Crossing Solutions at Roundabouts and Channelized Turn Lanes for Pedestrians with Vision Disabilities (2011)

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62 The objective of this chapter is to extend the analysis results from Chapter 5 to a broader and more applied context. Because of limited resources, only a small number of sites were repre- sented in the field experiment. But clearly, the crossing chal- lenges for pedestrians who are blind extend to other geometries and traffic patterns. This chapter attempts to provide this type of extension in two ways: 1. The development of pedestrian delay models that allow the analyst to predict the expected pedestrian delay at a cross- ing location based on traffic patterns and behavioral attri- butes of drivers and pedestrians. 2. A discussion on how to apply traffic simulation models to extrapolate the effects of other treatments to other sites, including treatment combinations not captured in the experimental field trials. This chapter presents the pedestrian delay models and dis- cussion of traffic simulation models consecutively. The reader should be aware that with limited field data, both areas of extension are to be treated with care. The analyst should always apply expert judgment in any treatment installation and eval- uation. Other national resources provide additional informa- tion on the effectiveness of different treatments (Fitzpatrick et al. 2006) and on case studies describing lessons learned from their installation (Zegeer et al. 2002). The approach for devel- oping pedestrian delay models has been separately published in Schroeder and Rouphail (2010). The principal focus of the two extensions is on pedestrian delay, not risk. This is a clear limitation that needs to be rec- ognized early on. The NCHRP Project 3-78A team attempted to follow similar approaches to predict the safety perfor- mance of a pedestrian crossing using regression and simulation techniques. The regression-based attempt was not successful due to the rare occurrence of O&M interventions. In order to develop a risk prediction model from field data, a different dependent variable would be needed that is readily observ- able for every participant. The section on simulation models does describe an approach for using simulation to extract sur- rogate safety measures and a way to model the unique aspects of how blind pedestrians interact with vehicles. However, the best measure of safety remains the field-measured rate of O&M interventions presented in Chapter 5. Chapter 7 discusses in more detail the interpretation of the results and the implica- tions for roundabout and CTL facility design. Delay Estimation Introduction The analysis results in Chapter 5 confirmed the hypothesis that pedestrian–vehicle interaction at unsignalized round- about and channelized turn lane crosswalks is characterized by a mix of pedestrians’ (crossable) gap acceptance and driver yielding behavior. Both represent crossing opportunities since pedestrians cross in between two vehicles (gap) or in front of a yielding vehicle. The crosswalks are typically marked with a zebra pattern or another form of marking (Rodegerdts et al. 2007) and feature a pedestrian splitter island to separate the interaction between different directions of moving traffic. State motor vehicle codes commonly give pedestrians the right- of-way within the crosswalk, suggesting that roundabouts and CTLs should be very accessible to pedestrians. But yielding laws can be misinterpreted, and the actual yielding behavior varies over a range of observed values at different sites and geometries (Fitzpatrick et al. 2006). Consequently, pedestrians are expected to experience some delay when attempting to cross at these locations. The interaction of the two modes therefore needs to be rep- resented by a “mixed-priority delay model” (Schroeder and Rouphail 2010) that acknowledges the mix of yielding and gap acceptance. The 2000 Highway Capacity Manual (TRB 2000), the guidebook for traffic operational analysis methodologies for the United States and many other countries, currently offers C H A P T E R 6 Study Extensions

no delay methodology for a mixed-priority crossing situation, where drivers sometimes yield to create crossing opportuni- ties but where pedestrians sometimes have to rely on their judgment of gaps in traffic to cross the street. The HCM gap- acceptance–based methods are limited to cases where pedestri- ans have full priority (100% of traffic yields) or where drivers have priority (no yields) and pedestrians are limited to cross- ings in gaps between moving vehicles only. An updated pedes- trian delay model that allows for a reduction of pedestrian delay due to driver yielding is being considered for the 2010 release of the HCM. However, the proposed theoretical model is not calibrated from field data and does not distinguish between different subpopulations of pedestrians. With currently available HCM pedestrian delay models, it is therefore not possible to represent the mixed-priority interaction that was observed at the studied CTL and round- about crosswalks. Furthermore, the HCM approach does not adequately capture the observed utilization rates of cross- ing opportunities. For example, a gap-acceptance–based delay model assumes that pedestrians utilize every cross- able gap, which was found not to be the case for blind pedes- trians. This section develops mixed-priority pedestrian delay models that capture the mix of yields and crossable gaps encountered and acknowledge the different utilization rates observed for different sites and by different participants. A more detailed description of the delay model development is given in Appendix K. Approach The mixed-priority delay models are developed on the prem- ise of the accessibility framework presented in Chapter 4. It is hypothesized that the rates of occurrence and utilization of yield and gap crossing opportunities are correlated to pedestrian delay. Using a multi-linear regression approach, the dependent variable, delay, can therefore be described as a function of the four probability parameters P(Y_ENC), P(CG_ENC), P(GO|Y), and P(GO|CG). Chapter 5 contains the raw data used to generate the results for each participant at each of the test sites, along with the average delay experienced by that participant. In the field experiments, blind participants crossed inde- pendently at three different single-lane roundabouts, two crosswalks at a two-lane roundabout, and two crosswalks at an intersection with CTLs. In each study, each participant crossed multiple times. Each trial consisted of four lane crossings at roundabouts (for example, entry–exit–exit–entry) and two lane crossings for the CTL (curb–island and island–curb). At each site, every pedestrian completed multiple trials to obtain an estimate of average crossing performance. These crossing- specific averages were used in the mixed-priority delay model development. Variable Definitions Many of the variables used in the delay model development are similar to the ones included in the Chapter 5 analysis and have been defined in Chapter 4. Initial independent variables included P(Y_ENC), P(CG_ENC), P(GO|Y), and P(GO|CG). The dependent variable for the models is the average pedes- trian delay from the time a trial started until a crossing was initiated. For model development, some additional explanatory vari- ables are defined. They are obtained by manipulating the orig- inal behavioral probabilities. • P(Y_and_GO): The probability of crossing in a yield, defined as the probability of encountering a yield multiplied by the probability of utilizing a yield: – P(Y_and_GO) = P(Y_ENC) ∗ P(GO|Y). • P(CG_and_GO): The probability of crossing in a crossable gap, defined as the probability of encountering a CG multi- plied by the probability of utilizing a CG: – P(CG_and_GO) = P(CG_ENC) ∗ P(GO|CG). • P(Cross): The probability of crossing, defined as the sum of the probabilities of crossing in a yield or crossing in a cross- able gap. – P(Cross) = P(Y_and_GO) + P(CG_and_GO) Different delay models were developed for the three types of sites: CTL, single-lane roundabout, and two-lane round- about. Some additional binary variables were defined to dis- tinguish between different sites, different crossings, different treatments, and pretest and posttest treatment periods. The model development uses a multi-linear regression approach to predict the dependent variable, delay, as a func- tion of various independent variables. All variables are given on a per-leg basis at the roundabout, and as a result, the total delay for a two-stage crossing at a roundabout is twice the estimate (assuming the probabilities are the same). CTL crossings are single-stage only. A histogram of the distribution of the delay variable showed significant skew to the left, suggesting a log- normal distribution. Consequently, all predictive probability variables were transformed by applying the natural logarithm of the variable. All regression is performed in SAS statistical analysis software (SAS 1999) using PROC GLM, a procedure to perform multi-linear regression. Results This section presents an overview of the resulting delay mod- els. Results are presented consecutively for the CTL, single-lane roundabout, and two-lane roundabout models, respectively. The results include the recommended delay equation for the three classes of crossings as well as a graphical representation 63

of the models. The graphs are only shown for illustrative pur- poses since only one or two dimensions can be shown at one time. For example, delay might be a function of four param- eters [(P(Y_ENC), P(GO|Y), P(CG_ENC), and P(GO|CG)], but assumptions need to be made on some variables in order to produce a visual plot of others. In application of the mod- els, analysts should always use the equation form of the model. For additional details on model development, the reader is directed to Appendix K. Channelized Turn Lane Delay Model A total of 30 participants (16 pretest and 14 posttest) were included in the analysis. Each observation represents the aver- age of 12 to 20 trials (6 to 10 round trips with two crossing tri- als each). With the distinction of the two studied crosswalks as well as pretest and posttest observations, the dataset thus con- tains 60 observations. One observation had to be excluded from the dataset since the participant did not encounter any yielding from drivers. As a result the final dataset contained 59 observations. Various model forms were tested and are discussed in detail in Appendix K. Model selection was guided by statistical sig- nificance (overall model significance, parameter significance, and adjusted R-square value), as well as practical significance (model simplicity, reasonableness of results, fit with field- observed data). Equation 1 shows the suggested pedestrian delay model. Equation 1. Suggested pedestrian delay model for CTL. where dp = average pedestrian delay (s) PCROSS = the natural logarithm of the probability of cross- ing [= P(Y_ENC) ∗ P(GO|Y) + P(CG_ENC) ∗ P(GO|CG)]. The suggested delay model for channelized turn lanes pre- dicts pedestrian delay as a function of the natural logarithm of PCROSS, which is calculated from the four individual proba- bility parameters. The overall model and the PCROSS parameter are significant (p < 0.0001). The adjusted R-square value sug- gests that 79.3% of the variability in the delay is explained by the model, which is very high given that inter-participant variability of crossing performance was very high. Figure 25 shows the fit of the model against field-observed data. Since the LN(PCROSS) term represents a combination of encounter and utilization parameters, it can be used to test the sensitiv- ity of the different probability components. The two curves contained in Figure 25 therefore show the predicted delay for 50% opportunity utilization (both crossable gaps and yields) and 100% utilization. The latter approximates the delay a sighted pedestrian may have experienced if encountering the same crossing opportunities. The curves were created by vary- ing P(Y_ENC) and P(CG_ENC) from 0 to 1.0 while keeping the values of P(GO|Y) and P(GO|CG) constant at 0.5 and 1.0. d LN Pp CROSS= − ( )0 89 17 75. .  64 This figure shows a chart of the developed mixed-priority delay model for the CTL. The chart plots the relationship between the probability of encountering yield and gap events on the x-axis and the pedestrian all crossing opportunities and pedestrians who only utilize 50% of opportunities. The graph further shows the field-observed data points for pretest and posttest, as well as the field-observed (theoretical) minimum delay for the pedestrians. 0 10 20 30 40 50 60 70 80 90 100 0% 20% 40% 60% 80% 100% Pe de s tr ia n D el a y an d M in De la y (s) . P(Y_ENC)=P(CG_ENC) Channelized Turn Lane Delay Model 50% Utilization 100% Utilization Raw Data- Pre Raw Data-Post Raw Data Min Delay Figure 25. Graphical comparison of CTL delay model against field data.

