Supporting Material to NCHRP Report 674 (2011)

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APPENDIX K: Details on Pedestrian Delay Models This Appendix was previously published as conference proceedings at the 89th Annual Meeting of the Transportation Research Board, January 10-14, 2010. The citation for this work is: Schroeder, Bastian J., and Nagui M. Rouphail. Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts. 89th Annual Meeting of the TRB, 2010. 174

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts 1 2 3 By 4 Bastian J. Schroeder, Ph.D* 5 Research Associate 6 Institute of Transportation Research and Education (ITRE) 7 North Carolina State University 8 Centennial Campus, Box 8601 9 Raleigh, NC 27695-8601 10 Tel.: (919) 515-8565 11 Fax: (919) 515-8898 12 Email: Bastian_Schroeder@ncsu.edu 13 14 Nagui M. Rouphail, Ph.D. 15 Director, Institute for Transportation Research and Education (ITRE) 16 Professor of Civil Engineering 17 North Carolina State University 18 Centennial Campus, Box 8601 19 Raleigh, NC 27695-8601 20 Tel.: (919) 515-1154 21 Fax: (919) 515-8898 22 Email: rouphail@eos.ncsu.edu 23 24 25 26 27 November 2009 28 29 Submitted for consideration for publication and presentation at the 89th Annual Meeting of the 30 Transportation Research Board, January 10-14, 2010 31 32 33 Word Count: 5,316 text words plus 2,000 for figures/tables (8*250) = 7,316 total 34 * Corresponding Author 35 36 37 --- This paper has been revised from its original submission --- 38 39 40 175

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts ABSTRACT 1 This paper presents an approach for developing mixed-priority pedestrian delay models at single-2 lane roundabouts using behavioral crossing data. Mixed-priority refers to crosswalk operations 3 where drivers sometimes yield to create crossing opportunities, but where pedestrians sometimes 4 have to rely on their judgment of gaps in traffic to cross the street. The models use probabilistic 5 behavioral parameters measured in controlled pedestrian crossings by blind pedestrians as part of 6 NCHRP project 3-78a. While blind pedestrians clearly represent a special population of 7 pedestrians, the developed delay model is structured to be applicable to other pedestrian 8 populations. Delay is predicted as a function of the probability of encountering a crossing 9 opportunity in the form of a yield or crossable gap, and the probability of utilizing that 10 opportunity, which are aggregated to an overall probability of crossing. The paper presents the 11 theoretical approach to estimating the probability parameters and uses a multi-linear log-12 transformed regression approach to predict the average pedestrian delay. The final delay model 13 explains 64% of the variability in the observed data and therefore represents a reasonable model 14 for predicting pedestrian delay at single-lane roundabouts. The paper concludes with a discussion 15 of how agencies can estimate the underlying probability parameters for existing or proposed 16 roundabouts using empirical and theoretical approaches, and how pedestrian crossing treatments 17 can be used in the context of the model to reduce average pedestrian delay. The research is 18 important in light of the ongoing debate of the accessibility of modern roundabouts to 19 pedestrians who are blind. However, the results have further application to the general evaluation 20 of pedestrian facilities at roundabouts, an application where existing Highway Capacity Manual 21 methods are limited. The probabilistic approach to predicting pedestrian delay is universal and 22 can be applied other pedestrian populations with the right probability parameters. Calibration to 23 other crossing geometries is feasible with future data collection. 24 25 176

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts INTRODUCTION 1 Modern roundabouts are a popular new form of intersection control in the US with over 1,500 2 existing and many more proposed (1). In contrast to older traffic circles, modern roundabouts are 3 compact, unsignalized, have low design speeds, and use a yield prioritization at the entering 4 approach with circulating traffic having the right-of-way. The strongest selling points for modern 5 roundabouts are a significant reduction in collisions compared to signalized intersections (2), 6 aesthetic appeal, and the ability to process varying traffic patterns without the need to adjust 7 signal parameters. 8 Many modern roundabouts are constructed in areas with pedestrian activity, including 9 downtown areas or suburban residential areas. Roundabout crosswalks are typically marked with 10 a zebra pattern or another form of marking (3) and feature a two-stage crossing with a splitter 11 island between entry and exit legs for pedestrian refuge. State motor vehicle codes commonly 12 give pedestrians the right of way within the crosswalk (4). This suggests that roundabouts should 13 be accessible to pedestrians. But yielding laws can be misinterpreted and the actual yielding 14 behavior varies over a range of observed values at different sites and geometries (2). 15 Consequently, pedestrians are expected to experience some delay when attempting to cross at 16 these locations. 17 The 2000 US Highway Capacity Manual (HCM) (5), the guide book for traffic 18 operational analysis methodologies for the US and many other countries, currently offers no 19 delay methodology for a mixed-priority crossing situation, where drivers sometimes yield to 20 create crossing opportunities, but where pedestrians sometimes have to rely on their judgment of 21 gaps in traffic to cross the street. The HCM gap acceptance-based methods are limited to cases 22 where pedestrians have full priority (100% of traffic yields) or where drivers have priority (no 23 yields) and pedestrians are limited to crossings in gaps only. An updated pedestrian delay model 24 that allows for a reduction of pedestrian delay due to drivers that yield is currently being 25 considered for the 2010 release of the HCM. However, the proposed theoretical model is not 26 calibrated from field data and does not distinguish between different sub-populations of 27 pedestrians. 28 In the context of building modern roundabouts, much national attention has been given to 29 pedestrians who are blind. Without the ability to see, blind travelers have to rely on auditory cues 30 177

