Assessing Interactions Between Access Management Treatments and Multimodal Users (2018)

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283 A P P E N D I X G : P E R F O R M A N C E R E L A T I O N S H I P D E V E L O P M E N T Performance Relationship Development Introduction This appendix describes the process used to develop performance relationships for two access management (AM) techniques. The two techniques are right-turn deceleration and TWLTL vs. non- traversable median. Each performance relationship quantitatively describes the effect of a technique on the performance of a specific travel mode (e.g., pedestrian, truck). The performance that is described is categorized as either safety or operations. For example, a performance relationship can describe the effect of right-turn deceleration lane presence on pedestrian safety. The data used to develop the performance relationships are summarized in Appendix F. The data are summarized on a technique-by-technique basis. For each technique, the presentation includes an overview of the study sites, data collection techniques, and data reduction procedures. The performance relationships that have been developed are described in this appendix on a technique- by-technique basis. The first section to follow describes the relationships for the right-turn deceleration technique. The second section describes the relationships for the TWLTL vs. non-traversable median technique. Right-Turn Deceleration This section describes the findings from an analysis of data describing the performance of a signalized intersection approach with and without a right-turn deceleration lane. The analysis was used to produce a set of performance relationships that predict intersection safety and operation. The objective and scope of the study are provided in Appendix E (in a section having the same title as this section). The first subsection to follow describes the procedures used to develop operations performance relationships. The second subsection describes the procedures used to develop the safety performance relationships. Each subsection describes the findings from an examination of the data, the statistical methods used to develop the relationships, and the procedures for using relationships in a practical application. Operations Relationships Based on Simulation Data This section describes the research undertaken to develop relationships for predicting the effect of right-turn deceleration lane presence on the operation of bicycles, transit vehicles, and trucks at a signalized intersection. Simulation data were used to develop these relationships. A simulation testbed was established using intersections without right-turn deceleration lanes to represent the “before” condition. A second testbed was based on the “before” condition intersections but they included right-turn deceleration lanes to represent the “after” condition. The set of sites represented in the database collectively include simulation results for a range of traffic characteristics, geometric design elements, and traffic control features. These data were evaluated to develop the performance relationships identified in the following list.

284  An operations-based performance relationship for bicycle travel;  An operations-based performance relationship for transit travel; and  An operations-based performance relationship for truck travel. These relationships describe the association between operational performance and right-turn lane presence. Data Overview The operations data produced from simulations were used to develop the operations performance relationships. One test bed was developed for each of two intersection sites. The test beds were simulated for a range of input variable combinations that uniquely described 5,184 simulation scenarios. The input variables are identified in the following list.  Right-turn deceleration length (0ft, 100ft, 200ft, and 300ft);  Traffic volume (i.e., motorized vehicle volume; left-turn, through, and right-turn; all vehicle types);  Bicycle volume;  Truck percentage (i.e., truck volume as a percentage of the traffic volume);  Right-turn percentage (i.e., right-turn volume as a percentage of the traffic volume);  Transit bus frequency (number of boarding stops);  Bus dwell time;  Signal cycle length; and  Right-turn on red operation (RTOR). A total of 10,368 observations were produced from the simulations (= 5,184 scenarios × 2 simulation runs per scenario). Of this total, 6912 observations had a non-zero bicycle volume and 6912 observations had a non-zero bus stop frequency. The key operations performance measures include:  Average bicycle delay (seconds per bicycle);  Average bus delay (seconds per bus); and  Average truck delay (seconds per truck). Additional information about the simulation data development and summary is provided in Appendix F. Examination of Operations Data The results of the simulation runs are summarized in this section. There is a separate subsection for each of the three travel modes addressed (i.e., bicycle, transit vehicle, and truck). Bicycle Operations Data Examination This section summarizes the findings from a review of the simulation results for the bicycle mode. Summary statistics for these results were previously provided in Table 129. The summary in this section focuses on an assessment of the percent change in performance associated with a 1 percent change in the factor value (i.e., sometimes referred to as performance “elasticity”). The results of the elasticity analysis are shown in Table 159.

285 As shown in Table 159, average bicycle delay does not appear to be significantly influenced by the following factors: right-turn deceleration lane length, right-turn-on-red operation, traffic volume, right- turn percentage, bicycle volume, truck percentage, bus stop frequency, or bus dwell time. Table 159. Factors affecting a change in operational performance – right-turn deceleration. Factor Effect of a Change in Factor Value or Presence on Delay Bicycle Bus Truck Right-turn deceleration lane presence -1.8% w/turn lane -17% w/turn lane -9.2% w/turn lane Right-turn deceleration lane length no effect -0.2% per +1% no effect Signal cycle length +1.10% per +1% +0.8% per +1% +1.1% per +1% Right-turn-on-red operation no effect -4.3% w/RTOR -2.9% w/RTOR Traffic volume no effect +0.5% per +1% +0.3% per +1% Right-turn percentage no effect no effect no effect Bicycle volume no effect no effect no effect Truck percentage no effect no effect no effect Bus stop frequency (stops per hour) no effect -0.1% per +1% no effect Bus dwell time no effect +0.1% per +1% no effect Note: For all factors except right-turn-on-red and right-turn lane presence, “no effect” means less than ±0.1 percent change in delay per +1 percent change in factor value. For right-turn-on-red and right-turn lane presence, “no effect” means less than ±1 percent change in delay. An increase in cycle length tends to increase the bicycle delay, keeping all other factors constant. A 1 percent increase in cycle length corresponds to a 1.1 percent increase in delay. Transit Operations Data Examination This section summarizes the findings from a review of the simulation results for transit vehicles. Summary statistics for these results were previously provided in Table 130. The summary in this section focuses on an assessment of the elasticity of bus delay, relative to a change in intersection design, traffic demand, or operation. The results of the elasticity analysis are shown in Table 159. As shown in Table 159, average bus delay does not appear to be significantly influenced by the following factors: right-turn percentage, bicycle volume, or truck percentage. Bus delay increases with an increase in cycle length, traffic volume, or bus dwell time. In contrast, bus delay tends to decrease with an increase in right-turn deceleration lane length or bus stop frequency. Bus delay tends to decrease if right- turn-on-red operation is used. Truck Operations Data Examination This section summarizes the findings from a review of the simulation results for trucks. Summary statistics for these results were previously provided in Table 131. The summary in this section focuses on an assessment of the elasticity of truck delay, relative to a change in intersection design, traffic demand, or operation. The results of the elasticity analysis are shown in Table 159. As shown in Table 159, average truck delay does not appear to be significantly influenced by the following factors: right-turn deceleration lane length, right-turn percentage, bicycle volume, truck percentage, bus stop frequency, or bus dwell time. Truck delay increases with an increase in cycle length or traffic volume. Truck delay tends to decrease if right-turn-on-red operation is used.

286 Statistical Methods Regression analysis was used to develop predictive relationships between the site characteristics and performance measures. The best fit was based on minimization of the squared residual values. The statistical software package, Stata 13, was used to estimate the model coefficients. A step-wise procedure was used to select the significant independent variables at a confidence level of 95 percent. The candidate independent variables included all scenario factors (e.g., signal cycle, access level, traffic volume, bicycle volume, and truck percentage). A graphical comparison of predicted and simulation-based values was used to evaluate each model’s goodness-of-fit. Following the presentation of the estimated model and the graphical illustration of goodness-of-fit, a series of figures are presented to illustrate the effects of each independent variable on performance. The predicted values depict the effect of the independent variable on performance when all other explanatory variables are set to equal their respective average value. The Stata command “margins” was used to produce these figures. Operations Performance Relationship Development The developed models are described in this section. The first section describes the relationship developed for bicycle operations. The second section describes the relationship developed for transit operations. The third section describes the relationship developed for truck operations. Bicycle Operations Relationship A linear regression model was developed to describe the relationship between average bicycle delay and various factors describing signalized intersection design, traffic demand, or operation. Table 160 shows the descriptive statistics of the data used for model development. Table 160. Statistics for variables in the bicycle operations model – right-turn deceleration. Variable Description Mean Std. Min. Max. y Average bicycle delay (seconds per bicycle) 21.43 4.85 14.44 29.37 x1 Right-turn deceleration lane indicator (1 if there is a right deceleration lane, 0 otherwise) 0.75 0.43 0 1 x2 Signal cycle length (seconds) 125 25 100 150 x3 Right-turn volume (vehicles per hour) 114.59 83.1 10 266 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 161. The R2 (i.e., 0.9424) indicates the developed model fits the bicycle delay data well.

287 Table 161. Predictive model calibration statistics, bicycle operations model – right-turn deceleration. Variable Description Coefficient Standard Error p-value Constant -1.9230 0.0779 <0.001 x1 Right-turn deceleration lane indicator (1 if there is a right deceleration lane, 0 otherwise) -0.3684 0.0324 <0.001 x2 Signal cycle length (seconds) 0.1882 0.0006 <0.001 x3 Right-turn volume (vehicles per hour) 0.0009 0.0002 <0.001 Number of observations 6912 R2 0.9424 The following equation represents the performance relationship for predicting bicycle delay. Equation 5 1.923 0.3684 ∙ 0.1882 ∙ 0.0009 ∙ where y equals the average bicycle delay, seconds per bicycle; and all other variables are defined in Table 161. This equation should not be used with variable values outside the ranges provided in Table 160. A comparison between the observed average bicycle delay and the predicted delay is shown in Figure 20. Figure 20. Predicted vs. observed bicycle delay – right-turn deceleration. Figure 21 illustrates the relationship between various model variables and bicycle delay. The presence of a right-turn deceleration lane was found to reduce the average bicycle delay by 0.37 seconds per bicycle. This reduction was found to be statistically significant; however, it is sufficiently small as to be insignificant on a practical basis.

288 a. Signal cycle length (seconds). b. Right-turn volume (veh. per hour). Figure 21. Influence of various factors on bicycle delay – right-turn deceleration. In general, average bicycle delay at signalized intersections is mainly determined by signal cycle length. The influences of other factors are very small because: (1) bicycles travel in a separate bicycle lane with little interference from motorized vehicles; (2) typically long bicycle headways minimize interactions between bicycles and turning vehicles; and (3) bicycles always have right-of-way and turning vehicles typically yield to bicycles. Transit Operations Relationship A regression model was developed to describe the relationship between the average bus vehicle delay and various factors describing signalized intersection design, traffic demand, or operation. Table 162 shows the descriptive statistics of the data used for model development. Table 162. Statistics for variables in the transit operations model – right-turn deceleration. Variable Description Mean Std. Min. Max. y Average bus delay (seconds per bus) 62.8 29.2 19.5 179 x1 Right-turn deceleration lane length (feet) 150 112 0 300 x2 Signal cycle length (seconds) 125 25.0 100 150 x3 Prohibition of right turn on red (RTOR) indicator (1 if RTOR is prohibited, 0 if enabled) 0.5 0.5 0 1 x4 Bus dwell time (seconds) 22.5 7.501 15 30 x5 Traffic volume (vehicles per hour per lane) 546 85.4 441 660 x6 Proportion right-turn vehicles 0.105 0.073 0.011 0.204 The estimated regression coefficients and p-values are given in Table 163. The R2 (i.e., 0.8682) indicates the developed model fits the bus delay data well.

289 Table 163. Predictive model calibration statistics, transit operations model – right-turn deceleration. Variable Description Coefficient Standard Error p-value Constant 1.7535 0.1690 <0.001 x1 Right-turn deceleration lane length (feet) -0.0053 0.0004 <0.001 x2 Signal cycle length (seconds) 0.3618 0.0093 0.001 x3 Prohibition of right turn on red (RTOR) indicator (1 if RTOR is prohibited, 0 if enabled) 0.1007 0.0296 <0.001 x4 Bus dwell time (seconds) 0.0147 0.0021 <0.001 x5 Traffic volume (vehicles per hour per lane) 0.0024 0.0002 <0.001 x6 Proportion right-turn vehicles 0.4736 0.2013 0.019 Number of observations 6912 R2 0.8682 The following equation represents the performance relationship for predicting bus delay. Equation 6 . . . . . . 0.3618 where y equals the average bus delay, seconds per vehicle; and all other variables are defined in Table 163. This equation should not be used with variable values outside the ranges provided in Table 162. In this study, the number of bus delay observations was limited because of low bus exposure (i.e., one or two local buses per hour) and limited simulation replications (i.e., two replications per scenario). Although the bus dwell time was uniformly distributed in simulations, the pattern of bus arrivals relative to the signal’s green indication was highly varied. This variation resulted in considerable variance of observed bus delay. The minimum bus delay, equal to the bus dwell time plus diverging and merging delay, led to clearly defined bounds at the low ends of observed and predicted bus delays. However, the upper end of bus delay was highly dependent on the bus arrival time relative to the start of green. A comparison between the observed average bus delay and the predicted delay is shown in Figure 22. The trend in the data suggests that the model underestimates bus delay slightly when the predicted bus delay exceeds 100s per bus.

290 Figure 22. Predicted vs. observed transit vehicle delay – right-turn deceleration. Figure 23 illustrates the relationship between various model variables and average bus delay. The trend in Figure 23a shows a nonlinear and negative relationship between right-turn deceleration lane length and average bus delay. Implementing a right-turn deceleration lane length is an effective treatment for improving bus operations at signalized intersections. The benefit of this lane increases with increasing lane length, but the percent reduction in delay becomes smaller as lane length increases. An increase of 100 feet in right-turn deceleration lane length, on average, tends to decrease average bus delay by 9.3 seconds per bus. Average bus delay increases with an increase in bus dwell time. On average, a one-second increase in bus dwell time tends to increase average bus delay by 0.26 seconds per bus. Because average bus delay is the summation of bus dwell time and signal control delay, an increase in bus dwell time should result in a similar increase in average bus delay, when keeping other factors constant. Thus, a one-second increase in dwell time should translate into about one-second increase in delay. The fact that this one-to-one relationship is not evident in the data may be caused by the variance in bus arrival patterns.

291 a. Right-turn deceleration lane length (feet). b. Signal cycle length (seconds). c. Right-turn-on-red operation. d. Bus dwell time (seconds). e. Traffic volume (veh. per hour per lane). f. Proportion right-turn vehicles. Figure 23. Influence of various factors on transit vehicle delay – right-turn deceleration.

292 Truck Operations Relationship A linear regression model was developed to describe the relationship between the average truck delay and various factors describing signalized intersection design, traffic demand, or operation. Average truck delay includes the delay to through and right-turning trucks at the intersection. Table 164 shows the descriptive statistics of the data used for model development. Table 164. Statistics for variables in the truck operations model – right-turn deceleration. Variable Description Mean Std. Min. Max. y Average truck delay (seconds per truck) 36.4 9.03 18.8 73.8 x1 Right-turn deceleration lane length (feet) 150 112 0 300 x2 Signal cycle length (seconds) 125 25.0 100 150 x3 Prohibition of right-turn on red (RTOR) sign indicator (1 if RTOR is prohibited, 0 if enabled) 0.5 0.500 0 1 x4 Bus stop frequency (bus stops per hour) 1 0.817 0 2 x5 Traffic volume (vehicles per hour per lane) 546 85.4 440 660 x6 Proportion right-turn vehicles 0.105 0.073 0.011 0.204 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 165. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable). Table 165. Predictive model calibration statistics, truck operations model – right-turn deceleration. Variable Description Coefficient Standard Error p-value Constant -2.2259 0.1759 <0.001 x1 Right-turn deceleration lane length (feet) -0.0084 0.0004 <0.001 x2 Signal cycle length (seconds) 0.2839 0.0008 <0.001 x3 Prohibition of right-turn on red (RTOR) sign indicator (1 if RTOR is prohibited, 0 if enabled) 0.1142 0.0246 <0.001 x4 Bus stop frequency (bus stops per hour) 0.0874 0.0151 <0.001 x5 Traffic volume (vehicles per hour per lane) 0.0065 0.0003 <0.001 x6 Proportion right-turn vehicles -10.4848 0.5133 <0.001 Number of observations 10,368 R2 0.9890 The following equation represents the performance relationship for predicting truck delay. Equation 7  . . ∙ . ∙ . ∙ . ∙ 0.2839 ∙ 10.4848 ∙   where y equals the average truck delay, seconds per vehicle; and all other variables are defined in Table 165. This equation should not be used with variable values outside the ranges provided in Table 164.

