The Pennsylvania State University. The Graduate School. Department of Civil and Environment Engineering

Transcription

1 The Pennsylvania State University The Graduate School Department of Civil and Environment Engineering EVALUATING DRIVERS STOP-LINE VIOLATION BEHAVIOR AT SIGNALIZED INTERSECTIONS A Thesis in Civil Engineering by Xinyu Zhou Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2017

2 The thesis of Xinyu Zhou was reviewed and approved* by the following: Martin Pietrucha Professor of Civil Engineering Thesis Advisor Eric Donnell Professor of Civil Engineering Vikash Gayah Assistant Professor of Civil Engineering Patrick Fox John A. and Harriette K. Shaw Professor of Civil Engineering Head of the Department of Department or Graduate Program *Signatures are on file in the Graduate School

3 iii ABSTRACT Stop lines are common at intersections; however, few studies have focused on the position of stopped vehicles with respect to the stop line. Often drivers will stop their vehicles over the line creating potential operational or safety problems. In this thesis, data collected from local intersections in State College, Pennsylvania, indicated that only 61 percent of the vehicles observed were in compliance and 13 percent of the vehicles observed were committing severe violations. The data were analyzed to characterize driver behavior related to stop location during red phases. Driver stop line violations were influenced by many factors in this study. Lane usage (right turn only) was associated with high violation rates. Minor roads, when compared to major roads, were more likely to have more severe violations, while morning periods had more minor violations than other time periods. Through only lanes or increased distance from the stop line to the crosswalk or curb extension line promoted higher rates of compliance. Improvements on having a good sight view, keeping enough sight distance and vehicle stop distance could be good choices on reducing severe stop line violations. Increasing the distance from a stop line to a crosswalk or curb extension line an additional 10 feet might provide enough space for the majority of the vehicles stopping at an intersection from entering the crosswalk or intersection area.

4 iv TABLE OF CONTENTS List of Figures... v List of Tables... vi Acknowledgements... vii Chapter 1 Background... 1 Existing problems and potential risks... 2 Literature review... 4 Definition for stop line and stop line violation... 4 Research on stop line related violations... 5 Vehicle length measurement method... 6 Sight distance for signalized intersection... 7 Summary... 8 Chapter 2 Methodology... 9 Data collection... 9 Vehicle violation measurement... 9 Data collection procedure Site selection Intersection geometric information Chapter 3 Data Analysis Data descriptions, summarization and sieve-filtration Model used for regression Group comparison for different variables Different time period Different usage lanes Different types of vehicles Major road or minor road Distance from stop line to crosswalk or curb extension line Chapter 4 Regression Model Results Intersection factors regression results Chapter 5 Conclusions Appendix A Selected intersection map views Appendix B Table of stop line violation data... 47

5 References v

6 vi LIST OF FIGURES Figure 1-1. The intersection of North Atherton Street and West Park Avenue from Google Maps Figure 1-2. The bus route through the intersection of North Atherton Street and West Park Avenue (Source: Google Maps) Figure 2-1. Position for measuring vehicles stop over stop line Figure 2-2. Illustration for collecting intersection violation data into a table Figure 2-3. Locations of the study intersections Figure 2-4. Distance between the curb extension line and a stop line Figure 4-1. Driver s sight view on major and minor road

7 vii LIST OF TABLES Table 2-1. Table of vehicle violation counting (with example) Table 2-2. Table of selected intersections Table 3-1. Table of sample size with different power value Table 3-2. Data description Table 3-3. Data summarization Table 3-4. Table of assumption test for Ordinal Logistic Model in Stata Table 3-5. Table of estimation of Multinomial Logistic Model in Stata Table 4-1. Results of the multinomial logit regression for intersection factors Table 4-2. Response of violation severity distribution when independent variables change

8 viii ACKNOWLEDGEMENTS Thanks to my advisor Professor Pietrucha, and I appreciate the help from my friends, Lingyu Li and Puttipan Seraneeprakarn.

9 1 Chapter 1 Background Stop lines are transverse road surface markings that inform drivers of where they should stop when approaching an intersection. Stop lines are placed to prevent vehicles from entering intersections at the wrong time, to force vehicles to yield to pedestrians and cyclists to allow them to cross the street safely, and to provide space for on-coming vehicles to make a left or right turn onto the adjacent lane. Vehicles should stop before the stop line when a traffic signal is in the red phase or there is a stop sign. However, in consulting several sources (e.g., the Pennsylvania Vehicle Code, the Pennsylvania Department of Transportation s (PennDOT) Bureau of Highway Safety and Traffic Engineering; the Pennsylvania State Police), there seems to be no consensus as to what constitutes compliant behavior. Specifically, which part of the vehicle (leading surface of front bumper or front axle) should be before which part of the stop bar (front or rear edge) for behavior to be compliant? The correct behavior is not clearly specified although the Pennsylvania Driver s Manual [1] states that drivers are allowed to move their vehicle over a stop line if there isn t adequate sight distance for them to get enough information to determine if it is safe for them to enter the cross street. Most drivers at signalized intersections will not have this problem. In their daily driving, however, many operators tend to stop over the stop line when they encounter a red indication, which could be dangerous for them and many of the other motor vehicle operators, pedestrians, and bicyclists using the intersection.

