Driver Behavior on Exit Freeway Ramp Terminals Based on the Naturalistic Driving Study

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Driver Behavior on Exit Freeway Ramp Terminals Based on the Naturalistic Driving Study

Mohannad Alyamani¹ and Yasser Hassan²

Abstract:Using trip data from the SHRP-2 Naturalistic Driving Study (NDS) database collected at 12 sites in three states across the United States, this paper investigates driver behavior at freeway exit ramp terminals. First, the study qualitatively assesses driver speed behavior as they navigate the speed change lane (SCL) and the ramp. Starting at the beginning of the SCL and continuing after diverging onto the ramp controlling curve, a trend of continuous vehicle deceleration was evident, which continued throughout the SCL and ramp. It was also evident that a portion of drivers have a tendency to diverge onto the SCL on the taper and before the SCL has begun, where this behavior is dominant on the taper-type SCL. In general, statistical analysis revealed that the speed measures of driver behavior follow a normal distribution. The speed and deceleration measures at the study sites were statistically and significantly different, with the differences likely related to the geometric characteristics of each site. The data were then used to develop prediction models for the speed and deceleration measures.

To account for the repeated measures induced by the same drivers in the dataset, linear-mixed models were developed for the speed and deceleration behavior measures.DOI:10.1061/JTEPBS.TEENG-7227.© 2022 American Society of Civil Engineers.

Author keywords: Freeway exit ramp terminal; Deceleration lane; Speed change lane (SCL); Driver behavior; Naturalistic Driving Study (NDS).

Introduction

Freeway interchanges, which are grade-separated intersections, are the only locations in freeways providing drivers with entrance and exit opportunities. Typically, interchanges are designed with ramps and speed change lanes (SCLs) to allow drivers entering/exiting a freeway to complete the merging/diverging maneuver without interrupting the freeway mainline traffic flow. Adequate design of ramp terminals is important to ensure that drivers merge onto or diverge off a freeway safely, efficiently, and conveniently. On the other hand, inadequate geometries of SCLs result in safety and operation problems such as conflicts or collisions between ramp and mainline traffic vehicles.

A review of the literature shows that the safety performance at interchange segments is a concern to highway engineers and agen- cies. A study by McCartt et al. (2004) indicated that around 18% of all US Interstate collisions, 17% of injury collisions, and 11% of fatal collisions in 2001 occurred at interchanges, although these segments account for less than 5% of total freeway mileage. Torbic et al. (2009) also analyzed data from the Fatality Analysis Report- ing System (FARS) and estimated that interchange-related fatal crashes constitute 21.8% of all US freeway-related fatal crashes.

Research on the design elements of interchange ramps has indicated that the design values of acceleration and deceleration SCLs

recommended in current North American’s design guides, which are the Green Book by the American Association of State Highway and Transportation Officials (AASHTO 2018) and the Canadian design guide by the Transportation Association of Canada (TAC 2017), are still mainly based on acceleration and deceleration characteristics of 1940-era passenger vehicles (Hassan et al. 2012).

As characteristics of today’s drivers and vehicles are different from those vehicles, questions have been raised about the appli- cability of the current recommended design values (Fitzpatrick and Zimmerman 2007). Another concern is that the design criteria used by AASHTO (2018) and TAC (2017) to determine the geometry of SCLs are still based on laws of kinematics and assumptions re- garding freeway and ramp operation speeds (Hassan et al. 2012).

Fitzpatrick et al. (2012) compared the lengths recommended in different editions of the AASHTO publications for the deceleration SCL and found that the lengths recommended in the 2004 edition of the Green Book which remained unchanged in the 2018 edition, are similar to those published in 1965. It was argued that the data for these parameters should be updated because it was collected in the 1930s (Fitzpatrick et al. 2012).

Literature Review

Many studies have been conducted on SCL safety and operation.

Cirillo (1970), for example, looked into the relationship between collisions and SCL length. The number of collisions on the SCL was shown to decrease as the length of the SCL increased. Bared et al. (1999) and Sharan et al. (2008) found similar results in their safety prediction models. El-Basha et al. (2007) collected speed profile data on deceleration SCLs and showed that the magnitude of speed differential between diverging and FRL vehicles depends on factors including SCL length. Brewer et al. (2011) used data collected by an instrumented vehicle to evaluate driver behavior measures on freeway ramps and SCLs including speed, acceleration, deceleration, use of throttle and brakes, and glancing. They concluded that the recommended SCL lengths at exit ramps in

1Lecturer, Dept. of Civil Engineering, Collage of Engineering and Islamic Architecture, Umm Al-Qura Univ., Makkah 24382, Saudi Arabia (corresponding author). ORCID: https://orcid.org/0000-0002-7762-1003.

Email: [email protected]

2Professor and Chair, Dept. of Civil and Environmental Engineering, Carleton Univ., 1125 Colonel By Dr., Ottawa, ON, Canada K2C 0R2.

ORCID: https://orcid.org/0000-0003-0135-1905. Email: yasser.hassan@

carleton.ca

Note. This manuscript was submitted on December 20, 2021; approved on August 31, 2022; published online on October 29, 2022. Discussion period open until March 29, 2023; separate discussions must be submitted for individual papers. This paper is part of theJournal of Transportation Engineering, Part A: Systems, © ASCE, ISSN 2473-2907.