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts to identify crossing opportunities. Research has shown that roundabouts can cause significant 1 challenges to this group of travelers, evident by long delays, missed crossing opportunities, and 2 risky situations (6, 7, 8). In the absence of a signal equipped with an accessible pedestrian signal 3 (APS), a pedestrian who is blind has a difficult time discerning between exiting and circulating 4 traffic and interpreting curved vehicle trajectories causing a confusing auditory environment.5 This paper presents an approach for estimating pedestrian delay at single-lane 6 roundabouts on the basis of observable behavioral parameters by pedestrians and drivers. The 7 analysis uses field-observed probabilities of yielding, gap occurrence, and the rate of utilization 8 of yield and gaps to develop statistical pedestrian delay models. The models are developed from 9 observations of blind pedestrian crossings at three single-lane roundabouts, but can be expanded 10 to other pedestrian populations and roundabout geometries from literature findings and traffic 11 flow theory concepts. The underlying performance assessment framework for (blind) pedestrian 12 crossings at roundabouts was previously published by the authors in (10) and (11). 13 BACKGROUND 14 The question of pedestrian delay at modern roundabouts, and more specifically the accessibility 15 of modern roundabouts to pedestrians who are blind is being investigated in two ongoing 16 research projects: National Cooperative Highway Research Program (NCHRP) Project 3-78a 17 (12) and a National Eye Institute Bioengineering Research Partnership investigating Blind 18 Pedestrian Access to Complex Intersections (13). The data used in this paper were collected for 19 those two projects. 20 Research on pedestrian behavior is typically of an observational nature, as researchers 21 observe and quantify behavior by pedestrians and drivers. This approach has been adopted in a 22 NCHRP-funded national survey of pedestrian crossing treatments (2) and research on the 23 operational performance of modern roundabouts (14). The latter project observed a total of 769 24 pedestrian crossing events at seven different roundabouts, but the dataset was deemed 25 insufficient to develop pedestrian delay models for roundabouts and no special pedestrian 26 populations were included in the study. 27 Other countries have developed methodologies for estimating the impact of pedestrians 28 on vehicular traffic, assuming pedestrian priority (15). Those approaches are conceptually 29 similar to the US HCM methods mentioned above (5), that quantify pedestrian delay at a vehicle-30 178

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts priority crossing or driver delay at pedestrian-priority crosswalk. A mixed-priority pedestrian 1 delay model will enable engineers to make predictions about the current or future operational 2 performance of a roundabout for this non-motorized mode. It further aids in comparing 3 pedestrian performance of a roundabout to a signalized intersection alternative. Finally, without 4 the ability to predict crossing performance for blind travelers, engineers cannot adequately 5 address requirements for the accessibility of modern roundabouts to pedestrians who are blind. 6 The American with Disabilities Act (ADA) of 1990 mandates equal access to public 7 facilities to all users of that facility, including those with mobility or vision impairments (16). 8 The US Access Board is tasked with interpreting the ADA legislation and issuing guidance to 9 engineers and planners to assure that the public right of way is accessible to and usable by 10 pedestrians with disabilities. The US Access Board has recognized the crossing challenges at 11 roundabouts and has proposed language that supports the installation of APS-equipped 12 pedestrian signals at multi-lane roundabouts (17). 13 Through the aforementioned blind pedestrian research projects (12, 13), crossing 14 behavior was studied through controlled experiments. In the studies, pedestrians would cross 15 repeatedly at the same crosswalk under supervision of an orientation and mobility (O&M) 16 specialist, resulting in extensive pedestrian-specific behavioral data sets than cannot be obtained 17 from uncontrolled observational studies. 18 In prior work, the authors have developed a framework for describing the accessibility of 19 modern roundabouts for blind pedestrians (11, 18). The accessibility framework is intended to 20 provide measures to quantify the crossing performance at these locations. In particular, the 21 crosswalk usability measures quantify the availability of crossing opportunities in the form of 22 yields and crossable gaps, the rate of utilization of those opportunities, and the delay and risk 23 experienced by pedestrians during the crossing. This paper expands on that prior work and 24 relates the performance outcome, delay, to the observed behavioral probability parameters. 25 METHODOLOGY 26 The data used for the delay model development were collected in controlled crossing 27 experiments with blind volunteers as part of two ongoing research projects (12, 13) investigating 28 the accessibility concerns of modern roundabouts to pedestrians with vision impairments. While 29 blind pedestrians represent a special pedestrian population, the approach allows the analyst to 30 179