10 2 Existing problems and potential risks Individual drivers may have a different understanding about where to stop relative to the location of the stop line when the traffic signal is red. Many drivers stop beyond the stop line and some of them even enter the pedestrian crosswalk, if one is present. This behavior happens every day at many signalized intersections and can also be seen at the street level view of an intersection found on Google Maps. Below is an example that shows the previously described problems in a more straightforward manner. Figure 1-1 is the intersection of West Park Avenue and North Atherton Street in State College, Pennsylvania. The black pickup truck is clearly passed the stop line and has even entered the pedestrian crosswalk, which could alter the path of a pedestrian crossing West Park Avenue and expose that person to the vehicle stream on the cross street, North Atherton Street. Atherton Street Figure 1-1. The intersection of North Atherton Street and West Park Avenue from Google Maps.

11 3 At that same intersection, buses need a larger radius to make a right turn from West Park Avenue onto North Atherton Street than what is provided by the constructed curb return. The path the bus follows is the red line shown in Figure 1-2, which requires the bus to take up two lanes, on both the approach and departure legs, to make a right-turn. If the vehicle on North Atherton Street trying to turn left onto West Park Avenue stops over the stop line, it will be much more difficult for buses to make the right turn and could elevate the risk of a side-swipe crash. The lane width for West Park Ave is about 10 feet (ft) (3.05m) for the right turn lane and 9ft (2.75m) for the other two lanes (the left turning approach and the receiving/departure leg). Vehicles from North Atherton Street turning right entering West Park Avenue need to slow more if there is a vehicle stopped over stop line on the left-turn lane of West Park Avenue. It is similar for vehicles from North Atherton Street turning left onto West Park Avenue. A larger radius is required if a vehicle occupies the space between the stop line of the left-turn lane on West Park Avenue and the crosswalk. Figure 1-2. The bus route through the intersection of North Atherton Street and West Park Avenue (Source: Google Maps).

12 4 In some cases, a vehicle stopped on a left turn lane needs to move backward to leave enough space for large vehicles (buses or large articulated trucks) to turn into the adjacent lane, which will usually cause some delay. This problem can be much more severe at intersections with narrow lane widths in urban areas during peak hours. The thesis will introduce the measurement of stop line violation, a stop line violation data collection method, a violation data analysis method, regression results of the analyzed data, and findings from the regression. Literature review Definition for stop line and stop line violation Stop lines are important in road design and operations. According to the Manual on Uniform Traffic Control Devices, 2009 edition (MUTCD 2009), [2] stop lines should be used to indicate the point behind which vehicles are required to stop in compliance with a traffic signal. It states the definition and the function of stop lines. The Pennsylvania Vehicle Code [3] states, vehicular traffic facing a steady red signal alone shall stop at a clearly marked stop line, or if none, before entering the crosswalk on the near side of the intersection, or if none, then before entering the intersection and shall remain standing until an indication to proceed is shown. The Pennsylvania Vehicle Code provides a definition of the compliance behavior at stop lines. According to the Pennsylvania Driver s Manual, [1] when there is a steady red light, drivers must stop before crossing the marked stop line or crosswalk. If the driver does not see any

13 5 lines, stop before entering the intersection. The Pennsylvania Driver s Manual also provides guidance on what drivers should do at stop lines. Research on stop line related violations In a study by Zegeer and Cynecki [4] examining pedestrian and motorcycle safety for the right turn on red (RTOR) condition, the use of offset stop lines (for drivers in the middle lanes who are stopped further back from the intersection than right-turning vehicles in the curb lane) were field tested as one of the developed countermeasures. Stop lines were determined to be a factor influencing whether drivers fail to make a full stop or yield to pedestrians as a part of a right turn on red maneuver along with other nine factors (e.g., signing, geometry). While many of the countermeasures that were developed seemed promising, the authors were not able to quantify how much each countermeasure would improve safety. Many studies have considered the stop line as part of the dilemma zone and focused on the behavior of vehicles crossing the dilemma zone during the yellow phase or vehicle violation of a red signal. Alterawi [5] developed a micro-simulation model and found reducing speeds of the vehicles as they approach the signal will greatly reduce red light violations. In this study, using speed reduction in advance of the stop line could reduce the effect of the dilemma zone by reducing the number of vehicles crossing at the onset of yellow or violating the red light by about 33 percent. For this work, the stop line is considered only as a marker to determine what percentage of vehicles crossed it during the yellow/red signal phases. Hulscher [6] performed research on vehicles traversing the stop-line after the termination of the yellow signal interval and derived timing algorithms based on the observed behaviors. Yousif, Alterawi, and Henson [7] discussed red light running in urban road networks after examining video recordings of traffic data and categorized drivers red light violation behavior. They found that around 30 percent of

14 6 the cycles were violated when drivers cross the stop line at the onset of the yellow and the red indications (18.9 percent pass through yellow and 11.3 percent run through red). They categorized red light violations into four categories as observed on site (dilemma zone, dilemma zone follower, single violation, and group violations). PennDOT s Bureau of Planning and Research [8] funded a project examining safer driver actions at stop signs, which analyzed drivers behaviors at stop signs in different situations and compared the changes in behavior before and after physical improvements at selected intersections. From the Phase I study of 32 intersections in Clearfield and Centre Counties, the location of physical obstructions around the intersections were determined to be important factors related to driver behavior, while other variables like stop bar and dashed-line pavement markings had little effect by themselves (the average stopping point for a stop sign located at an intersection was 7.85 ft from the extended cross street curb line, for a stop sign at a distance from (not adjacent to) the intersection that same distance was ft, for a stop sign with dashed edge-line on the major road, the distance was ft, and for a stop sign used in conjunction with a stop bar, the distance was 9.99 ft). However, in the Phase II study, examining 24 intersections where low-cost improvements were made, the post improvement ( STOP pavement marking painted, AT WHITE LINE sign mounted) operational effects were fairly minimal (the stop distance from edge of the road changes from ft to 9.55 ft for the STOP pavement marking, from ft to ft with the AT WHITE LINE sign, and from ft to ft with both improvements). Vehicle length measurement method One element of this thesis will involve estimating the portion of the vehicle over the stop bar in the field. There are many studies about how to measure vehicle length from field