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the Green Book were too short for the subject drivers in this experi- ment. On the other hand, Torbic et al. (2012) conducted a three- phase study involving crash analysis, observational field study, and driver behavioral study and concluded that the recommended minimum deceleration SCL in the 2004 Green Book were conservative. Chen et al. (2014) considered the impact of deceleration SCL length on traffic safety performance and operation. According to the results of the safety and operational analyses in this study, for one-lane exits, the minimum SCL length required for a design speed of 88.5km=h (55mi=h) is 152.4 m, while the minimum length required for design speeds of 96.5 and 104.6km=h (60 and 65mi=h, respectively) is 182.9 m. Clavi et al. (2015) found that the terminal geometry (i.e., type, width, and length) has an impact on the facility’s operational and safety performance. It was also shown that the choice of whether to design a tapered or parallel SCL had a significant impact on diverging drivers’speeds, with each SCL type producing a different level of interference with through traffic. Proterra and Bassani (2021) used driving simulation to examine driver behavior on exit terminals on horizontal curves.

The study showed that curve radius affects drivers’speeds at the beginning of the taper and at the diverging point and affects lateral vehicle control. Driver behavior was also impacted by the direction of the curve connecting the SCL and ramp.

Abdelnaby and Hassan (2014) argued that design of exit ramps must explicitly account for the expected safety performance resulting from the design decisions. Therefore, reliability analysis was utilized to develop a probabilistic, safety-explicit design approach that relates the different geometric and traffic conditions at a site to the expected safety performance based on a surrogate safety measure referred to as probability of non-compliance (PNC). However, due to data limitations, the study made assumptions related to drivers’diverging behavior. For example, as noted by Alarm and Hassan (2022), most existing research on driver behavior at freeway ramps had observed drivers from the moment they merged onto or diverged off a freeway to the moment they reached the ramp gore nose. While the study showed a significant relationship between PNC and actual safety performance, the identified data limitations highlighted the need for better driver behavior models.

Therefore, understanding and modeling driver merging and diverging behavior, and the impact of ramp and SCL geometry on this behavior, is a critical first step in validating current design recom- mendations or updating them to meet drivers’ expectations and needs, and in turn, ensure safe and comfortable freeway merging and diverging operations.

The major reason for the lack of complete data on drivers’ speeds and behavior at freeway ramp terminals is associated with limitations of traditional traffic data collection equipment. Laser guns are prone to erroneous conclusions due to bias, such as the cosine error. In addition, laser guns cannot track more than one vehicle at the same time or track the same vehicle over the entire length of the ramp and SCL. Fixed cameras also cannot cover long road segments unless they are deployed atop high structures such as neighboring buildings (Alamry and Hassan 2022). Furthermore, field data collected by laser guns and fixed cameras can be labor- intensive, time-consuming, and costly, particularly when comprehensive data are needed to be collected at several different locations and/or over a long time period.

Using data from the Strategic Highway Research Program 2 (SHRP-2) Naturalistic Driving Study (NDS) is an alternative approach to investigating driver behavior, especially over long and high-speed segments, such as the freeway ramp and SCL.

The NDS used inconspicuous data gathering equipment with no experimental control to generate detailed logs of all trips of more than 3,100 volunteer drivers for three years in six states in the USA:

Florida, Indiana, North Carolina, New York, Pennsylvania, and Washington (Xu et al. 2019). Based on such a large sample of par- ticipants for a long period without human intervention, the NDS has amassed considerable data about driving behaviors, thus providing more realistic data than traditional data collection techniques (Campbell 2012; Dingus et al. 2015). Recently, NDS data have gained significant interest among researchers to investigate driver behavior on ramp terminals. For example, researchers used NDS data in modeling the speed behavior on deceleration SCL (Xu et al. 2019) and in assessing the relationship between ramp design speed and drivers’ operating speed (Brewer and Stibbe 2019).

However, a review of the literature reveals that there has not been a study that comprehensively assesses all driver behavior measures at freeway ramp terminals. Thus, the authors first used NDS data to examine and model driver behavior at freeway entrance ramp terminals (Alyamani and Hassan 2021). This paper complements this latter study by extending the analysis and modeling to freeway exit ramp terminals.

Study Objectives

The main objective of this paper is to utilize the NDS data to investigate driver behavior at freeway exit ramp terminals, including ramp controlling curves (which will be referred to as ramp curve) and SCLs. Another objective of this research is to build a database that can be used to develop appropriate models for driver behavior measures on exit ramp terminals. As mentioned earlier, this is a missing critical first step in the implementation of reliability analysis for probabilistic, safety-explicit road design that can take advan- tage of these models. It is noted that this study is limited to freeway exit ramp terminals with single lane SCL.

Data Collection and Processing

To achieve this paper’s objectives, a research methodology was developed and consists of four phases: site selection and data collection, data processing, qualitative evaluation of driver behavior, and quantitative analysis and modeling of driver behavior measures.