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts distinguish between driver and traffic behavior and pedestrian characteristics. It can thus be 1 hypothesized what the delay would have been in a different behavioral context. For example 2 sighted pedestrians would have a higher rate of yield utilization (presumably 100%). However, 3 the blind pedestrian data set had the advantage that the full range of crossing performance was 4 observed (e.g. yield utilization ranging from 0% to 100%). The distribution of explanatory 5 variables across a range of values is a critical prerequisite for model development as discussed 6 below. 7 In the experiments, a total of 40 blind participants crossed independently at three 8 different roundabouts, with each site having a sample of 10-18 pedestrians. The pedestrians were 9 always accompanied by an O&M specialist and were familiarized with the roundabout and the 10 study design before crossing. Each pedestrian crossed the roundabout multiple times, where each 11 trial consisted of four lane crossings (for example entry-exit-exit-entry). Depending on the site, 12 each pedestrian completed four to six trials at the roundabout, resulting in 16 to 24 lane crossings 13 with half of the crossings at the entry and exit leg, respectively. The dataset used for model 14 development uses the average crossing performance for a single pedestrian at a given leg (entry 15 or exit), resulting in a total of 80 data points. Using the average of all trials for a participant 16 results in a more robust dataset. It assures a sufficient representation of accepted and rejected 17 opportunities for each pedestrian needed to calculated opportunity usability statistics. Overall, a 18 total of approximately 800 observations were used to generate the 80 data points. 19 20 Observational Variables 21 The following intermediate variables are calculated for each of the 80 data points. 22 • P(Yield): The probability of a vehicle yielding to the pedestrian, defined as the number 23 of yields divided by the number of yields plus the number of non-yielding vehicles that 24 cross the plane of the crosswalk while a pedestrian is waiting to cross. This parameter 25 describes driver behavior and does not include gap events. 26 • P(Y_ENC): The probability of encountering a yield event, defined as the number of 27 yields divided by the total number of events encountered by the pedestrian until he/she 28 completes the crossing. An event is defined as the interaction of a pedestrian with a single 29 vehicle. This measure is used to develop the pedestrian delay models. 30 180

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts • P(GO|Yield): The probability of yield utilization, defined by the number of crossings in 1 a yield divided by total number of yields encountered by the pedestrian. 2 • P(CG): The probability of a gap being crossable, defined as the number of crossable gaps 3 (CGs) divided by the number of all crossable plus non-crossable gaps. This parameter 4 describes gap occurrence and does not include any yields events. In this study, the CG 5 was calculated from the time required to cross at a walking speed of 3.5 ft/s (1.07) plus 2 6 seconds to account for start-up and clearance time. This is consistent with the pedestrian 7 critical gap definition in the HCM, given below in equation 3. 8 • P(CG_ENC): The probability of encountering a CG event, defined as the number of 9 crossable gaps divided by the total of all events (vehicles) encountered by the pedestrian. 10 P(GO|CG): The probability of crossable gap utilization, defined by the number of 11 crossings in a CG divided by total number of CGs encountered by the pedestrian. 12 • Observed Delay per Leg (sec.): The average pedestrian delay in seconds, defined as the 13 time difference between when the trial started and when the pedestrian initiated the 14 crossing at the leg. Note that a full crossing at the roundabout includes two legs and this 15 delay is given per leg! 16 • Minimum Delay (sec.): The minimum delay or waiting time until the first opportunity, 17 defined as the time difference between start of the trial and the first yield or crossable gap 18 encountered by the pedestrian. Presumably, this delay corresponds to the experience of a 19 sighted pedestrian who utilizes all yields and all crossable gaps (at the defined CG time). 20 21 The above variables are largely identical to measures used to define pedestrian 22 accessibility that were presented in (11). That paper used P(Yield), P(GO|Yield), P(CG), 23 P(GO|CG), but stopped short of relating those to pedestrian delay in a predictive model. For the 24 purpose of developing predictive delay models, it was necessary to define two additional 25 variables that describe the probability of encountering a yield and crossable gap. The measures 26 P(Y_ENC) and P(CG_ENC) use the same denominator: The total number of pedestrian-vehicle 27 interaction events, where one event is always defined as the interaction of one vehicle and one 28 pedestrian. With the same denominator, the two terms become additive and their sum by 29 definition is limited by 1.0. Figure 1 illustrates the definition of observational variables using a 30 hypothetical example of a pedestrian encountering 10 different vehicles (10 events). 31 181

1 2 2 3 4 4 5 6 7 7 8 8 9 10 Cross Yield Cross Cross Yield Cross Cross Cross Yield Cross Yield Cross Cross Cross = 10 Vehicles GO = 1 Crossing NY Y NY Y NY NY Y Y NY = 4/(4+5) = 4/9 = 44.4% non-CG CG non-CG CG non-CG = 3/(3+3) = 3/6 = 50.0% Y Y Y Y = 4/10 = 40.0% CG CG = 3/10 = 30.0% Rej. Y Rej. Y Rej. Y Rej. Y = 0/4 = 0.0% Rej. CG Rej. CG = 1/3 = 33.3% First Opportunity Delay = t(crossing) - t(start trial) Min. Delay (sec.) Min. Delay = t(first opp.) - t(start trial) P(GO|Yield) Yield Utilization (n=4) Utlz. CG P(GO|CG) CG Utilization (n=4) Delay (sec.) Gap Events (n=6) P(Y_ENC) Yield Encounters (n=10) CG P(CG_ENC) CG Encounters (n=10) # of Crossings Pedestrian Events (n=1) P(Yield) Yield Events (n=9) CG P(CG) Start of Trial MEASURES Veh. # # of Events Vehicle Events (n=10) 1 Figure 1: Graphical Illustration of Variable Definitions2 182