15 7 observations. Avery, Wang, and Rutherford [9] worked on an image-processing algorithm for length-based vehicle classification using an image stream captured by an uncalibrated video camera. They extracted the background and counted each vehicle, then measured the vehicle length in pixels, which provided an accuracy of more than 90 percent in their experiment results. An improved method for estimating vehicle lengths under congested traffic conditions was introduced by Qingyi Ai, ARCADIS US INC [10]. They used dual loop detectors to collect data and extract vehicle speeds, timestamps, and vehicle lengths using this information to develop a model to find vehicles operating status. The output of the improved method had only a 6.7 percent average error. A New England Section ITE technical committee [11] discussed an appropriate assumption for the average effective length of a passenger car equivalent in a queue. In their study, eight urban and suburban intersections were observed, using road markings to identify the intersection vehicle length in a queue. They found that the average effective length of a vehicle in a queue was slightly shorter at urban locations (22.5 ft on average) than suburban locations (24 ft), but the difference was negligible. Sight distance for signalized intersection In NCHRP Report 383: Intersection Sight Distance (ISD), [12] ISD Case III and Case IV are applicable for intersections with traffic signal control. Approach sight triangles provide the driver of a vehicle approaching an intersection an unobstructed view of any conflicting vehicles or pedestrians. The area of an approach sight triangle should be large enough so that drivers can see approaching vehicles and pedestrians in sufficient time to slow or stop and avoid a crash. Departure sight triangles provide adequate sight distance for a stopped driver on a minor roadway to depart from the intersection and enter or cross the major roadway. Departure sight triangles

16 8 should be provided in each quadrant of a controlled intersection. To determine whether an object is a sight obstruction in the sight triangle, a designer must consider both the horizontal and vertical alignment of both roadways, as well as the height and position of the obstructing object. For passenger vehicles, it is assumed that the driver s eye height is 3.5 feet and the height of an approaching vehicle is 4.25 feet above the roadway surface. Considering those factors, in the section of the report, Summary of Current AASHTO ISD Design Policy, for design speeds of 30 km/h, 40 km/h, 50 km/h, 60 km/h, and 70 km/h (the design speed range for most low-speed urban and rural roads), the ISD for crossing maneuver should be 40 m, 50 m, 55m, 65 m, and 75m, respectively, and the ISD for left-turn and right-turn maneuver should be 65 m, 90 m, 120 m, 160m, and 205m, respectively. Inadequate design and placement of stop lines relative to the geometry of these various sight triangles may be a factor in the violation patterns at individual intersections. Summary Stop line behavior is clearly mentioned in many references, but there are still many stop line violations that happen at many intersections every day. Several previous studies considered stop line location and stop line behavior as potential factors in relation to other safety problems; however, none of them tried to find what would cause stop line violations. In this study, stop line violations are considered strictly in terms of driver behavior and the factors that might influence that behavior. Using this approach, it is necessary to find the methods of characterizing the violation distance for each vehicle and the relevant sight distances to determine how intersection geometric factors might influence stop line violations.

17 9 Chapter 2 Methodology In this chapter, data collection methods are introduced in detail and the concepts employed, as a basis for the data collection, are clarified. Data related to the geometric design of the intersections will also be described and along with information on the vehicle violation data. Data collection Vehicle violation measurement In the Pennsylvania Vehicle Code [1] there is no description clearly delineating where vehicles should stop and what constitutes a violation for vehicles stopping over a stop line. In Figure 2-1, it can be seen that the front edge of the front bumper of the vehicle can be in front of the front edge or the rear edge of the stop line, but what is the compliant behavior? In this study, vehicles stopping (i.e., having the vehicle body intrude) after the leading edge of the stop line were considered in violation, and vehicles not encroaching on the leading edge of stop line were considered to be in compliance.

18 10 Lead Trail Figure 2-1. Position for measuring vehicles stop over stop line. In the study, the data were collected by observers, which made it difficult to measure a length value for the magnitude of the violation, so an estimate of the distance a vehicle exceeded the leading edge of the stop line was categorized as: 1) less than 25 percent of the overall vehicle length, 2) 25 to 50 percent of the overall vehicle length, 3) 50 to75 percent of the overall vehicle length, 4) over 75 percent of the overall vehicle length. Vehicles were divided into different groups by vehicle size: small (passenger cars and light trucks), medium (trucks or other large vehicles with 6 tires or more) or large (full size buses and articulated trucks).

19 11 Special cases Vehicles that passed the stop line once the red phase had started were counted as violations. This included vehicles that stopped in compliance at the beginning of the red phase, but then were driven over the stop line as time went by, or vehicles that stopped over the stop line that then moved back to a compliant position. Since right turns on red are allowed at most of the study intersections, some vehicles were often positioned over the stop line waiting for an adequate gap in the cross street traffic to make a right turn. This was not considered as a violation in this study. Method for recording vehicle violations Figure 2-2 is an example of the labeling that was used to segment the intersection into analysis zones, and Table 2-1 is the tabular form that was used to record violation data.