Site Selection and Data Collection

The availability of NDS data was the primary criterion for the selection of study sites for this study. To make the results as general as possible, sites in all six states covered by the NDS data were ex- amined. The numbers of drivers and trips available at each potential site were checked to ensure a relatively large and representative sample size on the ramp and the freeway mainline after screening out the trips that are unusable or correspond to unfavorable weather or traffic conditions. As a result, before accessing the actual trips, the initial screening of available sites in the planning phase relied solely on publicly available data on the total number of trips and unique drivers at each link in the NDS study. Subsequently, 12 exit ramp terminals in three states (Florida, Indiana, and New York) were selected. These 12 sites were made of four sites on I-275 (Tampa, Florida), two sites on I-69 (Bloomington, Indiana), and six sites on I-290 (Buffalo, New York). To maintain a reasonable acquisition cost of acquiring NDS data, a site was only included in the dataset if the records showed at least 80 trips were available at the site with at least 25 unique (different) drivers.

Except for one site, all of these criteria were met at the selected sites.

The required data were collected from multiple sources to create a dataset to analyze and model driver behavior at ramp terminals.

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First, detailed logs of the NDS trip data at the selected sites were the main dataset. This dataset, acquired from the Virginia Tech Transportation Institute (VTTI), included anonymized driver dem- ographic data (participant ID, vehicle ID, gender, age group, and education level) and time series file for each trip on the selected sites. The total number of trips acquired was 2,991 and were made by 1,041 unique (different) drivers. After excluding those trips that did not include essential information such as speed or GPS data, the final dataset of exit trips was comprised of 1,054 trips made by 639 unique drivers. Fig.1 presents the frequency distributions of the drivers’demographics for all exit trips and the unique drivers (excluding duplicates). Fig.S1 summarizes the number of trips and unique drivers on each study site in the Supplemental Materials.

Detailed instantaneous data collected from the vehicle’s data acquisition system were provided in a time series csv-file for each trip. The data included vehicle speed, lateral and longitudinal acceleration, GPS coordinates (longitude and latitude), another set of speed based on GPS, brake and gas pedal positions, the vehicle’s lateral lane position, and distance headway to front vehicles. All data records were provided at 0.1 s frequency except for the GPS data, which were provided at 1.0 s frequency. Finally, video logs of the front and rear views were also acquired. It should be noted that the absolute trip time was not shared for privacy reasons but only the trip date was provided. As a result, VTTI provided, at

the authors’request, two time-codes for each trip. The first code divided each day into four bins depending on whether the trip was performed during the daytime, nighttime, day-to-night transition, or night-to-day transition. The second code divided each day to eight 3-h time-bins with bins 2 and 5 corresponding to the morn- ing (6:00–9:00 AM) and afternoon (3:00–6:00 PM) peak traffic periods, respectively.

Traffic volume data on the study sites were extracted from the Roadway Information Database (RID) available from Iowa State University. Due to incomplete records for all study sites, attempts to extract the geometric design data from RID were unsuccessful.

For consistency, all geometric data for all study sites were collected from Google Maps and Google Earth. Table 1 summarizes the geometric data collected for the SCL, ramp, and freeway. In this table, the deceleration SCL length is measured from the end of taper (parallel-type) or to the point where pavement width is 3.6 m (taper-type) to the beginning of ramp curve as demonstrated in Fig.S2in the Supplemental Materials. It should be noted that it was attempted to cover different geometric characteristics of exit ramp terminals while balancing binary parameters such as SCL type. As shown in Table1, the final site selection that was dictated by NDS data availability allowed covering a wide range of ramp curve radius and SCL length but was not well balanced in terms of SCL type, ramp type, or posted speed limit.

Fig. 1.Frequency distribution of driver demographics on selected study sites.

Table 1.Geometric and traffic data of selected study sites

Site

SCL Ramp Freeway

Type LS Type AADT R LRC GR VL AADT GH

1 P 496.7 D 5,400 28.6 85.0 1.2 104.6 140,500 1.0

2 T 160.0 D 6,500 220.5 387.0 2.1 104.6 132,125 −0.6

3 T 250.2 D 3,975 25.4 40.3 −0.9 88.5 149,500 −1.2

4 P 215.7 D 6,923 505.2 512.6 −0.5 88.5 139,750 −2.0

5 P 148.5 OC 6,232 422.0 415.0 2.0 88.5 31,581 −1.6

6 P 259.6 OC 1,169 448.9 479.9 −1.2 88.5 18,255 0.6

7 P 200.8 OC 8,549 220.8 500.0 1.1 88.5 118,826 3.1

8 P 208.1 OC 8,924 226.3 596.8 −1.2 88.5 126,827 1.0

9 P 207.5 OC 8,973 223.0 497.9 0.4 88.5 126,827 0.5

10 P 141.1 OC 2,982 92.1 458.4 0.0 88.5 108,408 2.1

11 P 64.9 D 9,109 202.8 378.3 −1.8 88.5 93,653 −1.2

12 P 205.3 OC 4,862 250.2 577.1 0.3 88.5 93,653 0.8

Note:LSandLRC= length of SCL and ramp curve, respectively (m);GRandGH= average grade along the ramp curve and along of freeway lanes including SCL, respectively (%), which were estimated using the elevations of the beginning and end of the section of interest obtained using the elevation tool in Google Earth; AADT = average annual daily traffic (veh=d);R= radius of ramp controlling curve (m);V_L= posted speed limit on the freeway (km=h); P and T = parallel and taper SCL type, respectively; and D and OC = diagonal and outer connection, respectively.

