Pedestrian Gap Acceptance Behavior, A Case Study: Tehran

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Pedestrian Gap Acceptance Behavior, A Case Study: Tehran Mohammad Ali Arman Assistant Research, Traffic Laboratory, Iran University of Science and Technology. Narmak, 16846, Tehran, Iran. Phone: +98(21) 77803100 Fax: +98(21) 77240398 Email: [email protected] * Corresponding Author.

Amir Rafe Assistant Research, Traffic Laboratory, Iran University of Science and Technology. Narmak, 16846, Tehran, Iran. Phone: +98(21) 77803100 Fax: +98(21) 77240398 Email: [email protected]

Tobias Kretz Chief Technical Product Manager, PTV Group Haid-und-Neu-Str. 15, 76131 Karlsruhe, Germany Phone: +49 721 9651 7280 Email:[email protected]

Word Count = 5714 (Minus References) + 5 ×250 (Tables and Figures) = 6964 Word < 7000 Word. Number of References = 35.

Submission Date: July 30, 2014.

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ABSTRACT Pedestrians’ accidents with vehicles when they are trying to cross the streets are considered one of the most fatal accidents for pedestrians. So making a decision about accepting a proper gap is crucial for pedestrians. This paper, using video-taped data, investigates pedestrians’ gap acceptance in an unsignalized intersection and a midblock crosswalk in Tehran, Iran. Size of the accepted gaps, size and number of the rejected gaps and the waiting time are examined against pedestrians’ and traffic attributes, using statistical analysis and modeling approach. Statistical analysis revealed that gender, using cell-phone during crossing and accompanying a child strongly affects the pedestrian gap acceptance behavior. A latent variable, caution behavior, was defined based on some observable indicators and using structural equation modeling it was estimated and used as an input in a binary mixed logit model. Modeling approach shows pedestrian decision regarding acceptance or rejection of a gap to be highly influenced by the size of current gap, caution behavior and waiting time.

Keywords: Pedestrian gap Acceptance, Caution behavior, Behavioral modeling.

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1. INTRODUCTION Traffic accidents are one of the main reasons of injuries and deaths in developing countries. In road accidents, pedestrians are more vulnerable than other road users. According to official statistics, more than 28 percent of fatalities in Iran and 75 percent in Tehran are pedestrian-related(1). Two important points where pedestrian and vehicle accidents often occur are intersections and midblock crosswalk; so the analysis of gap acceptance at these facilities is very crucial for the improvement of pedestrian safety. To investigate the pedestrian gap acceptance, researchers use various parameters. These factors can be divided into two categories: pedestrian demographic characteristics such as age and gender, and environmental parameters including traffic flow characteristics, facility geometric design and interactive parameters between pedestrian and traffic flow (such as the pedestrian speed, group size, path and speed changes, waiting time, etc.)(2-6). Demographic characteristics are effective parameters in studies about pedestrian gap acceptance modelling, simulation and behavioral analysis. Some studies(2-16) have found that pedestrian demographic characteristics shows a significant effect on pedestrian gap acceptance behavior. Often they found men accept smaller gaps than women. Of course, in some cases it is vice versa(12, 16) and in some others(17) a significant difference between the two genders has not been achieved. Moreover, based on these studies, the average of the younger minimum gap is less than that of the older pedestrians. The second category of factors influencing pedestrian gap acceptance is the environmental parameters. As the waiting time increases, pedestrians become more aggressive and accept small gaps to cross the street(8, 9). On the other hand, according to(12, 16),those who are waiting a long time for crossing do not take high risks. Group size is another important factor in various studies that investigated gap acceptance in pedestrian crossing location(8, 11-13, 17, 18). Speeds of pedestrians in groups is demonstrated to be about 9% lower than that of a single pedestrians(19), moreover it found that pedestrian platoon has a significant contribution in reducing the gap size(13, 17). Speed of the pedestrian is another factor has been studied in gap acceptance studies(4, 11, 17, 18, 20). Findings have shown when the pedestrian try to accept smaller gap increase whose speed. Whenever there is an increase in walking speeds, the probability of crossing increases as well(21). Other factors in an effective pedestrian gap acceptance are traffic flow characteristics and properties of facilities. Vehicle Speed is one of the most important items in this category(4, 10, 15-17, 22-24). According to these studies, increase in the vehicle speed reduces the probability of pedestrian crossing. Although(16) in his studies found that pedestrians gap acceptance was better explained by the distance from the incoming vehicle, rather than by its speed. Other important factors in this category are the size and type of the vehicles(8, 12, 16, 17, 24), lane effects(10, 13, 22, 25, 26), illegal parking(16), weather condition(27-29), the presence of police enforcement(28, 29) and traffic volume(10, 20, 21, 27, 28). Pedestrians select various crossing patterns in diverse traffic conditions and according to their decision-making factors. They may cross a street as a one/two stage crossing when they find an appropriate gap in traffic or they may cross a street as a multi-stage crossing and lane by lane (rolling gap)(10, 25, 26). Discrete choice and regression models based on the combination of the above parameters are familiar models to demonstrate the size of accepted and critical gap and the probability of crossing(7, 8, 13, 16, 17, 22, 24-26, 28, 29). Also, some studies have investigated the critical gap and decision of crossing pedestrian using simulation(15) or field surveys(23, 28). This paper uses a statistical analysis and modelling approach in order to investigate the pedestrian gap acceptance behavior in Tehran, Iran. An integrated hybrid model structure is presented to estimate the size of gaps through a linear regression model, estimate caution behavior by a structural equation modeling technique and finally uses these two variables along with some other independent variables in a binary mixed logit model to estimate pedestrians’ gap acceptance behavior. Based on our knowledge it is the first time that such an integrated model is used to study the pedestrians gap acceptance behavior.