293 A comparison between the observed average truck delay and the predicted delay is shown in Figure 24. The fitted pattern suggests predicted truck delays are clustered at four stratifications that may be caused by unobserved factors (e.g., truck arrival pattern). Some outliers suggest the model may slightly underestimate truck delay when predicted truck delay is greater than 50 seconds per truck.   Figure 24. Predicted vs. observed truck-vehicle delay – right-turn deceleration. Figure 25 illustrates the relationship between various model variables and truck delay. Right-turn deceleration lane presence significantly reduces delay. The amount of the reduction is a function of the lane length. On average, an increase of 100 feet in right-turn deceleration lane length tends to reduce average truck delay by 1.8 seconds per truck. Bus stop frequency tends to slightly increase average truck delay at signalized intersections. Each additional bus stop tends to increase average truck delay by 0.19 seconds per truck. An increase in the proportion of right-turn vehicles tends to reduce average truck delay slightly. Every 1 percent increase results in 0.1 seconds less delay per truck. A high right-turn percentage corresponds to a low through volume (because total traffic volume is fixed). Thus, through truck delay decreases and right-turn truck delay increases with an increase in right-turn percentage. Since through truck volume is much higher than right-turn truck volume, the weighted average indicates an overall decrease in average truck delay.

294 a. Right-turn deceleration lane length (feet). b. Signal cycle length (seconds). c. Bus stop frequency (stops per hour). d. Traffic volume (veh. per hour per lane). e. Proportion right-turn vehicles. f. Right-turn-on-red operation. Figure 25. Influence of various factors on truck delay – right-turn deceleration.

295 Safety Relationships based on Simulated Conflict Data This section describes the research undertaken to develop relationships for predicting the effect of right-turn deceleration lane presence on the safety of transit vehicles and trucks. Simulated conflict data were used to develop these relationships. The simulation testbed established for the operations-focused study was used for this purpose (refer to the section titled Operations Relationships Based on Simulation Data). The set of sites represented in the database collectively include simulation results for a range of traffic volume, geometric design, and traffic control conditions. These data were evaluated to develop the performance relationships identified in the following list.  A safety-based performance relationship for transit travel; and  A safety-based performance relationship for truck travel. These relationships describe the association between safety performance and right-turn lane presence. Data Overview Traffic conflict data produced by the SSAM model were used to develop the safety performance relationships. One test bed was developed for each of two intersection sites. The test beds were simulated for a range of input variable combinations that uniquely described 5,184 simulation scenarios. A total of 10,368 observations (i.e., vehicle trajectories) were produced from the simulations (= 5,184 scenarios × 2 simulation runs per scenario). The key safety performance measures were retrieved from the trajectories using the SSAM model. Additional information about the simulation data development and summary is provided in Appendix F. Examination of Conflict and Crash Data A comparison between the simulated conflicts and the historical crash frequency was conducted to determine if the two measures were correlated. Although this study focused on the safety performance of buses and trucks, the count of bus- and truck-related crashes in the evaluation period (i.e., 2012 to 2016) was quite small. If fact, it was too small to obtain statistically valid results. Thus, the examination of the relationship between conflict frequency and crash frequency was expanded to include events associated with all vehicle types (i.e., it included all conflicts and all crashes, regardless of the involved vehicle type). The focus of this evaluation was the Florida site (i.e., Hillsborough Ave @ Florida Ave, Tampa). Crash data for a five-year period were used (i.e., 2012 to 2016) for the evaluation. The Oregon site (i.e., SE Division St. at SE 162nd Ave., Portland) was not included in this evaluation because there was not enough traffic data at the Oregon site to simulate the traffic conflicts in the five-year evaluation period. Conflict-Crash Data Examination I: Hourly Conflicts For this examination, the simulated hourly conflict frequency was compared with the annual crash frequency for each of four common hours of the average day. The annual crash frequency was computed as the count of crashes that occur during the subject hour at the target intersection (within a buffer of 500 feet from the intersection center) during the evaluation period, divided by the duration of the evaluation period (i.e., 5 years). The last column of Table 166 lists the observed annual crash frequency for each of the four hours.

296 Table 166. Simulated conflicts and observed crashes for hourly examination – right-turn deceleration. Day of Week Subject Hour Simulated Conflict Frequency, conflicts per hour Observed Average Annual Crash Frequency, crashes per year Tuesday 10:00 – 11:00 751.5 0.8 Tuesday 14:00 – 15:00 1242.2 1.2 Tuesday 17:00 – 18:00 1465.8 1.2 Tuesday 21:00 – 22:00 397.0 0.6 The hourly conflict frequency was computed for the same four hours for which crash data were obtained. Column 3 of Table 166 lists the conflict frequency for the four hours. The relationship between the conflict frequency and the crash frequency for the subject hours is presented in Figure 26. The regression results (R2 = 0.9629) indicate that the average annual crash frequency is linearly proportional to the simulated traffic conflict frequency. Figure 26. Relationship between hourly conflict frequency and average annual crash frequency – right-turn deceleration. Conflict-Crash Data Examination II: Equivalent Average Annual Daily Conflicts For this examination, the simulated hourly conflict frequency was converted into an estimate of the annual daily conflict frequency and then compared with annual crash frequency for the average day. The equivalent average annual daily conflict (EAADC) frequency was computed by dividing the simulated total conflict count for the analysis period by the total annual average hourly volume percentages representing the same hours as the analysis period. The following equation was used to compute the EAADC.

297 Equation 8 EAADC ∑ ∑ VolAADT 261 ∑ ∑ VolAADT 104 365 where EAADC = equivalent average annual daily conflict frequency, conflicts per day; is the number of simulated conflicts in a weekday hour ; is the number of simulated conflicts in a weekend hour ; is the traffic volume in a weekday hour ; and is the traffic volume in a weekend hour . A total of nine hours (four weekday hours and five weekend hours) were examined in this study. Column 4 of Table 167 lists the computed EAADC values for each of five years. Table 167. Simulated conflicts and observed crashes for daily examination – right-turn deceleration. Year Weekday Conflicts (four hours) Weekend Conflicts (five hours) EAADC, conflicts per day Observed Average Annual Crash Frequency, crashes per year 2012 4179.1 6266.1 21,358.3 28 2013 3835.4 6092.7 19,925.5 26 2014 3835.4 6092.7 19,925.5 29 2015 3890.8 5976.7 19,947.2 24 2016 3541.2 5159.4 17,787.1 18 The last column of Table 167 shows the observed annual crash frequency for each of five years. The relationship between the equivalent average annual daily conflicts and the annual crash frequency is presented in Figure 27. The regression model shows that the annual crash frequency is proportional to the equivalent average annual daily conflicts. The regression results (R2 = 0.746) indicate that the annual crash frequency is linearly proportional to the simulated conflict frequency.

298 Figure 27. Relationship between daily conflict frequency and average annual crash frequency – right-turn deceleration. Summary of Crash-Conflict Data Examinations Based on the two examinations, a plausible correlation between simulated conflicts and reported crashes was found. Accordingly, there is support for the use of simulated conflict frequency to assess the relative safety of the right-turn deceleration lane technique. Given the low occurrence of transit and truck- related crashes in the field data, it is assumed that the relationship between total crashes and total conflicts also holds for the subset of truck- and transit-related conflicts and crashes. Examination of Conflict Data The results of the SSAM conflict analysis are summarized in this section. There is a separate subsection for each of the two travel modes addressed (i.e., transit vehicle and truck). Transit Vehicle Conflict Data Examination This section summarizes the findings from a review of the SSAM conflict analysis results for the transit mode. Due to the small sample of bus-related conflicts in the simulation data, the analysis was based on total bus-related conflicts, which is the sum of the simulated rear-end, lane-change, and crossing conflicts. The summary in this section focuses on an assessment of the percent change in performance associated with a 1 percent change in the factor value (i.e., sometimes referred to as performance “elasticity”). The results of the elasticity analysis are shown in Table 168. Summary statistics for the bus conflict data were previously provided in Table 133.

299 Table 168. Factors affecting a change in safety performance – right-turn deceleration. Factor Effect of a Change in Factor Value or Presence on Conflict Frequency Transit Truck Right-turn deceleration lane presence +58% w/right-turn lane +0.8% w/right-turn lane Right-turn deceleration lane length -0.2% per +1% -0.1% per +1% Signal cycle length +0.1% per +1% +0.2% per +1% Right-turn-on-red operation +1.4% w/RTOR +1.6% w/RTOR Traffic volume +0.3% per +1% +1.6% per +1% Right-turn percentage no effect no effect Bicycle volume +0.3% per +1% no effect Truck percentage no effect +0.9% per 1% Bus stop frequency (stops per hour) +0.6% per +1% no effect Bus dwell time +0.1% per +1% no effect Note: For all factors except right-turn-on-red and right-turn lane presence, “no effect” means less than ±0.1 percent change in delay per +1 percent change in factor value. For right-turn-on-red and right-turn lane presence, “no effect” means less than ±1 percent change in delay. As shown in Table 168, transit-related conflict frequency does not appear to be significantly influenced by the following factors: right-turn percentage and truck percentage. Keeping all other factors constant, conflict frequency increases with the presence of a right-turn lane or right-turn-on-red operation. Conflict frequency also increases with an increase in cycle length, traffic volume, bicycle volume, bus stop frequency, and bus dwell time. In contrast, conflict frequency decreases with an increase in right-turn deceleration lane length. Truck Conflict Data Examination This section summarizes the findings from a review of the SSAM conflict analysis results for trucks. Due to the small sample of truck-related conflicts in the simulation data, the analysis was based on total truck-related conflicts, which is the sum of the simulated rear-end, lane-change, and crossing conflicts. The summary in this section focuses on an assessment of the elasticity of truck-related conflicts, relative to a change in intersection design, traffic demand, or operation. The results of the elasticity analysis are shown in Table 168. Summary statistics for these results were previously provided in Table 133. As shown in Table 168, truck-related conflict frequency does not appear to be significantly influenced by right-turn percentage, bicycle volume, bus stop frequency, or bus dwell time. Conflict frequency increases with the presence of a right-turn lane or right-turn-on-red operation. Conflict frequency also increases with an increase in cycle length, traffic volume, and truck percentage. In contrast, it decreases with an increase in right-turn deceleration lane length. Statistical Methods For model development, a negative binominal error distribution was assumed because the dependent variable consists of count data that have a variance that is greater than the mean. A log-linear model structure was used to describe the relationship between the independent variables and the dependent variable because the dependent variable is bounded to non-negative values. The statistical software package, Stata 13, was used to estimate the model coefficients. The maximum likelihood estimator (MLE) was used. A step-wise procedure was used to select the significant

300 independent variables at a confidence level of 95%. The candidate independent variables included a range of scenario factors (e.g., signal cycle, access level, traffic volume, bicycle volume, and truck percentage). A graphical comparison of predicted and simulation-based values was used to evaluate each model’s goodness-of-fit. Following the presentation of the estimated model and the graphical illustration of goodness-of-fit, a series of figures are presented to illustrate the effects of each independent variable on performance. The predicted values depict the effect of the independent variable on performance when all other explanatory variables are set to equal their respective average value. The Stata command “margins” was used to produce these figures. Safety Performance Relationship Development The developed models are described in this section. The first section describes the relationship developed for transit safety. The second section describes the relationship developed for truck safety. Transit Safety Relationship A log-linear regression model was developed to describe the relationship between transit-related conflict frequency and various factors describing signalized intersection design, traffic demand, or operation. A transit-related conflict is defined as any conflict event in which at least one bus is involved. Table 169 shows the descriptive statistics of the data used for model development. Table 169. Statistics for variables in the transit vehicle safety model – right-turn deceleration. Variable Description Mean Std. Min. Max. y Bus-related conflict frequency (conflicts per hour) 4.37 2.86 0 23 x1 Presence of right-turn deceleration lane indicator (1 if present, 0 otherwise) 0.75 0.433 0 1 x2 Right-turn deceleration lane length (feet) 150 112 0 300 x3 Bus stop frequency (bus stops per hour) 1.5 0.5 1 2 x4 Bus dwell time (second) 22.5 7.50 15 30 x5 Traffic volume (vehicles per hour per lane) 545 85.4 440 660 x6 Proportion right-turn vehicles 0.105 0.073 0.011 0.204 x7 Bicycle volume (bicycles per hour) 30.3 25.2 0 64 Note: Std. – standard deviation. The data used to estimate the transit vehicle safety model included only the results from the 6912 simulation runs with one or more bus stops per hour. The 3456 results having zero bus stops per hour were not used to estimate the model coefficients. The estimated regression coefficients in the model and associated p-values are given in Table 170. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable).

301 Table 170. Predictive model calibration statistics, transit vehicle safety model – right-turn deceleration. Variable Description Coefficient Standard Error p-value Constant -0.2542 0.0556 <0.001 x1 Presence of right-turn deceleration lane indicator (1 if present, 0 otherwise) 0.9798 0.0249 <0.001 x2 Right-turn deceleration lane length (feet) -0.0013 0.0001 <0.001 x3 Bus stop frequency (bus stops per hour) 0.4143 0.0134 <0.001 x4 Bus dwell time (second) 0.0034 0.0009 <0.001 x5 Traffic volume (vehicles per hour per lane) 0.0005 0.0001 <0.001 x6 Proportion right-turn vehicles -0.2251 0.0904 0.013 x7 Bicycle volume (bicycles per hour) 0.0048 0.0003 <0.001 α Overdispersion factor 0.0656 0.0053 <0.001 Number of observations 6,912 Log likelihood -15280.67 The following equation represents the performance relationship for predicting transit-related conflict frequency. Equation 9 . . ∙ . ∙ ∙ . ∙ . ∙ . ∙ . ∙ . ∙ where y equals the transit-related conflict frequency, conflicts per hour; and all other variables are defined in Table 170. This equation should not be used with variable values outside the ranges provided in Table 169. A comparison between the observed (i.e., simulated) transit-related conflict frequency and the predicted frequency is shown in Figure 28.

302 Figure 28. Predicted vs. observed transit-related conflict frequency – right-turn deceleration. Figure 29 illustrates the relationship between various model variables and transit-related conflict frequency. The influence of right-turn deceleration lane presence and length on conflict frequency has an interesting relationship. Conflict frequency is highest when a short turn lane is present (say less than 200 ft). The conflict frequency decreases with an increase in lane length. Mathematically, the conflict frequency associated with a 750-foot lane length equates to that incurred without a turn lane (i.e., no turn lane present). As the lane length increases beyond 750 feet, conflict frequency continues to decrease (below that associated with no turn lane present). The bus stop is located adjacent to the right-most lane near the intersection. With a right-turn deceleration lane present, a bus needs to return to the traffic stream from the right-turn deceleration lane after alighting and boarding occur. The return may cause traffic conflicts between the bus and vehicles in the outside through lane. In contrast, buses use the outside through lane for alighting and boarding when a right-turn lane is not present. In this situation, the aforementioned “return to traffic” is avoided and so are the associated bus-related conflicts. A higher proportion of right-turn vehicles is associated with fewer bus-related conflicts. In general, only the right-turn vehicle that is just ahead of (or behind) the bus has the potential to conflict with the bus. Thus, increases in right-turn percentage do not tend to increase conflicts between buses and right- turning vehicles. On the other hand, a higher right-turn percentage corresponds to a lower through-traffic volume. Accordingly, the conflicts between returning buses and through traffic, which are the predominant bus conflict type, tend to be reduced with an increase in the proportion of right-turn vehicles.

303 a. Right-turn deceleration lane length (feet). b. Bus stop frequency (bus stops per hour). c. Bus dwell time (seconds). d. Traffic volume (veh. per hour per lane). e. Proportion right-turn vehicles. f. Bicycle volume (bicycles per hour). Figure 29. Influence of various factors on transit-related conflicts – right-turn deceleration.

304 A crash modification function (CMFbus) based on transit-related conflict data was derived from Equation 9. This CMF describes the change in transit safety that occurs when a right-turn deceleration lane is added to a signalized intersection approach. The following equation shows the derived CMF. Equation 10 , 0.9798 0.0013∙ 2 where CMFbus is the crash modification factor for right-turn lane presence; , is the predicted hourly conflict frequency with a right-turn deceleration lane length of x2 feet, and is the predicted hourly conflict frequency without a right-turn lane. The base condition (i.e., the condition at which the CMF value is 1.0) is a right-turn lane that is 750 feet long. CMF values for a range of right-turn lane lengths are shown Figure 30. Figure 30. Right-turn deceleration lane length CMF, transit-related conflicts – right-turn deceleration. Truck Safety Relationship A log-linear regression model was developed to describe the relationship between truck-related conflict frequency and various factors describing intersection design, traffic demand, or operation. A truck conflict is defined as a conflict event that involves at least one truck. Table 171 shows the descriptive statistics of the data used for model development.