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Data Processing

As mentioned earlier, this paper uses 1,054 trips on freeway exits made by 639 unique drivers on 12 different exit ramp terminal sites.

Using Google Earth, the coordinates of the main points (beginning and end of SCL, and beginning, middle, and end of ramp curve) were determined at each site as demonstrated in Fig. S2 in the Supplemental Materials. A Python script was created to open each csv file corresponding to a trip in the dataset and match these coordinates with the GPS coordinates in the file to determine the time stamp in each trip where the vehicle was at each of these points.

Because speed data were available every 0.1 s while GPS data were available every 1.0 s, the time stamps for these vehicle locations were found by first gathering the closest GPS data record then in- terpolating based on vehicle speed. At the end of this step, the locations marked for each trip on an exit ramp were the beginning of SCL, end of SCL, which coincides with the beginning of ramp curve, middle of ramp curve, and end of ramp curve. All trips at each site were compiled in one Excel file with one worksheet corresponding to the speed profile of each trip along the ramp and SCL.

Another important point for each trip is the diverge point, which is defined here as the point at which the right-front corner of the vehicle starts to cross the lane marking between SCL and freeway right lane (FRL). The diverge point time stamp was found manually by cross-referencing the time stamp in the video logs and csv files.

Subsequently, the speeds at the diverge point, beginning, middle, and end of the ramp curve were extracted for each trip and compiled in one file. The distance traveled over the SCL from the diverge point to the end of the SCL (referred to as deceleration distance) was also extracted for each trip. Finally, knowing the speed at the diverge point and the end of SCL (which is the same as the beginning of the ramp curve) and the deceleration distance, the average deceleration rate along the SCL was computed. It should be noted that regardless of whether the change of speed is referred to as acceleration or deceleration, the negative and positive signs are used in this paper to correspond to slowing down and speeding up, respectively.

Qualitative Assessment

General Speed Behavior

Based on the entire trip trajectory over the SCL and ramp of the study sites, the driver speed behavior was qualitatively assessed.

A MATLAB script was created to read the Excel file for each site, calculate the distance between each two successive points with known latitude and longitude in each trip, sum these distances to determine the total distance for each timestamp in each trip from a specific reference point, and plot all speed and deceleration profiles against the total travel distance from the reference point at each site. The reference point for all trips was taken 50 m before the taper to capture whether the trip started diverging on the taper or on the SCL. This point was set upstream the taper to capture all points on the SCL and ramp for each trip. The exiting vehicle speeds at this reference point were compared to the speeds at a longer distance upstream the taper (200 m) using pairedt-test. The results indicated that the null hypothesis that speeds are equal at the 50 and 200 m points should not be rejected at 5% level of significance on most sites. Moreover, only one site with a statistically significant difference of speed between the two points had a mean speed difference between the two points just over2.00km=h. It should be noted that the analysis in this section uses the GPS speed at 1.0 s frequency because the latitude and longitude were available at this

same frequency and to avoid the very high accelerations or decel- erations that appear when using speed measurements at 0.1 s frequency.

Fig.2shows an example of speed and deceleration profiles at one exit site, which is Site 2 in Table1. Again, the figure shows the main points at the site (beginning of taper, beginning of SCL, beginning of ramp, and end of ramp) as vertical lines. In addition, the diverge point is marked as a circle in the speed profile for each trip.

For clarity, only 15 trips are shown in the figure out of 97 available trips at Site 2. The figure shows the general trend of driver speed behavior at exit sites as the vehicle moves along the FRL, SCL, and ramp. Some vehicles initially start deceleration on the FRL, as evidenced in the negative accelerations before the diverge point.

The deceleration increases almost at a linear rate as the vehicle pro- gresses on the SCL and ramp. As the vehicle approaches the end of the ramp, where the speed drops to zero for most trips due to traffic control, both the deceleration and rate of increasing deceleration become higher. It is noted also that some trips in the figure had relatively low initial speeds on the FRL, and drivers in such trips may increase their speed on the SCL. This behavior was investi- gated and can be attributed to different reasons related to traffic congestion, weather conditions, and diverging from an inner lane.

The general deceleration behavior in Fig.2can be divided into three regions. The first region starts on the FRL, where drivers decelerate at a relatively low rate. This region extends to a point close to the end of SCL, where the second region starts, and drivers adopt increasingly higher deceleration rates. The third region is close to the end of the ramp where drivers have to decelerate at much higher rates, as they have to slow down significantly or stop due to traffic control. These regions can be seen in the distinct linear regression trend lines drawn for the speed profiles of each trip shown in Fig. 3. The trend of drivers decelerating at an initial low rate followed by a higher one is consistent with the assumption used by AASHTO in calculating the length of deceleration SCL (Fitzpatrick et al. 2012). However, the drivers in this study used Fig. 2.Example of speed and deceleration profiles at exit Site 2.

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the low rate on the whole length of SCL on 11 sites out of a total of 12 sites. This may be due to the geometry of the sites where the ramps are mostly straight or have flat curves. This indicates that the assumption of using two different deceleration rates in calculating SCL is not valid for most sites in this study, where one rate of deceleration better fits the data. This finding is consistent with what has been reported by Brewer et al. (2011) who showed that the AASHTO assumption of initial 3-s coasting on deceleration SCL was not valid. However, this paper did not study whether the adopted deceleration on the SCL involved application of brakes or only releasing the throttle.