20 12 6 B ave N A st 3 Figure 2-2. Illustration for collecting intersection violation data into a table.

21 13 Table 2-1. Table of vehicle violation counting (with example). date time cycle no observations intersection weather & temperature compliance less than 25% [25%,50%) [50%,75%) m 5 6l l greater than or equal to 75% In Figure 2-2, for example, each lane is marked with a lane number. If there was no vehicle stopped on lane 1 during the red signal of cycle 1, the lane number 1 was filled in the table where column is no observations and the row cycle 1. If a small sized vehicle in lane 5 encroached on the line but the encroachment did not exceed 25 percent of vehicle length during the red phase of cycle 1, the lane number 5 was filled into the cell under the less than 25% column as shown in Table 2-1. For medium (denoted as m ) and large sized vehicles (denoted as l ), the category of that vehicle was added after lane number, like the 6l or 4m entries in Table 2-1. Data collection procedure Field data collection consisted of observations of vehicle behavior in and around the State College area. Observers collected driver behavior data manually on weekdays. Violation behavior

22 at ten different intersections, at different time periods on weekdays (AM peak 7:30-9:30, mid-day 11:30-13:30, and PM peak 16:00-18:00) was recorded using the method described previously. 14 Site selection Ten signalized intersections were selected from those in the local State College area. Some intersections had been observed to be problematic in terms of stop line encroachment behavior. These were included as part of the study. A group of randomly selected intersections, without known encroachment behavior, were also included as part of the study. The selected intersections are shown in Table 2-2. The street view of each intersection is included in the appendix, with the place marked where observers stood to record the data. Table 2-2. Table of selected intersections. MAJOR ROAD MINOR ROAD RIGHT TURN ON RED 1 Blue Course Dr Martin St 2 N Atherton St Blue Course Dr & Clinton Ave 3 N Atherton St W Park Ave NO TURN ON RED on northbound Atherton St 4 N Atherton St Curtin Rd NO TURN ON RED on Curtin Rd 5 N Atherton St White Course Dr 6 N Atherton St W College Ave 7 E Park Ave University Dr 8 E Park Ave Porter Rd & Fox Hollow Rd 9 W Beaver St S Allen St NO TURN ON RED for all directions 10 W Beaver St S Garner St NO TURN ON RED for all directions In Figure 2-3, all the study intersections are marked with black circle on a street grid generated from Google Maps. Intersections number 1, 2, 3 and 4 are far from campus major activity areas compared to the other six intersections. Intersections 1 and 2 are located close to a residential area, and 3 and 4 are in the campus functional area. Intersections 8, 9 and 10 are on

23 15 Beaver Avenue and College Avenue and have more pedestrian traffic compared to the other intersections. For intersections 5, 6 and 7 on Atherton Street, buses turn into a narrow width receiving lane, and for intersection 7, vehicles enter a parking area from the Atherton Street corridor. Figure 2-3. Locations of the study intersections. Intersection geometric information For stop lines at different intersections, the distance between the stop line and the delineation of the extended curb line varies. Drivers may make their judgment about where to stop their vehicle according to this distance. If the distance is longer, it may be likely that there are more violations than when this is a shorter distance. In Figure 2-4, the red arrows depict the

24 16 distance between the stop line and the curb extension line. The distance measured was from the mid-point of the stop line for the lane to the curb extension line in front of each individual lane. In the figure, the two lanes have different offsets between the stop line and the extended curb line. Therefore, for each observed location, each lane had the offset distance noted. Distance between stop line and curb extension line Figure 2-4. Distance between the curb extension line and a stop line.

25 17 Chapter 3 Data Analysis In this chapter, a description of the data analysis is provided. This analysis determines the violation rates and violation magnitude (i.e., how far over the line each vehicle encroached) for each intersection to determine differences within and between each intersection. The analysis also considered how some factors (such as time period in a day, major or minor road, bus route) might have influenced driver behavior. Prior to the formal analysis, based the observation of the actual intersection stop line violations, the experimenter estimated that the ratio of probable violations for three levels of severity would be about 60 percent for vehicles in compliance, 25 percent for slight violations, and 15 percent for severe violations. When setting alpha to be 0.1 (mentioned in the model used for the regression part) and using only a one-tailed test, the required sample size for ordinal outcome on is in the following table [13]. Table 3-1. Table of sample size with different power value power Sample size Since only three hours of data were collected for each intersection, which means less than 180 signal cycles were recorded for each intersection (in most cases one cycle will last for more than one minute), and in some cases, there were no vehicles to be observed during a red indication throughout the cycle, the sample sizes may not be adequate to determine the statistical

26 18 significance of the results in all cases. Therefore, the descriptive data were examined in detail to determine if there were any relationships between driver behavior and some of the factors mentioned previously. Data descriptions, summarization and sieve-filtration For the regression, the dependent variable was the different severity level of stop line violation, described below, and intersection numbers, time periods, lane usage, vehicles types, major/minor road designation, and the distance from the stop line to the curb extension line were considered as potential independent variables (will be discussed in group comparison part). A data description and a summary of the data are provided in the following table: Table 3-2. Data description. variable name Lane usage time minor road distance from stop line to crosswalk /curb extension line vehicle size variable type categorical categorical categorical categorical /continuou s categorical variable value variable description l left turn only lane r right turn only lane t through only lane t+l shared through/left turn lane t+r shared through/right turn lane t+l+r shared through/left turn/right turn lane 1 7AM-9 AM 2 11AM-1PM 3 5PM-7PM 0 major road 1 minor road 1 distance less than 10 ft 2 distance from 10ft to 20ft 3 distance from 20ft to 30ft 4 distance greater than 30ft s small-sized vehicle m medium-sized vehicle l large-sized vehicle