The two curves are plotted against the raw average delay data for pretest and posttest conditions. Finally, the figure contains the theoretical average minimum delay for each data point. In interpreting the figure, the raw data should be compared against the 50% utilization curve, while the minimum delay data should be compared against the 100% utilization curve. The figure shows that the general trends of the model delay curves fall within the area of observed data, as was suggested by the high model adjusted R-square value. The exponential model form predicts high delays when PCROSS is in the range of 0 to 20%, corresponding to a very low occurrence of cross- ing opportunities (since utilization is fixed). As the availabil- ity of crossing opportunities increases, the delay drops, which is supported by the field data. The distinction between pretest (filled circles) and posttest (hollow circles) shows a general trend toward higher PCROSS and lower delay after treatment installation. In this context it is important to emphasize that the treatment effect is not explicitly included in the model. While this was tried in model development, the treatment dummy variable was not significant with the PCROSS variable also in the model. This indicates that any treatment effect is implicitly represented in the variability of PCROSS. This finding gives confidence to the model form and allows its application beyond the treatments tested by varying the underlying probability terms. One example for this type of sensitivity analysis is the 100% utilization curve that hypothesizes the delay experienced by a (sighted) pedestrian who utilizes every opportunity. The trend for that curve fits well with the observed minimum delay raw data, which represents the minimum theoretical delay if the very first crossing opportu- nity was always utilized by a participant. Single-Lane Roundabout Delay Model A total of 40 participants were included in the analysis from three different single-lane roundabout sites. Each observation represents the average of four or more crossing trials at a par- ticular site. With the distinction of entry versus exit crossings, the dataset contained 80 observations. However, four obser- vations had to be excluded since these participants had one or more zero observations because they either didn’t encounter any crossable gaps or because no drivers yielded for them. As a result, the final dataset contained 76 observations. No treat- ments were installed at any of the tested single-lane round- abouts, and consequently there is no posttreatment data. Various model forms were tested and are discussed in detail in Appendix K. Model selection was guided by statistical sig- nificance (overall model significance, parameter significance, and adjusted R-square value) as well as practical significance (model simplicity, reasonableness of results, fit with field- observed data). Equation 2 shows the suggested pedestrian delay model. Equation 2. Suggested pedestrian delay model for single- lane roundabouts. where dp = average pedestrian delay (s) PCROSS = probability of crossing [= P(Y_ENC) ∗ P(GO|Y) + P(CG_ENC) ∗ P(GO|CG)]. The suggested delay model for channelized turn lanes pre- dicts pedestrian delay as a function of the natural logarithm of PCROSS, which is calculated from the four individual proba- bility parameters. The overall model and the PCROSS parame- ter are significant (p < 0.0001). The adjusted R-square value suggests that 63.6% of the variability in the data is explained by the model, which is very high given that inter-participant variability of crossing performance was very high. Figure 26 shows the fit of the model against field-observed data. Since the LN(PCROSS) term represents a combination of encounter and utilization parameters, it can be used to test the sensitivity of the different probability components. The two curves contained in Figure 26 therefore show the pre- dicted delay for 50% opportunity utilization (both crossable gaps and yields) and 100% utilization. The latter approxi- mates the delay a sighted pedestrian might have experienced if encountering the same crossing opportunities. The curves were created by varying P(Y_ENC) and P(CG_ENC) from 0 to 1.0 while keeping the values of P(GO|Y) and P(GO|CG) constant at 0.5 and 1.0. The two curves are plotted against the raw average delay data for pretest and posttest conditions. Finally, the figure contains the theoretical average minimum delay for each data point. In the interpretation of the figure, the raw data should be compared against the 50% utilization curve, while the minimum delay data should be compared against the 100% utilization curve. The figure shows that the general trends of the model delay curves fall within the area of observed data, as was suggested by the high model adjusted R-square value. The exponential model form predicts high delays when PCROSS is low, correspon- ding to a very low occurrence of crossing opportunities (since utilization is fixed). As the availability of crossing opportuni- ties increases, the delay drops, which is supported by the field data (black circles). Similar to the CTL model, the 100% uti- lization curve fits well with the observed minimum delay data. Two-Lane Roundabout Delay Model The two-lane roundabout model utilized different inde- pendent variables that are consistent with the revised analysis framework for two-lane approaches presented in Chapter 4. The reader may recall that crossing a two-lane roundabout requires the consideration of three different event conditions d LN Pp CROSS= − ( )0 78 14 99. .  65

for each lane (crossable gap, non-crossable gap, and yield) resulting in nine different combinations. A crossable situa- tion is defined as encountering either a yield or a crossable gap. From these nine combinations, four yield crossable sit- uations in both lanes: Yield–Yield, Yield–CG, CG–Yield, and CG–CG. There are four other combinations that have cross- able situations in only one of the lanes (Yield–non-CG, CG–non-CG, non-CG–Yield, and non-CG–CG). The remain- ing combination has a non-crossable gap in both lanes. These combinations introduce new probability terms that are defined below: • PA_Dual: This is the probability of encountering a cross- able situation (i.e., crossable gap or yield) in both lanes. • PU_Dual: This is the probability of utilizing a situation that has a crossable situation (crossable gap or yield) in both lanes. • P_Dual_Cross: This is the probability of crossing when both lanes have a crossable situation, defined as PA_Dual times PU_Dual. A total of 31 participants were included in the analysis, including pretest (18 participants) and posttest treatment (13). Each observation represents the average of 16 crossing trials [four round trips, each with crossing trials from curb to splitter island at entry (exit), from splitter island to curb at exit (entry), and going back] at each of two approaches of the two-lane roundabout. However a few of the observations had to be excluded from the dataset since the participant did not encounter any yields from drivers. As a result the final dataset contained 124 observations Various model forms were tested and are discussed in detail in Appendix K. Model selection was guided by statistical sig- nificance (overall model significance, parameter significance, and adjusted R-square value) as well as practical significance (model simplicity, reasonableness of results, fit with field- observed data). Equation 3 shows the suggested pedestrian delay model. Equation 3. Suggested pedestrian delay model for two- lane roundabouts. where dp = average pedestrian delay (s) PDual_Cross = probability of crossing when both lanes have a crossable situation in the form of a crossable gap or a yield (= PA_Dual ∗ PA_Dual). The suggested delay model for channelized turn lanes pre- dicts pedestrian delay as a function of the natural logarithm of PDUAL_CROSS, which is calculated from the availability and encounter probability of dual crossing opportunities. The d LN Pp Dual CROSS= − ( )1 9 21 0. . _ 66 0 10 20 30 40 50 60 70 80 90 100 0% 20% 40% 60% 80% 100% Pe de st ria n D e la y & M in . D e la y (s) P(Y_ENC)=P(CG_ENC) Single-Lane Roundabout Delay Model 50% Utilization 100% Utilization Raw Data - D elay Raw Data - M in. Delay This figure shows a chart of the developed mixed-priority delay model for the single-lane roundabout. The chart plots the relationship between the probability of encountering yield and gap events on the x-axis and the pedestrian delay in seconds on the y-axis. The graph shows two curves, representing pedestrians with 100% utilization of all crossing opportunities and pedestrians who only utilize 50% of opportunities. The graph further shows the field-observed data points for pretest and posttest as well as the field-observed (theoretical) minimum delay for the pedestrians. Figure 26. Graphical comparison of single-lane roundabout delay model against field data.