305 Table 171. Statistics for variables in the truck-related safety model – right-turn deceleration. Variable Description Mean Std. Min. Max. y Truck-related total conflicts (conflicts per hour) 28.8 12.8 7 73 x1 Right-turn deceleration lane length (feet) 150 112 0 300 x2 Signal cycle length (second) 125 25.0 100 150 x3 Prohibition of right turn on red (RTOR) indicator (1 if RTOR is prohibited, 0 if enabled) 0.50 0.50 0 1 x4 Bus stop frequency (bus stops per hour) 1.00 0.82 0 2 x5 Traffic volume (vehicles per hour per lane) 545 85.4 440 661 x6 Proportion right-turn vehicles 0.10 0.07 0.01 0.20 x7 Proportion trucks 0.04 0.01 0.03 0.06 x8 Bicycle volume (bicycles per hour) 27.7 22.5 0 58 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 172. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable). Table 172. Predictive model calibration statistics, truck safety model – right-turn deceleration. Variable Description Coefficient Standard Error p-value Constant 0.54482 0.01891 <0.001 x1 Right-turn deceleration lane length (feet) -0.00037 0.00002 <0.001 x2 Signal cycle length (second) 0.00176 0.00008 <0.001 x3 Prohibition of right turn on red (RTOR) indicator (1 if RTOR is prohibited, 0 if enabled) -0.00799 0.00396 0.043 x4 Bus stop frequency (bus stops per hour) 0.00828 0.00242 0.001 x5 Traffic volume (vehicles per hour per lane) 0.00277 0.00002 <0.001 x6 Proportion right-turn vehicles 0.25284 0.02712 <0.001 x7 Proportion trucks 23.995 0.15967 <0.001 x8 Bicycle volume (bicycles per hour) 0.00042 0.00009 <0.001 α Overdispersion factor 0.00516 0.00054 <0.001 Number of observations 10,368 Log likelihood -32370.396 The following equation represents the performance relationship for predicting truck-related conflict frequency. Equation 11 . . ∙ . ∙ . ∙ . ∙ . ∙ . ∙ . ∙ . ∙

306 where y equals the truck-related conflict frequency, conflicts per hour; and all other variables are defined in Table 172. This equation should not be used with variable values outside the ranges provided in Table 171. A comparison between the observed (i.e., simulated) truck-related conflict frequency and the predicted frequency is shown in Figure 31. Figure 31. Predicted vs. observed truck-related conflict frequency – right-turn deceleration. Figure 32 illustrates the relationship between various model variables and truck-related conflict frequency. Right-turn deceleration lane presence significantly reduces truck-related conflict frequency. The amount of the reduction is a function of the lane length. On average, an increase of 100 feet in right- turn deceleration length reduces conflict frequency by 4 percent (= 100 – 100 × exp[-0.00037 × 100]). When this predictive model is used to evaluate an intersection approach with no right-turn deceleration lane, the length of the right-turn deceleration lane is entered as “0” feet (i.e., variable x1 = 0.0).

307 a. Right-turn deceleration lane length (feet). b. Bus stop frequency (bus stops per hour). c. Traffic volume (veh. per hour per lane). d. Proportion right-turn vehicles. e. Bicycle volume (bicycles per hour). f. Proportion trucks. Figure 32. Influence of various factors on truck-related conflicts – right-turn deceleration.

308 A crash modification function (CMFtruck) based on truck-related conflict data was derived from Equation 11. This CMF describes the change in truck safety that occurs when a right-turn deceleration lane is added to a signalized intersection approach. The following equation shows the derived CMF. Equation 12 , . ∙ where CMFtruck is the crash modification factor for right-turn deceleration lane length, , is the predicted hourly conflict frequency with a right-turn deceleration lane length of x1 feet, and is the predicted hourly conflict frequency without a right-turn lane. The base condition (i.e., the condition at which the CMF value is 1.0) is no right-turn lane present. CMF values for a range of right-turn lane lengths are shown Figure 33. Figure 33. Right-turn deceleration lane length CMF, truck-related conflicts – right-turn deceleration. TWLTL vs. Non-Traversable Median This section describes the findings from an analysis of data describing the performance of streets with either a TWLTL or non-traversable median (NTM). The analysis was used to produce (1) a set of performance relationships that predict the safety and operation of the TWLTL, and (2) a set of relationships that predict the safety and operation of the NTM. When both sets of relationships are used together, the results can be compared to obtain information about the relative performance of the two median types. The objective and scope of the study are provided in Appendix E (in a section having the same title as this section). The first subsection to follow describes the procedures used to develop operations performance relationships. The second subsection describes the procedures used to develop the safety performance relationships. Each subsection describes the findings from an examination of the data, the statistical

309 methods used to develop the relationships, and the procedures for using relationships in a practical application. Operations Relationships Based on Simulation Data This section describes the research undertaken to develop relationships for predicting the operation of bicycles and trucks on urban and suburban streets. A simulation testbed was established using several different prototype street segments. One-half of the segments included a TWLTL, the other one-half of the segments included a NTM. The set of sites represented in the database collectively include simulation results for a range of traffic characteristics, geometric design elements, and traffic control features. These data were evaluated to develop the performance relationships identified in the following list.  An operations-based performance relationship for bicycle travel on a street with a TWLTL;  An operations-based performance relationship for bicycle travel on a street with a NTM;  An operations-based performance relationship for truck travel on a street with a TWLTL; and  An operations-based performance relationship for truck travel on a street with a NTM. These relationships describe the association between performance and various factors for both the TWLTL and the NTM. This section describes the research undertaken to develop the aforementioned relationships. The first section provides a brief overview of the database that was used for relationship development. The second section describes the findings from an exploratory data analysis that was intended to identify the database variables that influence bicycle or truck operation. The third section describes the statistical methods used to develop the performance relationships as predictive models. The fourth section describes the model development results for bicycles and trucks. Data Overview The operations data produced from simulation were used to develop the performance relationships. Four simulation test beds were developed as the basis for the simulation runs. A total of 288 simulation scenarios were developed using these test beds. Each scenario represented a different combination of the factors identified in the following list.  Access management treatment (TWLTL or Non-Traversable Median);  Access density;  Through-traffic volume (i.e., through motorized vehicle volume; all vehicle types);  Bicycle volume;  Truck percentage;  Signal cycle length at the downstream intersection; and  Segment length. A total of 2801 observations were produced from the simulations. Of this total, 1489 observations had non-zero bicycle volume. They were used to develop the bicycle-speed predictive relationship. The key operations performance measures include:  Average bicycle speed (mph); and  Average truck speed (mph).

310 A detailed description of the data elements in the database is provided in Appendix F. Examination of Operations Data The results of the simulation runs are summarized in this section. There is a separate subsection for each of the two travel modes addressed (i.e., bicycle and truck). Bicycle Operations Data Examination This section summarizes the findings from a review of the simulation results for the bicycle travel mode. Summary statistics for these results were previously provided in Table 136. The summary in this section focuses on an assessment of the percent change in performance associated with a 1 percent change in the factor value (i.e., sometimes referred to as performance “elasticity”). The results of the elasticity analysis are shown in Table 173. Table 173. Factors affecting a change in operational performance – TWLTL vs. non-traversable median. Factor Effect of a Change in Factor Value or Presence on Speed Bicycle Speed Truck Speed NTM TWLTL NTM TWLTL Signal cycle length -0.3% per +1% -0.5% per +1% -0.2% per +1% -0.3% per +1% Segment length +0.3% per +1% +0.4% per +1% +0.3% per +1% +0.4% per +1% Access density no effect no effect no effect no effect Traffic volume no effect -0.1% per +1% -0.5% per +1% -0.5% per +1% Bicycle volume no effect no effect no effect no effect Truck percentage no effect no effect no effect no effect Note: “no effect” means less than ±0.1 percent change in delay per +1 percent change in factor value. As shown in Table 173, bicycle speed does not appear to be significantly influenced by the following factors: access density, traffic volume, bicycle volume, and truck percentage. An increase in cycle length tends to decrease bicycle speed, keeping all other factors constant. On a street with a non-traversable median, a 1 percent increase in cycle length corresponds to a 0.3 percent decrease in speed. In contrast, a 1 percent increase in segment length corresponds to a 0.3 percent increase in bicycle speed. Truck Operations Data Examination This section summarizes the findings from a review of the simulation results for the truck travel mode. Summary statistics for these results were previously provided in Table 136. The summary in this section focuses on an assessment of the elasticity of truck speed relative to a change in segment length, cycle length, access density, or volume. The results of the elasticity analysis are shown in Table 173. As shown in Table 173, truck speed does not appear to be significantly influenced by traffic volume, bicycle volume, or truck percentage. On a street with a non-traversable median, a 1 percent increase in segment length tends to increase truck speed by 0.3 percent, keeping all other factors constant. In contrast, an increase in cycle length or access density corresponds to a decrease in truck speed.

311 Statistical Methods Based on the examination of operations data, linear regression models were developed to explore the relationship between operations performance measures and independent variables (scenario factors). The statistical software package Stata 13 was used to estimate the model coefficients using the ordinary least squares (OLS) estimator. A step-wise procedure was used to select the significant independent variables at a confidence level of 95%. The candidate independent variables included a range of scenario factors (e.g., signal cycle, access level, traffic volume, bicycle volume, and truck percentage). A graphical comparison of predicted and observed values were used to evaluate each model’s goodness-of-fit. Following the presentation of the estimated model and the graphical illustration of goodness-of-fit, a series of figures are presented to illustrate the effects of each independent variable on performance. The predicted values depict the effect of the independent variable on performance when all other explanatory variables are set to equal their respective average value. The Stata command “margins” was used to produce these figures. Operations Performance Relationship Development The developed models are described in this section. It consists of four subsections. One subsection is used to describe the model for each of the following four combinations of travel mode and median type.  Bicycle speed along street with TWLTL;  Bicycle speed along street with non-traversable median;  Truck speed along street with TWLTL; and  Truck speed along street with non-traversable median. Bicycle Operations Relationship – TWLTL A log-linear regression model was developed to describe the relationship between bicycle speed and various factors describing street design, traffic demand, or operation. The model discussed in this section predicts speed associated with a TWLTL design. Table 174 shows the descriptive statistics of the data used for model development. Table 174. Statistics for variables in the bicycle operations model, TWLTL – TWLTL vs. non- traversable median. Variable Description Mean Std. Min. Max. y Bicycle speed (mph) 8.78 1.83 5.32 11.2 x1 Signal cycle length (seconds) 123 25.0 100 150 x2 Segment length (miles) 0.34 0.13 0.22 0.48 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 175. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable).

312 Table 175. Predictive model calibration statistics, bicycle operations model, TWLTL – TWLTL vs. non-traversable median. Variable Description Coefficient Standard Error p-value Constant 2.6007 0.0077 <0.001 x1/x2 Signal cycle length (seconds) divided by segment length (miles) -0.0011 <0.0001 <0.001 Number of observations 721 R2 0.9928 The following equation represents the performance relationship for predicting bicycle speed on a street with a TWLTL. Equation 13 . . ∙ / where y equals the bicycle speed, miles per hour; and all other variables are defined in Table 175. This equation should not be used with variable values outside the ranges provided in Table 174. Equation 13 is based on a bicycle free-flow speed of 11 miles per hour. The use of this equation for other free-flow speeds will require multiplying the result (i.e., y) by the proportion “new free-flow speed” divided by 11. A comparison between the observed and predicted bicycle speed is shown in Figure 34. The trend line shown suggests that the model slightly overestimates the observed bicycle speed for speeds above 10 miles per hour and speeds less than 7 miles per hour. Figure 34. Predicted vs. observed bicycle speed for TWLTL – TWLTL vs. non-traversable median. Figure 35 illustrates the relationship between various model variables and bicycle speed. The trend lines indicate that an increase in segment length corresponds to higher bicycle speed. In contrast, an increase in cycle length corresponds to lower bicycle speed. The regression analysis indicated that the influence of traffic volume on bicycle speed is not significant.

313 Segment length (miles) Figure 35. Influence of various factors on bicycle speed for TWLTL – TWLTL vs. non-traversable median. Bicycle Operations Relationship – NTM A log-linear regression model was developed to describe the relationship between bicycle speed and various factors describing street design, traffic demand, or operation. The model discussed in this section predicts speed associated with a non-traversable median design. Table 176 shows the descriptive statistics of the data used for model development. Table 176. Statistics for variables in the bicycle operations model, non-traversable median – TWLTL vs. non-traversable median. Variable Description Mean Std. Min. Max. y Bicycle speed (mph) 9.26 1.45 5.89 11.2 x1 Signal cycle length (seconds) 125 25.0 100 150 x2 Segment length (miles) 0.35 0.13 0.22 0.48 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 177. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable).

314 Table 177. Predictive model calibration statistics, bicycle operations model, non-traversable median – TWLTL vs. non-traversable median. Variable Description Coefficient Standard Error p-value Constant 2.5207 0.0079 <0.001 x1/x2 Signal cycle length (seconds) divided by segment length (miles) -0.0007 0.0001 <0.001 Number of observations 768 R2 0.9922 The following equation represents the performance relationship for predicting bicycle speed on a street with a non-traversable median. Equation 14 . . ∙ / where y equals the bicycle speed, miles per hour; and all other variables are defined in Table 177. This equation should not be used with variable values outside the ranges provided in Table 176. Equation 14 is based on a bicycle free-flow speed of 11 miles per hour. The use of this equation for other free-flow speeds will require multiplying the result (i.e., y) by the proportion “new free-flow speed” divided by 11. A comparison between the observed and the predicted bicycle speed is shown in Figure 36. The trend line shown suggests that the model slightly overestimates the observed bicycle speed for speeds in excess of 10 miles per hour. Figure 36. Predicted vs. observed bicycle speed for non-traversable median – TWLTL vs. non- traversable median. Figure 37 illustrates the relationship between various model variables and bicycle speed. The trend lines indicate that an increase in segment length corresponds to higher bicycle speed. In contrast, an

315 increase in cycle length corresponds to lower bicycle speed. The regression analysis indicated that the influence of traffic volume on bicycle speed is not significant. Segment length (miles) Figure 37. Influence of various factors on bicycle speed for non-traversable median – TWLTL vs. non-traversable median. An interesting trend in bicycle speed can be found by comparing the trend lines in Figure 35 and Figure 37. For shorter street segments, bicycle speed is higher on a street with a non-traversable median than it is on a street with a TWLTL. This trend reverses for longer street segments. The trend lines for TWLTL and for NTM cross at a segment length of around 0.5 miles, which is the upper limit segment length in the data used to calibrate the model. The data support the trend noted for shorter street segments (i.e., bicycle speed on NTM is higher than that on a TWLTL). The trend noted for longer street segments is based on an extrapolation of the model beyond the range of segment length represented in the data. Truck Operations Relationship – TWLTL A regression model was developed to describe the relationship between truck speed and various factors describing street design, traffic demand, or operation. The model discussed in this section predicts speed associated with a TWLTL design. Table 178 shows the descriptive statistics of the data used for model development.

316 Table 178. Statistics for variables in the truck operations model, TWLTL – TWLTL vs. non- traversable median. Variable Description Mean Std. Min. Max. y Truck speed (mph) 15.2 3.29 6.33 24.5 x1 Signal cycle length (seconds) 124 25.0 100 150 x2 Segment length (miles) 0.34 0.13 0.22 0.48 x3 Traffic volume (vehicles per hour per lane) 488 71.1 348 648 x4 Truck volume (trucks per hour) 45.4 18.4 15 88 x5 Access density (access points per mile) 13.7 4.72 8.33 22.7 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 179. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable). Table 179. Predictive model calibration statistics, truck operations model, TWLTL – TWLTL vs. non-traversable median. Variable Description Coefficient Standard Error p-value Constant 4.9656 0.1064 <0.001 x1 Signal cycle length (seconds) -0.0405 0.0020 <0.001 1/x2 Reciprocal of segment length (miles) -0.0784 0.0034 <0.001 ln(x3) Natural logarithm of traffic volume (vphpl) -0.2520 0.0178 <0.001 ln(x4) Natural logarithm of truck volume (trucks per hour) -0.0316 0.0062 <0.001 x5 /x2 Access density (access points per mile) divided by segment length (miles) -0.0006 0.0002 <0.001 Number of observations 1649 R2 0.9822 The following equation represents the performance relationship for predicting truck speed on a street with a TWLTL. Equation 15 0.0405 ∙ . . / . ∙ . ∙ . ∙ / where y equals the truck speed, miles per hour; and all other variables are defined in Table 179. This equation should not be used with variable values outside the ranges provided in Table 178. This equation is based on a truck free-flow speed of 40 miles per hour. The use of this equation for other free-flow speeds will require multiplying the result (i.e., y) by the proportion “new free-flow speed” divided by 40. A comparison between the observed and the predicted truck speed is shown in Figure 38. The fitted line suggests the model tends to be a reliable predictor of truck speed. However, there are some scenarios where it underestimates truck speed when the predicted speed is in the range of 12mph to 13 mph.