27 19 Table 3-3. Data summarization. compliance violation severe violation total compliance violation severe violation description Time % 29% 12% AM % 26% 13% NOON % 24% 14% PM Intersection % 24% 11% Park Ave& Atherton St % 26% 11% White course Dr & Atherton St % 27% 16% Porter Rd & Park Ave % 26% 9% University Dr & Park Ave % 24% 14% Blue course Dr & Martin St % 26% 13% Beaver Ave & Allen St % 29% 7% College Ave & Atherton St % 25% 21% Curtin Rd & Atherton St % 25% 13% Garner St & Beaver Ave % 28% 16% Blue course Dr & Atherton St Lane l % 25% 16% left turn lane r % 27% 20% right turn lane t % 24% 8% through lane t_and_l % 30% 18% shared left/through lane t_and_r % 27% 14% shared right/through lane t_and_l _and_r % 36% 15% shared left/through/right lane

28 Table 3-3 continued compliance violation severe violation total compliance violation severe violation 20 description Minor road % 27% 17% minor road % 26% 11% major road distance from crosswalk/curb extension line % 24% 9% less than 10 ft % 28% 17% ft % 31% 22% ft % 34% 28% greater than 30 ft vehicle size s % 26% 14% small-sized vehicle M % 38% 2% medium-sized vehicle l % 30% 3% large-sized vehicle total % 26% 13% In the data summarization table, vehicle violations not less than 25 percent of the overall vehicle length were combined into three violation category severities, as there were not enough data in each level of violation severity for the regression. From the table, the numbers of violating vehicles for the medium-sized and large-sized categories are too small (31, 20, 1 for mediumsized vehicle and 131, 59, 5 for large-sized vehicle), therefore vehicle size was not considered as a valid factor for data analysis. The data set is also small for the shared left/through/right lane in the lane usage category; therefore, that lane usage configuration was ignored. In ordered logistic regression, each record should be listed in the table, the original Excel file had 6277 records, 6181 records after filtering the vehicle size categories and shared left/through/right category.

29 21 Model used for regression A Multinomial Logistic Regression Model is a classification method that generalizes logistic regression to multiclass problems and is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). The probabilities of Multinomial Logistic Regression are shown as follows: 1 vehicle in compliance y = { 2 violation with less than 25% of vehicle length 3 violation with at least 25% of vehicle length (1) ln Pr (y i) k = β Pr (y 1 ) 0 i,k X k Pr(y 1 ) + Pr(y 2 ) + Pr(y 3 ) = 1 (2) Where Pr (y i ) = prob(y i = i) is response probability, y i from (1), i= 2 or 3, y 1 status is set as a pivot; β i,k = vector of coefficient for factor k and outcome level i to be estimated; and X k = vector of independent variables, k is the indicator for each independent variable, X 0 is for constant variable. Ordinal Logistic Regression Model, also called an Ordered Logit Model, is a regression model for ordinal dependent variables, used as a special case of Multinomial Logistic Model. This type of model is used to see how well a response can be predicted by other factors. In this study, vehicle stop line violations have different severities, and the objective of this analysis is to find out the relationship between different violation severity levels and an intersection s characteristics. Ordinal Logistic Models are widely used in transportation research. Many studies on injury severity use this method. The model can reflect how the changes in independent variables

30 influence changes in the output; therefore, when the response needs to be characterized according to different levels, an Ordinal Logistic Model is a good choice if the regression fits the assumptions [14] : 1. The dependent variable is measured on an ordinal level; 2. One or more of the independent variables are either continuous, categorical or ordinal; 3. No multi-collinearity (i.e., two or more variables are highly correlated with each other); and 4. Proportional odds (i.e., each independent variable has an identical effect at each cumulative split of the ordinal dependent variable). As described in chapter 2, drivers stop line violations were measured at five different levels (compliance, less than 25 percent of the vehicle length, 25 to 50 percent of the vehicle length, 50 to 75 percent of the vehicle length, and greater than 75 percent of the vehicle length). Ordinal Logistic Regression was used to find the relationship between the violation and the many potential factors that could influence driver behavior. The formula of the regression and variables are explained as follows: where logit(p i ) = log ( i 1 p i 1 i 1 p i ) = α + β X i (3) p i = prob(y i = i) is response probability, y i is the i level(s) of y; α = intercept parameter; β = vector of coefficients to be estimated; and X i = vector of independent variables, and are discussed relative to the in-group comparisons for the different variables in the following sections. All the variables listed in the following steps were tested using Ordinal Logistic Regression to find which factors contributed most to the violation behaviors. Most of the factors 22