overall model and the PCROSS parameter are significant (p < 0.0001). The adjusted R-square value suggests that 78.7% of the variability in the data is explained by the model, which is very high given that inter-participant variability of crossing performance was very high. Figure 27 shows the fit of the model against field-observed data. Since the LN(PDUAL_ROSS) term represents a combination of encounter and utilization parameters, it can be used to test the sensitivity of the different probability components. The two curves contained in Figure 27 therefore show the predicted delay for 50% opportunity utilization and 100% utilization. The latter approximates the delay a sighted pedestrian might have experienced if encountering the same crossing opportu- nities. The curves were created by varying PA_Dual from 0 to 1.0 while keeping the values of PU_DUAL constant at 0.5 and 1.0. The two curves are plotted against the raw average delay data for pretest and posttest conditions. Finally, the figure contains the theoretical average minimum delay for each data point. In the interpretation of the figure, the raw data should be compared against the 50% utilization curve, while the min- imum delay data should be compared against the 100% uti- lization curve. The figure again shows a predicted decrease in delay with increase in the availability of dual crossing opportunities. The shape of the curves is characteristic of the logarithmic model form. In a comparison to the field-observed delay (filled cir- cles), the 50% utilization curve appears to overpredict delay. This is because the field-observed utilization rates (of dual events) for blind pedestrians were very high at this site, on the order of 90% for both pretest and posttest. Consequently, the field-observed delay matches more closely with the 100% utilization curve, as it should. The 100% utilization curve expectedly is shifted downward compared to the 50% curve, corresponding to lower delay at the same PA_Dual encounter rate. The 100% curve matches well with the field-observed minimum delay values. The field-observed data for the posttest with PHB and RCW installed show no observations at PA_Dual less than 40%, whereas the pretest data is distributed over almost the entire range. The corresponding delay figures for the posttest data points are low and match the predicted delay model. Consequently, the delay improvements of the PHB and RCW treatments are consistent with the increased PA_Dual prob- abilities. Model Comparison This section compares the selected mixed-priority delay models for the three facility types. Since the models for CTLs and single-lane roundabouts use the same variable definitions 67 0 10 20 30 40 50 60 70 80 90 100 0% 20% 40% 60% 80% 100% Pe de st ria n De la y an d M in . D el ay (s ) PA_Dual Two-Lane Roundabout Delay Model 50% Utilization 100% Utilization Raw Data - Pre Raw Data - Post PHB Raw Data - Post RCW Raw Data - Min Delay This figure shows a chart of the developed mixed-priority delay model for the two-lane roundabout. The chart plots the relationship between the probability of encountering a dual crossing opportunity (gap or yield in both lanes) on the x-axis and the pedestrian delay in seconds on the y-axis. The graph shows two curves, representing pedestrians with 100% utilization of all crossing opportunities and pedestrians who only utilize 50% of opportunities. The graph further shows the field-observed data points for pretest and posttest (RCW and PHB), as well as the field-observed (theoretical) minimum delay for the pedestrians. Figure 27. Graphical comparison of two-lane roundabout delay model against field data.

and model form, they are directly comparable. The two-lane roundabout model uses revised definitions for explanatory variables, but a general comparison is still possible. Table 11 shows the final delay models for the three sites for comparison. All three models use natural-log transformed explanatory variables [LN(PCross) and LN(PDual_Cross)] with negative coefficients. Since the natural log of a low number is a large negative number [e.g., ln(0.1) = –2.3], this results in a high positive prediction (of delay) at low probabilities. With increasing probabilities the absolute value of the natural log decreases, thus dropping the predicted delay. A greater coeffi- cient therefore results in higher delays at low probabilities. For example, the fact that the CTL model has a higher absolute value coefficient (–17.75) compared to the single-lane round- about (–14.99) indicates that CTL delay is always higher than the single-lane roundabout. However, due to the nature of the model, the relative difference is greater at low probabilities than at higher ones since the natural log decreases in absolute value [e.g., ln(0.9) = –0.1]. As with a conventional linear regression model, the intercept shifts the curve upward (pos- itive coefficient) or downward (negative coefficient). How- ever, due to the relatively low absolute value of the intercept compared to the coefficient for Ln(PCross), the effect of the intercept on model form is negligible. In other words, in the general model for y = a + b ∗ ln(x), the parameter “b” in this case weighs much more heavily than parameter “a.” Following this discussion, the models predict greater delay for channelized turn lanes than for single-lane round- abouts, assuming the same traffic patterns and pedestrian behavior. While the dependent variable for the two-lane roundabout model is slightly different, its coefficient (–21.0) suggests that delays are greater at two-lane roundabouts than at the other sites, assuming that traffic patterns and user behavior are fixed. These comparisons are illustrated in Figure 28, which shows the three delay curves as a function of the explanatory variables LN(PCross) and LN(PDual_Cross) on the x-axis. As discussed above, the curve for two-lane roundabout delay is always higher than the CTL curve, which in turn pre- dicts higher delays than the single-lane roundabout curve. Due to the natural-log transformed model form, the relative difference between the curves decreases with higher probabil- ities of crossing. All three curves expectedly approach a delay of zero as those probabilities approach 1.0 or 100%. 68 CTL Single-Lane Roundabout Two-Lane Roundabout Intercept 0.89 –0.78 1.7* Ln(PCross) –17.75** –14.99 ** n/a Ln(PDual_Cross) n/a n/a -21.0** Pr>F <.0001 <.0001 <.0001 DF 1 1 1 R-Square 0.796 0.641 0.785 Adj. R-square 0.793 0.636 0.783 * Significant at p < 0.05 ** Significant at p < 0.01 Table 11. Comparison of delay models for three facility types. 0 10 20 30 40 50 60 70 80 90 100 0 0.2 0.4 0.6 0.8 1 Pe de st ria n De la y (s) P(Cross) or P(Dual_Cross) Delay Model Comparison CTL Single-Lane RBT Two-Lane RBT This figure shows a comparison chart of the three developed mixed-priority delay models for the channelized turn lane, single-lane roundabout, and two-lane roundabout. The chart plots the relationship between the probability of encountering a (dual) crossing opportunity on the x-axis and the pedestrian delay in seconds on the y-axis. RBT = roundabout. Figure 28. Delay model comparison for three facility types.

The comparison does not mean that all two-lane round- abouts will always produce higher delays than any single-lane roundabout or CTL. It merely says that a pedestrian will expe- rience higher delay at a two-lane roundabout than a single-lane roundabout (or CTL) when encountering the exact same traf- fic patterns and driver behavior and is furthermore capable of making the same judgments about gaps and yields. The actual performance of a particular site and the relative difference to other sites depends on the underlying probabilities that make up PCross and PDual_Cross. An approach for estimating these is dis- cussed in the next section. Model Application The mixed-priority pedestrian delay models presented in this section can theoretically be applied to other sites with dif- ferent geometries, traffic volumes, and pedestrian behavior. Clearly the application of any model beyond its realm of cal- ibration can be risky, and professional judgment should be applied. In general, these models are not intended to serve as the sole determinant of pedestrian accessibility and should not be used in isolation. As this report discusses, pedestrian delay is only one aspect of accessibility, with pedestrian risk being another that is equally if not more important. Clearly, the risk to pedestrians or the fact that a crossing may be avoided entirely if the real or perceived risk is too high needs to be con- sidered first and foremost. Further, Chapter 2 of this report discusses the other components of the crossing task, which include locating the crosswalk, aligning to cross, deciding when to cross, and maintaining alignment after the crossing is ini- tiated. The delay models are focused on the third component and therefore do not capture any additional delays that may occur when a pedestrian is challenged to locate the intended crossing point. Selecting Delay Thresholds The application of delay models is associated with the chal- lenge of defining thresholds for what is considered an accept- able wait time and whether these thresholds differ by facility type. The Highway Capacity Manual (TRB 2000) uses delay to stratify LOS for (sighted) pedestrians and other modes at signalized and unsignalized starting points. Logically, the HCM LOS tables could represent a starting point for the dis- cussion of acceptable delay thresholds. The HCM table for signalized and unsignalized pedestrian crossings is presented in Table 12. The table shows a stratification of LOS from A (best) to F (worst) using ranges of average delay per pedestrian for the crossing. From the HCM exhibits it is evident that the pre- sumed level of acceptable delay is greater at a signalized inter- section because the presence of the signal is associated with a certainty that a crossing opportunity will eventually present itself. Consequently, pedestrians may be more willing to accept greater delay at signals. However, the table recognizes quali- tatively that the likelihood of pedestrian risk taking (i.e., jay- walking against the signal or accepting short gaps in traffic) increases with higher pedestrian delay. The HCM LOS strat- ification does not distinguish between one-stage and two- stage crossings, so it is assumed here that the thresholds are intended to be applied to the entire crossing, which in the case of roundabouts represents the sum of delay experienced at the entry and exit leg. At channelized turn lanes, the total cross- ing delay accordingly includes the delay at the main inter- section and any additional CTLs that are in the path of the pedestrian. It is important to emphasize here that (blind) pedestrian delay can also be measured directly from field observations, which is usually the preferred approach. Any theoretical model is participant to variability and error, and direct field mea- surements are likely to provide a more unbiased estimate of delay or any other parameter. In the absence of field data, the remaining challenge in the application of the mixed-priority delay models is to identify appropriate model inputs. This is the focus of the next sections. Estimating Probability Parameters The probability parameters that are used as the explana- tory variables in the mixed-priority delay models can be esti- mated directly from field measurements or can be gleaned from the appropriate literature and traffic flow theory concepts. As with any model application, the use of field-measured prob- abilities is preferable since these give the analyst the greatest confidence. It is recognized that field measurements are often beyond the scope and budget of such analysis and are further precluded for newly planned locations. Field studies are also not applicable for sensitivity analyses that explore the poten- tial impact of implementing pedestrian treatments to improve accessibility at a particular location. 69 Delay Range (s/ped) LOS Signalized Unsignalized Likelihood of Noncompliance A <10 <5 Low B ≥10–20 ≥5–10 C >20–30 >10–20 Moderate D >30–40 >20–30 E >40–60 >30–45 High F >60 >45 Very high Table 12. Pedestrian LOS stratification, adopted from the HCM (TRB 2000).