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The rest of this paper is organized as follows: data collection method and site description are explained in section 2. Section 3 deals with the representative statistics and data analysis. Theoretical model is presented in section 4 and the results are discussed in section 5. Finally, Section 6 will be the concluding remarks.

2. DATA COLLECTION AND SITE DESCRIPTION Video recording was used to collect data of the pedestrians’ crossing behaviors in two selected facilities in South Sohrevardi St. in Tehran, Iran. The survey period includes the peak hour(7:00–8:30 a.m.) and off-peak hour(8:30–10:00 a.m.). One of these facilities is an unsignalized intersection and another one is a midblock crosswalk. Two considerations have been taken for facility selection: first, both facilities are selected in a street as near as possible to each other to avoid social differences in study; second, there were enough high building near facility to provide suitable view for camera installation. On the whole, 1163 accepted gaps and 1435 rejected ones were observed and studied in unsignalized intersection respectively along with 1208 accepted gaps and 1812 rejected gaps in midblock crosswalk.

3. REPRESENTATIVE STATISTICS AND DATA ANALYSIS As described previously, Data were collected using video recordings. Based on these videos, pedestrian physical and behavioral attributes, conflict condition and vehicle and traffic flow features were collected. 3.1 Pedestrian Attributes Pedestrian attributes are basically classified in two main groups: pedestrian physical characteristics and pedestrian behavioral attributes. Like most of the other studies, age and gender are the only two pedestrian physical characteristics. Pedestrian behavioral attributes include using cellphone, holding bags or briefcases, walking in groups and with children. In unsignalized intersection, the behaviors of 623pedestrians were observed and analyzed. This number was 607 in midblock crosswalk. Because pedestrians’ ages were estimated from the videos, this property breaks up into three discrete categories: young, middle-aged and old. Table 1, summarizes the gender and age distribution of pedestrians in two types of facilities studied in this paper as well as corresponding’s size of accepted gaps. TABLE 1 Data of Observations Based on Facility Type, Gender and Age Young Unsignalized Intersection Midblock Crosswalk

Unsignalized Intersection Midblock Crosswalk

a: Data Summary Based on Facility Type, Gender and Age Males Females Middle-aged old Young Middle-aged 375 (60.3%)

110 (29.2%)

197 (52.4%)

112 (30.2%)

196 (52.9%)

68 (18.4)

78 (31.4%)

9.37

41 (16.7%)

236 (38.8%) 63 (16.9%)

73 (30.9%)

11.09 11.43

8.89

9.03 8.33

128 (51.9%)

123 (52.3%)

40 (16.8%)

b: Accepted Gap Size by Facility Type, Gender and Age in Seconds Average Size of Accepted Gap 85th Percentile Size of Accepted Gap Males Females Males Females MiddleMiddleMiddleMiddleold Young old Young old Young aged aged aged aged 9.44

8.41

old

247 (39.7%)

371 (61.2%)

Young

35 36 37

4

8.97

11.03

13.98 15.4

12.62

9.63 10.4

8.41

9.52

13.89

14.25 16.43

12.78

12.98 12.3

12.54

12.94

old

14.21

16.98

13.48 13.73

12.62

13.33

15.56

Table 1b, summarized the size of accepted gaps based on gender, age groups and facility type. Women generally take larger gaps and are less risky; moreover, the accepted gaps in midblock