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts Figure 1 shows a timeline of a pedestrian encountering 10 hypothetical vehicle events. 1 The timeline proceeds from left to right, from the start of the experimental trial until the last 2 vehicle that interacts with the pedestrians crossed the plane of the crosswalk. Of the ten vehicles, 3 vehicles 2, 4, 7, and 8 yielded to the pedestrian, but none of these yields were utilized. Vehicles 1, 4 3, 5, 6, 8, and 9 didn't yield even though a pedestrian was waiting at the crosswalk. No yield 5 information is available for vehicle 10, since the pedestrian had already crossed by the time it 6 crossed the plane of the crosswalk. Consequently, the variable P(Yield) is calculated from four 7 yields divided by a total of nine drivers that could have yielded and equals 44.4%. In contrary, 8 the variable P(Y_ENC)=40% is calculated by diving four yields by a total of 10 vehicles 9 encountered in the trial. 10 The temporal separation between vehicles 2-3, 5-6, and 9-10 constituted three crossable 11 gaps, the last of which was utilized by the pedestrians. The gap from the start of the trial to 12 vehicle 1, and the gaps between vehicles 4-5 and 8-9 were below the crossable gap threshold. 13 The measure P(CG)=50.0% is calculated by dividing three crossable gaps by six total gaps 14 encountered. P(CG_ENC)=30.0% is calculated by dividing three crossable gaps by a total of ten 15 events. 16 The rates of yield and crossable gap utilization are calculated at P(GO|Yield)=0.0% and 17 P(GO|CG)=33.3%, respectively. The reasons for not utilizing one of these crossing opportunities 18 may include uncertainty about driver intent or high levels of ambient noise. Delay is defined as 19 the temporal duration from the time the trial starts until the pedestrian initiates the crossing. The 20 Minimum Delay is less, calculated as the time spent waiting until the first crossing opportunity, 21 which in this case is the yield by vehicle 2. 22 23 Site Description 24 All three studied roundabouts have one circulating lane and single-lane entries and exits. The 25 major approaches at the roundabouts are arterial streets with a mix of commuter and local traffic. 26 All three roundabouts have university or city bus stops in close proximity and thus exhibit at 27 least some heavy vehicle activity. Site DAV-CLT is located at the intersection of 9th Street and 28 Davidson Street in Charlotte, NC in a downtown residential area and has an inscribed diameter 29 of 100-120 feet (30.5-36.6m). The major approach at DAV-CLT has an approximate Average 30 Annual Daily Traffic (AADT) of 9,900 vehicles. Site PS-RAL is located at the intersection of 31 183

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts Pullen Road (AADT 15,000) and Stinson Drive in Raleigh, NC near a major university with an 1 inscribed diameter of 88 feet (26.8m). Site ULY-GOL is located at the intersection of Golden 2 Road (AADT 15,000) and Ulysses Drive in Golden, CO in a suburban business district and has 3 an inscribed diameter of 100 feet (30.5m). Figure 2 shows aerial views of all three sites. The 4 studied crosswalks are highlighted. 5 6 184

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts 1 a) DAV-CLT b) PS-RAL c) ULY-GOL Figure 2: Aerial views of Comparison roundabouts (Source: www.bing.com) 2 3 4 185

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts Descriptive Statistics 1 Table 1 shows a summary of the comparison of the three roundabouts for the described measures. 2 The three studied single-lane roundabouts exhibit considerable differences in the performance 3 assessment. Site ULY-GOL shows higher P(Yield) rates than the remaining two sites, with 4 DAV-CLT having the lowest yielding rates. The likelihood of encountering a yield, P(Y_ENC), 5 follows a similar trend. The rates of yield utilization are comparable for PS-RAL and ULY-GOL, 6 with a slightly lower rate observed for DAV-CLT. 7 Table 1: Summary Comparison of Three Single-Lane Roundabouts 8 Site ID DAV-CLT PS-RAL ULY-GOL ENTRY EXIT ENTRY EXIT ENTRY EXIT P(Yield) Mean 10.8% 11.8% 41.5% 18.2% 65.6% 20.2% Std.Dev 8.9% 7.9% 32.8% 17.9% 36.1% 17.2% P(Y_ENC) Mean 5.8% 6.7% 37.9% 28.1% 51.1% 29.6% Std.Dev 4.8% 5.0% 17.8% 14.4% 18.4% 13.7% P(GO|Yield) Mean 64.1% 70.4% 83.0% 87.8% 82.8% 76.0% Std.Dev 41.2% 44.1% 20.4% 14.1% 20.1% 26.1% P(CG) Mean 62.1% 60.9% 53.5% 50.2% 53.7% 29.8% Std.Dev 14.2% 12.9% 28.1% 23.5% 21.6% 12.2% P(CG_ENC) Mean 29.8% 27.8% 17.7% 20.5% 26.3% 20.6% Std.Dev 6.9% 6.7% 8.9% 9.7% 12.4% 8.4% P(GO|CG) Mean 66.3% 60.3% 52.0% 63.6% 83.2% 86.8% Std.Dev 20.6% 17.9% 41.3% 26.6% 23.7% 23.4% Delay (sec.) Mean 26.6 24.0 10.5 11.6 10.9 13.0 Std.Dev 17.0 9.7 8.9 6.8 7.3 7.9 Delay >Min (sec.) Mean 18.8 17.2 5.6 6.1 2.8 2.7 Std.Dev 15.5 9.6 7.2 5.8 2.1 2.3 9 The rates of gap availability show the reverse trend from the yielding data with DAV-10 CLT showing the highest availability of crossable gaps, followed by PS-RAL and ULY-GOL. 11 The rate of gap utilization is highest at ULY-GOL, followed by DAV-CLT and PS-RAL. 12 13 186