The delay models for channelized turn lanes and single- lane roundabouts are based on the variable PCross, which is a function of the four probability terms P(Y_ENC), P(CG_ ENC), P(GO|Y), and P(GO|CG). For two-lane roundabouts, the explanatory variable is PDual_Cross, which is a function of the availability and utilization of crossing opportunities in both lanes, PA_Dual and PU_Dual. An analyst can apply the delay models to new sites and conditions by estimating these param- eters from field measurements or literature sources. For the field measurement of the explanatory variables, the rate of driver yielding and the availability of crossable gaps can be measured using manual tally and stopwatch methods described in the ITE Manual of Transportation Studies (1994) or other sources. The estimation of yield and gap utilization rates is more difficult for blind pedestrians since it requires controlled field experiments. In the absence of field data, the results from this research can be used in the interim, which is discussed in more detail below. For sighted pedestrians, uti- lization rates of or near 1.0 can be assumed. For other special pedestrian populations, including children and the elderly, analyst judgment will be required until further research char- acterizes their behavior. A basic sensitivity analysis can ensure that a range of values are considered. In the absence of field data, probabilities can also be estimated from the literature, which includes findings from this research and other field studies, as well as theoretical traffic flow relationships. Crossable Gap Encounters. The availability of crossable gaps can be estimated using traffic-flow theory concepts based on traffic volume and an assumed headway distribu- tion. Assuming random arrivals, one can use the negative exponential distribution to estimate the probability of observ- ing a time headway greater than tc seconds, per Equation 4. This equation assumes random arrivals of vehicles. For non- random arrivals, other distributions are available (May 1990). Equation 4. Estimating P(CG_ENC) from traffic flow theory (May 1990). where tc = critical headway for crossable gap (s) tavg = average headway, defined as tavg = (3,600 s/h)/(vph). In the absence of pedestrian platoons, the critical gap for pedestrians can be calculated by Equation 5 following the HCM methodology. Equation 5. Pedestrian critical gap after HCM Equa- tion 18-17 (TRB 2000). t L S tc p s= + P CG ENC P headway t ec tc tavg_( ) = ≥( ) = − where L = crosswalk length (ft), Sp = average pedestrian walking speed (ft/s), and ts = pedestrian start-up and clearance time (s). Using the above relationship, the probability of observing a crossable gap in a stream of 400 vph at a 14-ft lane at a round- about and a corresponding critical headway of tc = 14/3.5 + 2 = 6 s is: Yield Encounters. The probability of encountering a yielding vehicle is a function of driver courtesy and is also dependent on the geometry of the site, particularly the result- ing vehicle operating speeds. More yields are expected where vehicle speeds are low and where drivers expect the presence of pedestrians, including university campuses and down- town areas. Most field studies estimate the probability of yielding based on the number of vehicles that could have yielded, P(Yield). Note that this is different from the proba- bility P(Y_ENC) used in the delay model, which is calculated on the basis of all encountered vehicles and is a better rep- resentation of the flow rate that a pedestrian is likely to experience. A reasonable approach for estimating P(Y_ENC) from P(Yield) is to subtract the probability of crossable gaps from the total number of vehicle events: Equation 6. Estimating yield encounters from yield probabilities. This approach ensures that the sum of PY_ENC and PCG_ENC is less than or equal to 1.0, as is required by definition. The reader is referred to Chapter 4 for more detail on these event definitions. Probability estimates for the probability of yielding (PYield) are available from research. A recent national survey on round- about operations (Rodegerdts et al. 2007) has estimated yield probabilities for many single-lane and two-lane roundabouts. Table 13 shows observed ranges for single-lane approaches from that research along with findings from this project. The table shows significant variation across yielding rates for the studied sites. The averages and ranges from NCHRP Report 572 represent five single-lane roundabouts. These were the only studied sites that featured notable pedestrian activity. It appears that the single-lane roundabout yielding rates observed during this project are much lower than the ones observed in that project. A potential explanation for this is the different levels of pedestrian use and associated driver courtesy. The statistics do, however, point to the general trend that yield- ing rates at the exit lane are often lower than at the entry lane. P P PY ENC Yield CG ENC_ _%= −( ) 100 P CG Enc P headway e e tc tavg_ . %( ) = ≥( ) = = =− −6 51 369s 70

A comparison between roundabouts and the CTL studies under NCHRP Project 3-78A further points to low CTL yield- ing behavior at the tested sites. It is expected that a wider range of rates would be observed with a greater sample of CTL sites with varying geometry. Gap and Yield Utilization. The remaining explanatory probability variables are the rates of utilization for yield and crossable gap opportunities. It was hypothesized above that most sighted pedestrians would be assumed to accept most or all first yield and crossable gap opportunities. Their rates of utilization for those events would therefore be assumed to equal 1.0. For blind pedestrians, utilization rates much lower than 100% have been observed in this research as well as in prior studies. Individual differences and unique audi- tory characteristics of different sites are expected to affect these rates. Tables 14 and 15 summarize the utilization rates observed at single-lane roundabout and CTL crossings in this research, respectively. Two-lane roundabouts are dis- cussed separately. The tables show average utilization rates for all sites in the range of 50% to 80%. The utilization rates are highest at the GOL-PRE single-lane roundabout. The statistics further show a large range of these values across study participants, making it difficult to generalize for the entire population of blind pedes- trians. If a user chooses to apply the average utilization rate, higher delays (due to lower utilization rates) can be expected for half of the population of blind travelers. As discussed in Chap- ter 5, the installation of crossing treatments at the CTL had some impact on the utilization statistics. The installation of sound strips only (SS-ONLY) resulted in a slight decrease of yield utilization. The added use of a flashing beacon (SS+FB) increased both yield and crossable gap utilization. Numerical Illustration for Single-Lane Roundabout. This section presents an example calculation for a single-lane roundabout that will be used by a population of blind pedes- trians. The delay equation for a single-lane roundabout was given previously by Equation 2, which expands to: where all terms are as defined previously. To estimate the delay at a site, the analyst would first esti- mate the availability of yield and crossable gap opportunities. In this context, it is critical that these two probabilities use the same common denominator in the total number of vehicle d LN P LN P p CROSS Y = − − ( ) = − − 0 78 14 99 0 78 14 99 . . . . _   ENC GO Yield CG ENC GO CGP P P +( )_ 71 Single-Lane Roundabouts CTL NCHRP Report 572 NCHRP Project 3-78A Averages Average Range DAV-CLT PS-RAL GOL-PRE NCHRP Project 3- 78A Sites Entry Lane Curb–island 85% 65%–100% Island–curb 90% 50%–100% 10.8% 41.5% 65.6% Exit Lane Curb–island 71% 17%–100% Island–curb 85% 33%–100% 11.8% 32.8% 36.1% 26.1% Table 13. Yield probabilities (PYield), for single-lane approaches. Single-Lane Roundabout DAV-CLT PS-RAL GOL-PRE Avg. Range Avg. Range Avg. Range P(GO|Y) Entry lane 64.1% 0%–100% 83.0% 50%–100% 82.8% 36%–100% Exit lane 70.4% 0%–100% 87.8% 60%–100% 76.0% 25%–100% P(GO|CG) Entry lane 66.3% 25%–100% 52.0% 0%–100% 83.2% 33%–100% Exit lane 60.3% 33%–100% 63.6% 19%–100% 86.8% 40%–100% Table 14. Yield and crossable gap utilization rates at studied single-lane roundabouts.

events. By definition, the sum of PY_ENC and PCG_ENC can there- fore never exceed 1.0, which would correspond to every vehi- cle event constituting a crossing opportunity. Since the two probabilities are related, it is expected that an increase in yielding will correspond to a lower fraction of encountered events being crossable gaps. For the example, assume peak hour conflicting traffic flow at the site is 800 vph and the pedestrian critical gap is esti- mated at 6 s. At 800 vph, the average headway between vehi- cles is 3600/800, or 4.5 s. The probability of encountering a crossable gap greater than 6 s in this traffic stream is given by: It is further assumed that the analyst knows from field studies that 30% of the remaining traffic is expected to yield. The probability of encountering a yield is therefore given by (100% – 26.4%) ∗ 30% = 22.1% of vehicle encounters. Referring to Table 15, the analyst estimates that the utiliza- tion rates for yields and crossable gaps are 40% and 30%, respectively. This is about half of the average rates found in this research, and was selected to represent a more conserva- tive and less skilled blind traveler: Since this delay estimate is per crossing leg, the total approach delay is estimated at 52.0 s on average, which falls within HCM LOS = F for unsignalized crossings. This assumes that the behavioral parameters at the entry and exit legs are exactly the same. This simplifying assumption was only done for this example. In reality, the analyst should carefully con- sider the differences between entry and exit legs, including traffic volumes, vehicle speeds, and yielding behavior. As a comparison, a sighted pedestrian would have experienced a delay of: Consequently, the delay for a blind pedestrian with the assumed lower utilization rates would be 2.6 times higher than d LNp = − − +( ) =0 78 14 99 0 221 1 0 0 264 1 0 10 1. . . . . . .   s d LNp = − − +( ) =0 78 14 99 0 221 0 4 0 264 0 3 26 0. . . . . . .   s P CG ENC P headway e e tc tavg_ . .( ) = ≥( ) = = =− −6 2664 5s . %4 for a sighted pedestrian facing the same traffic conditions and driver behavior. A pedestrian treatment that improves driver yielding from 30% to say 75% would increase PY_ENC to (100% – 26.4%) ∗ 75% = 55.2% and would improve the delay for the blind pedestrian to: Compared to the baseline delay of 26.0 s, this pedestrian treatment resulted in a 33.6% reduction in delay to the blind travelers. The total delay for both legs is reduced to 34.6 s. The treatments also helped sighted pedestrians and reduced their delay from 10.1 s to only 2.6 s on average: The analyst can easily perform additional sensitivity analy- ses to test the hypothesized effects of other treatments or changes in the conflicting traffic volumes. Estimating Probabilities for Two-Lane Approaches. Since the probability terms for two-lane roundabouts are different than for single-lane approaches, their estimation is discussed separately. The two-lane roundabout crossing process is characterized by the availability and utilization of dual crossing opportunities, which can be in the form of either a yield or a crossable gap in both conflicting lanes at the same time. The mixed-priority delay equation given above expands to: where all terms are as defined previously. The probability of encountering either a crossable gap or a yield in both lanes, PA_Dual, is calculated as follows. 1. The analyst calculates the likelihood of encountering a crossable gap in each lane, based on the estimated per-lane traffic volumes using Equation 4. The resulting probabil- ities are PCG1 and PCG2, for lanes 1 and 2, respectively. Lane 1 is defined to be the one closest to the pedestrian. 2. The analyst estimates the probability of yielding in each lane, PYield_Lane1 and PYield_Lane2, from field observations or literature. 3. The analyst calculates the probabilities of encountering a yield event in each lane PY_ENC1 and PY_ENC2 using Equation 6 and the results of steps 1 and 2. 4. The analyst estimates the probability of encountering a dual crossing opportunity in both lanes by the following equation: d LN P LN P p DualCROSS A Du = − ( ) = − 1 9 21 0 1 9 21 0 . . . . _   al U DualP _( ) d LNp = − − +( ) =0 78 14 99 0 552 1 0 0 264 1 0 2 3. . . . . . .   s d LNp = − − +( ) =0 78 14 99 0 552 0 4 0 264 0 3 17 3. . . . . . .   s 72 Average Range P(GO|Y) PRE 51.9% 0%–100% POST-SS-ONLY 40.5% 10%–75% POST-SS+FB 64.6% 20%–100% P(GO|CG) PRE 61.8% 4%–100% POST-SS-ONLY 68.2% 6%–100% POST-SS+FB 89.3% 58%–100% Table 15. Yield and crossable gap utilization rates at studied channelized turn lanes.