31 23 in the study are categorical variables. Variables with a p-value less than 0.10 were considered valid factors and kept in the model. Otherwise, the variable was removed from the model. Before using a model, any underlying assumptions related to that model must be tested to determine if those assumptions are true. If any of the assumptions related to Ordinal Logistic Regression fail to hold, then a Multinomial Logistic Regression could be used as an alternative analysis method. The four assumptions mentioned in previous paragraph that need to be tested are: 1. The dependent variable is measured on an ordinal level; 2. One or more of the independent variables are either continuous, categorical or ordinal; 3. No multi-collinearity (i.e., two or more variables are highly correlated with each other); and 4. Proportional odds (i.e., each independent variable has an identical effect at each cumulative split of the ordinal dependent variable). For the first two assumptions, the dependent variable, stop line violation, was recorded in an ordinal level, and all the independent variables are either categorical or continuous. For all the selected variables (time period, lane usage, minor road, and distance from stop line to crosswalk or curb extension line), time period was not related to other spatial factors; minor road has different usage lanes and different distance from stop line to crosswalk or curb extension lane, which might be correlated but not highly correlated; lane usage-left turn only lane and the distance from stop line to crosswalk or curb extension line might be highly correlated. Some approaches have both a left turn and a through only lane. The distance between left turn lane and through only lane was 7 ft to 8 ft, while the range of each unit change in distance variable is only 10 ft. Therefore, the two factors could not be in the regression at the same time, and the left turn only lane was to be removed if both would be valid in regression.

32 24 The last assumption, proportional odds, is a key assumption of ordinal regression. This assumption is that the effects of any explanatory variables are consistent across the different thresholds. In this study, with the formula (1) from Chapter 3: vehicle in compliance 1 y = { violation with less than 25% of vehicle length 2 violation with at least 25% of vehicle length 3 The logarithms of the odds can be written as: log p 1 p 2 +p 3 -vehicle in compliance log p 1+p 2 p 3 -vehicle in compliance and less than 25% of vehicle length violation (4) and the proportional odds assumption is the logarithms form an arithmetic sequence, the number of times that logarithms must be added, which is some linear combination of other dependent variables in this study. The statistic software, Stata, was used to develop the regression, which could be used to test this proportional odds assumption. Before the regression analysis was performed, the omodel logit command was used to test the proportional odds assumption of the data source to make sure Ordinal Logistic Model can be used on all categories.

33 25 Table 3-4. Table of assumption test for Ordinal Logistic Model in Stata. iteration 0 log likelihood= iteration 1 log likelihood= iteration 2 log likelihood= iteration 3 log likelihood= Ordered logit estimates Number of obs: 6181 LR chi2(10): Prob > R2: Log likelihood: Pseudo R2: severelevel Coef. Std. Err. z P> z 95% Conf. Interval T T R T L T_and_L D D D minor _cut _cut (Ancillary parameters) Approximate likelihood-ratio test of proportionality of odds across response categories: chi2(10): Prob>chi2: As can be seen in Table 3-4, the analysis yielded a chi-square (10) [with 10 degrees of freedom] result of 43.88, a probability greater than chi-square less than Given this result, the distance from the vehicle in compliance to slightly in violation (less than 25 percent of vehicle length) is not equal to the distance from slightly violation to severe violation (greater than 25 percent of vehicle length). Since Ordinal Logistic Regression could not meet the proportional odds assumption, therefore, Multinomial Logistic Regression was used.

34 Table 3-5. Table of estimation of Multinomial Logistic Model in Stata. iteration 0 log likelihood= iteration 1 log likelihood= iteration 2 log likelihood= iteration 3 log likelihood= Iteration 4 log likelihood= Multinomial logistic regression Number of obs: 6181 LR chi2(22): Prob > R2: Log likelihood: Pseudo R2: severelevel variables Coef. Std. Err. z P> z 95% Conf. Interval 1 Base outcome 2 T T R T L T_and_L D D D minor _cons T T R T L T_and_L D D D minor _cons Table 3-5 lists all variables for the Multinomial Logistic Regression, the detailed regression result will be updated in Chapter 4.

35 27 Group comparison for different variables There are many intersection factors (time, geometric design, etc.) that might influence drivers stop line behaviors. Each intersection factor that is considered in the model will be discussed in the following section, and a description table of all the factors and data summarization table are presented after the discussion. Different time period As vehicle violation data was collected during different time periods, it was thought that there might be some relationship between time of day and drivers behavior. Drivers might display different performance characteristics (e.g., level of attention/alertness, search and scan behavior) in the morning or in the afternoon, and drivers might behave differently under different traffic conditions. Drivers might be hurrying to get to work in the morning and perform more aggressively on the road. Three time periods (7:00 a.m. to 9:00 a.m., 11:00 a.m. to 1:00 p.m., and 5:00 p.m. to 7:00 p.m.), were tested as categorical factors in the model. Different usage lanes It was also theorized that different lane usage configurations might have different levels of violation as drivers might exceed the stop line frequently in a right turn lane that does not allow a right turn on red, as they usually move forward to see traffic conditions at intersections where a right turn on red is allowed. Lanes were divided into through lanes, left turn lanes, right turn lanes (only considering lanes that do not allow right turn on red), shared right/through, shared left/through, and shared left/through/right. Lane usage was also a categorical variable.

36 28 Different types of vehicles It was thought that there might be some difference in behavior by operators of oversize vehicles. For example, larger vehicle drivers should be more concerned about their vehicle size and stop in compliance more frequently than normal length vehicles. However, in the data collection, the estimated percentage of the vehicle length is used, but it would have been more accurate if the actual encroachment distance could have been measured. Vehicle types were considered as a categorical factor. Major road or minor road Drivers on the major road or the minor road of an intersection may think differently about where to stop their vehicles. For example, drivers might violate less often on the major road as there is a greater volume of traffic around them. The major or minor road was used as an indicator factor in the model. Distance from stop line to crosswalk or curb extension line If the distance from a stop line to a crosswalk is excessive, drivers might violate more often as they are very far away from the curb extension line. This distance was tested as a both a categorical and continuous variable. Some drivers might stop based on their own judgments, which might be much closer to the intersection and exceed stop lines. These results were then compared to each other. The distance was divided into four groups: less than 10 ft to the crosswalk, 10 ft to 20 ft to the crosswalk, 20 ft to 30 ft and more than 30 ft to the crosswalk. If there was no crosswalk, the distance to the curb extension line was used as the distance reference.