317 Figure 38. Predicted vs. observed truck speed for TWLTL – TWLTL vs. non-traversable median. Figure 39 illustrates the relationship between various model variables and truck speed. The regression analysis indicated that truck volume and access point density have an influence on truck speed. Specifically, an increase in truck volume reduces truck speed. The rate of reduction is largest when truck volume is less than about 40 trucks per hour. As truck volume increases beyond 40 trucks per hour, the rate of reduction becomes smaller. For a segment length of 0.22 miles, an increase of 10 access points per mile tends to reduce truck speed by 0.36 mph on streets with a TWLTL. This rate of reduction becomes smaller as segment length increases.

318 a. Access density (access points per mile). b. Signal cycle length (seconds). c. Traffic volume (vehicles per hour per lane). d. Truck volume (trucks per hour). e. Segment length (miles). Figure 39. Influence of various factors on truck speed for TWLTL – TWLTL vs. non-traversable median.

319 Truck Operations Relationship – NTM A linear regression model was developed to describe the relationship between truck speed and various factors describing street design, traffic demand, or operation. The model discussed in this section predicts speed associated with a non-traversable median design. Table 180 shows the descriptive statistics of the data used for model development. Table 180. Statistics for variables in the truck operations model, non-traversable median – TWLTL vs. non-traversable median. Variable Description Mean Std. Min. Max. y Truck speed (mph) 15.8 2.89 7.87 23.2 x1 Signal cycle length (seconds) 125 25.0 100 150 x2 Segment length (miles) 0.35 0.13 0.22 0.48 x3 Traffic volume (vehicles per hour per lane) 491 74.1 350 655 x4 Truck volume (trucks per hour) 45.8 18.8 18 91 x5 Access density (access points per mile) 10.9 3.19 8.33 18.2 Note: Std. – standard deviation. The estimated regression coefficients in the model and associated p-values are given in Table 181. The p-value for each coefficient is listed in the last column of the table. The values are all quite small, indicating that each model coefficient is significantly different from zero (i.e., that the associated variable has a strong correlation with the dependent variable). Table 181. Predictive model calibration statistics, truck operations model, non-traversable median – TWLTL vs. non-traversable median. Variable Description Coefficient Standard Error p-value Constant 5.1667 0.1205 <0.001 x1 Signal cycle length (seconds) -0.0313 0.0023 <0.001 1/x2 Reciprocal of segment length (miles) -0.0591 0.0050 <0.001 ln(x3) Natural logarithm of traffic volume -0.3033 0.0204 <0.001 ln(x4) Natural logarithm of truck volume -0.0261 0.0072 <0.001 x5 /x22 Access density (access points per mile) divided by squared segment length (miles) -0.0002 0.0001 <0.001 Number of observations 1152 R2 0.9850 The following equation represents the performance relationship for predicting truck speed on a street with a non-traversable median. Equation 16 0.0313 ∙ . . / . ∙ . ∙ . ∙ / where y equals the truck speed, miles per hour; and all other variables are defined in Table 181. This equation should not be used with variable values outside the ranges provided in Table 180.

320 This equation is based on a truck free-flow speed of 40 miles per hour. The use of this equation for other free-flow speeds will require multiplying the result (i.e., y) by the proportion “new free-flow speed” divided by 40. A comparison between the observed and the predicted truck speed is shown in Figure 40. The fitted line suggests the model tends to be a reliable predictor of truck speed. Figure 40. Predicted vs. observed truck speed for non-traversable median – TWLTL vs. non- traversable median. Figure 41 illustrates the relationship between various model variables and truck speed. The regression analysis indicated that truck volume and access point density have an influence on truck speed. Specifically, an increase in truck volume reduces truck speed. The rate of reduction is largest when truck volume is less than about 40 trucks per hour. As truck volume increases beyond 40 trucks per hour, the rate of reduction becomes smaller. For a segment length of 0.22 miles, an increase of 10 access points per mile tends to reduce truck speed by 0.38 mph on streets with a TWLTL. This rate of reduction becomes smaller as segment length increases. An interesting trend in truck speed can be found by comparing the trend lines in Figure 39 and Figure 41. For shorter street segments, truck speed is higher on a street with a non-traversable median than it is on a street with a TWLTL. This trend reverses for longer street segments. The trend lines for TWLTL and for NTM cross at a segment length of around 0.5 miles, which is the upper limit segment length in the data used to calibrate the model. The data support the trend noted for shorter street segments (i.e., truck speed on NTM is higher than that on a TWLTL). The trend noted for longer street segments is based on an extrapolation of the model beyond the range of segment length represented in the data.

321 a. Access density (access points per mile). b. Signal cycle length (seconds). c. Traffic volume (vehicles per hour per lane). d. Truck volume (trucks per hour). e. Segment length (miles). Figure 41. Influence of various factors on truck speed for non-traversable median – TWLTL vs. non-traversable median.

322 Safety Relationships Based on Crash Data This section describes the research undertaken to develop relationships for predicting the safety of truck and transit vehicles on urban and suburban streets. A cross-sectional database was assembled to evaluate the safety effects of the TWLTL and NTM on transit vehicles and trucks. The set of sites represented in the database collectively include a range of traffic characteristics, geometric design elements, and traffic control features. Data for sites having a flush-painted median were also included in the database. These sites were grouped with those having a TWLTL because both median types can be characterized as “traversable.” Hereafter, the two classes of median type addressed are the NTM and the traversable median (TM). The assembled data were used to develop the performance relationships identified in the following list.  A crash-based safety performance relationship for transit travel on a street with a TM;  A crash-based safety performance relationship for transit travel on a street with a NTM;  A crash-based safety performance relationship for truck travel on a street with a TM; and  A crash-based safety performance relationship for truck travel on a street with a NTM. Each relationship has the form of a safety prediction model that includes (1) a safety performance function (SPF) to quantify the safety effect of segment length and AADT, and (2) a series of crash modification factors (CMFs) to quantify the safety effect of various site characteristics (e.g., lane width). The SPF and CMFs are used together to compute the predicted average transit- or truck-related crash frequency. Models of this type that are applicable to the overall traffic stream (i.e., all vehicle types combined) are provided in Part C of the Highway Safety Manual (AASHTO, 2010). This section describes the research undertaken to develop the aforementioned relationships. The first section provides a brief overview of the database that was used for relationship development. The second section describes the findings from an exploratory data analysis that was intended to identify the database variables that influence truck or transit safety. The third section describes the statistical methods used to develop the performance relationships as predictive models. The fourth and fifth sections describe the model development results for transit vehicles and trucks, respectively. The last section provides guidelines for using the models to evaluate transit-related and truck-related safety for streets with either a TM or NTM. Data Overview The database assembled for performance relationship development includes data for 214 study sites. Each site represents a two-way street segment located between two signalized intersections. Of the 214 segments, 96 segments have a non-traversable median and total 28 miles in length. There are 118 segments with a traversable median; they total 42.2 miles in length. The 214 segments are collectively located in urban or suburban areas of six states. Crash data were obtained for the most recent five-year period that records were available. This time period varied among the agencies contacted. However, in most cases, the crash data obtained correspond to the years 2012 to 2016. There are a total of 172 transit-related crashes and 369 truck-related crashes included in the database. The crashes included in the database are transit-related and truck-related crashes occurring along the segment. Crashes related to other vehicle types and those associated with signalized intersections were excluded from the database. A detailed description of the data elements in the database is provided in Appendix F.

323 Examination of Crash Data As a precursor to model development, the database was examined graphically to identify the possible association between specific site characteristics and crash rate. The insights obtained from this examination were used to (1) determine which characteristics are likely candidates for representation in the model and (2) guide the functional form development for the performance relationship. The discussion in this subsection is not intended to indicate conclusive results or recommendations. The recommended predictive models (and associated trends) are documented in a subsequent section. The paragraphs to follow describe the findings from the graphical examination of each geometric design element. The examination focused on “total” crashes (i.e., all severities combined). Identifying trends in a figure with one point for each segment was often difficult because of the large number of clustered data points. To improve the examination of trends in the data, the data were sorted by the design element dimension of interest to form groups of segments with similar dimension value. Then, the total crash frequency and the total million entering vehicles were computed for each group. These two values were then used to compute the group crash rate. Each group was sized to have the about same total exposure (i.e., weight). It was determined that limiting each figure to five to ten data points (one point for each group) would minimize data overlap and facilitate an examination of trends in the data. Lane Width The findings from the examination of average lane width are shown in Figure 42. Figure 42a shows the relationship for transit-related crashes and Figure 42b shows the relationship for truck-related crashes. The trend lines shown represent the line of best fit to the data points, based on regression analysis. The trend lines indicate that crash frequency decreases with an increase in lane width. This trend is logical and consistent with that found for the overall traffic stream on arterial streets (Lord et al. 2015). However, the slope of the line is steeper for transit- and truck-related crashes than for the overall traffic stream. For example, a one-foot increase in lane width is shown to be correlated with a 40-percent reduction in the transit-related and truck-related crash rates. In contrast, a one-foot increase in lane width typically associates with a 2- to 4-percent reduction in overall traffic stream crash rate. a. Transit-related crashes. b. Truck-related crashes. Figure 42. Examination of lane width and crash rate – TWLTL vs. non-traversable median.

324 Median Width The findings from the examination of non-traversable median width are shown in Figure 43. Figure 43a shows the relationship for transit-related crashes and Figure 43b shows the relationship for truck-related crashes. A relationship was not found for traversable median width. The trend lines indicate that crash frequency decreases with an increase in median width. This trend is logical and consistent with that found for the overall traffic stream on arterial streets (AASHTO 2010; Lord et al., 2015). However, the slope of the line is steeper for transit- and truck-related crashes than for the overall traffic stream. For example, a one-foot increase in width is shown to be correlated with a 5- percent reduction in the transit-related and truck-related crash rates. In contrast, a one-foot increase in median width typically associates with a 0.1 to 0.6 percent reduction in overall traffic stream crash rate. Further examination of the data in Figure 43 suggests that the change in crash rate is greatest for median widths less than about 25 feet. For medians wider than 25 feet, there appears to be negligible change in crash rate with a change in median width. a. Transit-related crashes. b. Truck-related crashes. Figure 43. Examination of median width and crash rate – TWLTL vs. non-traversable median. Combined Shoulder and Bike Lane Width The findings from the examination of combined outside shoulder width and bike lane width are shown in Figure 44. Figure 44a shows the relationship for transit-related crashes and Figure 44b shows the relationship for truck-related crashes. The average widths of the outside shoulder and bike lane were added to produce one value representing both sides of the roadway. If a roadway had no bike lane, then the value used represents just the average shoulder width. The trend lines indicate that crash frequency decreases with an increase in shoulder plus bike lane width. This trend is logical and consistent with that found for the overall traffic stream on arterial streets (Lord et al., 2015). However, the slope of the line is steeper for transit- and truck-related crashes than for the overall traffic stream. For example, a one-foot increase in width is shown to be correlated with a 20- percent reduction in the transit-related and truck-related crash rates. Figure 44a shows a data point for 10.2-foot width that does not fit the trend in the other data points. Further examination of the data in Figure 44a suggested that there may be a “minimum” point such that shoulder plus bike lane width is associated with the smallest crash rate at widths of about 7 feet. For widths of 7 feet or more, there may be a slight increase in crash rate with increasing width.

325 a. Transit-related crashes. b. Truck-related crashes. Figure 44. Examination of average outside shoulder width plus bike lane width and crash rate – TWLTL vs. non-traversable median. Commercial Driveway Density The findings from the examination of commercial driveway density are shown in Figure 45. Figure 45a shows the relationship for transit-related crashes and Figure 45b shows the relationship for truck-related crashes. The driveway density values used for this examination represent the count of driveways with access to all turn movements (i.e., full-access driveways) and those that prohibit some movements (i.e., partial-access driveways). The trend lines indicate that crash frequency increases with an increase in driveway density. This trend is logical and consistent with that found for the overall traffic stream on arterial streets (AASHTO 2010; Lord et al., 2015). The trend lines suggest that a one unit increase in driveway density is shown to be correlated with a 1 percent and 4 percent increase in the transit-related and truck-related crash rates, respectively. A similar trend was found for office driveway density. a. Transit-related crashes. b. Truck-related crashes. Figure 45. Examination of commercial driveway density and crash rate – TWLTL vs. non- traversable median.

326 Partial-Access Driveway Presence This examination investigated whether the prohibition of some driveway turn movements had an effect on transit or truck safety. A driveway for which one or more movements were prohibited is considered a “partial-access driveway.” A driveway with access to all turn movements is considered a “full-access driveway.” The count of commercial and office driveways was used for this examination. The findings from the examination of partial-access driveway presence are shown in Figure 46. The independent variable for this examination is the ratio of partial-access driveways to total driveways on each segment. For example, if a street has three full-access driveways and two partial-access driveway, the ratio is 0.4 (= 2/[3+2]). The trend lines in Figure 46 indicate that crash frequency decreases with an increase in the partial- access driveway ratio. This trend is logical and consistent with that found when comparing the predicted crash frequency for four-leg stop-controlled intersections with that for three-leg stop-controlled intersections using the predictive methods in Part C of the Highway Safety Manual (AASHTO, 2010). a. Transit-related crashes. b. Truck-related crashes. Figure 46. Examination of partial-access driveway presence and crash rate – TWLTL vs. non- traversable median. Public Street Approaches The findings from the examination of public street approach density are shown in Figure 47. The approach density values used for this examination represent the count of public street approaches along the segment (excluding those at the boundary signalized intersections). Almost all of the public street approaches included in the database allow all turn movements (i.e., they provide full access). The trend lines indicate that crash frequency increases with an increase in approach density. This trend is logical and consistent with that found for driveway density. The trend lines suggest that a one unit increase in approach density is shown to be correlated with a 3 percent and 2 percent increase in the transit-related and truck-related crash rates, respectively.

327 a. Transit-related crashes. b. Truck-related crashes. Figure 47. Examination of public street approach density and crash rate – TWLTL vs. non- traversable median. Statistical Methods This section describes the activities undertaken to develop the performance relationships (i.e., models) for predicting transit-related and truck-related crash frequency as a function of median type. The subsections to follow provide an overview of the modeling approach and an overview of the statistical analysis methods used to calibrate the models. Modeling Approach As indicated in a previous section, four models were planned for development. These models would collectively address the two vehicle types (i.e., transit and truck) and two median types (i.e., TM and NTM) of interest. A preliminary analysis of the data indicated that the sample size for some of the model combinations was too small to develop a reliable model. To overcome this issue, it was decided that separate models would be independently developed for each of the two vehicle types, and that a combined modeling approach would be needed to develop semi-independent models for the two median types. Thus, the model development plan was revised to include development of two vehicle-type models; each model having a safety performance function (SPF) for the traversable and the non-traversable median types. The two models are identified in the following list:  Transit vehicles, with a SPF for traversable medians and a SPF for non-traversable medians; and  Trucks, with a SPF for traversable medians and a SPF for non-traversable medians. The general form of each model is shown in the following equations. Equation 17 , . . . , . . . , Equation 18 , . . . , . . . , where

328 Nm = predicted average crash frequency for a road segment with median type m (m = TM: traversable median; NTM: non-traversable median), crashes/yr; Ls = length of segment, miles; NSPF,m = predicted crash frequency for base conditions on a segment with median type m, crashes/mile/year; CMFi = crash modification factor for traffic characteristic, geometric element, or traffic control feature i (applicable to all median types); and CMFm,i = crash modification factor for traffic characteristic, geometric element, or traffic control feature i and median type m. The SPF’s associated with these models are defined as: Equation 19 , , 1000 1000 Equation 20 , , 1000 1000 where AADT = overall annual average daily traffic (AADT) volume for segment (including transit vehicles and trucks), veh/d; AADTv = AADT for vehicle type v (v = tv: transit vehicle; tk: truck) for street segment, veh/d; bi = calibration coefficient for condition i; and all other variables are as previously defined. The CMFs in the middle term of Equation 17 are shown to be the same as the CMFs in the middle term of Equation 18. That is, the functional form and calibration coefficient associated with each CMF is the same, regardless of median type. This approach recognizes that some design elements or traffic control features have a similar influence on segment crash frequency, regardless of whether the median is traversable or non-traversable. Before it was determined that a common CMF is appropriate for both equations, a preliminary regression analysis was undertaken to determine if the regression coefficient associated with each CMF was significantly different when applied only traversable median segments, relative to when it was applied only to non-traversable median segments. If the two coefficients were not significantly different, then one coefficient was used for both median types (to create a common CMF). The use of common CMFs has the advantage of maximizing the sample size available to estimate the CMF coefficient. In this manner, the data for both median types are pooled to provide a more efficient estimate of the CMF coefficient. The use of common CMFs in the two equations required the use of a combined regression modeling approach. With this approach, the regression analysis evaluated both models simultaneously and used the total log-likelihood statistic to determine the best-fit calibration coefficients. The regression analysis is described in more detail in subsequent section. Model Fit Statistics It was assumed that segment crash frequency is Poisson distributed, and that the distribution of the mean crash frequency for a group of similar segments is gamma distributed. In this manner, the distribution of crashes for a group of similar segments can be described by the negative binomial distribution. The variance of this distribution is computed using the following equation.