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts The overall delay is comparable for PS-RAL and ULY-GOL, but highest at DAV-CLT, a 1 trend mirrored by the Delay>Min statistics. Interestingly, the highest delay is evident at the site 2 with the lowest availability of yields and a lower rate of yield utilization. At similar crossable 3 gap and gap utilization rate across the three sites, this may suggest that the lack of yielding at the 4 site contributes to delay difference. This point is explored further on the delay model 5 development for individual participants. 6 The results in Table 1 point to a high level of inter-subject variability as evident in high 7 observed standard deviations. With high standard deviations, the interpretation of the 8 accessibility of a single site is challenging. But for the purpose of model development, the 9 observed variability is considered an asset. For example, if no variability in yielding was 10 observed, it would be impossible to use that variable to predict pedestrian delay. The critical 11 point in this context is that the observed variability (in yielding) is correlated with pedestrian 12 delay. Consequently, if the model development process shows that an increasing likelihood of 13 yielding results in reduced pedestrian delay, the yield probability becomes an important 14 explanatory variable in the delay prediction model. 15 MODEL DEVELOPMENT 16 For the purpose of model development, some additional performance measures are defined in 17 this section that are used as independent variables in model development, in addition to the ones 18 already defined above. The dependent variables are the two delay variables as defined previously. 19 The following three variables are obtained by summation and multiplication of the intermediate 20 behavioral probability parameters. 21 • P(Yield_and_GO): The probability of crossing in a yield, defined as the probability of 22 utilizing a yield multiplied by the probability of encountering a yield: 23 P(Y_and_GO) = P(Y_ENC)*P(GO|Y). 24 • P(CG_and_GO): The probability of crossing in a crossable gap, defined as the 25 probability of utilizing a CG multiplied by the probability of encountering a CG: 26 P(CG_and_GO) = P(CG_ENC)*P(GO|CG). 27 • P(Crossing): The probability of crossing, defined as the sum of the probabilities of 28 crossing in a yield and crossing in a crossable gap. 29 P(Crossing): = P(Y_and_GO) + P(CG_and_GO) 30 187

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts 1 Additional independent variables used in the analysis are: 2 • Site_Gol: Dummy variable that identifies the site as GOL-PRE if Site_Gol=1. 3 • Site_RAL: Dummy variable that identifies the site as PS-RAL if Site_RAL=1. By 4 definition, if Site_Gol=Site_Ral=0 then the data refers to an observation at DAV-CLT. 5 • ENTRY: Dummy variable denoting that the observation represents the average of events 6 at the roundabout entry if ENTRY=1. 7 8 A total of 40 subjects were included in the analysis from three different sites. Each 9 observation represents the average of four or more lane crossings at a particular site. With the 10 distinction of entry versus exit crossings, the dataset contains 80 observations. However, four 11 observations had to be excluded because these subjects had one or more zero observations. This 12 can occur because they either didn't encounter any crossable gaps or because no drivers yielded 13 for them. As a result, the final data set contained 76 observations. Descriptive statistics for the 14 data set in Table 2 suggest that a range of values was observed for most probability terms, 15 suggesting a good basis for model development. 16 Table 2: Descriptive Statistics for Delay Model Data Set 17 Variable Site N Mean Std Dev Min Max P(Y_ENC) All 76 27.7% 18.8% 1.7% 66.7% P(GO|Yield) All 76 61.4% 37.0% 0.0% 100.0% P(CG_ENC) All 76 24.7% 8.3% 4.8% 44.4% P(GO|CG) All 76 71.5% 28.0% 0.0% 133.3%* p(yield_and_go) All 76 21.7% 18.5% 0.0% 58.3% p(CG_and_go) All 76 17.5% 8.6% 0.0% 44.4% p(Crossing) All 76 39.2% 21.1% 12.1% 88.9% Entry All 76 48.7% 50.3% 0.0% 100.0% Delay All 76 15.5 10.6 3.5 58.3 Delay_overMin All 76 7.8 9.1 0.1 46.0 * A value of P(GO|CG)>1.0 can occur when a pedestrian utilizes a "non-crossable" gap 18 that is below the selected CG threshold. 19 20 The model development uses a multi-linear regression approach to predict the dependent 21 variable, delay, as a function of various independent variables. All variables are given on a per 22 leg basis at the roundabout and as a result the total delay at the crossing is the sum of predicted 23 entry and exit delays. A histogram of the distribution of the delay variable showed significant 24 skew to the left, suggesting a log-normal distribution. Consequently, all predictive probability 25 188