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crosswalk were smaller for both sexes. Age is another factor that leads pedestrians to become more cautious. This factor was more effective on women. While changing age group from young to middleaged and from middle-aged to old result in a10.6% and 19.9% increase in accepted gap size between men in unsignalized intersection, these percentages are respectively17.7% and 29.4% for women in this facility. This could be interpreted as age cautiousness effect. A similar pattern could be seen in midblock crosswalk: the above-mentioned percentages are 5.4% and 11% in midblock crosswalk facility for men and 9.4% and 21.1% for women. It’s clear that aging effect has been more meaningful among women. Other studies in India have reported similar results regarding accepting larger gaps by females and elders compared to males and youth(10). In order to check the variables effect on waiting time and the size of accepted gap, multi-way ANOVA was used. The overall results are shown at the end of these discussions, in Table 4. As mentioned previously, four variables are considered as pedestrians’ behavior for the purpose of investigating their effect on the size of accepted gap. One of them that based on our knowledge is not broadly studied, is using cell-phone during crossing(30, 31). Generally, 41.2% of pedestrians in unsignalized intersection facility and 39.7% of them in midblock crosswalk facility used their cell-phone during crossing. In unsignalized intersection facility, 23.8% of pedestrians who confront with interaction with one or more vehicle used their cell-phone during crossing and this percentage was 20.4 in midblock crosswalk facility. This conduct is more prevalent among males (1.34 times more than females) and the youth act in this way approximately 2.1 times more than middle-aged people and 2.9 times more than elderlies. Based on traffic accident data in Tehran in 2013, in average 38.1% of all the pedestrians who were involved in a crash used their cellphone in the time of accident. Furthermore, 43.2% of fatal pedestrian accidents involved people who used their cell-phone during crossing across street(1). A similar effect of using cell-phones on pedestrian injuries and fatalities have been reported in other studies(32). In both genders and in all age groups, using cell-phones widened the accepted gaps. According to the results derived from Table 4, when the simultaneous effects of gender, age and using cell-phones during crossing are checked, F-value becomes larger compared to the effect of any of these variables individually or even in comparison with any of their paired composition. Calculating the percentage change of accepted gap size in different age groups and genders that used their cell-phones during crossing shows that the most substantial increase is in age variation from the middle-aged to the elderly and also it is more remarkable in women compared to men. While the average and 85th percentile of the size of the accepted gap for men who used their cell-phones are 10.1 and 15.2 seconds, these numbers are 12.0 and 15.8 for women. Moreover, young women normally need 11.6 seconds for crossing and elders need larger gaps with the size of 16.0 seconds on average. A study conducted to examine the effect of using cell-phones during crossing in Seattle showed 7.3% of pedestrians speaking with cell-phone during crossing and 11.2% of them text messaging, and it concluded that these pedestrians need 1.87 seconds bigger gaps (18%) to cross the street(31). Next variable considered in this paper and found to be effective is accompanying a child during crossing. According to Shariat et al., studies in Tehran shows an average walking speed of children to be 0.93 meters per second and relatively 16% slower compared to that of the adults with average speed of 1.11 meters per second(33). Consequently it is reasonable to reduce the speed of the adults when they accompany a child and seek to find larger gaps. Moreover, it is suggested that adults become more cautious regarding accident risk when they accompany a child. From a gender perspective, this study found that in most cases children walked with a female (63.4%). Men’s average and 85th percentile of accepted gap when they accompany a child are 11.7 and 16.4 seconds respectively; these numbers are 13.2 and 17.9 seconds for women. As could be concluded and presented in Table 4, through ANOVA results, considering gender and child accompaniment along with each other is more effective than any of these individual variables. Middle-aged pedestrians go along with a child more than other age groups and consist 78.3% of all the observations, but the statistical evidence shows difference between sizes of accepted gap by different age groups of pedestrians who accompany a child. Results of Table 4, indicates that if a pedestrian carries a bag or a briefcase, it does not have any effect on the size of accepted gap. These variables include bags that a single pedestrian could carry easily; other cases were too rare to be included in the study. The last pedestrian behavior variable investigated in this paper is walking in groups. Pedestrians may walk alone, in pairs, or in bigger groups when crossing the streets. Total observations consist of