Equation 7. Estimating yield encounters from yield probabilities. where PA_Dual = probability of encountering crossing opportunity in both lanes, PY_ENC1 = probability of encountering a yield in lane 1, PY_ENC2 = probability of encountering a yield in lane 2, PCG1 = probability of encountering a crossable gap in lane 1, and PCG2 = probability of encountering a crossable gap in lane 2. The results from this research can again be used as guid- ance for the estimation of the probability of utilizing a dual crossing opportunity. Table 16 summarizes field-observed probabilities of encountering and utilizing dual crossing oppor- tunities for the studied two-lane roundabout in the pretest condition. The analyst can follow the procedure above to estimate the PA_Dual and PU_Dual probabilities for a two-lane round- about and calculate the predicted average pedestrian delay using Equation 3 for two-lane approaches. A numerical exam- ple is not provided but is consistent with the example presented for single-lane roundabouts. Impacts of Pedestrian Crossing Treatments The underlying hypothesis of the NCHRP Project 3-78A analysis framework and these delay models is that there exists the ability to represent the impact of pedestrian crossing treat- ments through changes in the probability terms. This allows the analyst to quantify the impact of any treatment on pedes- trian delay. Chapter 5 presented a detailed discussion of the measured impacts for the pedestrian treatments studied in this research. Consistent with the discussion in Chapter 2, various pedestrian treatments not tested in this research have a similar ability to reduce pedestrian delay. P P P P P P P A Dual Y ENC Y ENC Y ENC CG CG _ _ _ _= + + 1 2 1 2 1    Y ENC CG CGP P_ 2 1 2+  Among the most common treatments are those intended to increase the probability of drivers to yield to pedestrians, which was one of the key focus areas of NCHRP Report 562 (Fitzpatrick et al. 2006). While data collection in that research was focused on midblock crossings, the results provide an overview of the average and range of yielding rates observed for different treatments across the country. The reader is encouraged to consult that and similar research for further information. Delay Model Discussion The previous section demonstrated the application of a framework based on pedestrian and driver behavioral param- eters for estimating pedestrian delay at single- and two-lane roundabouts as well as at channelized turn lanes. The under- lying dataset was obtained from controlled experiments using more than 100 blind participants at seven different sites. The focus on blind pedestrians provided a framework that distin- guished between available crossing opportunities and the actual utilization of these opportunities. A dataset containing only sighted pedestrians would not be expected to capture the utilization effect. The resulting delay models are statistically significant and produce good estimates of pedestrian delay that match observed field data. The underlying probability terms can be estimated from field observations for other sites or can be estimated from literature or traffic flow theory concepts. The resulting models allow the analyst to distinguish delay encoun- tered at CTLs, single-lane roundabouts, and two-lane round- abouts. It further allows the analyst to represent the impact of pedestrian crossing treatments on delay. Extension to Safety Modeling As discussed earlier in this chapter and emphasized through- out this report, delay is only one factor when evaluating the accessibility and usability of a crosswalk. Another, potentially more critical aspect is the safety or risk associated with cross- ing at a particular location. This report uses the measure of O&M interventions to quantify the risk involved in crossing decisions by blind study participants. Clearly, it would be desirable to develop study extension tools for the assessment of pedestrian safety, similar to the delay models described above. The development of predictive models for pedestrian risk or safety is constrained by a limitation of the risk perfor- mance measure of O&M interventions. Since interventions are very rare events, it is difficult to apply the regression-based modeling approach to this measure. The reason is that most of the observations result in a dependent variable value of zero (no interventions) while being associated with a range of underlying yield, gap, and utilization probability terms. 73 Average Range PA_Dual PRE 55.8% 15%–93% POST-RCW 76.9% 57%–100% POST-PHB 89.3% 72%–100% PU_Dual PRE 90.0% 44%–100% POST-RCW 98.1% 94%–100% POST-PHB 98.3% 83%–100% Table 16. Field-observed performance at two-lane roundabout.

The resulting usable dataset for non-zero intervention cross- ing events is therefore very small. Recognizing that the event of an O&M intervention can be treated as a binary event (yes/no), it would be feasible to apply a logistic regression approach to these data. However, it is unclear how useful such models would be to practitioners. An alternative and potentially more promising approach for safety modeling is feasible with the introduction of new dependent variables for pedestrian risk. Since the biggest lim- itations of the O&M intervention measure are its binary nature and rare occurrence, a revised variable should be con- tinuous and frequently observable. In particular, the project team discussed the use of two vari- ables that meet these criteria. The first is the theoretical time to collision of pedestrian and vehicle in seconds, which is calcu- lated from the speed and position of the vehicle at the instant the pedestrian steps into the crosswalk. The second is the nec- essary deceleration rate in feet per second squared that is nec- essary for the vehicle to come to a stop before the crosswalk. This measure is also calculated from the speed and position of the vehicle at the time the pedestrian steps into the cross- walk. This metric is further related to standard engineering sig- nal timing practice, where a similar deceleration rate is used to calculate the length of the yellow interval at signals (ITE 2009). The development of these measures requires real-time field measures of vehicle speed and position that were not avail- able in this study. The feasibility of this approach has been demonstrated in other research (Schroeder 2008), where it was used to develop predictive models for driver yielding and pedestrian gap acceptance at unsignalized crossings. The approach is being explored in ongoing research on the acces- sibility of complex intersections to pedestrians who are blind (NIH 2010). Simulation Approach The NCHRP Project 3-78A analysis framework fits within the context of modern microsimulation tools. These software tools work on the basis of algorithms that describe driver behavioral rules for car following, lane changing, gap accept- ance, and routing. Many of the commercially available prod- ucts further allow the user to code both motorized and non- motorized transportation modes. The models differ in the specifics of how the interaction between vehicles and pedes- trians is modeled and how much flexibility the user has in modifying and calibrating behavioral parameters. However, most models apply some sort of a gap acceptance algorithm to model pedestrians selecting gaps in traffic or to model driv- ers yielding to pedestrians. Depending on the model, the user also may have the ability to model mixed-priority situations where some drivers yield and some pedestrians cross in large gaps, as was discussed in the previous section. This distinc- tion is critical to the implementation of the NCHRP Project 3-78A analysis framework. Furthermore, it will be necessary to represent different populations of drivers (courteous or not) and pedestrians (blind and sighted) to adequately cap- ture the crosswalk interaction as observed in this study. Assuming that a particular model can adequately address these aspects and can be calibrated to represent specific behav- ioral and traffic conditions, a simulation analysis is ideally suited to extrapolate performance results to other geometry and traffic patterns. The approach is also ideally suited for con- ducting sensitivity analyses of different parameters. In effect, a simulation-based analysis represents a second option for extending the field results from NCHRP Project 3-78A to other conditions. The first extension is of course the use of the delay models discussed in the previous section. Simulation has the added benefit that it can evaluate unique traffic characteristics, the impacts of nearby intersections, or the use of pedestrian signals (or PHBs) at the crosswalk in question. Finally, simu- lation models are increasingly used to perform surrogate safety analysis based on vehicle trajectories (FHWA 2008). It is beyond the scope of this project to discuss in detail the variety of simulation tools available and to what extent they capture the interaction of pedestrians and vehicles at cross- walks. The focus of this section is to discuss the use of simu- lation analysis in two principal ways: 1. How to represent the analysis framework in simulation and findings from a sensitivity analysis of different behav- ioral and traffic-related model parameters. The objective is to guide other efforts of those who wish to further extend results from this research in a simulation environment. This section is primarily based on the work published in Schroeder and Rouphail (2007). 2. A detailed analysis of different signalization options at single-lane and two-lane roundabouts, including a com- parison of PHB and conventional signals, one-stage and two-stage crossings, and different crosswalk geometries. The analysis is performed using calibrated representative models of a single-lane and a two-lane roundabout and explores operations for a range of vehicle and pedestrian volumes. The emphasis is on pedestrian-induced vehicle delay and queuing impacts with the objective to provide decision support for agencies that are considering signal- ization as one of the treatments at roundabout pedestrian crossings. This section is primarily based on the work pub- lished in Schroeder, Rouphail, and Hughes (2008). Applying the Framework to Simulation The NCHRP Project 3-78A analysis framework uses the principles of gap and yield availability as well as the rate of uti- lization of both types of crossing opportunities. The availabil- 74