329 Equation 21 where V[X] = crash frequency variance for a group of similar locations, crashes2; N = predicted average crash frequency, crashes/yr; X = reported crash count for y years, crashes; y = time interval during which X crashes were reported (i.e., evaluation period), yr; and K = inverse dispersion parameter (= 1/k, where k = overdispersion parameter). The nonlinear regression procedure (NLMIXED) in the SAS software was used to estimate the proposed model coefficients. This procedure was used because the proposed predictive model is both nonlinear and discontinuous. The log-likelihood function for the negative binomial distribution was used to determine the best-fit model coefficients. Equation 21 was used to define the variance function for all models. The procedure was set up to estimate model coefficients based on maximum-likelihood methods. Several statistics were used to assess model fit to the data. One measure of model fit is the Pearson χ2 statistic. This statistic is calculated using the following equation. Equation 22 where χ2 = Pearson chi-square statistic; n = number of observations (i.e., segments or intersections in database); V[Xi] = crash frequency variance for a group of similar locations, crashes2; Ni = predicted average crash frequency for observation i, crashes/yr; Xi = reported crash count for yi years for observation i, crashes; and yi = time interval during which Xi crashes were reported for observation i, yr. This statistic follows the χ2 distribution with n – p degrees of freedom, where n is the number of observations and p is the number of model variables (McCullagh and Nelder, 1983). This statistic is asymptotic to the χ2 distribution for larger sample sizes. The root mean square error sp is a useful statistic for describing the precision of the model estimate. It represents the standard deviation of the estimate when each independent variable is at its mean value. This statistic can be computed using the following equation. Equation 23 ∑ where sp = root mean square error of the model estimate, crashes/yr; and all other variables are as previously defined. The scale parameter φ is used to assess the amount of variation in the observed data, relative to the specified distribution. This statistic is calculated by dividing Equation 22 by the quantity n – p. A scale parameter near 1.0 indicates that the assumed distribution of the dependent variable is approximately equivalent to that found in the data (i.e., negative binomial). Another measure of model fit is the coefficient of determination R2. This statistic is commonly used for normally distributed data. However, it has some useful interpretation when applied to data from other

330 distributions when computed in the following manner (Kvalseth, 1985). This coefficient is computed using the following equation. Equation 24 1.0 ∑ ∑ where = average crash frequency for all n observations, crashes; and all other variables are as previously defined. The last measure of model fit is the dispersion-parameter-based coefficient of determination Rk2. This statistic was developed by Miaou (1996) for use with data that exhibit a negative binomial distribution. It is computed using the following equation. Equation 25 1.0 where k = overdispersion parameter (= 1/K, where K = inverse dispersion parameter); and knull = overdispersion parameter based on the variance in the observed crash frequency. The null overdispersion parameter knull represents the dispersion in the reported crash frequency, relative to the overall average crash frequency for all sites. This parameter can be obtained using a null model formulation (i.e., a model with no independent variables but with the same error distribution, link function, and offset in years y). Transit Safety Performance Relationship Development This section describes the development of models for predicting transit-related crash frequency on urban and suburban street segments. These models are not applicable to the evaluation of other travel modes (e.g., trucks) or facility types. The models are developed to predict total crash frequency (i.e., all severities). One variation of the model is applicable to segments with a traversable median and a second variation of the model is applicable to segments with a non-traversable median. This section consists of four subsections. The first subsection describes the structure of the safety predictive models as used in the regression analysis. The second subsection describes the regression statistics for each of the estimated models. The third subsection describes the estimated safety performance functions. The fourth subsection describes the estimated CMFs. Model Development This section describes the proposed prediction models and the methods used to calibrate them. The regression model is generalized to accommodate the analysis of segments with either a traversable median or a non-traversable median. The generalized form shows all the CMFs in the model. Indicator variables are used to determine which CMFs are applicable to each observation in the database based on the associated median type. The following generalized regression model is described using the following equations. A. If the observation corresponds to a segment with a traversable median (i.e., m = TM), the following model is used. Equation 26 , , ,

331 With Equation 27 , , 1000 1000 Equation 28 , / 46 where Ny,TM = predicted average number of crashes for y years for a road segment with a traversable median, crashes; y = time interval for reported crashes (i.e., evaluation period), yr; Ls = length of segment, miles; NSPF,TM = predicted crash frequency for base conditions on a segment with a traversable median; crashes/mile/yr; CMFWlsb = crash modification factor for lane width and shoulder width; CMFDcox,TM = crash modification factor for commercial driveways, office driveways, and public street approaches on a segment with a traversable median; AADT = overall annual average daily traffic (AADT) volume for segment (including local public transit vehicles and trucks), veh/d; AADTtv = AADT for local public transit vehicles, veh/d; ncom = number of commercial driveways on the segment (two-way total; including driveways with full access and those with partial access), driveways; noff = number of office driveways on the segment (two-way total; including driveways with full access and those with partial access), driveways; nxstrt = number of unsignalized public street approaches on the segment (two-way total; including approaches with full access and those with partial access), approaches; bi,TM = calibration coefficient for condition i for segments with a traversable median; and bi = calibration coefficient for condition i. . B. If the observation corresponds to a segment with a non-traversable median (i.e., m = NTM), the following model is used. Equation 29 , , , , with Equation 30 , 1000 1000 Equation 31 , , , , 25 20 Equation 32 , / 23 where

332 Ny,NTM = predicted average number of crashes for y years for a road segment with a non-traversable median, crashes; NSPF,NTM = predicted crash frequency for base conditions on a segment with a non-traversable median; crashes/mile/yr; CMFWm,NTM = crash modification factor for median width on a segment with a traversable median; Wm,NTM = median width (measured from near edges of traveled way in both directions), ft; CMFDcox,NTM = crash modification factor for commercial driveways, office driveways, and public street approaches on a segment with a non-traversable median; and all other variables as previously defined. The value of “46” in Equation 28 and “23” in Equation 32 is the base access point approach density (in units of access points per mile) for the segments with traversable and non-traversable median type, respectively. These values were computed as the average density of those segments in the database. The value of “20” in Equation 31 is the base median width (in units of feet) for the segments with non- traversable medians. The term “min{X, Y}” is used in Equation 31 to indicate that the smaller value of variables X and Y are used in the calculation. This term is used in equations to follow with similar meaning. The following CMF is used in both the TM and NTM models. Equation 33 12 , 7 1.5 2 12 , 7 1.5 where Wl = lane width (average for all through lanes), ft; Ws = paved outside shoulder width (average for both travel directions), ft; Wb = bike lane width (average for both travel directions), ft; and all other variables as previously defined. The value of “12” in Equation 33 is the base lane width (in units of feet) for the segments. Similarly, the value of “1.5” is the base shoulder width (in units of feet). This width corresponds to the “effective” shoulder width for a typical curb-and-gutter section. Equation 33 includes an interaction term that accounts for an interaction between shoulder width and lane width. The interaction term effectively adjusts the coefficient value for lane width as a function of shoulder width. Similarly, it adjusts the coefficient value for shoulder width as a function of lane width. This type of interaction between lane width and shoulder width has previously been incorporated in a CMF for the overall traffic stream on rural two-lane highways (Bonneson et al., 2006). The regression model described by Equation 26 to Equation 33 represents the “final” model form. This form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described by these equations represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded. CMFs for other variables were also examined but were not found to be helpful in explaining the variation in the observed crash frequency among sites. These variables include:  Parking presence;  Residential driveway density;  Industrial driveway density;  Number of transit stop facilities on the segment;

333  Number of through lanes; and  Presence of a mid-segment crosswalk. This finding does not rule out the possibility that these factors have an influence on segment safety. It is possible that their effect is sufficiently small that it would require either (1) a larger database (with more observations and a wider range in variable values) to detect using regression, or (2) the use of a before– after study that isolates the individual effect of one factor on crash frequency. Five segments were found to have one or more transit-related crashes during the evaluation period, but the segment was not located on a public transit route. It is possible that the vehicle type was miss-coded on the crash report or that the involved transit vehicle was a school bus or intercity bus. Regardless, the database includes only the volume of public transit vehicles, so the volume for this segment is zero. Because the natural log function in Equation 27 and Equation 30 is undefined at zero, these five segments (and the seven transit-related crashes) were removed from the database to avoid computational errors. Model Estimation The predictive model calibration process was based on a combined regression modeling approach, as discussed in the section titled Modeling Approach. With this approach, the two median-type models and CMFs (represented by Equation 26 to Equation 33) are calibrated using a common database. This approach is needed because the lane width and shoulder width CMF and the AADT coefficients in the SPFs are common to both median-type models. The results of the combined regression model calibration are presented in Table 182. Calibration of this model focused on transit-related total crash frequency (i.e., all severities). The Pearson χ2 statistic for the model is 225 and the degrees of freedom are 200 (= n − p = 209 − 9). As this statistic is less than χ2 0.05, 200 (= 234), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.29. An alternative measure of model fit that is better suited to the negative binomial distribution is Rk2. The Rk2 for the calibrated model is 0.72 . Table 182. Predictive model calibration statistics, transit-related crashes – TWLTL vs. non-traversable median. Model Statistics Value R2 (Rk2): 0.29 (0.72) Scale Parameter φ: 1.08 Pearson χ2: 225 (χ20.05, 200 = 234) Inverse Dispersion Parameter K: 7.14 Observations n: 209 segments (165 crashes) Standard Deviation sp: ±0.22 crashes/yr Calibrated Coefficient Values Variable Inferred Effect of… Value Std. Error t-statistic b0 Non-traversable median -1.868 1.162 -1.61 b2 Local public transit AADT 0.698 0.168 4.14 b1 AADT (excluding local public transit volume) 0.684 0.307 2.23 b0,TM Traversable median -0.460 0.254 -1.81 bWm,NTM Width of non-traversable median -0.0576 0.0237 -2.43 bWl Lane width -0.724 0.171 -4.24 bWx Lane width and shoulder width interaction 0.0719 0.0282 2.55 bWsb Outside shoulder width and bike lane width -0.0165 0.0577 -0.29 bDcox Commercial driveways, office driveways, and public street approaches 0.0153 0.00626 2.44

334 The t-statistics listed in the last column of Table 182 indicate a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model, and its trend was found to be logical and consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The findings from an examination of the coefficient values and the corresponding CMF or SPF predictions are documented in a subsequent subsection. Estimated SPFs This section describes the fit statistics and inverse dispersion parameter for each component model. Model for Traversable Median. The statistics for the traversable median model are presented in Table 183. Calibration of this model focused on transit-related total crash frequency (i.e., all severities). The Pearson χ2 statistic for the model is 133.8 and the degrees of freedom are 109 (= n − p = 118 − 9). As this statistic is less than χ20.05, 109 (= 134.4), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.34. The Rk2 for the calibrated model is 0.71. Table 183. Predictive model calibration statistics, transit-related crashes, TM segments – TWLTL vs. non-traversable median. Model Statistics Value R2 (Rk2): 0.34 (0.71) Scale Parameter φ: 1.14 Pearson χ2: 133.8 (χ20.05, 109 = 134.4) Inverse Dispersion Parameter K: 5.21 Observations n: 118 segments (96 crashes) Standard Deviation sp: ±0.23 crashes/yr The coefficients in Table 182 were combined with Equation 27 to obtain the calibrated SPF for segments with a traversable median. The form of the model is described by the following equation. Equation 34 , 2.328 0.684 1000 0.698 1000 The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 48. The lane width, shoulder width, and access point density are such that the associated CMFs have a value of 1.0. The trends in the figure indicate that transit-related crash frequency increases with both transit and overall AADT volume. This trend is consistent with that from the urban street segment SPF for the overall traffic stream that is provided in the Highway Safety Manual (AASHTO, 2010). The calibrated CMFs used with this SPF are described in a subsequent section.

335 Figure 48. Predicted transit-related crash frequency, TM segments – TWLTL vs. non-traversable median. The fit of the calibrated model is shown in Figure 49. This figure compares the predicted and reported crash frequency in the calibration database. The thick trend line shown represents a “y = x” line. A data point would lie on this line if its predicted and reported crash frequencies were equal. The two thin lines identify the 90th-percentile confidence interval (= 95–5). The data points shown represent the reported crash frequency for the segments used to calibrate the corresponding component model. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency. Figure 49. Predicted vs. reported transit-related crash frequency, TM segments – TWLTL vs. non- traversable median.

336 Each data point shown in Figure 49 represents the average predicted and average reported crash frequency for a group of 10 segments (i.e., 10 sites). The data were sorted by predicted crash frequency to form groups of sites with similar crash frequency. The purpose of this grouping was to reduce the number of data points shown in the figure and, thereby, to facilitate an examination of trends in the data. The individual site observations were used for model calibration. Model for Non-Traversable Median. The statistics for the non-traversable median model are presented in Table 184. Calibration of this model focused on transit-related total crash frequency (i.e., all severities). The Pearson χ2 statistic for the model is 90.9 and the degrees of freedom are 82 (= n − p = 91 − 9). As this statistic is less than χ20.05, 82 (= 104.1), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.17. The Rk2 for the calibrated model is 0.73. Table 184. Predictive model calibration statistics, transit-related crashes, NTM segments – TWLTL vs. non-traversable median. Model Statistics Value R2 (Rk2): 0.17 (0.73) Scale Parameter φ: 1.01 Pearson χ2: 90.9 (χ20.05, 82 = 104.1) Inverse Dispersion Parameter K: 7.92 Observations n: 91 segments (69 crashes) Standard Deviation sp: ±0.20 crashes/yr The coefficients in Table 182 were combined with Equation 30 to obtain the calibrated SPF for segments with a non-traversable median. The form of the model is described by the following equation. Equation 35 , 1.868 0.684 1000 0.698 1000 The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 50. The lane width, shoulder width, median width, and access point density are such that the associated CMFs have a value of 1.0. The trends in the figure indicate that transit-related crash frequency increases with both transit and overall AADT volume. This trend is consistent with that from the urban street segment SPF for the overall traffic stream that is provided in the Highway Safety Manual (AASHTO, 2010). The calibrated CMFs used with this SPF are described in a subsequent section.

337 Figure 50. Predicted transit-related crash frequency, NTM segments – TWLTL vs. non-traversable median. The fit of the calibrated model is shown in Figure 51. This figure compares the predicted and reported crash frequency in the calibration database. The thick trend line shown represents a “y = x” line. A data point would lie on this line if its predicted and reported crash frequencies were equal. The two thin lines identify the 90th percentile confidence interval (= 95–5). The data points shown represent the reported crash frequency for the segments used to calibrate the corresponding component model. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency. Figure 51. Predicted vs. reported transit-related crash frequency, NTM segments – TWLTL vs. non- traversable median.