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66.5% of alone crossings, 16.8% of pairs, 7.3% of groups with three people and 9.4% of groups consisting more people. As shown in the collected data, for groups up to three persons, the accepted gap size becomes larger along with the group size, but it is not the case for groups consisting more than three persons. A considerable reduction in the size of accepted gap is observed in such groups. Table 2, represents average and 85th percentile of accepted gap based on group size. TABLE 2 Accepted Gap Size Based on Group Size

Average Size of Accepted Gap 85th Percentile Size of Accepted Gap

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Walking Alone

Walking in Pairs

Walking in Groups with Three People

9.6 13.41

9.92 13.81

10.56 14.29

Walking in Groups with More than Three people 9.76 13.57

An assumption that could be discussed and verified statistically is that the size of the accepted gap in group members depends on the group formation rationale. Three main group formation rationales could be found according to pedestrians’ behaviors. Groups can be formed based on one or more of these rationales: a) Pedestrians basically walk together in a group and cross the street in this form. b) Long waiting time as a result of high vehicular flow speed or volume is imposed on pedestrians and during this time a group is shaped that cross the street in the first appropriate gap. c) A pedestrian or a group of them accept a suitable gap and cross the street, while another pedestrian joins them through a sudden acceleration. Whenever t-test did not show any statistical differences between the average sizes of the accepted gaps by group types (a) and (c), the average size of the accepted gap by group type (b) is approximately 11.3% smaller than the other two groups. With respect to the group formation rationale in group type (b), it seems that waiting times led pedestrians to become more aggressive and risk-taking, therefore accepting smaller gaps. Furthermore, group type (b) is mostly formed by three or more people and the above-mentioned rationales regarding the acceptance of smaller gaps by such group sizes could be valid in case of group type (b) as well. Two-way ANOVA was used to check the differences among the sizes of accepted gaps based on group sizes and group formation rationale. The results showed that the size of accepted gap differed significantly across four groups sizes, and it was also different among three group formation F  2, 2368   11 .59, p  va lue  6.76 e  4 rationales, F  2, 2 3 68   6 .37 5, p  va lue  0 .01 1 6 . As groups usually consist of different pedestrians with different behaviors, it is difficult to judge them based on behavioral features like using cell-phones or holding bags and briefcases. However, observations show that women are more cross in groups compared to men. Whereas 38.1% of women cross the street in groups, this percentage is 30.5 for men. In addition, compared to other age categories, number of the youth in groups is low, although most of the pedestrians that join a group based on pattern (c) are young. In contrast, elders cross in groups more than other age categories and they mainly belong to type (b). The larger the group size the slower is the crossing and there is not any exception for large groups as there was in case of the size of accepted gap. Among the remarkable rationales for group formation, group type (c) is interesting: the numbers of those pedestrians with any slackening behavior in their crossing, like using cell-phones or accompanying a child, are relatively very low in this type of groups. Although men with more walking speed and accepting smaller gaps are often more agile than women, in case of joining and forming groups type (c) women are more numerous. This behavior could be interpreted in a sense that women are more cautious than men and prefer crossing safely in groups. The number of 1163 accepted gaps for 451 pedestrians leads to a gap acceptance rate of 1.87 per person in unsignalized intersections. This rate equals 1.99 in midblock crosswalk. Therefore, it can be inferred that some pedestrians had to accept more than one gap to fully cross the street. Since both facilities are divided in to two way streets, pedestrians may involve in conflicts with vehicles in slowlane or passing-lane before (conflict on the left side) or after (conflict on the right side) reaching to safety. In some cases, pedestrian did not wait for the street to be cleared and started crossing just after finding a proper gap in the nearest lane. In such kind of behavior, known as rolling gap (25), a pedestrian may stop in the middle of the street after one successful gap acceptance and look for a suitable gap in

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the next lane; or s/he may cross the next lane immediately because it has been cleared after his/her firstline crossing. 18.7% and 26.5% of all the observed pedestrians exhibited the rolling gap behavior in unsignalized intersection and midblock crosswalk respectively. The number of males showing such behavior in both facilities were considerably more than females, with 82.8% and 84.6% of all the rolling gap behaviors in unsignalized intersection and midblock crosswalk. Among the observed rolling gap behavior in unsignalized intersections and midblock crosswalks, in 29.7% and 31.1% of cases pedestrians had to find a proper gap in passing-lane after crossing slow-lane and in the rest of the cases passing-lane become clear during their first-line crossing. As the comparison between the accepted gaps in slow-lane and passing-lane illustrates, lane types exert a significant effect in unsignalized intersection, t  716   19.98, p  value  2.2 e  16 and