37 29 Chapter 4 Regression Model Results For the purposes of the model, the distance from the stop line to the curb extension line was recorded as a continuous variable and was used as a dummy variable (four distance ranges were set: less than 10 ft, 10 to 20 ft, 20 to 30 ft, 30 ft and more) in the regression. Intersection factors regression results As the distance from stop line to curb extension line can be considered as a continuous variable or transferred into dummy variables, the regression compared regressions using both scenarios. Table 4-1 shows the regression with the larger absolute of log likelihood.

38 30 Table 4-1. Results of the multinomial logit regression for intersection factors. iteration 0 log likelihood= iteration 1 log likelihood= iteration 2 log likelihood= iteration 3 log likelihood= iteration 4 log likelihood= Ordered logit estimates Number of obs 6181 LR chi2(14) Prob > R Log likelihood Pseudo R severelevel Coef. Std. Err. z P> z 95% Conf. Interval 1 (base outcome) T R T D D D minor _cons T R T D D D minor _cons From Table 4-1, the probability of each severity level can be calculated from the following formula: ln p 2 p 1 = T R T D D D minor (5) ln p 3 p 1 = T R T D D D minor (6)

39 Based on equation (5) and (6), the ratio of p 2 to p 1 and p 3 to p 1 can be calculated, and the sum of p 1, p 2, and p 3 is 1, then p 1, p 2, and p 3 will be clear. The table below shows the unit change in each category (e.g. from no right turn only lane to right turn only lane) and how the distribution of different levels of violations would respond to that unit change. For example, the percentage of each severity level in base condition in the table are calculated by setting T1, R, D1, D2, D3 and minor to 0, and S to 1 (description of each condition in the table) in equation (5) and (6) : ln p 2 p 1 = = , ln p 3 p 1 = = ). Then get the ratio between p 1, p 2, and p 3: p 2=exp( )p 1, 31 p 3=exp( )p 1, p 1:p 2:p 3=1: : , which is about 0.43:0.37:0.20. Table 4-2. Response of violation severity distribution when independent variables change. condition Base condition compliance slightly violation severe violation 43% 37% 20% description major road with through only lane and the distance from stop line to crosswalk/curb extension lane D4 not in AM T1 43% 44% 13% base with time from not AM to AM R 26% 33% 41% base with right turn lane D1 71% 23% 6% base distance change from D4 to D1 D2 63% 27% 10% base distance change from D4 to D2 D3 54% 32% 15% base distance change from D4 to D3 minor 40% 35% 25% base change from major road to minor road From the Table 4-1 and Table 4-2, the base condition is a vehicle stopping on the through only lane of a major road in the morning period, with more than 30 ft from the stop line to the crosswalk or curb extension line. Morning time (T1 with a positive coefficient for y 2) compared

40 32 to other time period (noon and P.M.), increases the percentage of slightly violations. The p-value of A.M. is for severe violations, which is too large to explain how the morning period would influence the severe violation. It seems like people drive a little bit more aggressively in the morning, but this does not have a great influence on stop line violations. For different lane usage, the right turn lane has positive coefficients for two outcomes. As mentioned in Chapter 3, drivers are more likely to move forward on a right turn lane during the red phase. As right turn on red is allowed at many intersections, many drivers will move over the stop line and wait for a chance to make a right turn. This pre-turn RTOR action might influence drivers behaviors at intersections where a right turn on red is not allowed but the right turning vehicles still overrides the stop bar. On a through only lane (with a negative coefficient for both the slight violation and severe violation outcomes), drivers are more likely to keep their vehicles behind the stop line or just on the stop line. For left turn lanes, which are not shown in the table because of a higher p-value, some stop lines for left turn lanes are set back farther than the through lane, but some are the same as the through lane. This inconsistency (i.e., potential nonuniformity) in application and appearance could influence stop line violation, but there were not enough intersections with this diverse practice to perform a formal analysis. The driver behavior in these instances might also be influenced by the variance in the distance from the stop line to the crosswalk or curb extension line. Another reason that left turn lane is not a valid factor may be that some drivers stop over the stop line waiting for a chance to make a left turn, but they cannot make the left turn during the green phase. For the mixed usage lanes, many shared left/through lanes are a mixed condition of left turn only and through only lanes, which are more complicated than left turn only lanes, therefore not on the table. Shared right/through lanes, which are more common than shared left/through lanes and might have a higher percentage of turning vehicles, are not included in the table. This may be due to the random placement at the front of the queue of a through moving vehicle. As these vehicles are more likely to comply with the stop