ity parameters represent characteristics of the traffic stream and are a function of traffic volumes, speed, and driver behavior. The utilization parameters are pedestrian behavior attrib- utes that describe a pedestrian’s ability and willingness to cross in a yield or gap situation. The analysis framework further uses the performance measure of delay and risk to quantify the pedestrian’s ability to cross at a particular location. The four availability and utilization probability parameters serve as inputs when the analyst sets up the simulation model. The analyst codes these after defining model geometry, traf- fic control strategies (signals), volumes, and other inputs. The remaining delay and risk performance measures are model outputs that are calculated from the simulation. It is beyond the scope of this report to describe the details of simulation mod- eling and the wide variety of modeling and calibration param- eters that are available to the analyst. The FHWA has extensive resources available through the “Traffic Analysis Toolbox” (2010) that the analyst can use for further information on sim- ulation modeling, calibration, and validation. The remainder of this section focuses on the proposed approach for modeling the interaction between pedestrians and vehicles. Modeling Treatments Based on the framework described above, the purpose of a treatment is to enhance or minimize delay and risk for pedes- trians without negatively affecting traffic flow. It was hypothe- sized and demonstrated that the functional effect of a treatment can be described through a combination of the four underlying probability parameters. This can be done in one of four ways: 1. Increasing the occurrence of driver yielding: Previous research implies that slower speeds, increased driver aware- ness, and education/enforcement may be able to achieve this. Some natural speed reduction also occurs at high flows. Treatments addressing yielding could include warning signs, flashing lights, or raised crosswalks. 2. Increasing the occurrence of crossable gaps: It is unclear if there are treatments whose sole purpose is an increase in the availability of crossable gaps, but a number of situa- tions will have an impact, including upstream signals or more conservative driver behavior. Ultimately, the biggest factor affecting this parameter is the amount of conflict- ing traffic. 3. Increasing the probability of yield utilization: Treat- ments may help blind pedestrians and others to more reli- ably detect the presence of yielding vehicles or increase their level of confidence in accepting yields. The list of potential treatments includes pavement sound strips, sur- face treatments, and automated yield detection technology. 4. Increasing the probability of gap utilization: There may be treatments that enable pedestrians to perform better gap judgment so as to decrease the frequency of risky or overly conservative decisions. Examples include improved lighting conditions and automated gap detec- tion technology. The functional effect of a treatment installation is repre- sented in simulation through a net increase (or decrease) in one or more of the probability terms. The proposed approach for modeling treatments is therefore implicit, through changed behavioral parameters, rather than explicit, through a build- ing block included in the simulation tool. The one exception to this approach is when a treatment involves the use of sig- nalized traffic control. This aspect is discussed toward the end of this chapter. Setting up Behavioral Parameters This section discusses how the four probability parameters could be implemented in a simulation. Differences among drivers and pedestrians are best represented through the use of multiple vehicle and pedestrian classes. For example, two driver classes may be modeled: those with and those without the propensity to yield. Similarly, two or more pedestrian classes may be modeled with different gap acceptance thresh- olds. In particular, the four probability parameters would be modeled as follows: • The availability of yielding should be modeled through the use of multiple vehicle classes. The gap acceptance algo- rithm at the crosswalk that effectively tells drivers to look for gaps in the pedestrian traffic will lead a potential yielder to slow in the presence of a pedestrian. The vehicle classifi- cation of whether or not a driver is a potential yielder is sto- chastically assigned to each vehicle as it enters the simulated system. Note that these are actually “potential yielders” since some vehicles tagged as yielders may not encounter a pedestrian at the crosswalk or may be too close to the cross- ing to be able to yield when the pedestrian shows up. This probability will vary for the entry and exit legs of a round- about and for different sites. Simulation models vary in their ability to apply customized gap acceptance algorithms for different simulated crossings. • The availability of a crossable gap is determined from the headway distribution of traffic upon entering the system. This probability is implicit in the individual vehicle gener- ation, and the gap sizes can be tracked by the model at any point in the simulated system. Some tools may have the flexibility of coding a custom headway distribution. Fur- ther, the headway arrivals at a crosswalk will be affected by upstream signals. If significant vehicle platooning is observed at a crosswalk, this effect should be accounted for in the simulation. 75

• The propensity to utilize yields is also stochastically assigned to each pedestrian as he or she arrives at the crossing loca- tion. This value will depend on whether the simulated pedestrian is blind or sighted (also assigned stochastically based on their respective volumes) and whether natural or augmented yield detection systems are in place. This aspect of the interaction is likely to be the most challenging to rep- resent in simulation. • The utilization of crossable gaps is handled through a gap acceptance algorithm, and different gap thresholds will be assigned to different populations of pedestrians. The chal- lenge here lies with the fact that most simulation gap accept- ance algorithms are based on minimum gaps, to the effect that a pedestrian will always utilize any gap greater than the minimum. To represent a utilization rate of less than 100%, additional customization may be necessary, which depends on the particular model used. Model Calibration and Validation The quality of the simulation analysis results relies on cor- rect modeling inputs and adequate calibration and validation of model outputs. Model inputs are defined as those param- eters that always need to be collected in order to develop a simulation model. These parameters include detailed site geometry, origin–destination traffic and pedestrian volumes, traffic composition, and signal timing. In addition, calibration parameters are available that have default settings included in the model but that can and should be customized by the user. These include speed distribution, gap acceptance behavior, gap distribution, yielding behavior, and yield utilization. In most cases, these parameters are adjusted (i.e., calibrated) to ensure that the model accurately represents field conditions. Finally, validation parameters are model outputs that allow the modeler to compare the model to field conditions or other models. Validation parameters include travel time, delay, queuing, and risk. In other words, model validation is achieved by altering calibration parameters and comparing the valida- tion parameters to field conditions; input parameters stay constant throughout the calibration/validation process. For model validation, simulation outputs are either com- pared to field-collected data or to outputs from other software packages for roundabouts and signalized intersections. These traffic analysis models are mostly designed for the analysis of vehicle traffic and are limited in their ability to model mixed- priority pedestrian–vehicle interaction. Consequently, the use of these traffic analysis tools is primarily to ensure that the vehicle operations in the simulation are modeled correctly. The analyst will have to rely on field observations or expert judgment to validate pedestrian results. The following list of model input parameters needs to be collected to set up the initial simulation model: • Geometry: The general geometry of the particular round- about or CTL is often available in the form of a design draw- ing or a scaled aerial photograph. Geometric data of the site include correct lane widths and crosswalk locations. • Origin/destination (O/D) volumes by lane: The typical simulation analysis uses traffic and pedestrian volumes for a duration of one hour. The flows in the model should rep- resent actual turning percentages by approach (and by lane in the case of a two-lane roundabout). • Traffic composition: The traffic composition at each site includes the percentage of heavy vehicles and the presence of special driver and/or pedestrian classes (yield/no yield or safe/risky). • Signal timings: Where applicable, signal timings in the model are based on the actual signal timing plan for the intersection or, if necessary, on field measurements of average green times. In some cases, as in the evaluation of proposed treatments, signal timing reflects the proposed operation of the signal. The following parameters are used for calibration to match the operations in the model to field conditions. • Speeds: The modeler can input field-collected data on aver- age vehicle speeds on the approaches upstream of the cross- walk, the entry to the roundabout, in the circulating lane of the roundabout, and in the turn lane. If actual speed data cannot be obtained, the posted speed limit can be used to infer a speed distribution on the approaches, and the liter- ature (FHWA 2000, AASHTO 2004) can be used to approx- imate speeds in the roundabout or turn lane. • Gap acceptance: Gap acceptance parameters for pedestrian crossings and for vehicle merges (into the roundabout or downstream traffic at a CTL) can be obtained either from field data or from sources in the literature. The model can include distributions of gap acceptance times by coding multiple vehicle and/or pedestrian classes. In this fashion it is possible to model pedestrians who make risky decisions, pedestrians with average behavior, and pedestrians with poor gap detection (who need very long gaps to cross). • Driver yielding (potential): Different classes of drivers will be coded to achieve a certain percentage of potential yield- ers. Driver behavior will be based on observations at the site with help from sources in the literature. • Yield detection: As discussed previously, some blind pedes- trians may not be able to accurately detect drivers yielding for them at the crosswalk. The proportion of this group of pedestrians is a calibration parameter. • Headway distribution: Modeling a user-defined headway distribution may be necessary in some occasions, for exam- ple if an upstream signal causes platoon arrivals of vehicles or if class changes on campus cause pedestrians to arrive in groups. 76

