Speed change upon arrival is also a three-category variable. Two dummy variables were set by the model. The first dummy variable is expressed by slower vs. unchanged with 0 denoting unchanged and 1 denoting slower. The second dummy variable is expressed by faster vs. unchanged with 0 denoting unchanged and 1 denoting faster. Both dummy variables are fixed coefficients based on the results of the model.

The first dummy variable has significantly decreasing effect (-1.295). The estimation of the standard deviation is 0.517. However, it did not pass the test showing that the first dummy variable is a fixed variable. Therefore, the odds of the IRLR of those samples whose arriving speed has slowed down are 27.4% (

The second dummy variable has significantly increasing effect (-11.360). The estimation of the standard deviation is 2.501. However, it did not pass the test showing that the first dummy variable is a fixed variable. Therefore, the odds of the IRLR of those samples whose arriving speed has accelerated is 85819.37(

1368 samples including pedestrians, bicycle riders, and electric bicycle riders were collected in this study. A RPLM of IRLR behaviour of pedestrian and cyclists at the signalized intersection in the urban was developed. The results indicate that no. of people waiting upon arrival, no. of people crossing upon arrival, pedestrians vs. electric bicycle riders, arrival phase, and speed change upon arrival have significant effects on the IRLR behaviour. Four variables, no. of people waiting upon arrival, no. of people crossing upon arrival, pedestrians vs. electric bicycle riders, and straight vehicles in road vs. far left turn, produce statistically significant random parameters. Two variables, close left turn vs. far left turn and speed change upon arrival, result in fixed parameters.

The present outcomes might be helpful for the proposal of traffic management countermeasures to decrease intersection-crossing risk behaviours:

(

(

(

In conclusion, the findings of this research would be useful for transportation engineers to better understand the behaviour of pedestrians to find related solutions for the problem. And it is also helpful in developing more accurate and reliable pedestrian and cyclist simulation models. There are still several limitations in the present study which should be addressed in future work. First, data from three intersections makes it difficult to be representative of most intersections and this may limit the transferability of the research. Modeling with an increased sample size should have a better transferability. Second, the phasing and timing variables of the intersctions may be also important to road users’ behaviours, which are not considered in present research. Future studies including the phasing and timing variables are needed to better understand how those factors influence IRLR behaviours. Third, only the factors’ effects on the behaviour of IRLR have been analyzed in this study. There is need for a further study on the rule and factors of waiting time of the waited pedestrians and cyclists.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was jointly supported by the Fundamental Research Funds for the Central Universities [No. 2018JBM023