338 Estimated CMFs Several CMFs were calibrated in conjunction with the SPFs. All of them were calibrated using total crash data (i.e., all severities). Collectively, they describe the relationship between various geometric factors and crash frequency. These CMFs are described in this section and, where possible, compared with the findings from previous research as means of model validation. Lane Width and Shoulder Width CMF. The lane and shoulder width CMF is described using the following equation. Equation 36 0.724 12 0.0165 , 7 1.5 2 0.0719 12 , 7 1.5 This CMF is applicable to segments with a traversable or non-traversable median. The lane widths used to calibrate this CMF ranged from 9.5 to 12.7 feet. The sum of the outside shoulder width and bike lane width ranged from 0.0 to 12.0 feet A sensitivity analysis was conducted by computing the CMF values for a range of lane, shoulder, and bike lane widths. The analysis revealed that the CMF equation provided a good fit to the data. However, the formulation was not well-bounded such that it predicted implausibly small CMF values at the largest lane and shoulder widths. To overcome this boundary limitation, it was determined that the CMF for shoulder plus bike lane widths in excess of 6 feet should be equal to the value obtained for 6 feet. Similarly, the CMF for lane widths in excess of 12 feet should be equal to the value obtained for 12 feet. The lane and shoulder width CMF is shown in Figure 52. The x-axis in Figure 52b represents the sum of the average outside shoulder width and the average bike lane width. The trend line shown in either figure indicates that the CMF value decreases with increasing width. The slope of the lane width trend line is steepest when the shoulder is narrow. Similarly, the slope of the shoulder width trend line is steepest when the lane is narrow. It is rationalized that street segments with a larger lane width provide more lateral separation between transit vehicles and the vehicles in adjacent lanes and thus a reduced susceptibility to sideswipe crashes. Segments with a wider outside shoulder (or bike lane) provide storage for transit vehicles to pick up passengers and additional pavement in which to complete turn maneuvers with greater separation from vehicles in adjacent lanes. a. Lane width. b. Shoulder plus bike lane width. Figure 52. Lane and shoulder width CMF, transit-related crashes, both median types – TWLTL vs. non-traversable median.

339 A review of the research literature indicates that the correlation between pavement width and transit- related crash frequency has been investigated by McCummings and Chimba (2013). The regression model they developed included a term for lane width and for shoulder width. The relationship between crash frequency and lane width obtained from their model is shown in Figure 52a. It is shown for a 4-foot outside shoulder width, which is the average shoulder width in the data used to calibrate their model. Similarly, the relationship between crash frequency and shoulder width obtained from their model is shown in Figure 52b. It is shown for a 12-foot lane width, which is the average lane width in the data used to calibrate their model. The trend line associated with McCummings and Chimba is shown in both figures to be consistent with the value predicted by Equation 36. Median Width CMF. The median width CMF is described using the following equation. Equation 37 , 0.0576 , , 25 20 This CMF is applicable to segments with a non-traversable median. The median widths used to calibrate this CMF ranged from 6.0 to 62 feet. The median width CMF is shown in Figure 53. The trend line shown indicates that the CMF value decreases with increasing width. However, the trend line is horizontal for median widths in excess of 25 feet suggesting that transit-related crash frequency is not highly correlated with the width of wide medians. This trend was initially noted in the discussion associated with Figure 43. Figure 53. Median width CMF, transit-related crashes, non-traversable median type – TWLTL vs. non-traversable median. A review of the research literature indicates that the correlation between median width and transit vehicle crash frequency has been investigated by McCummings and Chimba (2013). The regression model they developed included a term for median width. The relationship between crash frequency and median width obtained from their model is shown in Figure 53. This trend line is shown in both figures to be generally consistent with the value predicted by Equation 37.

340 Access Point CMF. The access point CMF is described using the following two equations. The first equation is used for segments with a traversable median. The second equation is used for segments with a non-traversable median. Equation 38 , 0.0153 / 46 Equation 39 , 0.0153 / 23 This CMF is applicable to segments with a traversable or non-traversable median. The count of commercial driveways, office driveways, and public street approaches is an input to this CMF. The count includes driveways and approaches with full access to all movements as well as those with partial access. The total number of these access points is converted to a density value in the equation (i.e., access points per mile). The access point density used to calibrate the CMF for traversable medians ranged from 0 to 98 access points per mile. The access point density used to calibrate the CMF for non-traversable medians ranged from 0 to 73 access points per mile. The access point CMF is shown in Figure 54. The trend line shown indicates that the CMF value increases with an increase in the density of access points. This trend is consistent with the predictive models for access points that are provided in Chapter 12 of the Highway Safety Manual (AASHTO, 2010). This trend was initially noted in the discussion associated with Figure 45 and Figure 47. Figure 54. Access point CMF, transit-related crashes, both median types – TWLTL vs. non- traversable median. Truck Safety Performance Relationship Development This section describes the development of models for predicting truck-related crash frequency on urban and suburban street segments. These models are not applicable to the evaluation of other travel modes

341 (e.g., transit vehicles) or facility types. The models are developed to predict total crash frequency (i.e., all severities). One variation of the model is applicable to segments with a traversable median and a second variation of the model is applicable to segments with a non-traversable median. This section consists of four subsections. The first subsection describes the structure of the safety predictive models as used in the regression analysis. The second subsection describes the regression statistics for each of the estimated models. The third subsection describes the estimated safety performance functions. The fourth subsection describes the estimated CMFs. Model Development This section describes the proposed prediction models and the methods used to calibrate them. The regression model is generalized to accommodate the analysis of segments with either a traversable median or a non-traversable median. The generalized form shows all the CMFs in the model. Indicator variables are used to determine which CMFs are applicable to each observation in the database based on the associated median type. The following generalized regression model is described using the following equations. A. If the observation corresponds to a segment with a traversable median (i.e., m = TM), the following model is used. Equation 40 , , , , with Equation 41 , , 1000 1000 Equation 42 , , , , / 39 Equation 43 , , , , / 7 where Ny,TM = predicted average number of crashes for y years for a road segment with a traversable median, crashes; y = time interval for reported crashes (i.e., evaluation period), yr; Ls = length of segment, miles; NSPF,TM = predicted crash frequency for base conditions on a segment with a traversable median; crashes/mile/yr; Cstate = calibration factor for specific states represented in the database; CMFWl = crash modification factor for lane width; CMFWsb = crash modification factor for shoulder width; CMFFDcox,TM = crash modification factor for full-access commercial driveways, office driveways, and public street approaches on a segment with a traversable median; CMFPDcox,TM = crash modification factor for partial-access commercial driveways, office driveways, and public street approaches on a segment with a traversable median; AADT = overall annual average daily traffic (AADT) volume for segment (including local public transit vehicles and trucks), veh/d;

342 AADTtk = AADT for trucks, veh/d; nF,com = number of commercial driveways on the segment (two-way total; including only driveways with full access), driveways; nF,off = number of office driveways on the segment (two-way total; including only driveways with full access), driveways; nF,xstrt = number of unsignalized public street approaches on the segment (two-way total; including only approaches with full access), approaches; nP,com = number of commercial driveways on the segment (two-way total; including only driveways with partial access), driveways; nP,off = number of office driveways on the segment (two-way total; including only driveways with partial access), driveways; nP,xstrt = number of unsignalized public street approaches on the segment (two-way total; including only approaches with partial access), approaches; bi,TM = calibration coefficient for condition i for segments with a traversable median; and bi = calibration coefficient for condition i. . B. If the observation corresponds to a segment with a non-traversable median (i.e., m = NTM), the following model is used. Equation 44 , , , , , with Equation 45 , 1000 1000 Equation 46 , , , , 25 20 Equation 47 , , , , / 5 Equation 48 , , , , / 18 where Ny,NTM = predicted average number of crashes for y years for a road segment with a non-traversable median, crashes; CMFWm,NTM = crash modification factor for median width on a segment with a traversable median; Wm,NTM = median width (measured from near edges of traveled way in both directions), ft; CMFFDcox,NTM = crash modification factor for full-access commercial driveways, office driveways, and public street approaches on a segment with a non-traversable median; CMFPDcox,NTM = crash modification factor for partial-access commercial driveways, office driveways, and public street approaches on a segment with a non-traversable median; and all other variables as previously defined. The value of “39” in Equation 42 base access point approach density (in units of access points per mile) for full-access access points on TM segments. The value of “7” in Equation 43 is the base access point

343 approach density for partial-access access points on TM segments. The values of “5” and “18” in Equation 47 and Equation 48, respectively, have similar definitions for NTM segments. These values were computed as the average density of those segments in the database. The value of “20” in Equation 46 is the base median width (in units of feet) for the segments with non- traversable medians. The term “min{X, Y}” is used in Equation 46 to indicate that the smaller value of variables X and Y are used in the calculation. This term is used in equations to follow with similar meaning. The same coefficient “b1” is used for both AADT terms in Equation 41 and Equation 45. Preliminary regression analyses using two coefficients (one for each term) revealed that they were highly correlated and, as a result, of uncertain value. The confidence intervals for both variables overlapped significantly, so it was decided that the best option to overcome the correlation issue was to use the same variable for both terms. The following equations are used in both the TM and NTM models. Equation 49 12 Equation 50 , 7 1.5 Equation 51 where Wl = lane width (average for all through lanes), ft; Ws = paved outside shoulder width (average for both travel directions), ft; Wb = bike lane width (average for both travel directions), ft; Iwi = indicator variable for Wisconsin (= 1.0 if site is in Wisconsin, 0.0 otherwise); and all other variables as previously defined. The value of “12” in Equation 49 is the base lane width (in units of feet) for the segments. Similarly, the value of “1.5” is the base shoulder width (in units of feet). This width corresponds to the “effective” shoulder width for a typical curb-and-gutter section. The regression model described by Equation 40 to Equation 51 represents the “final” model form. This form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described by these equations represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded. CMFs for other variables were also examined but were not found to be helpful in explaining the variation in the observed crash frequency among sites. These variables include:  Parking presence;  Residential driveway density;  Industrial driveway density;  Number of through lanes; and  Presence of a mid-segment crosswalk. This finding does not rule out the possibility that these factors have an influence on segment safety. It is possible that their effect is sufficiently small that it would require either (1) a larger database (with more

344 observations and a wider range in variable values) to detect using regression, or (2) the use of a before– after study that isolates the individual effect of one factor on crash frequency. Model Estimation The predictive model calibration process was based on a combined regression modeling approach, as discussed in the section titled Modeling Approach. With this approach, the two median-type models and CMFs (represented by Equation 40 to Equation 51) are calibrated using a common database. This approach is needed because the lane width CMF, shoulder width CMF, and the AADT coefficients in the SPFs are common to both median-type models. The results of the combined regression model calibration are presented in Table 185. Calibration of this model focused on truck-related total crash frequency (i.e., all severities). The Pearson χ2 statistic for the model is 228 and the degrees of freedom are 205 (= n − p = 214 − 9). As this statistic is less than χ2 0.05, 205 (= 239), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.37. The Rk2 for the calibrated model is 0.84. The t-statistics listed in the last column of Table 185 indicate a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model, and its trend was found to be logical and consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The findings from an examination of the coefficient values and the corresponding CMF or SPF predictions are documented in a subsequent subsection. Table 185. Predictive model calibration statistics, truck-related crashes – TWLTL vs. non- traversable median. Model Statistics Value R2 (Rk2): 0.37 (0.84) Scale Parameter φ: 1.07 Pearson χ2: 228 (χ20.05, 205 = 239) Inverse Dispersion Parameter K: 6.39 Observations n: 214 segments (369 crashes) Standard Deviation sp: ±0.60 crashes/yr Calibrated Coefficient Values Variable Inferred Effect of… Value Std. Error t-statistic bwi Location in Wisconsin 0.614 0.439 1.40 b0 Non-traversable median -2.472 0.525 -4.71 b1 AADT and AADTtk 0.596 0.105 5.69 b0,TM Traversable median -0.380 0.224 -1.70 bWm,NTM Width of non-traversable median -0.0311 0.0196 -1.59 bWl Lane width -0.0614 0.132 -0.47 bWsb Outside shoulder width and bike lane width -0.0951 0.0301 -3.16 bFDcox Full-access commercial driveways, office driveways, and public street approaches 0.0401 0.00800 5.01 bPDcox Partial-access commercial driveways, office driveways, and public street approaches 0.0293 0.00859 3.42

Estimated SPFs This section describes the fit statistics and inverse dispersion parameter for each component model. Model for Traversable Median. The statistics for the traversable median model are presented in Table 186. Calibration of this model focused on truck-related total crash frequency (i.e., all severities). The Pearson χ2 statistic for the model is 131 and the degrees of freedom are 109 (= n − p = 118 − 9). As this statistic is less than χ20.05, 109 (= 134.4), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.42. The Rk2 for the calibrated model is 0.79. Table 186. Predictive model calibration statistics, truck-related crashes, TM segments – TWLTL vs. non-traversable median. Model Statistics Value R2 (Rk2): 0.42 (0.79) Scale Parameter φ: 1.12 Pearson χ2: 131 (χ20.05, 109 = 134.4) Inverse Dispersion Parameter K: 5.81 Observations n: 118 segments (100 crashes) Standard Deviation sp: ±0.23 crashes/yr The coefficients in Table 185 were combined with Equation 41 to obtain the calibrated SPF for segments with a traversable median. The form of the model is described by the following equation. Equation 52 , 2.852 0.596 1000 0.596 1000 The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 55. The lane width, shoulder width, and access point densities are such that the associated CMFs have a value of 1.0. The trends in the figure indicate that truck-related crash frequency increases with both truck and overall AADT volume. This trend is consistent with that from the urban street segment SPF for the overall traffic stream that is provided in the Highway Safety Manual (AASHTO, 2010). The calibrated CMFs used with this SPF are described in a subsequent section. Figure 55. Predicted truck-related crash frequency, TM segments – TWLTL vs. non-traversable median.

346 The fit of the calibrated model is shown in Figure 56. This figure compares the predicted and reported crash frequency in the calibration database. The thick trend line shown represents a “y = x” line. A data point would lie on this line if its predicted and reported crash frequencies were equal. The two thin lines identify the 90th-percentile confidence interval. The data points shown represent the reported crash frequency for the segments used to calibrate the corresponding component model. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency. Figure 56. Predicted vs. reported truck-related crash frequency, TM segments – TWLTL vs. non- traversable median. Each data point shown in Figure 56 represents the average predicted and average reported crash frequency for a group of 10 segments (i.e., 10 sites). The data were sorted by predicted crash frequency to form groups of sites with similar crash frequency. The purpose of this grouping was to reduce the number of data points shown in the figure and, thereby, to facilitate an examination of trends in the data. The individual site observations were used for model calibration. Model for Non-Traversable Median. The statistics for the non-traversable median model are presented in Table 187. Calibration of this model focused on truck-related total crash frequency (i.e., all severities). The Pearson χ2 statistic for the model is 97.6 and the degrees of freedom are 87 (= n − p = 96 − 9). As this statistic is less than χ20.05, 87 (= 109.8), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.32. The Rk2 for the calibrated model is 0.81.

347 Table 187. Predictive model calibration statistics, truck-related crashes, NTM segments. Model Statistics Value R2 (Rk2): 0.32 (0.81) Scale Parameter φ: 1.03 Pearson χ2: 97.6 (χ20.05, 87 = 109.8) Inverse Dispersion Parameter K: 6.02 Observations n: 96 segments (269 crashes) Standard Deviation sp: ±0.23 crashes/yr The coefficients in Table 185 were combined with Equation 45 to obtain the calibrated SPF for segments with a non-traversable median. The form of the model is described by the following equation. Equation 53 , 2.472 0.596 1000 0.596 1000 The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 57. The lane width, shoulder width, median width, and access point densities are such that the associated CMFs have a value of 1.0. The trends in the figure indicate that truck-related crash frequency increases with both truck and overall AADT volume. This trend is consistent with that from the urban street segment SPF for the overall traffic stream that is provided in the Highway Safety Manual (AASHTO, 2010). The calibrated CMFs used with this SPF are described in a subsequent section. The fit of the calibrated model is shown in Figure 58. This figure compares the predicted and reported crash frequency in the calibration database. The thick trend line shown represents a “y = x” line. A data point would lie on this line if its predicted and reported crash frequencies were equal. The two thin lines identify the 90th-percentile confidence interval. The data points shown represent the reported crash frequency for the segments used to calibrate the corresponding component model. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency. Figure 57. Predicted truck-related crash frequency, NTM segments – TWLTL vs. non-traversable median.

348 Figure 58. Predicted vs. reported truck-related crash frequency, NTM segments – TWLTL vs. non- traversable median. Each data point shown in Figure 58 represents the average predicted and average reported crash frequency for a group of 10 segments (i.e., 10 sites). The data were sorted by predicted crash frequency to form groups of sites with similar crash frequency. The purpose of this grouping was to reduce the number of data points shown in the figure and, thereby, to facilitate an examination of trends in the data. The individual site observations were used for model calibration. Estimated CMFs Several CMFs were calibrated in conjunction with the SPFs. All of them were calibrated using total crash data. Collectively, they describe the relationship between various geometric factors and crash frequency. These CMFs are described in this section and, where possible, compared with the findings from previous research as means of model validation. Lane Width CMF. The lane width CMF is described using the following equation. Equation 54 0.0614 12 This CMF is applicable to segments with a traversable or non-traversable median. The lane widths used to calibrate this CMF ranged from 9.5 to 12.7 feet. The lane width CMF is shown in Figure 59. The trend line shown indicates that the CMF value decreases with increasing width. Segments with a wider lane provide more lateral separation between trucks and vehicles in adjacent lanes. A wider lane should also better allow turn maneuvers with greater separation from vehicles in adjacent lanes.