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a similar results found in midblock crosswalk where: t  748   14.67, p  value  2.2 e  16 . Although women are less risk-taking when involving themselves in more than one gap in every direction of street, in emergencies their waiting time to cross the street is less than men (in average 5.6 seconds compared to 6.7 seconds) and they accept more risky gaps (in average 5.2 seconds compared to 5.8 seconds). The direction of conflict was found not to be effective on the size of the accepted gap even while considering the facility type or people’s gender; however, in an analogues pattern between two genders and two facilities, pedestrians wait less time for finding gaps when they are involved in a right side conflict. A similar pattern to that of the size of the accepted gap could be seen regarding waiting time. Although gender and aging effected waiting time, facility type was not found to be meaningful in pedestrians’ waiting time. Based on the collected data, average and 85th percentile of waiting time for men are 9.3 and 26.5 seconds and statistically equal in both facilities (based on t-test). These numbers are 10.7 and 27.6 seconds for women. The results of multi-way ANOVA for checking different variables’ effects on waiting time are presented in Table 4. As expected, elders showed more patience and had the longest waiting time, while the youth were more impetuous compared to others. Again multi-way ANOVA was used to check the effect of different variables on waiting time and the results are presented in Table 4. As could be seen, both variables of gender and age are effective and their simultaneous effect is stronger. Using cell-phones has the same effect on both the size of accepted gap and waiting time, producing an increase in both variables. Pedestrian which used their cell-phones during gap acceptance crossing approximately wait 8.8% more than others. Considering the combinational effect of using cell-phones along with age and gender simultaneously is more operative than considering each of them separately. Whenever the average waiting time of young, middle-aged and elderly women are 10.2, 10.7 and 12.2 seconds and women use their cell-phone these averages rise to 11.1, 11.9 and 13.5 seconds for these age groups. Similarly, accompanying a child leads to longer waiting times for both genders but not with an equal effect (11.3% increase for men and 20.2% increase for women). As ANOVA test indicates, child accompaniment is more effective on waiting time compared to using cell-phones, whether they are evaluated solely or along with gender. Holding bags or briefcases again did not affect the waiting time. Although grouping does not matter to waiting time, still the longer the waiting time, the larger the group size will be. Whilst it is expected that the waiting time and number of rejected gaps make the same sense for pedestrians, Pearson correlation between these two is 0.543. Again ANOVA test was used to check the relationship between different variables and the number of rejected gap by each pedestrian. Contrary to the size of accepted gap and waiting time, the number of accepted gap is not affected by gender. Similar results were gained regarding facility type, using cell-phone and holding bags or briefcases. No statistically significant differences were observed between the youth and the middle-aged, but the elders meaningfully rejected more gaps compared to other age groups. Finally, child accompaniment led to more gap rejection and it could be a result of more caution from adults for protecting children. As only age groups and child accompaniment were found to affect the number of rejected gaps, the simultaneous effect of these variables on the number of rejected gap was not considered in ANOVA test. The results are presented in Table 4. Five video cameras were used simultaneously to record pedestrian behaviors in sidewalks in both sides of the street and in the crosswalk. Moreover, the approaching vehicles were recorded from approximately 50 meters before reaching the crosswalk in both directions. Investigating pedestrians’ speeds in sidewalks and crosswalks using t-test revealed that they changed their speed in the street

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where: t  2445   17.72, p  value  2.2 e  16 . Table 3 summarizes the average and 85th percentile of pedestrians’ speeds in sidewalk and crosswalk based on gender and age group. TABLE 3 Summary of Pedestrians Speed Study Results Young

Sidewalk

Crosswalk

Average Speed 85 Percent Speed Average Speed 85 Percent Speed

Males Middleaged

Old

Young

Females Middleaged

Old

1.15

1.11

1.04

1.09

1.05

1.00

1.19

1.14

1.06

1.11

1.09

1.03

1.24

1.20

1.11

1.16

1.12

1.06

1.29

1.23

1.13

1.18

1.16

1.09

5 6 7 8 9 10 11 12 13 14 15 16

As described earlier, pedestrians increase their speed on the crosswalk, but this increase is not equal among both genders and age groups. Whereas males raise their speed relatively to 8%, 6.7% of increase was seen among females. Here again the multi-way ANOVA was used to evaluate the effect of different variables on acceleration from sidewalk to crosswalk and the results are shown in Table 4. Gender was found to be the most effective factor on speed acceleration behavior. Age, using cell-phone, child accompaniment and holding bags or briefcases are all effective factors in speed increase as well. Facility type is the only ineffective factor in this analysis and simultaneous consideration of gender with each of the other factors (except facility type) was found to be impressively more effectual. The most effective combination of factors is gender-child accompaniment. Using cell-phone, accompanying a child and holding bags or briefcases resulted to 0.8%, 1.5% and 1.3% less speed increase among men and these rates were 2.2%, 3.4% and 1.7% for women.