41 33 line requirement, a more detailed dataset with a greater variance in the mix of through and right turning vehicles would need to be collected and analyzed. Distance variables (distance from stop line to crosswalk or curb extension line): D1, D2, and D3 have negative coefficients. D1 with about and on severe level 2 and 3, which made a smaller p 2/p 1 and p 3/p 1 ratio compared to base condition D4 (distance over 30 ft). D2 with about and on severe level 2 and 3, D3 with about and on severe level 2 and 3. As the absolute value of coefficients from D1 to D2 and D2 to D3 decreased in severe level 2, which means the ratio p 2/p 1 for D1 is smaller than D2 and much smaller than D3, it is also same for severe level 3. The percentage of vehicles in compliance is the largest on D1, followed by D2, and then D3, which could be explained more directly by table 4-2. When the distance from a stop line to a crosswalk or curb extension line increases, the average violation severity level tends to go up (71, 63, 54, and 43 percent for vehicles in compliance; 23, 27, 32, and 37 percent for slight violations; and 6, 10, 15, and 20 percent for severe violations when distance increases to a higher range). This may be caused by a desire by drivers to be able to see the cross-street geometry and cross-street traffic, which could be attributable to their own safety concerns. Alternatively, on high-speed approaches, some drivers may not be using the pavement markings, which are harder to see from a distance, as a cue to place their vehicle in the lane when having to reduce speed quickly to come to a stop.

42 34 Major road Sight triangle Minor road Figure 4-1. Driver s sight view on major and minor road. Vehicles on minor roads with the coefficient of on severe level 3, which means the ratio p 3/p 1 will slightly increase compared to other factors. The coefficient of minor road for severe level 2 is , it is really small (less than 10 percent of coefficients of other variables) and with a higher p-value (0.661), therefore, there were no obvious relationship between minor roads and slightly violations. Many drivers behave more aggressively on these narrower roads than on the wider streets, especially when the minor roads have lower traffic volumes in relation to RTOR and other behaviors. Also, from Figure 4-1, since major road crosssections are wider than those for the minor roads, even though both the major and minor roads have the same offset distance from the stop line to a crosswalk, drivers might still have difficulty placing their vehicle given their approach speed, as described above, or their ability to divide their attention when placing their vehicle at the intersection given the many different decisions they are making as they approach an intersection. Therefore, drivers might need to exceed the stop line much more to get a better sight view and make a decision.

43 35 Chapter 5 Conclusions The regression results show that intersections have different levels of average violation severities, which can be explained by multiple intersection factors. The distance from the stop line to the crosswalk or curb extension line and lane usage are the most influential followed by whether the driver is on a major or minor road. Morning periods see an increase in slight violations, but there are no differences for the other time periods regarding stop line violations. For a single use lane, right turn only are the lanes that have the most severe average violation level as most drivers cross onto or pass the stop line when they stop at a red signal. Left turn only lanes have more situationally-based variance depending on operational issues (e.g., signal phasing and timing, opposing vehicle volumes): vehicles are in compliance, stop on or over the stop line, or fail to make a turn during a green signal and get caught in a non-compliant position, which makes it hard to predict different results regarding stop line violation. The results are more complicated for shared usage lanes. Shared through/left/right turn lanes are the most complex, then shared through/right turn lanes and shared through/left lanes, as the first arriving vehicle making up the queue will be influenced by what that vehicle s post signal release maneuver will be. Major or minor roads have some effects on drivers stop line violations, but not that much when compared to the lane usage effects discussed above. So it is important to consider sight lines, sight distances, and stop line distances for right turn only lanes and some shared lanes to ensure that the majority of the vehicles maintain a compliant (i.e., safe) distance to the intersection. For minor roads, stopping sight distance values in excess of the minimum may have some effects on reducing high severity level violations.

44 36 From the Table 4-2, if the distance from the stop line to the crosswalk or curb extension line is less than 10 ft (D1), 71 percent of the vehicles were in compliance and 23 percent had slight violations. For distance from 10 ft to 20 ft (D2), the percentage will be 63 percent for vehicle in compliance and 27 percent for slightly violations. Given a small vehicle with a length of about 15 ft, for which a 25 percent of that length is about 3.75 ft, 50 percent of vehicle length would be 7.5 ft, this would mean that if the distance from the stop line to crosswalk or curb extension line were increased to 10 ft, it would cause an eight percent decline in vehicle compliance and a four percent increase in slight violations, which is worse on the total percentage of vehicle in compliance and with slightly violations. However, 25 percent of vehicle length (3.75 ft) or even 50 percent of vehicle length (7.5ft) is much shorter than 10 ft, meaning that the majority of vehicles would have enough stop distance to the intersection. It might be helpful to set stop lines 10 to 20 ft instead of less than 10 ft behind crosswalks or curb extension lines to avoid most vehicles violating the stopping operational criteria. Since the data were collected by a single observer recording behaviors by sight view, the study results are limited in terms of precision and sample size. In future work, more factors could be analyzed with a larger sample size and more precise methods. For the intersections used in this study, spatial factors are much more related to stop line violations than the other factors studied, which could provide some guidance for road designers.

45 37 Appendix A Selected intersection map views Appendix A provides satellite map views of ten selected intersections with street names and the location where observer the observer stood to record driver behavior information. This is denoted by the red dot on each map, the map view is directly from Google Maps with north being the top of the map. The following is each satellite map view of each intersection: 1. Park Avenue and Atherton Street

46 2. White Course Drive and Atherton Street 38

47 3. Porter Road and Park Avenue 39

48 4. University Drive and Park Avenue 40

49 5. Martin St and Blue Course Drive 41

50 6. Beaver Avenue and Allan Street 42

51 7. College Avenue and Atherton Street 43

52 8. Curtin Road and Atherton Street 44

53 9. Garner Street and Beaver Avenue 45

54 10. Blue Course Drive and Atherton Street 46