349 Figure 59. Lane width CMF, truck-related crashes, both median types – TWLTL vs. non-traversable median. A review of the research literature indicates that the correlation between lane width and truck-related crash frequency has been investigated by Daniel and Chien (2004). The regression model they developed included a term for pavement width, which included lane and shoulder width. The relationship between crash frequency and lane width obtained from their model is shown in Figure 59. This relationship is shown to be consistent with the value predicted by Equation 54. Shoulder Width CMF. The shoulder width CMF is described using the following equation. Equation 55 0.0951 1.5 This CMF is applicable to segments with a traversable or non-traversable median. The sum of the outside shoulder width and bike lane width that was used to calibrate this CMF ranged from 0.0 to 12.0 feet. The shoulder width CMF is shown in Figure 60. The x-axis represents the sum of the average outside shoulder width and the average bike lane width. The trend line shown indicates that the CMF value decreases with increasing width. Segments with a wide shoulder, bike lane, or both, provide storage for trucks to park while making deliveries and additional pavement in which to complete turn maneuvers with greater separation from vehicles in adjacent lanes.

350 Figure 60. Shoulder width CMF, truck-related crashes, both median types – TWLTL vs. non- traversable median. A review of the research literature indicates that the correlation between shoulder width and truck- related crash frequency has been investigated by Daniel and Chien (2004). The regression model they developed included a term for pavement width, which included lane and shoulder width. The relationship between crash frequency and shoulder width obtained from their model is shown in Figure 60. This relationship is shown to be consistent with the value predicted by Equation 55. Median Width CMF. The median width CMF is described using the following equation. Equation 56 , 0.0311 , , 25 20 This CMF is applicable to segments with a non-traversable median. The median widths used to calibrate this CMF ranged from 6.0 to 62 feet. The median width CMF is shown in Figure 61. The trend line shown indicates that the CMF value decreases with increasing width. However, the trend line is horizontal for median widths in excess of 25 feet, suggesting that truck-related crash frequency is not highly correlated with the width of wide medians. This trend was initially noted in the discussion associated with Figure 43.

351 Figure 61. Median width CMF, truck-related crashes, non-traversable median type – TWLTL vs. non-traversable median. A review of the research literature did not lead to the identification of prior studies of the relationship between median width and truck-related crash frequency. The trend obtained from Equation 56 is logical and consistent with that found for the overall traffic stream on arterial streets (Lord et al., 2015). However, the slope of the line is steeper for truck-related crashes than for the overall traffic stream suggesting that medians less than 25-feet wide have a more significant effect on truck safety than on passenger car safety. Full Access Point CMF. The full access point CMF is described using the following two equations. The first equation is used for segments with a traversable median. The second equation is used for segments with a non-traversable median. Equation 57 , 0.0401 , , , / 39 Equation 58 , 0.0401 , , , / 5 This CMF is applicable to segments with a traversable or non-traversable median. The count of commercial driveways, office driveways, and public street approaches is an input to this CMF. The count includes driveways and approaches with full access to all movements. The total number of these access points is converted to a density value in the equation (i.e., access points per mile). The access point density used to calibrate the CMF for traversable medians ranged from 0 to 94 access points per mile. The access point density used to calibrate the CMF for non-traversable medians ranged from 0 to 26 access points per mile. The access point CMF is shown in Figure 62. The trend line shown indicates that the CMF value increases with an increase in the density of access points. This trend is consistent with the predictive models for access points that are provided in Chapter 12 of the Highway Safety Manual (AASHTO, 2010). This trend was initially noted in the discussion associated with Figure 45 and Figure 47.

352 Figure 62. Full access point CMF, truck-related crashes, both median types – TWLTL vs. non- traversable median. Partial Access Point CMF. The partial access point CMF is described using the following two equations. The first equation is used for segments with a traversable median. The second equation is used for segments with a non-traversable median. Equation 59 , 0.0293 , , , / 7 Equation 60 , 0.0293 , , , / 18 This CMF is applicable to segments with a traversable or non-traversable median. The count of commercial driveways, office driveways, and public street approaches is an input to this CMF. The count includes driveways and approaches with partial access (i.e., some turn movements are prohibited). The total number of these access points is converted to a density value in the equation (i.e., access points per mile). The access point density used to calibrate the CMF for traversable medians ranged from 0 to 33 access points per mile. The access point density used to calibrate the CMF for non-traversable medians ranged from 0 to 61 access points per mile. The access point CMF is shown in Figure 63. The trend line shown indicates that the CMF value increases with an increase in the density of access points. This trend is consistent with the predictive models for access points that are provided in Chapter 12 of the Highway Safety Manual (AASHTO, 2010). This trend was initially noted in the discussion associated with Figure 45 and Figure 47. The regression coefficient in this CMF (i.e., 0.0293) is smaller than it counterpart in Equation 57 and Equation 58 (i.e., 0.0401). This trend indicates that the CMF value increases at a smaller rate when a partial-access driveway is added to a segment, relative to the case where a full-access driveway is added.

353 It implies that a partial-access driveway has a smaller effect on truck safety than a full-access driveway. This safety benefit of partial-access driveways was initially noted in the discussion of Figure 46. Figure 63. Partial access point CMF, truck-related crashes, both median types – TWLTL vs. non- traversable median. Safety Prediction Method This section presents the final version of the crash prediction models. The presentation is divided into four subsections. The subsections are identified in the following list.  Transit safety prediction method;  Transit safety prediction method – sensitivity analysis;  Truck safety prediction method; and  Truck safety prediction method – sensitivity analysis. The first and third subsections describe a predictive method. Each predictive method includes SPFs and CMFs that are specific to median type (i.e., traversable or non-traversable median) of the subject street segment. Both sets of SPFs and CMFs will need to be used to facilitate a comparison of the level of safety associated with each median type. The two predictive methods described in this section provide estimates of the average crash frequency of transit-related and truck-related crashes, as may be influenced by alternative cross sections and access densities. This information can be used to inform the project development and safety management processes. However, the “overall” safety of the street should always be considered in the decision- making process. In this regard, overall safety is described in terms of the safety of all travel modes and vehicle types that use the street and its adjacent sidewalks. The Highway Safety Manual (AASHTO, 2010) provides safety prediction methods that can be used to quantify the overall safety of a street segment.

354 Transit Safety Prediction Method This section describes the transit safety prediction method as sequence of steps that are completed to evaluate the influence on segment design on transit-related crash frequency. The associated crash prediction model predicts total crash frequency (i.e., all severities) for urban and suburban street segments with two-way traffic flow. Tables that describe the typical crash distribution by crash type and by severity category can be used to estimate the average crash frequency by crash type or severity. Step 1 – Apply SPF. At the start of this step, the analyst decides whether the analysis will focus on a segment with one median type or whether a change in median type is being considered. If the analysis is focused on one median type, then just the SPF and CMFs that are applicable to that median type are used. If the analysis is focused on the safety effect of a change in median type, then the SPFs and CMFs applicable to both median types are used. The calibrated SPFs for TM and NTM segments are shown in Equation 61 and Equation 62, respectively. These equations are used compute the predicted crash frequency for base conditions. SPF for TM segments Equation 61 , 2.328 0.684 1000 0.698 1000 SPF for NTM segments Equation 62 , 1.868 0.684 1000 0.698 1000 where NSPF,TM = predicted crash frequency for base conditions on a segment with a traversable median; crashes/mile/yr; NSPF,NTM = predicted crash frequency for base conditions on a segment with a non-traversable median; crashes/mile/yr; AADT = overall annual average daily traffic (AADT) volume for segment (including local public transit vehicles and trucks), veh/d; and AADTtv = AADT for local public transit vehicles, veh/d. Step 2 – Apply CMFs. The CMFs that can be used with the SPFs are shown in this section. The associated equations are used to compute the CMF value that adjusts the SPF prediction when non-base conditions are of interest to the analyst. Lane Width and Shoulder Width CMF. The lane and shoulder width CMF is computed using the following equation. Equation 63 0.724 , 12 12 0.0165 , 6 1.5 2 0.0719 , 12 12 , 6 1.5 where CMFWlsb = crash modification factor for lane width and shoulder width; Wl = lane width (average for all through lanes), ft; Ws = paved outside shoulder width (average for both travel directions), ft; and Wb = bike lane width (average for both travel directions), ft.

355 This CMF is applicable to segments with a traversable or non-traversable median. The lane widths used to calibrate this CMF ranged from 9.5 to 12.7 feet. The sum of the outside shoulder width and bike lane width ranged from 0.0 to 12.0 feet. The term “min{X, Y}” is used in Equation 63 to indicate that the smaller value of variables X and Y are used in the calculation. This term is used in equations to follow with similar meaning. Median Width CMF. The median width CMF is computed using the following equation. Equation 64 , 0.0576 , , 25 20 where CMFWm,NTM = crash modification factor for median width on a segment with a traversable median; and Wm,NTM = median width (measured from near edges of traveled way in both directions), ft. This CMF is applicable to segments with a non-traversable median. The median widths used to calibrate this CMF ranged from 6.0 to 62 feet. Access Point CMF. The access point CMF is computed using the following two equations. The first equation is used for segments with a traversable median. The second equation is used for segments with a non-traversable median. Equation 65 , 0.0153 / 46 Equation 66 , 0.0153 / 23 where CMFDcox,TM = crash modification factor for commercial driveways, office driveways, and public street approaches on a segment with a traversable median; CMFDcox,NTM = crash modification factor for commercial driveways, office driveways, and public street approaches on a segment with a non-traversable median; ncom = number of commercial driveways on the segment (two-way total; including driveways with full access and those with partial access), driveways; noff = number of office driveways on the segment (two-way total; including driveways with full access and those with partial access), driveways; nxstrt = number of unsignalized public street approaches on the segment (two-way total; including approaches with full access and those with partial access), approaches; and Ls = length of segment, miles. This CMF is applicable to segments with a traversable or non-traversable median. The count of commercial driveways, office driveways, and public street approaches is an input to this CMF. The count includes driveways and approaches with full access to all movements as well as those with partial access. The total number of these access points is converted to a density value in the equation (i.e., access points per mile). The access point density used to calibrate the CMF for traversable medians ranged from 0 to 98 access points per mile. The access point density used to calibrate the CMF for non-traversable medians ranged from 0 to 73 access points per mile.

356 Step 3 – Compute Predicted Crash Frequency. The CMF and SPF values from the preceding steps are used in this step to compute the predicted total average crash frequency. Equation 67 and Equation 68 are provided for segments with traversable and non-traversable median, respectively. Predicted Crash Frequency for TM segments Equation 67 , , , Predicted Crash Frequency for NTM segments Equation 68 , , , , where Np,TM = predicted average crash frequency for a road segment with a traversable median, crashes/yr; Np,NTM = predicted average crash frequency for a road segment with a non-traversable median, crashes/yr; and C = local calibration factor. Step 4 – Apply Crash Severity Distribution (optional). The crash severity distribution is listed in Table 188. The proportion associated with a given crash severity category Ps is obtained from the corresponding row of the table and the column that coincides with the subject median type. Table 188. Crash severity distribution, transit-related crashes – TWLTL vs. non-traversable median. Severity Category Crash Severity Distribution by Median Type Non-Traversable Median Traversable Median KABC (i.e., fatal and injury) 0.26 0.20 PDO 0.74 0.80 Note: K – fatal, A – incapacitating injury, B – non-incapacitating injury, C – possible injury, PDO – property-damage- only. Step 5 – Apply Crash Type Distribution (optional). The crash type distribution is listed in Table 189. The proportion associated with a given crash type Pt is obtained from the corresponding row of the table and the column that coincides with the subject median type. Table 189. Crash type distribution, transit-related crashes – TWLTL vs. non-traversable median. Category Crash Type Crash Type Distribution by Median Type Non-Traversable Median Traversable Median Multiple Vehicle Right angle 0.07 0.24 Rear end 0.35 0.17 Sideswipe, same direction 0.34 0.37 Other 0.05 0.04 Single Vehicle Parked vehicle 0.07 0.11 Other 0.12 0.07 Total: 1.00 1.00

357 Step 6 – Compute Predicted Crash Frequency by Crash Type and Severity (optional). The predicted crash frequency for a given severity category is computed using the following equations. For TM Segments Equation 69 , , , , For NTM Segments Equation 70 , , , , where Np,TM,s = predicted average crash frequency for severity category s (s = KABC or PDO) for a road segment with a traversable median, crashes/yr; Np,NTM,s = predicted average crash frequency for severity category s (s = KABC or PDO) for a road segment with a non-traversable median, crashes/yr; Ps,TM = proportion of crash severity s for a road segment with a traversable median; and Ps,NTM = proportion of crash severity s for a road segment with a non-traversable median. These two equations are used once for each severity category (i.e., KABC or PDO) of interest. The proportion used in the previous equation was obtained in Step 4. The predicted average crash frequency was computed in Step 3. The predicted crash frequency for a given crash type category is computed using the following equations. For TM Segments Equation 71 , , , , For NTM Segments Equation 72 , , , , where Np,TM,t = predicted average crash frequency for crash type t (see Table 189 for types) for a road segment with a traversable median, crashes/yr; Np,NTM,t = predicted average crash frequency for crash type t (see Table 189 for types) for a road segment with a non-traversable median, crashes/yr; Pt,TM = proportion of crash type t for a road segment with a traversable median; and Pt,NTM = proportion of crash type t for a road segment with a non-traversable median. This equation is used once for each crash type of interest. The crash types are listed in Table 189. The proportion used in the previous equation was obtained in Step 5. The predicted average crash frequency was computed in Step 3. The predicted crash frequency for a given combination of crash type and severity is computed using the following equations. For TM Segments Equation 73 , , , , , , For NTM Segments

358 Equation 74 , , , , , , where Np,TM,t,s = predicted average crash frequency for crash type t and severity category s for a road segment with a traversable median, crashes/yr; and Np,NTM,t = predicted average crash frequency for crash type t and severity category s for a road segment with a non-traversable median, crashes/yr. Transit Safety Prediction Method - Sensitivity Analysis This section describes the findings from a sensitivity analysis of selected factors that influence the transit-related predicted average crash frequency. Comparison of Median Types. The transit safety prediction method was used to compute the predicted average crash frequency for the two median types addressed by the method. The objective of this comparison is to illustrate how the method could be used to identify the conditions for which each median type is safer, from the perspective of transit-related crash frequency. In this regard, the method calculations were repeated for a range of access point densities to illustrate the sensitivity of the predictions to access point density. The findings from this analysis are listed in Table 190. Note that different numbers will be obtained for different traffic volume levels or design conditions. Table 190. Comparison of transit-related average crash frequency for alternative median types – TWLTL vs. non-traversable median. Traversable Median 1 Non-Traversable Median 1 Access Point Density, ap/mi Access Point CMF Transit Crash Freq., cr/mi/yr Overall Traffic Stream Crash Freq.,4 cr/mi/yr Access Point Density, ap/mi 2 Access Point CMF Transit Crash Freq., cr/mi/yr Overall Traffic Stream Crash Freq.,4 cr/mi/yr Full Partial Full Partial 0 0 0.495 0.20 17.32 0 0 0.704 0.44 8.87 10 2 0.595 0.24 19.68 2 8 0.820 0.51 9.26 20 4 0.715 0.28 22.04 4 15 0.941 0.59 9.62 30 5 0.845 0.33 23.88 6 22 1.079 0.68 9.91 40 7 1.015 0.40 25.89 8 30 1.258 0.79 10.24 50 9 1.220 0.48 27.54 10 37 1.443 0.90 10.46 60 11 1.465 0.58 29.55 12 45 1.681 1.05 10.79 70 13 1.760 0.70 31.56 14 52 1.929 1.21 11.08 80 14 2.082 0.82 33.04 16 59 2.213 1.39 11.31 Notes: 1 – Predicted average crash frequency based on 12-ft lane width, 1.5-ft shoulder width, no bike lane, 20-ft median width, 200 transit vehicles per day, overall traffic stream AADT of 40,000 veh/d. 2 – Assumes that 20 percent of the access points on the traversable median segment will be consolidated for the non-traversable median segment (i.e., 20 percent reduction in access point density with non-traversable median). 3 – TM: traversable median; NTM: non-traversable median. 4 – Predicted average crash frequency obtained by using the methods in Chapter 12 of the HSM (AASHTO, 2010). Table 190 lists the assumed full and partial access point densities for each median type. The ratio of partial to full access points in a given row is based on the ratio found in the database assembled for model estimation. The access point density for the non-traversable median is based on the assumption that

359 20 percent of the access points on the traversable median segment would be consolidated. This assumption was intended to reflect the type of consolidation that often occurs when the median is converted from traversable to non-traversable. Columns 4 and 9 of Table 190 list the predicted transit-related average crash frequency for the traversable and non-traversable median types, respectively. A row-by-row comparison of the predicted values shows that the transit-related crash frequency is higher for the non-traversable median than it is for the traversable median. This trend is likely due to the increase in total pavement surface width provided by the traversable median. The paved surface of the traversable median can be used by drivers to provide greater separation between the transit vehicle and the vehicles in adjacent lanes. With a traversable median, drivers in an inside lane that desire to pass a transit vehicle in the outside lane can shift closer to the far edge line (perhaps even encroach on the paved median) to avoid a possible sideswipe collision. The aforementioned benefit of a traversable median is shown in Figure 64 for the situation where a transit vehicle is pulling away from the curb and encroaching on the inside traffic lane. The passenger car in the inside lane is shown in Figure 64a to be “pinched” between the transit vehicle and curb of the raised median. The car will have to brake sharply to avoid a collision. In contrast, the car is shown in Figure 64b to swerve safely into the flush median to avoid the sideswipe collision with the transit vehicle. A similar safety benefit was found for the presence of a wide outside shoulder, as shown previously in Figure 52b. a. Non-traversable median (less flexible). b. Traversable median (more flexible). Figure 64. Lateral separation flexibility afforded by the traversable and non-traversable median – TWLTL vs. non-traversable median.