Finally, the following simulation outputs are proposed for model validation: • Travel times: Simulation tools can estimate travel times on user-specified segments that can be used to compare actual travel times obtained in the field and so validate uncongested operations at the sites. Travel time data can be obtained as an average over the analysis period, sepa- rated by pedestrian/vehicle class or as raw data for each individual pedestrian/vehicle. • Delay times: Vehicle and pedestrian delays in the defined travel time segments are estimated by subtracting the theo- retical (undelayed) travel time from the actual travel time through a given segment. These data can be obtained as an average over the analysis period separated by pedestrian/ vehicle class or as raw data for each individual pedestrian/ vehicle and can be used to validate congested operations. It is also possible to validate using stopped delay. • Queue lengths: The simulation tools generally provide estimates of average vehicle queues at a specified location that can be compared with field measurements. This mea- sure may be most helpful in validating approach queuing at roundabouts. • Driver yielding (actual): It is hypothesized that the num- ber of actual yielders is significantly lower than the num- ber of potential yielders entered in the model. In order for a yield to occur, the event of an approaching potential yielder needs to coincide with the presence of a pedestrian at the crosswalk and with sufficient time for the driver to decelerate at a comfortable rate. By comparing the fraction of actual yield events, the analyst can validate the assump- tions used to derive the relationship between actual and potential yielders. Measures of Risk from Simulation It is further possible to use a simulation-based analysis approach to obtain an estimate of pedestrian risk by extracting the occurrence of pedestrian–vehicle conflicts. The FHWA surrogate safety assessment methodology (SSAM) is a post- processing tool that can interpret outputs from simulation tools and quantify the number of conflicts observed in the simulation (FHWA 2008). A conflict in this case is defined by one of sev- eral performance measures, including the time to collision. A methodology for estimating pedestrian–vehicle conflicts from simulation independent of SSAM is discussed in Schroeder and Rouphail (2006), which is also included in Appendix I. Illustrative Example This section is intended to demonstrate the proposed approach for modeling the interaction of pedestrians and drivers at unsignalized crosswalks in simulation. To illustrate the use of multiple vehicle and pedestrian classes, the two populations are divided into several groups. Vehicles are cat- egorized as either yielding or non-yielding drivers, P(Y). Pedes- trians are categorized into blind and sighted groups and within those groups in categories with different gap acceptance parameters—risky, typical, and conservative—where critical gap times are increasing in that order. It will generally be assumed that most sighted pedestri- ans will make typical decisions, while blind pedestrians will be more strongly represented at either extreme. As crossing treat- ments are implemented at a facility, more pedestrians will shift away from risky and conservative decisions, thereby reducing conflicts and delay, respectively. In the following, we will assess the operational impacts of six treatment functionalities: • No control (NC): This configuration represents the default interaction in a simulation model without any interaction between modes. Delay is a function of car-following param- eters only, and risk is the result of random arrivals at the conflict point. • Unassisted crossing (UA): Pedestrians and drivers are assigned priority rules that govern the interaction. Pedes- trians have different gap acceptance parameters, and some drivers will yield if encountering a pedestrian. No further treatments are implemented. • Yield sign for drivers (YS): The likelihood of drivers yield- ing is increased through treatments such as a raised cross- walk, warning signs, pedestrian flashers, enforcement, or education measures. It is assumed that the treatment has no effect on pedestrian behavior. • Vehicle detection (VD): Some treatments will help blind pedestrians to more effectively detect the arrival of a vehicle. The assumption is that this will enable them to make bet- ter (safer and more efficient) crossing decisions. Examples include a gap-detection system and noise-generating rum- ble strips. It is assumed that driver behavior is not affected. • Yield sign and vehicle detect (YSVD): This treatment cat- egory combines YS and VD treatments to increase driver yielding and improve the vehicle detection capabilities of blind pedestrians. Examples include a combination of auto- mated vehicle detection with a pedestrian flasher or rumble strips in the approach of a raised crosswalk. • Perfect information (PI): This configuration represents per- fect unsignalized crossing conditions from a pedestrian per- spective. Pedestrian delay and risk are minimized because 100% of vehicles yield to pedestrians. This form of driver behavior may represent a strictly enforced right-of-way law. The six treatment scenarios are implemented in the simu- lation at a CTL location for a one-way, one-lane pedestrian crossing, using assumed run-specific pedestrian and driver 77

attributes (Table 17). For illustrative purposes the implemen- tation was tested and executed in the VISSIM simulation package (PTV 2005), but the approach should be applicable to other simulation tools as well. It is assumed that the typical pedestrian has a critical lag of 6 s, which is considered safe compared to the actual crossing time of about 5 s at a walking speed of 4 ft/s. Accordingly, con- servative pedestrians are assigned a longer critical lag value (12 s) and risky pedestrians have a short critical lag of only 3 s. The resulting delay and risk measures of effectiveness (MOEs) from 10 simulation replications per scenario are shown in Table 18. The tables suggest that an increased likelihood of drivers yielding (case YS) decreases the percentage of conflicts. Improv- ing VD for pedestrians appears to slightly increase observed conflicts compared to the unassisted case. Looking at the large standard deviations of the risk estimates, it cannot be stated if this is a real effect at the given sample size. This suggests the need for large sample sizes in the model repetitions to show significant effects when evaluating actual treatments. In comparison, the delay MOEs suggest that as drivers yield more, delay for pedestrians decreases while driver delay increases. The table also indicates that the percent of actual driver yields is considerably less than the specified percent of theoretical yielders. This finding is expected at low pedes- trian volumes since the majority of drivers do not encounter a pedestrian waiting at the crosswalk. This observation sug- gests challenges to estimating the required model input of potential yielders [P(Y)] from field observations of actual yielders. This sample analysis shows that it is possible to use micro- simulation models to extract conflict and delay data for pedestrian–vehicle interaction as a function of run-specific attributes of the two groups. The approach describes the inter- action of the two modes in terms of four probability param- eters: the likelihood of crossable gap occurrence [P(G)], the likelihood of gap detection [P(GD)], the likelihood of driver yielding [P(Y)], and the likelihood of yield detection [P(YD)]. From a preliminary analysis, it appears that the delay and conflict estimates produced by the model in fact follow expec- tations. For further information the reader is referred to the paper included in Appendix I. Simulation-Based Analysis of Signalized Crosswalks The aforementioned approach for describing pedestrian– vehicle interaction in a microsimulation environment applies to all unsignalized crosswalks, where the interaction is gov- erned by the four assumed probability parameters. For sig- nalized crossings, simulation tools already incorporate algo- rithms to replicate the way real-world traffic signals function and operate. Consequently, these built-in algorithms should be used when a signalized crosswalk is to be evaluated. 78 Run-Specific Attributes Pedestrians Drivers 50 Sighted Pedestrians per Hour 50 Blind Pedestrians per Hour 300 Vehicles per Hour Treatment Functionality (Assume 100% Yield Detection) P(C) P(A) P(R) P(C) P(A) P(R) P(Y) NC No Information n/a n/a n/a n/a n/a n/a 0% UA Unassisted Crossing 5 90 5 10 70 20 20% YS Yield Sign for Drivers 5 90 5 10 70 20 50% VD Vehicle Detect for Pedestrians 5 90 5 0 90 10 20% YSVD Yield Sign and Vehicle Detect 5 90 5 0 90 10 50% PI Perfect Information, Everybody Yields 0 100 0 0 100 0 100% P(C) Probability of conservative pedestrian crossing behavior. Pedestrian will accept gaps of 12 s or more. P(A) Probability of average pedestrian crossing behavior. Pedestrian will accept gaps of 6 s or more. P(R) Probability of risky pedestrian crossing behavior. Pedestrian will accept gaps of 3 s or more. P(Y) Probability of drivers yielding to pedestrians (percentage of potential yielders). Table 17. Input parameters for simulation scenarios.

Depending on the specific signal strategy (i.e., a conven- tional signal versus a pedestrian hybrid beacon), it may be nec- essary to customize the signal control logic to some extent. The analyst should have a thorough understanding of how the signal is or will be implemented in the field before attempting to represent it in simulation. Particular attention should be paid to whether the signal operates in “free” operation or whether it is in some way coordinated with other pedestrian signals (two-stage crossing) or with the vehicle signal at the main intersection (for channelized turn lanes). The analyst should further consider whether actual driver and pedestrian behavior is consistent with the way it is intended by the signal. For example, it was observed at the PHB installa- tion in this project that some pedestrians crossed before the “Walk” phase came on while others waited until the “Flashing Don’t Walk” before they felt comfortable crossing. In other words, pedestrians used the signal as a crossing aid, but by no means as the sole means of determination for stepping into the roadway. Similarly, some drivers were observed to proceed despite a red signal indication. For modeling the vehicular impact of the PHB signal, it is of particular importance to ade- quately represent driver behavior. That signalization strategy is intended to result in more efficient vehicle operations by allow- ing drivers to proceed during the “Flashing Red” phase if no pedestrian is in the crosswalk. Clearly, the estimated vehicle delay for this strategy is principally tied to the level of under- standing of and compliance with this phasing scheme. With these considerations in mind, simulation tools can readily be used to estimate the effect of signals on pedestrian and vehicle delay. Even without fully capturing the behav- ioral aspects related to the signal, a simulation-based analy- sis is a great tool for a relative comparison of different signal strategies. Pedestrian Signals at Roundabouts This section summarizes a detailed sensitivity analysis of pedestrian signalization options for modern roundabouts performed in simulation. The discussion is based on work published in Schroeder et al. (2008), which is included in Appendix L for quick reference. The objective of this sensitivity analysis is to explore the pedestrian-induced impacts of different signalization strategies at modern roundabouts in a simulation environment. The analysis focuses on six analysis dimensions: 1. Roundabout geometry: The analysis includes a single- lane and a two-lane roundabout. 2. Crosswalk location: The analysis includes three alterna- tive crosswalk geometries. The proximal crossing is the stan- dard crosswalk location set back from the circulating lane by one vehicle length (∼20 ft). The zigzag configuration moves the exit portion of the crosswalk to a distance of three vehicle lengths (∼60 ft) from the circulating lane to 79 Measures of Effectiveness (Average of 10 VISSIM Runs) Actual Driver Yield – % Yield Pedestrian Risk Lead, % Pedestrian Risk Lag, % Pedestrian Delay (s) Vehicle Delay (s) Treatment Functionality (Assume 100% Yield Detection) Avg. Std. Dev. Avg. Std. Dev. Avg. Std. Dev. Avg. Std. Dev. Avg. Std. Dev. NC No Control 0.0% 0.00% 27.0% 5.20% 19.3% 2.40% 0.0 0.00 2.4 – UA Unassisted Crossing 3.8% 0.99% 2.1% 0.70% 0.5% 0.70% 4.4 0.28 3.1 0.32 YS Yield Sign for Drivers 9.3% 1.16% 1.0% 0.80% 0.2% 0.70% 4.1 0.20 4.2 0.29 VD Vehicle Detect for Pedestrians 3.7% 0.84% 2.7% 1.40% 0.2% 0.70% 4.3 0.37 3.1 0.27 YSVD Yield Sign and Vehicle Detect 9.0% 1.33% 1.0% 1.00% 0.2% 0.70% 3.9 0.27 4.2 0.31 PI Perfect Information, Everybody Yields 15.0% 2.00% 0.0% 0.00% 0.0% 0.00% 3.5 0.30 5.4 0.41 Table 18. Measures of effectiveness from simulation.