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts variables were transformed by applying the natural logarithm of the variable. All regression is 1 performed in SAS statistical analysis software using PROC GLM, a procedure to perform multi-2 linear regression. 3 RESULTS 4 The analysis includes a range of models to explain the dependent variable as a function of the 5 behavioral probability terms. Table 3 shows seven models for the Delay dependent variable. 6 Table 3: Regression Results for Dependent Variable Delay 7 Model A Model B Model C Model D Model E Model F Model G+ Estimate Estimate Estimate Estimate Estimate Estimate Estimate Intercept -15.40 *** 0.90 -11.21 ** 9.31 ** -4.45 * -1.54 -0.78 ln_y_enc -4.65 *** -2.35 * ln_GO_given_y -5.78 *** -3.54 *** ln_cg_enc -3.48 ** -2.62 ln_GO_given_CG -9.32 *** -8.66 *** ln_yield_and_go -6.11 *** -3.33 *** ln_gap_and_go -9.20 *** -6.03 *** ln_cross -15.75 *** -14.99 *** Entry 1.29 site_gol 13.21 *** 14.97 *** -12.43 *** 1.97 site_ral 8.30 ** 13.71 *** -17.34 *** -3.29 Pr > F <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 DF 7 4 3 3 2 3 1 R-Square* 0.779 0.679 0.634 0.460 0.640 0.683 0.641 Adj. R-Square* 0.755 0..659 0.619 0.436 0.630 0.670 0.636 + Represents Suggested Model 8 * Significant at p < 0.1 9 ** Significant at p < 0.05 10 *** Significant at p < 0.01 11 12 The delay models in Table 3 suggest a good overall fit, with most variables having a 13 significant explanatory effect on the response. The variable ENTRY is not significant in any 14 model, including others that are not shown. This is explained, because differences in behavior at 15 entry and exit leg are already captured in the probability terms. Model A and several other 16 models suggests a significant effect of the site dummy variables with variables SITE_RAL and 17 SITE_GOL shifting the overall delay curve upward relative to site DAV_CLT. This finding is 18 significant, because the descriptive statistics in Table 1 suggested that this site had the highest 19 overall delay. The model results suggest that the high observed delays at DAV_CLT are 20 189

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts explained by the relative lack of crossing opportunities and that the delays at PS_RAL and 1 ULY_GOL would have been much higher with more traffic (fewer crossable gaps) and less 2 courteous driver behavior (fewer yields). 3 The goal of this analysis is the development of a universal pedestrian delay model for 4 single-lane roundabouts. Therefore, additional models were tested without the site effects. The 5 guiding principles for the final model were significant parameter estimates, a high adjusted R-6 Square value, and a relatively simple model form. When removing the site variables from Model 7 A, the four probability terms in Model B lose statistical validity. Consequently, the remaining 8 models use the pooled probability terms. Model E and G both represent viable alternatives, 9 predicting delay as a function of P(Yield_and_Go) and P(CG_and_GO) and the overall 10 probability P(Cross), respectively. Both models have comparable adjusted R-Square values and 11 significant parameter estimate. Ultimately, model G was selected, because it provides a better fit 12 with the data at low probability values. In turn Model E was overly optimistic at low 13 probabilities. Both models converge in the higher probability ranges (See Figure 3). 14 The recommended model G predicts pedestrian delay as a function of P(Cross), which is 15 calculated from the four individual probability parameters. The overall model and the P(Cross) 16 parameter are significant p<0.0001. The adjusted R-Square value suggests that 63.6% of the 17 variability in the data is explained by the model, which is very high given that inter-subject 18 variability of crossing performance was very high. Equation 1 shows the suggested pedestrian 19 delay model. 20 Equation 1: Suggested Pedestrian Delay Model (Model G) 21 )(99.1478.0 CROSSp PLNd ∗−−= 22 23 where, 24 dp = average pedestrian delay (s) 25 PCROSS = Probability of Crossing 26 = P(Y_ENC)*P(GO|Yield)+P(CG_ENC)*P(GO|CG) 27 28 Figure 3 plots the predicted pedestrian delay as a function of P(Cross), which is the sum 29 of the PY&GO and PCG&GO model parameters. The different data points were obtained by 30 strategically varying P(Y_ENC) and P(CG_ENC) for a fixed utilization of 31 P(GO|YIELD)=P(GO|CG)=0.5. The figure shows that the general trends of the model delay 32 curves fall within the cloud of observed data (blue crosses). The figures shows that in a 33 190

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts comparison of Models E (green triangle) and G (blue squares) with field-observed delays, the 1 latter fits the data better in the lower P(Y_ENC) and P(CG_ENC) region. 2 3 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pe de st ria n D el ay & M in im um D el ay (s ec .) P(Y_ENC) = P(CG_ENC) Model E - 50% Utilization Suggested Model G - 50% Utilization Raw Data - Delay Suggested Model G - Perfect Utilization Raw Data - Min. Delay 4 Figure 3: Graphical Comparison of Model 5 against Field Data 5 Figure 3 further plots the curve for suggested model G corresponding to perfect 6 opportunity utilization of P(GO|YIELD)=P(GO|CG)=1.0 (red filled circles). This curve may 7 approximate the behavior of a sighted pedestrian, assuming that this group of pedestrians has 8 identical thresholds for crossable gaps. Given that the definition used for crossable gap is 9 consistent with the HCM, the resulting delay should be an appropriate, albeit conservative 10 estimate. The perfect utilization curve generally fits well with the observed minimum delay times 11 (red hollow circles), which were calculated by subtracting the Delay_OverMin from the 12 observed delay for each subject. 13 14 191