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TABLE 4 Multi-way ANOVA Test for Relation between Explanatory Variables and Size of Accepted Gap, Waiting Time, Number of Rejected Gaps and Percentage of Speed Increase in Crosswalk Size of Accepted Gap Gender Age Facility Type Cell-phone Child Accompaniment Bag Walking in Group Gender × Age Gender × Cell-phone Gender × Age × Cell-phone Gender × Child Accompaniment Test Degree of Freedom

5 6 7

Waiting Time

Number of Rejected Gaps

F Value

Pr (>F)

F Value

Pr (>F)

F Value

Pr (>F)

42.24 26.96 15.68 122.45 225.01 2.06 98.8 406.0 225.62 408.65 515.39

.75e-11 2.15e-7 7.6e-5 2e-16 2e-16 0.15 2e-16 2e-16 2e-16 2e-16 2e-16

5.41 3.93 0.25 9.79 12.21 0.426 26.97 16.05 42.8 61.29

0.02 0.047 0.617 1.79e-3 4.92e-4 0.514 2.42e-7 6.55e-5 8.89e-11 1.06e-14

2.79 5.15 0.03 0.397 49.05 2.11 -

0.094 0.023 0.863 0.528 4.1e-12 0.146 -

5607

1219

1223

Percentage of Speed Increase in Crosswalk F Value Pr(>F) 20.18 17.2 2.87 9.96 11.13 7.86 98.5 108.53 49.68 31.75

7.7e-6 3.59e-5 0.09 1.64e-3 8.74e-4 5.12e-3 2e-16 2e-16 3.03e-12 2.17e-8 1219

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3.2 Traffic Condition and Vehicles’ Attributes During 3 hours of data collection from 7 a.m. to 10 a.m., traffic condition was in peak and off-peak periods. The average of vehicle speed in unsignalized intersection in peak and off-peak periods were 31.5 k/h and 38.6 k/h respectively and these numbers were 34.7 k/h and 39.8 k/h in midblock location. Moreover, the traffic volume in peak and off-peak periods in signalized intersections were 1288 and 845 vehicles per hour and these numbers were 1235 and 796 in the midblock facility. All the observed vehicles in this study have been classified into four groups: Private Cars, Taxis, Buses and Motorbikes. Although the type of conflicting vehicle is not effective on the size of accepting gap, it affects decision-making regarding acceptance or rejection of a certain gap. More than 91% of conflicts with a bus result to a reject gap. This number was even more for conflicts between a pedestrian and a motorbike, where in more than 98.5% of cases pedestrians reject gaps in conflict with motorbikes. High rate of rejection gaps in conflicts with buses could be related to their size, because pedestrians are more cautious in these cases. On the other hand, in conflicts with motorbikes, motorists usually have more speed and do some tricky maneuvers to pass faster and pedestrian do not prefer to get involved in such hazardous situations. In unsignalized intersections, in 22.7% and 75% of all the observations pedestrians conflict with a taxi and private car respectively. These rates were 18.2% and 77.3% in midblock crosswalk. In both facilities in average 60% of conflicts with taxies and 52% of conflicts with private cars eventuated to gap rejections.

4. THEORETICAL MODEL In order to estimate the pedestrian gap acceptance behavior in our study, a Hybrid Binary Mixed Logit model was accommodated and used. A regression and a structural equation model (SEM) component are used to estimate the gap size and pedestrian cautious behavior respectively. The outputs of these two components were used as inputs along with other independent variables in utility function of a mixed logit model. The first part of this model structure is a linear regression model that estimates gap size based on independent variables. In this study, a SEM technique was used to estimate a latent variable named cautious behavior, based on three observable indicators: gender, percentage of speed acceleration from sidewalk to crosswalk and the number of rejected gaps. Previous studies in both psychology(34) and traffic safety(35) show caution and risk perception to be different among genders. Consequently, gender was considered as an indicator in this latent variable. It was assumed that the more the speed acceleration rate the greater the cautious behavior because pedestrians were more likely to pass the street faster. As it was shown in section 3, child accompaniment requires more caution; therefore those elders and pedestrians who accompany a child reject more gaps, and the number of the rejected gaps involved as the third indicator. A binary mixed logit model is used to estimate pedestrian decision-making regarding the acceptance or rejection of gaps. As we could not judge about pedestrian utility or regret regarding the rejected gaps, a utility function estimated the accepted gaps and the utility of rejected ones was assumed to be zero. As the only important difference between utilities is in binary choice models, a comprehensive utility function for the accepted gaps could reflect the choice behavior perfectly. Utility and probability function of choice model proposed in this paper are presented in equations 1 and 2 below:

UAccn GS    x C  Un*

45 46 47

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 e PAccn     1  eUn*  Where:

  f    d  

(1) (2)

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1

U Acc n is the utility of accepting a certain gap for pedestrian n . GS

2 3 4 5

is the gap size that is the output of regression model and  is its corresponding coefficient.  is the latent variable that reflects pedestrians’ caution and is estimated using SEM technique and  is its corresponding coefficient. x is the vector of other independent variables in utility function and  is corresponding vector of coefficients

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of these variables and C and  are model constant and error term respectively. In addition,

7

PAccn represents the probability of accepting a gap; therefore 1  PAcc n  is the probability of rejection. f   is

8 9

the density function and Un is calculated with equation 3 and indicates pure difference between utility of accepting and rejecting.

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*

Un*  UAccn URejn

(3)

5. RESULTS AND DISCUSSION For testing the model, fitness likelihood ratio test (443.2), Rho-square (0.323), Craig-Uhler (0.292) and Theil’s tests (0.136) were used. The results show that all the tests revealed superior prediction power of the proposed model. Theil’s test has been used to control the overall model accuracy. The entire model has 17 variables and the estimated model was based on 3911 observation of accepted and rejected gaps. The ratio of observation to variables is about 230 in proposed model. Table 5 illustrates the model estimation results. The first variable in regression model is conflict lane. This is a dummy variable: it takes one if the conflict lane is the passing-lane; otherwise, it equals to zero. Due to a higher speed in passing-lane, a positive coefficient for this variable was expected which resulted in smaller gaps in this lane. With respect to section 3, conflict direction is not an effective variable on the size of gap. To verify this claim, Pearson correlation test was used to check the correlation between this variable and the gap size. As shown in Table 5, there was not a correlation, and consequently this variable could excluded from regression model with certainty. Despite based on ANOVA results facility is not effective on size of accepted gap but this variable is meaningful in regression model. Facility type appears in this model in form of a dummy variable that equal to one for unsignalized intersection and zero for midblock location. The estimated coefficient is positive and it could be a result of lower speed and consequently larger gaps in unsignalized intersection. Gap size is measured by the elapsed time between passing of the rear of one vehicle to that of the next. Hence, whenever the size of the passing vehicle was bigger, the remaining time for a pedestrian to complete a gap acceptance maneuver was smaller. Accordingly, the length of the passed vehicle appeared with a positive coefficient in the model and it has a remarkable correlation with the gap size. Similarly, the higher speed of the upcoming vehicle leaves smaller crossing opportunity for pedestrians and they need bigger gaps to pass. This is confirmed by the coefficient of variable “Speed of Upcoming Vehicle”. Finally however model constant is large, its t-test represents that it is not very meaningful in regression model compared to independent variable. SEM model scaled to one for gender and loading factor for the other two estimated variables. Based on the results, gender is the most important factor in pedestrian caution behavior and the rate of speed acceleration is more important compared to the number of rejected gaps based on loading factor and t-test. However, t-test indicates that the number of rejection gap in significant in the model. The first variable in choice model is age. Although age is continues variable, the age of pedestrians was recorded discretely, and accordingly this variable was presented in a discrete form in the model. Random coefficient based on normal distribution was estimated for age dummies which indicated taste variation among each age group. According to results, age coefficient is positive with high variance for the youth, while it becomes negative with very small variance as pedestrians become more aged. It could be interpreted as youth tendency to accept larger variety of gap sizes and more cautious behavior among elders. T-test