Deceleration Distance and Diverge Location

Among the driver behavior measures extracted for each trip is the deceleration distance, which is then used to calculate a normalized deceleration distance (LDec;N) as the distance from the diverge point to the end of SCL divided by SCL length. The measure readily indicates the location of the diverge point where a value of LDec;N >1.0indicates that the driver of this trip started the diverging maneuver by changing lane from FRL to taper before reaching the SCL. Otherwise, the driver would have performed the diverging maneuver on the SCL. Fig.4shows the frequency distribution of LDec;N for all trips in this study. As shown in the figure, a considerable portion (54.3%) of the trips showed early diverging that took place on the taper (LDec;N >1.0). Some differences can be noted when splitting the analyses by SCL type and traffic condition such as the histograms in parts (b) to (e). Specifically, for taper SCL, 52.5% and 64.1% of the trips had the diverge point on the taper during peak and off-peak traffic conditions, respectively, while the corresponding percentages for parallel SCL were 56.6% and 51%. This finding seems consistent with what was reported by Torbic et al. (2012) although a higher percentage was reported in the latter study to have diverged on the taper.

Quantitative Analysis

Descriptive Statistics

Different driver speed behavior measures were built into an analysis dataset in this paper considering the continuous change of speed along the SCL and ramp curve. These measures include diverge speed (VD), speed at beginning of ramp curve (VBRC) which is the same as the speed at the end of SCL, speed at middle of ramp curve (VMRC), speed at end of ramp curve (VERC). Additional

measures related to the diverging behavior are the normalized deceleration distance (LDec;N), average deceleration from diverge point to the end of SCL (d). Table 2 summarizes the descriptive statistics of all these measures.

As shown in the table, all speed measures on the one taper SCL site with88.50km=h (55mi=h) posted speed limit are lower than the corresponding measures on parallel SCL sites during off and on-peak conditions. For this posted speed limit also, drivers on the taper SCL site utilized a much higher deceleration than the parallel SCL sites. A possible reason for this behavior on this taper SCL is the sharp ramp curve and short ramp corresponding to Site 3 as shown in Table1. In contrast, an opposite trend for most speed measures can be observed on the sites with104.59km=h (65mi=h) posted speed limit. Also, close values of the mean and median deceleration are observed on the taper and parallel SCL sites under this speed limit. The table also shows that drivers mostly utilized the full length of the deceleration SCL, with the meanLDec;Nvery close to 1.0 and the median value exceeding 1.0 in most cases. The lowest utilization of SCL length was in the case of parallel SCL and posted speed limit of104.59km=h (65mi=h), in which case most drivers still utilized over 90% of the SCL length during both off and on-peak traffic conditions. It should be noted that although the taper SCL at this posted speed limit is shorter than the one at88.50km=h (55mi=h) posted speed limit, it has a much longer ramp curve with flatter radius. This may indicate that the perception of short and ramp curve had a higher impact on driver behavior than the SCL length.

Equality of Variance and Mean

As shown in Table2, some differences expectedly exist in the mean and standard deviations of each driver behavior measure depending on traffic condition and SCL type. To examine the significance of these differences, one-way Analysis of Variance (ANOVA) in SPSS was used to test the hypotheses related to equality of variance and equality of mean. For equality of variance, the null hypothesis that samples being tested have an equal variance was tested using Levene statistic. For equality of mean, the null hypothesis that samples being tested have an equal mean was tested in ANOVA using the F-statistics. The level of significance used in all tests was 5%.

First, the effect of traffic condition was tested by setting a null hypothesis that on- and off-peak conditions at each exit site have equal variance and mean of each measure. As shown in Table3, the Levene test showed that the null hypothesis of equality of variance should not be rejected for most sites, with the biggest potential dis- crepancy corresponding toVD, where the null hypothesis was not rejected for seven sites (out of 12). For the remaining measures, the number of sites where the null hypothesis should not be rejected ranged from 12 (forVMRC) to 9 (forVBRC). Similarly, ANOVA results, also summarized in Table3, indicated that the null hypothesis should not be rejected for a number of sites ranging from 11 (for VMRC) to 10 (ford). ForVD, where the effect of traffic conditions is expected to be most pronounced, the null hypothesis was not rejected on eight sites. Thus, similar to the findings of Alyamani and Hassan (2021) for entrance sites, it is concluded that all measures on these specific exit sites in this study had the same variance and mean for on and off-peak traffic conditions.

Second, the individual sites were compared to test the significance of the differences of the mean and variance by location. Both null hypotheses related to equality of variance and mean on all 12 exit sites should be rejected whether the analysis covered all data combined or whether the data were split by traffic conditions.

Similar conclusions were reached when the data were split by speed Fig. 3.Example of linear regression trends of speed profiles at exit

Site 2.

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limit or by SCL type, i.e., comparing only sites that have the same speed limit or same SCL type, respectively. As a result, there is strong evidence that the speed and deceleration measures have different means and variances on the study sites. These differences are not explained by traffic condition, speed limit, or SCL type alone.