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts 0.0 10.0 20.0 30.0 40.0 50.0 60.0 0 10 20 30 40 50 60 Pr ed ic te d D el ay & M in .D el ay Field Observed Delay & Min.Delay Delay Model G Comparison with Field Data Delay (Blind) Min. Delay (Sighted) 1 Figure 4: Field Observed versus Predicted Delay and Min. Delay 2 Figure 4 plots the field-observed and predicted delay and minimum delay for all 76 data 3 points. The delay corresponds to the actual crossing experience of the blind study participants. 4 The minimum delay approximates the corresponding crossing experience of sighted pedestrians 5 encountering the same number of yields and crossable gaps, but having perfect opportunity 6 utilization. 7 Figure 5 shows a sensitivity analysis of the four base probability parameters (P(Y_ENC), 8 P(GO|Yield), P(CG_ENC), and P(GO|CG) against the field-observed range of those data. In each 9 of the sub-figures, one of the probability parameters was varied from 0.0 to 1.0 (shown on the x-10 axis), while keeping the other three fixed at two varying levels. The first level uses the field 11 average for that parameter for all subjects as shown in Table 2. The second level again assumes 12 perfect utilization, approximating the delay for a sighted pedestrian. 13 14 192

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pe de st ri an D el ay (s ec .) P(Y_ENC) Sensitivity : P(Y_ENC) Raw Data Model G - Field Averages Model G - Perfect Utiliz. 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pe de st ri an D el ay (s ec .) P(GO|Yield) Sensitivity : P(GO|Yield) Raw Data Model G - Field Averages Model G - Perfect Utiliz. 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pe de st ri an D el ay (s ec .) P(GO|CG) Sensitivity : P(GO|CG) Raw Data Model G - Field Averages Model G - Perfect Utilz. 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pe de st ri an D el ay (s ec .) P(CG_ENC) Sensitivity : P(CG_ENC) Raw Data Model G - Field Averages Model G - Perfect Utilz. 1 Figure 5: Model 5 Sensitivity versus Field Data 2 3 The plots in figure 5 show how the delay model responds to changes in one of the four 4 probability terms. The greatest sensitivity is evident for rates of yield and gap encounter, 5 P(Y_ENC) and P(CG_ENC), suggesting that changes in these parameters have the biggest 6 impact on the predicted delay. The sensitivity curves for the utilization curves are flatter, 7 suggesting that improvements to the ability (or willingness) of pedestrians to utilize crossing 8 opportunities has less of an effect than changing the overall occurrence of these opportunities. 9 All plots generally show a good fit with observed field data. The worst fit is evident for the 10 P(CG_ENC) plot, where the majority of field observations are clustered towards a low gap 11 occurrence rate. With increasing probability levels, the predicted pedestrian delay decreases. The 12 delay estimate for perfect utilization is expectedly below the field averages. 13 14 193

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts DISCUSSION 1 The delay model presented in equation 1 above can be used to predict the delay at single-lane 2 roundabouts by estimating the four probability parameters P(Y_ENC), P(GO|YIELD), 3 P(CG_ENC), and P(GO|CG) that ultimately feed into the model parameters. In order to apply the 4 model to predict delay at single-lane roundabouts, theses parameters therefore need to be field-5 measured or derived from literature, previous studies, and traffic theory. 6 The rate of driver yielding and the availability of crossable gaps can easily be measured 7 in the field using manual tally and stop watch methods described in the ITE Manual of 8 Transportation Studies (19) or other sources. In the absence of field data, a recent NCHRP 9 Report (14) has collected data on driver yielding behavior at US roundabouts that can be used for 10 guidance. The availability of crossable gaps can be estimated using traffic flow theory concepts 11 based on traffic volume and an assumed headway distribution. Using a negative exponential 12 distribution, the probability of observing a headway greater than tc seconds is given by (20): 13 Equation 2: Estimating P(CG_ENC) from Traffic Flow Theory (20) 14 .)( avg c t t c etheadwayP − =≥ 15 16 where, 17 tc = critical headway for crossable gap (sec.) 18 tavg = average headway, defined as tavg=(3,600sec/hour) / (V vehicles/hour) 19 20 In the absence of pedestrian platoons, the critical gap for pedestrians can be calculated by 21 equation 3 following the HCM (5) methodology: 22 Equation 3: Pedestrian Critical Gap after HCM2000 Equation 18-17 (5) 23 s p c tS Lt += 24 25 where, 26 L = crosswalk length (ft) 27 Sp = average pedestrian walking speed (ft/s), and 28 ts = pedestrian start-up and clearance time (s) 29 30 Using the above relationship, the probability of observing a crossable gap in a stream of 31 400 vehicles per hour at a 14 foot-lane at a roundabout and a corresponding critical headway of 32 tc=14/3.5+2=6 seconds is: 33 194