provide additional queue storage on the exit leg. The distal crossing location moves the entire crosswalk to a distance of five vehicle lengths (∼100 ft) from the circulating lane. 3. Signal staging: The analysis includes single-stage and two- stage phasing schemes as appropriate. 4. Signalization strategy: The analysis includes a conven- tional pedestrian signal and a pedestrian hybrid beacon (i.e., HAWK signal). The analysis assumes full understanding of and compliance with the signal phases, which is reason- able for a relative comparison. For an absolute assessment of the delay impact, some variation in behavior should be considered. 5. Vehicle volumes: The analysis considers a range of vehi- cle volumes, categorized as below capacity, at capacity, and slightly above capacity. 6. Pedestrian volumes: The analysis considers two levels of pedestrian volumes (10 and 50 pedestrians per hour) rel- ative to the baseline of no pedestrians. Appendix L provides a more detailed description of the dif- ferent model scenarios. Table 19 summarizes the tested com- binations of the dimensions of roundabout geometry, cross- walk location, and signal staging. The table demonstrates that some of the combinations were not tested because they were considered impractical. For example, a two-stage crossing at a single-lane roundabout proximal crosswalk is expected to result in low compliance and therefore wasn’t tested. Similarly, a one-stage crossing was not tested for the zigzag configuration since the elongated splitter island provides a natural separation between the two stages of the crossing. For each of the checked cells, the analysis considered all combinations of the remaining three dimen- sions (signalization strategy, vehicle volumes, and pedestrian volumes). In addition, the analysis included an additional vol- ume sensitivity that was intended to capture the effect of even higher pedestrian flows of up to 300 pedestrians/hour. The analysis used the average results from 10 simulation replica- tions in each scenario. All runs evaluated the effect of one sig- nalized crosswalk being installed at the busiest approach to the roundabout. The analysis results provide a quantitative comparison of different signalization options for pedestrian crossings at one-lane and two-lane roundabouts, all of which intended to improve access for blind pedestrians. Table 20 highlights a subset of the results for the case of 50 pedestrians/hour cross- ing at the signalized two-lane roundabout crosswalk. Results are shown for below-capacity and at-capacity vehicle vol- umes. These two-lane roundabout scenarios were selected because they directly relate to the most likely application of roundabout pedestrian signals. Additional results are pro- vided in Appendix L. The results indicate that innovative signalization treat- ments, including the PHB and two-stage crossings, can sig- nificantly decrease vehicle delay. With 50 pedestrians/hour at the two-lane roundabout, a proximal single-stage pedestrian- actuated signal resulted in pedestrian-induced vehicle delays of 14.2 s per vehicle in the below-capacity scenario and 68.4 s for the at-capacity case. The use of a PHB at the same location 80 Crosswalk Location Crosswalk Staging Single-Lane Roundabout Two-Lane Roundabout One stage Yes Yes Proximal Crossing Two stage No Yes One stage No NoZigzag Crossing Two stage Yes Yes One stage Yes No Distal Crossing Two stage No Yes Two-lane Roundabout, 50 peds/hour Below Capacity At Capacity Crosswalk Location Signal Staging Signal Strategy Delay per Vehicle (s) % Change over Base Delay per Vehicle (s) % Change over Base Ped. signal 14.2 Base 68.4 BaseSingle stage PHB 6.3 –56% 39.4 –42% Ped. signal 4.1 –71% 24.4 –64% Proximal Two stage PHB 1.5 –89% 5.5 –92% Ped. signal 3.9 –73% 23.4 –66%Zigzag Two stage PHB 1.3 –91% 7.0 –90% Ped. signal 2.8 –80% 5.9 –91% Distal Two stage PHB 1.2 –92% 0.0* –100% * This scenario actually resulted in a net decrease of the total roundabout delay, explained by the fact that the signal was metering demand on a busy approach. Number was limited to a positive range for this table. Table 19. Test matrix of treatment combinations (source: Schroeder et al. 2008). Table 20. Sample results of roundabout signalization sensitivity analysis.

reduced that delay by 56% and 42% to 6.3 s and 39.4 s, respectively. The use of a two-stage phasing at the same prox- imal location resulted in delay reductions of 71% and 64% over the base case even if a regular pedestrian signal was used. The PHB resulted in further delay benefits and reductions of 89% and 92% over the base case. Modified crossing geometries such as a zigzag or distal crosswalk resulted in similar delay savings for both a regular pedestrian signal and the PHB phasing scheme. In all cases the PHB resulted in additional delay savings. The modified exit leg geometry for the zigzag and distal crosswalk locations can further reduce spillback potential into the circulating lane due to added vehicle storage at the roundabout exit lane. The detailed analysis results in Appendix L discuss the average and maximum vehicle queues at the crosswalk in light of the avail- able queue storage. The analysis further suggested a non-monotonic relation- ship between the treatment effects and the levels of vehicle volumes. Pedestrian-induced vehicle delays appeared to be greatest as traffic volumes approached roundabout capacity. The need for innovation in pedestrian signal application is therefore less pronounced at low traffic volumes but should be a key consideration at busy roundabout junctions. As vehicle volumes increase, pedestrian signals become even more important from an accessibility perspective. The most promising approach for minimizing the impacts on vehicu- lar traffic while ensuring access for blind pedestrians appears to be a strategic reduction of the vehicle red indication. The authors showed that this can be achieved by shortening the crossing distance through a two-stage crossing or through the introduction of a “Flashing Red” phase in a PHB phasing scheme. A sensitivity analysis of the effect of increasing pedestrian volumes supported the hypothesis that vehicle and pedestrian delay impacts increase at a diminishing rate as signal opera- tions approach the limit of maximum number of actuations per hour. Pedestrian and vehicular delays generally appear to plateau at volumes in excess of 200 pedestrians/hour. This suggests an application for signalization as a means of con- trolling pedestrian interference to vehicular operations—an interesting twist to the existing pedestrian signal warrant that evaluates only the available crossing opportunities for pedes- trians within a given time interval. Clearly, this assumes per- fect pedestrian compliance with the signal phasing. Discussion This chapter has discussed two extensions of the NCHRP Project 3-78A field results for application to other locations, geometries, and traffic volumes. The first part of this chap- ter presented empirically derived mixed-priority pedestrian delay models that can be used to estimate pedestrian delay at single-lane roundabouts, two-lane roundabouts, and CTLs. The explanatory variables in these delay models are consis- tent with the four behavioral probability parameters defined in Chapter 4 and used in the Chapter 5 evaluation of field results. The second part presented the concept of using these four probability terms in a microsimulation environment for further extension analysis. Microsimulation tools have the advantage that the analyst can readily explore the impacts of different geometries, traffic volumes, and pedestrian and driver behavior on selected performance measures. The constraint of both approaches is their limited applica- bility to measures of pedestrian safety. The chapter briefly touched on the ability to extract surrogate safety measures from simulation in the form of pedestrian–vehicle conflicts or near collisions. This approach is the focus of an ongoing national effort by FHWA but has yet to be extensively vali- dated. This research has demonstrated that it is possible to extract pedestrian–vehicle conflict data from simulation and further that the rate of conflicts is responsive to changes in the four underlying probability parameters. Presumably, changes in these parameters represent the implicit impacts of pedes- trian crossing treatments. However, while there is confidence in the delay measures resulting from such analysis, the risk measures are at this point strictly theoretical. The concept of predicting pedestrian–vehicle conflicts from simulation requires extensive field validation to build confi- dence in the approach. While this research recorded a field measure of risk in the form of O&M interventions, its occur- rence and variability across participants makes it challenging to perform such validation. Further, while some of the tested treatments showed a significant impact on these O&M inter- ventions, additional observations are needed to validate a simulation-based safety performance assessment. 81