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indicated that age is statistically meaningful in the model. As described in section 3, using cell-phones has adverse effects on the accepted gap size. As the normal distribution of coefficient and big variance revealed, effects of this variable consisted of high degrees of variation. It could be a result of different effects of using cell-phones among genders and age groups. This parameter was shown to be very significant by values of coefficient and t-test. One of the most effective variables in this model is accompanying a child. This variable appeared with strong negative coefficient and the smaller variance (in the entire model) with normal distribution. With respect to section 3, holding bags or briefcases is not an effective variable on the size of the accepted gap. In Table 5, a star mark is used to indicate that this variable is not significant in the model even in 85% of confidence level. A random coefficient was estimated for the gap size based on the lognormal distribution. Because everyone prefers larger gaps, it is not reasonable to estimate a negative coefficient for this variable; consequently lognormal distribution is acceptable. In addition, coefficient variance becomes very small and, based on t-test, less significant compared to the coefficient mean; therefore pedestrians’ taste variation is very limited regarding the gap size. On the other hand, based on the fact that pedestrians’ behavior is in not completely rational, the same caution behavior is not expected from all the pedestrians. Estimations of a normal random coefficient with big variance compared to mean, reflect this fact according to some situational and personal conditions (e.g. hurry). Longer waiting time leads to more aggression and risk-taking behavior, so the pedestrians with longer waiting time are more encouraged to accept even the small gaps. To consider this suggestion, a random coefficient based on negative lognormal distribution was estimated for this variable. Similar to the coefficient estimated for the gap size, here variance is very small compared to the mean and results to a limited taste variation among pedestrians. In section 3, described increase in group size leads to accepting larger gaps but it is not the case for groups larger than three persons. So it seems that taste variation is considerable in this case. A random coefficient based on normal distribution was estimated to reflect this fact. As t-test shows, group size is less significant compared to other variables in choice model. Finally, the model constant estimated fixed because a random constant pose heteroscedasticity in utility of choice alternative and this situation is not addressed in this model. TABLE 5 Model Estimation Results Regression Model Variables Conflict Lane(Dummy) Conflict Direction (Dummy) Facility Type (Dummy) Length of Pervious Vehicle Speed of Upcoming Vehicle Model Constant

Coefficient

t-test

DV-IV Correlation*

-0.82

-8.44

0.602 0.083 0.489 0.591 0.598 -

Not involved in the Model 0.72 1.02 1.27 -8.68

4.48 6.19 5.69 -2.12

Structural Equation Modeling (SEM) Variables Gender Percentage of Speed Increase From Sidewalk To Crosswalk Number of Rejected Gaps

Loading Factor

t-test

1

-

0.84

7.88

0.61

4.45

Mixed Binary Logit Model Variables

Coefficient Mean

t-test

Coefficient Variance

t-test

Selected Distribution Function

1.72 0.33 -1.25

5.86 4.99 -6.16

0.67 0.22 0.05

4.17 4.12 3.68

Normal Normal Normal

-1.83 -2.12 -0.26* 3.46 2.78 2.51

-5.15 -9.68 -1.49 11.31 5.55 6.23

0.71 0.08 1.12e-5* 0.22 1.25 0.47

3.49 3.26 1.37 2.88 3.37 3.01

Normal Normal Normal Lognormal Normal Negative Lognormal

Age Young (Dummy) Middle-age (Dummy) Old (Dummy) Using Cell-phone (Dummy) Child accompaniment (Dummy) Holding Bag (Dummy) Gap Size Caution Behavior Waiting Time

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1.17 4.53 1.11 3.12 Normal Group Size 0.65 2.43 Model Constant DV-IV Correlation*: Correlation between dependent variable (Gap Size) and each of independent variables.

6. CONCLUSION This paper tried to report an experimental analysis of pedestrians’ gap acceptance decisions in unsignalized intersections and midblock crosswalks. The statistical analysis of pedestrian decisions regarding acceptance or rejection of a gap at waiting times, revealed that gender, using cell-phones and child accompaniment to be extremely effective on pedestrians’ behavior. A linear regression model was used to predict the size of gap that pedestrians have to evaluate based on their norms. The gap size was determined by traffic conditions and then evaluated through pedestrians' behavioral norms. Structural equation modelling technique was used to estimate a latent variable. This variable is considered in this paper as an index of pedestrian caution behavior and it was demonstrated that gender and percentage of speed increase in the street are the most dominant variables in this behavior. Finally binary mixed logit model revealed that although the gap size is very important by itself, behavioral factors of pedestrians highly affect their judgment to accept or reject a gap and it is in contrast to some pervious findings like Yannis(16). Caution behavior, child accompaniment and using cellphones were found to be the most important behavioral factors in the present study. As expected, the longer the waiting time, the more aggressive will be the pedestrians’ behavior, leading to acceptance of smaller gaps.

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