Modeling Driver Behavior Measures

Modeling Approach and Variables

According to the findings of the previous section, the obvious differences in speed limit and SCL type between the different sites cannot fully explain the differences between the means and

variances at the different sites. It is more likely that this disparity is the result of the geometric characteristics of the study sites when taken together. As a result, the next step in the analysis was to model the relationship between these driver behavior measures and the geometric features. The assumption of independence of the observations, which is required for regular linear regression, is not valid because the trips collected in this study involve duplicate or repeated trips by many drivers including repeated trips at the same site. As a result, the repeated-measures approach was followed to develop linear mixed-effects (LME) models that account for the correlation of repeated observations (Wu 2009). Generally, a LME model includes a fixed-effects portion that quantifies the effects of the different independent variables, and a random-effects portion that accounts for the potential that different subjects would (a)

(b) (c)

(d) (e)

Fig. 4.(a) Histograms of normalized deceleration distance: All trips; (b) histograms of normalized deceleration distance: On-peak; taper SCL;

(c) histograms of normalized deceleration distance: On-peak; parallel SCL; (d) histograms of normalized deceleration distance: Off-peak; taper SCL; and (e) histograms of normalized deceleration distance: Off-peak; parallel SCL.

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have different regression constants and/or slopes of one or more independent variable. The analysis performed in this paper utilizes the linear mixed model option in SPSS. The first set of models cov- ers the speed profiles on ramp curve (VRC) and SCL from diverge point (VSCL). In addition, models are developed for the instantaneous speed parametersVBRC,VMRC,VERC, andVDand the deceleration parametersLDec;N andd.

The independent variables considered in developing the models are shown in Table4. Traffic volume (AADT) was not taken as an independent variable given that there was no statistically significant difference in the mean value of the driver behavior measures during on and off-peak traffic. More variables were initially included to account for the driver gender and site state (Florida, Indiana, or New York). However, these variables were subsequently removed from all models either because they were insignificant or because they did not improve the quality of any model.

Each model was developed by randomly selecting only 85% of the input records, with the remaining 15% being kept for model Table 2.Summary descriptive statistics at study sites

VL SCL Type On/off Peak Statistic VD VBRC VMRC VERC L_Dec;N d

All Data μ 88.14 77.85 67.25 41.69 0.98 −0.37

Median 89.34 79.47 68.72 37.48 1.02 −0.32

σ 12.82 14.86 15.04 22.43 0.26 0.66

88.50 Taper Off-peak μ 80.63 49.53 39.14 21.91 1.04 −0.70

Median 81.07 48.99 38.62 19.74 1.05 −0.72

σ 9.71 10.39 12.28 13.07 0.06 0.26

On-peak μ 73.27 45.44 35.74 22.01 1.06 −0.60

Median 75.69 42.49 33.74 23.79 1.04 −0.65

σ 17.60 10.46 11.47 12.58 0.11 0.38

Parallel Off-peak μ 88.89 80.55 70.67 46.41 0.96 −0.41

Median 89.03 80.02 69.72 41.65 1.02 −0.31

σ 9.55 10.13 11.29 22.67 0.28 0.81

On-peak μ 83.95 79.23 70.20 43.68 1.01 −0.19

Median 88.38 80.85 70.11 40.28 1.06 −0.23

σ 17.08 13.04 12.75 22.51 0.29 0.43

104.59 Taper Off-peak μ 98.99 92.13 74.31 27.68 0.98 −0.30

Median 97.45 92.66 75.31 27.99 1.00 −0.32

σ 8.90 8.60 8.47 13.66 0.11 0.33

On-peak μ 97.95 91.02 73.30 27.27 0.99 −0.32

Median 96.87 91.26 74.44 32.83 0.99 −0.29

σ 8.02 7.12 8.61 12.87 0.08 0.22

Parallel Off-peak μ 96.33 66.99 55.04 32.16 0.90 −0.39

Median 97.99 68.43 53.31 31.17 0.95 −0.41

σ 12.78 14.48 12.57 11.85 0.13 0.22

On-peak μ 93.38 71.05 53.78 28.04 0.90 −0.32

Median 92.68 72.18 54.07 26.03 0.94 −0.34

σ 12.59 7.50 9.24 7.39 0.10 0.22

Note:VL= posted speed limit on the freeway (km=h);VBRC= speed at beginning of ramp curve which is also end of SCL (km=h);VMRC= speed at middle of ramp curve (km=h);VERC= speed at end of ramp curve;VD= diverge speed (km=h);L_Dec;N= normalized deceleration distance = distance traveled on SCL divided by SCL length;d= average deceleration from diverge point to end of SCL (m=s²);μ= mean value; andσ= standard deviation.