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts %3.51.)sec6( 9 6 . ===≥ −− eeheadwayP avg c t t 1 2 The estimation of yield and gap utilization rates is more difficult for blind pedestrians, 3 since it requires controlled field experiments. In the absence of field data, the results from the 4 three roundabouts used in this analysis that were presented in Table 1 can be used as a starting 5 point. For sighted pedestrians utilization rates of or near 1.0 can be assumed. For other special 6 pedestrian populations, including children and the elderly analyst judgment will be required. A 7 basic sensitivity analysis can assure that a range of values are considered. 8 The sensitivity of the model to the different probability parameters that was presented in 9 Figure 5 can inform the debate on how to reduce pedestrian delay through the use of pedestrian 10 crossing treatments. An extensive national survey of different pedestrian crossing treatments and 11 their impact on driver yielding behavior is found in NCHRP Report 562 (14). For example, a 12 treatment that enhances driver yielding from 10% to 30% while keeping the availability of 13 crossable gaps fixed at 20% would presumably decrease the pedestrian delay for sighted 14 pedestrians (perfect utilization) from 13.0 to 4.6 seconds, and the delay for a blind pedestrian 15 (assumed 50% utilization) from 23.3 to 15.0 seconds. 16 Pedestrian crossing treatments tested in (14) included some with red signal indication, 17 some with yellow flashing beacons, and other static signs that are all intended to increase driver 18 yielding. The results suggested a large variability of the effectiveness of different treatments 19 depending on site-specific parameters. In other research (7) driver yielding behavior was found 20 to increase with decreasing vehicle speeds. Consequently, low roundabout design speeds and 21 traffic calming treatments may be the most effective treatment to assure pedestrian accessibility. 22 This hypothesis is supported by the model response to increases in P(Y_ENC) shown in Figure 5.23 The forthcoming report of NCHRP Project NCHRP 3-78 (12) will include field-observed 24 data on the effect of special blind pedestrian treatments in enhancing both the availability and 25 utilization of crossing opportunities. Following the delay framework, any treatment that 26 improves one or more of the underlying probability parameters will reduce overall pedestrian 27 delay. 28 195

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts CONCLUSION 1 This paper demonstrated the application of a framework based on pedestrian and driver 2 behavioral parameters to develop a mixed-priority delay models for pedestrian crossings at 3 single-lane roundabouts. Mixed-priority refers to crosswalk operations where drivers sometimes 4 yield to create crossing opportunities, but where pedestrians sometimes have to rely on their 5 judgment of gaps in traffic to cross the street. The underlying data set was obtained from 6 controlled experiments including 40 blind pedestrians at three different single-lane roundabouts. 7 It can however be readily adopted to sighted pedestrians or other special populations by varying 8 the appropriate probability parameters. The use of data from blind pedestrians proved to be 9 extremely valuable, since it allowed the distinction between available crossing opportunities and 10 the actual utilization of these opportunities. A dataset containing only sighted pedestrians 11 expectedly would not have captured the utilization effect, since sighted pedestrians would likely 12 utilize the first opportunity that is presented to them. The delay to sighted pedestrians can be 13 predicted with the developed model by assuming perfect utilization. However, the model further 14 allows the analyst to consider pedestrian populations with less-than perfect rates of opportunity 15 utilization. In addition to fully blind participants, the approach is therefore adoptable to people 16 with low vision or children, who have been shown to have difficulty judging the speed and 17 distance of oncoming traffic (9). 18 The resulting mixed-priority delay model is statistically significant and produces good 19 estimates of pedestrian delay that match observed field data. It is applicable to situation where 20 pedestrian delay is governed by a mix of pedestrian gap acceptance and driver yielding behavior. 21 The underlying probability terms can be estimated from field observations for other sites, or can 22 be estimated from literature or traffic flow theory concepts. In future research, the authors hope 23 to expand the data collection and analysis to other unsignalized crossing locations, including 24 multi-lane roundabouts, which pose more severe crossing difficulties for both blind and sighted 25 pedestrians. 26 The authors recognize that the material presented here has potential implications for the 27 ongoing national debate in the US on the accessibility of modern roundabouts to pedestrians who 28 are blind. The focus of this paper is not to make policy statements, but rather to contribute to that 29 debate. The question of roundabout treatments and signalization are much discussed in the 30 roundabout engineering and accessibility communities and go far beyond the scope of this paper. 31 196

Schroeder and Rouphail: Mixed-Priority Pedestrian Delay Models at Single-Lane Roundabouts The authors hope that the developed delay models can assist with that discussion by offering 1 readers a methodology for quantifying and predicting (blind) pedestrian delay at roundabouts. 2 However, it is emphasized that the approach presented here disregards the implications on 3 pedestrian safety, which is at least equally important to delay. The readers are encouraged to 4 consult the final report for NCHRP project 3-78a (11) for a more complete discussion of these 5 accessibility issues. 6 ACKNOWLEDGMENTS 7 The authors would like to thank the National Institutes of Health and the National Academies of 8 Science for their financial support and the members of the project teams, who have provided 9 continuous feedback to the research efforts. The authors would further like to acknowledge staff 10 at Western Michigan University and Accessible Design for the Blind, who were instrumental in 11 running the studies. The authors would also like to thank the Cities of Charlotte, NC, Raleigh, 12 NC, and Golden, CO for facilitating the data collection efforts. 13 The NIH project described was supported by Grant Number R01EY12894 from the 14 National Eye Institute. This content is solely the responsibility of the authors and does not 15 necessarily represent the official views of the National Eye Institute or the National Institutes of 16 Health. 17 18 197

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