Table 3. Equality of variance and mean: number of sites with equal variance or mean during on and off-peak conditions

Measure Equality of variance Equality of mean

VBRC 11 9

VMRC 12 11

VERC 12 10

VD 7 8

L_Dec;N 11 11

d 10 10

Table 4.Summary of independent variables

Variable Description

VD Diverging speed (km=h)

LS SCL length (m): as mentioned earlier,LSis measured from the end of taper (parallel-type) or from the point where pavement width is 3.6 m (taper-type) to the beginning of ramp curve

LST SCL and taper length (m): combined length of SCL and taper

LT Taper length (m): length of taper at the beginning of SCL L_Dec;N Normalized deceleration: this variable is one of the driver behavior measures modeled as a dependent variable and is also used as independent variable in predictingVDandd SCLT SCL type: binary variable for the type of SCL: 0 = taper-

type and 1 = parallel-type

RampT Ramp type: binary variable for the type of ramp: 0 = diagonal-type and 1 = outer connection-type

V_L;C Speed limit code: binary variable for posted speed limit on the freeway: 0 is equivalent to88.5km=h (55mi=h) and 1 is equivalent to104.59km=h (65mi=h)

GH Grade along the main freeway lanes GR Grade along the ramp curve LRC Length of ramp curve (m) R Radius of ramp curve (m)

L_R;N Normalized travel distance on ramp curve: used in modeling speed profile on ramp curve (VRC); calculated as the distance from the beginning of ramp curve to the current point of the vehicle on the ramp divided byLRC

D_R;N Normalized travel distance on SCL: used in modeling speed profile on SCL (VSCL); calculated as the distance traveled from the diverge point to the end of SCL divided byLS

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testing. All relevant parameters were considered with random effects considered for the regression constant only. Independent variables that were insignificant at 5% level of significance were checked one-by-one for the potential of contributing to random effects and were removed if they were still insignificant. When a model with all significant independent variables is reached, the model was checked to assess whether including each variable in random effects would improve the quality of the model based on the values of Akaike’s Information Criterion (AIC) and Schwarz’s Bayesian Criterion (BIC). Generally, lower AIC and BIC values imply a better model. Finally, the contribution of each variable in the model was checked by removing them one-by-one and check- ing the quality of the model. If a significant variable can be removed without degrading the model quality (based on AIC and BIC), the variable was kept out of the model.

Using the 15% sample that was not included in the modeling process, the models were tested as the final step in evaluating their performance and accuracy. Model testing involved applying the fixed-effects equation in each model to predict the dependent variable and calculating the root mean square error (RMSE) as follows:

RMSE¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PðO_i−P_iÞ²

n r

ð1Þ

whereOiis the observed value of the dependent variable;Piis the predicted value; and n is the number of records in the testing sample.

Developed Models

Table5summarizes the final recommended models for the speed profilesVSCLandVRCand for the driver behavior measuresVBRC, VMRC,VERC,VD,LDec;N, andd, using the data for on and off-peak traffic combined. It is noted that splitting the data records to off- and on-peak traffic did not yield better models based on the values of RMSE, which is consistent with previous findings based on ANOVA where no significant differences were found between the driver behavior measures for peak and off-peak conditions.

Generally, accounting for one independent variable in random effects (referred to in the table as random-effects slope) improves the model quality for all models except forVBRC,VMRC, andd. In the case ofVSCL, the independent variable included in random effects wasDR;N. On the other hand,LRCandLTwere the independent variables included in random effects in the cases ofVRC and LDec;N, respectively. It is also noted that all variances of regression

constant [Uð1;1Þ] or independent variable coefficient [Uð2;2Þ] were statistically significant in all models at 5% level of significance, which confirms the need to account for the random effects in modeling. Furthermore, the value ofUð1;1Þis relatively high in most speed models, which further confirms the need to account for the random effects in modeling. The correlation between the variances in each model is reflected in the covarianceUð2;1Þ, which was also statistically significant at 5% level of significance.

The table also shows theRMSEfor each model, which was calculated using the 15% of the data records not used in the model development. As shown in the table, the RMSEis lower for the VRC model than the VSCL model indicating better prediction of the ramp curve speed profile compared to SCL speed profile. The same trend is observed by comparingRMSEvalues for the instantaneous speed models, whereRMSEdecreases in the direction of vehicle travel fromVDtoVERC. The models forVSCL,VRC, andVD

also had higher values ofUð1;1Þthan any other instantaneous ramp curve speed, indicating greater variability among individual drivers.

Conclusions

As previously stated, the current design guidelines for ramps and ramp terminals are primarily based on acceleration and deceleration characteristics from the 1940s, with no data-based assessment of how modern vehicles and drivers behave at this road element.

This context makes a number of assumptions about the speed of the ramp and the speed of the freeway, as well as the rate at which diverging vehicles decelerate and the acceptable speed differential between diverging and freeway vehicles. Furthermore, with these assumptions, the design criteria are deterministic because they only consider a single value for each parameter, which is typically taken as a conservative percentile value.

A safety-explicit, probabilistic design approach based on reliability analysis can be used to overcome the inadequacies of current design guidelines. This approach requires reliable driver behavior models to estimate the expected number of crashes at a location with specific geometric characteristics. It can be argued that earlier work on safety-explicit probabilistic design for freeway ramp terminals used rudimentary driver behavior models based on a database with some limitations (Abdelnaby and Hassan 2014;Fatema and Hassan 2013;Fatema et al. 2014). To overcome this limitation, this paper presented a comprehensive study of driver behavior at freeway exit ramp terminals using trip data from the SHRP-2 NDS. To assess driver speed behavior through the SCL and ramp over 1,000 trips on 12 different sites in three different US states, the Table 5.Summary of recommended models

Fixed effects

Random effects

RMSE Slope Uð1;1Þ Uð2;1Þ Uð2;2Þ

VSCL¼127.64−8.93ð1−SCLTÞ−9.87ð1−RpTÞ−20.03ð1−V_L;CÞ−0.04LS−0.06LT− 8.18DR;N−1.23GH

D_R;N 1.99×10³ −97.50 94.56 9.16 VRC¼82.80−9.36ð1−RampTÞ−0.04LRCþ0.04R−3.86GRþ25.73L_R;N−64.02L²_R;N LRC 3.79×10⁴ −7.38 0.015 7.68 VD¼106.65−7.9ð1−SCLTÞ−15.54ð1−V_L;CÞ−0.02LSþ5.72LDec;N NA 109.83 NA NA 9.39 VBRC¼110.02−10.47ð1−SCLTÞ−7.49ð1−RampTÞ−29.34ð1−V_L;CÞ−0.07LSþ0.05R NA 17.06 NA NA 8.82

VMRC¼45.21þ0.015LRCþ0.1R NA 41.51 NA NA 8.16

VERC¼66.25−35.5ð1−RampTÞ−0.06LRCþ0.07R NA 68.81 NA NA 6.41

d¼−1.13−0.12ð1−RampTÞ−0.18ð1−V_L;CÞ þ0.001LS−0.002LTþ0.001Rþ0.64LDec;N NA 0.35 NA NA 0.59 LDec;N¼0.77þ0.13ð1−SCLTÞ þ0.003LT LT 0.03 −9.4×10⁴ 3.34×10⁵ 0.99 Note: Random Effects Slope = independent variable considered in random effects as random slope in addition to the random intercept;Uð1;1Þ= variance of intercept;Uð2;2Þ= variance of slope;Uð2;1Þ= covariance of intercept and slope; NA = not applicable because no independent variable was included in random effects; all speeds are in km=h; and deceleration is in m=s².

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data was first analyzed qualitatively. It was shown that vehicles continuously decelerate from the beginning of the SCL until the beginning of ramp curve, where they continue decelerating for some distance. Then, the deceleration tends to drop down quickly in conjunction with the middle of the ramp curve. The drivers’selection of deceleration seemed to follow three different rates with a trend of increasing deceleration as vehicles progress on the SCL and ramp. These trends of deceleration are consistent with other recent research (Brewer et al. 2011) but not consistent with the AASHTO assumption of two distinct deceleration rates on the SCL.

A portion of drivers were also found to diverge from the FRL to SCL on the taper, and this portion is much higher on taper-type SCL compared to parallel-type.

Different driver behavior measures were extracted to quantify speed at different points on the ramp terminal and other diverging measures. Namely, the measures extracted were, diverge speedVD, speed at beginning of ramp curve (VBRC) which is the same as the speed at the end of SCL, speed at middle of ramp curve (VMRC), speed at end of ramp curve (VERC), normalized deceleration distance (LDec;N), and average deceleration from diverge point to end of SCL (d). Performing several statistical tests showed no statistically significant differences for each of these measures during peak and off-peak traffic conditions. However, there was strong evidence that the means and variances of all measures were significantly different on the different sites. The SCL type or freeway speed limit alone could not explain this difference but rather is the result of the general geometric characteristics at each site.

Subsequently, regression models were developed for each of these measures. Because repeated trips in the NDS data were performed by the same drivers, the models were developed using a mixed modeling technique which can account for the repeated measures.

The developed models confirmed the need to account for random effects resulting from repeated trips by the same drivers.

The site selection in this study attempted to ensure balanced variability in geometric characteristics. Although good variability in the continuous parameters (such as SCL length and ramp curve radius), the representation of SCL and ramp types was not ideal.

Still, the developed models represent a considerable contribution in the literature. It is recommended that these models, along with the models developed earlier for entrance ramps (Alyamani and Hassan 2021), should be integrated in reliability analysis of ramp terminals to develop a safety-explicit probabilistic design approach.

In that approach, the designer would be able to assess the PNC and the expected number of collisions associated with a specific design.

Hence, the design is not assessed as safe or unsafe but rather assessed on a scale of relative safety that allows examination of the feasibility of the design decisions. Another extension to the work presented in this paper is to compare the behavior of familiar and unfamiliar drivers with each site. Given the privacy constraints in accessing NDS data, assumptions will have to be made in iden- tifying familiar and unfamiliar drivers. For example, drivers who navigated a site more than one time may be assumed as familiar drivers while those navigating it only once may be assumed as unfamiliar drivers.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. (https://insight.shrp2nds.us/login /auth). Some or all data, models, or code used during the study were

provided by a third party. Direct requests for these materials may be made to the provider as indicated in the Acknowledgments.

Acknowledgments

The authors would like to thank and gratefully acknowledge the financial support from the Saudi Arabian Cultural Bureau in Canada and Umm Al-Qura University. The authors also thank Virginia Tech Transportation Institute (VTTI) for their help in providing the naturalistic driving behavior data. The findings and conclusions of this paper are those of the authors and do not necessarily represent the views of the VTTI, SHRP-2, the Transportation Research Board, or the National Academy of Science.

Supplemental Materials

Figs.S1andS2are available online in the ASCE Library (www .ascelibrary.org).

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