360 Columns 5 and 10 of Table 190 list the predicted overall traffic stream average crash frequency for the traversable and non-traversable median types, respectively. These estimates were obtained using the safety prediction methodology in Chapter 12 of the HSM (AASHTO, 2010). A row-by-row comparison of the predicted values shows that the overall traffic stream crash frequency is lower for the non- traversable median than it is for the traversable median. This trend reflects the fact that the non- traversable median provides significant safety benefit to passenger cars, which represent a majority of the vehicles using urban arterial streets. It is a reminder that the “overall” safety of the street should always be considered in the decision-making process. Pavement Width Alternatives. The lane and shoulder width CMF was used to compute the CMF value for alternative lane and shoulder width combinations. The objective of this comparison is to illustrate the use of the predictive method to explore alternative allocations of cross section width. In this regard, the calculations were repeated for a range of lane and shoulder widths for a given pavement width. The findings from this analysis are listed in Table 191. Table 191. Comparison of alternative lane and shoulder width combinations, transit vehicle safety – TWLTL vs. non-traversable median. Width of Four Lanes and Shoulder1, ft Average Lane Width, ft Average Shoulder Width, ft Lane and Shoulder Width CMF 49 10 4.5 1.708 10.5 3.5 1.862 11 2.5 1.757 11.5 1.5 1.436 51 10 5.5 1.260 10.5 4.5 1.476 11 3.5 1.497 11.5 2.5 1.315 12 1.5 1.000 12.5 0.5 1.017 Note: 1 - Total lane plus shoulder width shown is based on the presence of four through lanes and no bike lanes. The last column of Table 191 lists the CMF value computed using the lane and shoulder width CMF. A CMF value of 1.0 is computed for the base lane width (12 ft) and base shoulder width (1.5 ft). CMF values less than 1.0 correspond to conditions that produce a reduction in crash frequency, relative to base conditions. Similarly, CMF values larger than 1.0 correspond to conditions that produce an increase in crash frequency. The values in the last column of the table equal or exceed 1.0. This trend suggests that a reduction in lane width is likely to produce an increase in transit-related crash frequency, regardless of the shoulder width. It is interesting to note that the largest CMF value for the 51-foot pavement width corresponds to the 11-foot lane width and 3.5-f-foot shoulder width combination (i.e., 1.497). Also, the CMF value of 1.260 for 10-foot lane width and 5.5-foot shoulder width is smaller than that for 11.5-foot lane width and 2.5- foot shoulder width (i.e., 1.315). These trends suggest that transit vehicles benefit more from wider lanes than wider shoulders. However, if narrow lanes are needed to achieve other project objectives, it is advisable to provide a shoulder (or bike lane) width of 5-feet or more to mitigate the adverse effects of lane width-reduction on transit vehicle safety.

361 Truck Safety Prediction Method This section describes the truck safety prediction method as sequence of steps that are completed to evaluate the influence on segment design on truck-related crash frequency. The associated crash prediction model predicts total crash frequency (i.e., all severities) for urban and suburban street segments with two-way traffic flow. Tables that describe the typical crash distribution by crash type and by severity category can be used to estimate the average crash frequency by crash type or severity. Step 1 – Apply SPF. At the start of this step, the analyst decides whether the analysis will focus on a segment with one median type or whether a change in median type is being considered. If the analysis is focused on one median type, then just the SPF and CMFs that are applicable to that median type are used. If the analysis is focused on the safety effect of a change in median type, then the SPFs and CMFs applicable to both median types are used. The calibrated SPFs for TM and NTM segments are shown in Equation 75 and Equation 76, respectively. These equations are used compute the predicted crash frequency for base conditions. SPF for TM segments Equation 75 , 2.852 0.596 1000 0.596 1000 SPF for NTM segments Equation 76 , 2.472 0.596 1000 0.596 1000 where NSPF,TM = predicted crash frequency for base conditions on a segment with a traversable median; crashes/mile/yr; NSPF,NTM = predicted crash frequency for base conditions on a segment with a non-traversable median; crashes/mile/yr; AADT = overall annual average daily traffic (AADT) volume for segment (including local public transit vehicles and trucks), veh/d; and AADTtk = AADT for trucks, veh/d. Step 2 – Apply CMFs. The CMFs that can be used with the SPFs are shown in this section. The associated equations are used to compute the CMF value that adjusts the SPF prediction when non-base conditions are of interest to the analyst. Lane Width CMF. The lane and shoulder width CMF is computed using the following equation. Equation 77 0.0614 12 where CMFWl = crash modification factor for lane width; and Wl = lane width (average for all through lanes), ft. This CMF is applicable to segments with a traversable or non-traversable median. The lane widths used to calibrate this CMF ranged from 9.5 to 12.7 feet. Shoulder Width CMF. The lane and shoulder width CMF is computed using the following equation. Equation 78 0.0951 1.5

362 where CMFWsb = crash modification factor for shoulder width; Ws = paved outside shoulder width (average for both travel directions), ft; and Wb = bike lane width (average for both travel directions), ft. This CMF is applicable to segments with a traversable or non-traversable median. The sum of the outside shoulder width and bike lane width ranged from 0.0 to 12.0 feet. Median Width CMF. The median width CMF is computed using the following equation. Equation 79 , 0.0311 , , 25 20 where CMFWm,NTM = crash modification factor for median width on a segment with a traversable median; and Wm,NTM = median width (measured from near edges of traveled way in both directions), ft. This CMF is applicable to segments with a non-traversable median. The median widths used to calibrate this CMF ranged from 6.0 to 62 feet. The term “min{X, Y}” is used in Equation 79 to indicate that the smaller value of variables X and Y are used in the calculation. Full Access Point CMF. The full access point CMF is computed using the following two equations. The first equation is used for segments with a traversable median. The second equation is used for segments with a non-traversable median. Equation 80 , 0.0401 , , , / 39 Equation 81 , 0.0401 , , , / 5 where CMFFDcox,TM = crash modification factor for full-access commercial driveways, office driveways, and public street approaches on a segment with a traversable median; CMFFDcox,NTM = crash modification factor for full-access commercial driveways, office driveways, and public street approaches on a segment with a non-traversable median; nF,com = number of commercial driveways on the segment (two-way total; including only driveways with full access), driveways; nF,off = number of office driveways on the segment (two-way total; including only driveways with full access), driveways; nF,xstrt = number of unsignalized public street approaches on the segment (two-way total; including only approaches with full access), approaches; and Ls = length of segment, miles. This CMF is applicable to segments with a traversable or non-traversable median. The count of commercial driveways, office driveways, and public street approaches is an input to this CMF. The count includes driveways and approaches with full access to all movements. The total number of these access points is converted to a density value in the equation (i.e., access points per mile). The access point density used to calibrate the CMF for traversable medians ranged from 0 to 94 access points per mile. The

363 access point density used to calibrate the CMF for non-traversable medians ranged from 0 to 26 access points per mile. Partial Access Point CMF. The partial access point CMF is computed using the following two equations. The first equation is used for segments with a traversable median. The second equation is used for segments with a non-traversable median. Equation 82 , 0.0293 , , , / 7 Equation 83 , 0.0293 , , , / 18 where CMFPDcox,TM = crash modification factor for partial-access commercial driveways, office driveways, and public street approaches on a segment with a traversable median; CMFPDcox,NTM = crash modification factor for partial-access commercial driveways, office driveways, and public street approaches on a segment with a non-traversable median; nP,com = number of commercial driveways on the segment (two-way total; including only driveways with partial access), driveways; nP,off = number of office driveways on the segment (two-way total; including only driveways with partial access), driveways; nP,xstrt = number of unsignalized public street approaches on the segment (two-way total; including only approaches with partial access), approaches; and Ls = length of segment, miles. This CMF is applicable to segments with a traversable or non-traversable median. The count of commercial driveways, office driveways, and public street approaches is an input to this CMF. The count includes driveways and approaches with partial access (i.e., some turn movements are prohibited). The total number of these access points is converted to a density value in the equation (i.e., access points per mile). The access point density used to calibrate the CMF for traversable medians ranged from 0 to 33 access points per mile. The access point density used to calibrate the CMF for non-traversable medians ranged from 0 to 61 access points per mile. Step 3 – Compute Predicted Crash Frequency. The CMF and SPF values from the preceding steps are used in this step to compute the predicted total average crash frequency. Equation 84 and Equation 85 are provided for segments with traversable and non-traversable median, respectively. Predicted Crash Frequency for TM segments Equation 84 , , , , Predicted Crash Frequency for NTM segments Equation 85 , , , , , where Np,TM = predicted average crash frequency for a road segment with a traversable median, crashes/yr;

364 Np,NTM = predicted average crash frequency for a road segment with a non-traversable median, crashes/yr; and C = local calibration factor. Step 4 – Apply Crash Severity Distribution (optional). The crash severity distribution is listed in Table 192. The proportion associated with a given crash severity category Ps is obtained from the corresponding row of the table and the column that coincides with the subject median type. Table 192. Crash severity distribution, truck-related crashes – TWLTL vs. non-traversable median. Severity Category Crash Severity Distribution by Median Type Non-Traversable Median Traversable Median KABC (i.e., fatal and injury) 0.32 0.32 PDO 0.68 0.68 Note: K – fatal, A – incapacitating injury, B – non-incapacitating injury, C – possible injury, PDO – property-damage- only. Step 5 – Apply Crash Type Distribution (optional). The crash type distribution is listed in Table 193. The proportion associated with a given crash type Pt is obtained from the corresponding row of the table and the column that coincides with the subject median type. Table 193. Crash type distribution, truck-related crashes – TWLTL vs. non-traversable median. Category Crash Type Crash Type Distribution by Median Type Non-Traversable Median Traversable Median Multiple Vehicle Right angle 0.03 0.21 Rear end 0.32 0.33 Sideswipe, same direction 0.42 0.24 Other 0.06 0.13 Single Vehicle Parked vehicle 0.02 0.02 Other 0.15 0.07 Total: 1.00 1.00 Step 6 – Compute Predicted Crash Frequency by Crash Type and Severity (optional). The predicted crash frequency for a given severity category is computed using the following equations. For TM Segments Equation 86 , , , , For NTM Segments Equation 87 , , , , where Np,TM,s = predicted average crash frequency for severity category s (s = KABC or PDO) for a road segment with a traversable median, crashes/yr;

365 Np,NTM,s = predicted average crash frequency for severity category s (s = KABC or PDO) for a road segment with a non-traversable median, crashes/yr; Ps,TM = proportion of crash severity s for a road segment with a traversable median; and Ps,NTM = proportion of crash severity s for a road segment with a non-traversable median. These two equations are used once for each severity category (i.e., KABC or PDO) of interest. The proportion used in the previous equation was obtained in Step 4. The predicted average crash frequency was computed in Step 3. The predicted crash frequency for a given crash type category is computed using the following equations. For TM Segments Equation 88 , , , , For NTM Segments Equation 89 , , , , where Np,TM,t = predicted average crash frequency for crash type t (see Table 193 for types) for a road segment with a traversable median, crashes/yr; Np,NTM,t = predicted average crash frequency for crash type t (see Table 193 for types) for a road segment with a non-traversable median, crashes/yr; Pt,TM = proportion of crash type t for a road segment with a traversable median; and Pt,NTM = proportion of crash type t for a road segment with a non-traversable median. This equation is used once for each crash type of interest. The crash types are listed in Table 193. The proportion used in the previous equation was obtained in Step 5. The predicted average crash frequency was computed in Step 3. The predicted crash frequency for a given combination of crash type and severity is computed using the following equations. For TM Segments Equation 90 , , , , , , For NTM Segments Equation 91 , , , , , , where Np,TM,t,s = predicted average crash frequency for crash type t and severity category s for a road segment with a traversable median, crashes/yr; and Np,NTM,t = predicted average crash frequency for crash type t and severity category s for a road segment with a non-traversable median, crashes/yr. Truck Safety Prediction Method - Sensitivity Analysis This section describes the findings from a sensitivity analysis of selected factors that influence the truck-related predicted average crash frequency. Comparison of Median Types. The truck safety prediction method was used to compute the predicted average crash frequency for the two median types addressed by the method. The objective of this

366 comparison is to illustrate how the method could be used to identify the conditions for which each median type is safer, from the perspective of truck-related crash frequency. In this regard, the method calculations were repeated for a range of access point densities to illustrate the sensitivity of the predictions to access point density. The findings from this analysis are listed in Table 194. Note that different numbers will be obtained for different traffic volume levels or design conditions. Table 194. Comparison of truck-related average crash frequency for alternative median types – TWLTL vs. non-traversable median. Traversable Median 1 Non-Traversable Median 1 Access Point Density, ap/mi Full Access Point CMF Partial Access Point CMF Transit Crash Freq., cr/mi/yr Overall Traffic Stream Crash Freq.,4 cr/mi/yr Access Point Density, ap/mi 2 Full Access Point CMF Partial Access Point CMF Transit Crash Freq., cr/mi/yr Overall Traffic Stream Crash Freq.,4 cr/mi/yr Full Partial Full Partial 0 0 0.210 0.814 0.11 17.32 0 0 0.818 0.590 0.47 8.87 10 2 0.313 0.864 0.18 19.68 2 8 0.887 0.746 0.65 9.26 20 4 0.467 0.916 0.29 22.04 4 15 0.961 0.916 0.87 9.62 30 5 0.697 0.943 0.44 23.88 6 22 1.041 1.125 1.15 9.91 40 7 1.041 1.000 0.70 25.89 8 30 1.128 1.422 1.58 10.24 50 9 1.554 1.060 1.11 27.54 10 37 1.222 1.747 2.10 10.46 60 11 2.319 1.125 1.75 29.55 12 45 1.324 2.209 2.88 10.79 70 13 3.462 1.193 2.78 31.56 14 52 1.434 2.713 3.83 11.08 80 14 5.168 1.228 4.27 33.04 16 59 1.554 3.331 5.09 11.31 Notes: 1 – Predicted average crash frequency based on 12-ft lane width, 1.5-ft shoulder width, no bike lane, 20-ft median width, 1600 trucks per day, overall traffic stream AADT of 40,000 veh/d. 2 – Assumes that 20 percent of the access points on the traversable median segment will be consolidated for the non-traversable median segment (i.e., 20 percent reduction in access point density with non-traversable median). 3 – TM: traversable median; NTM: non-traversable median. 4 – Predicted average crash frequency obtained by using the methods in Chapter 12 of the HSM (AASHTO, 2010). Table 194 lists the assumed full and partial access point densities for each median type. The ratio of partial to full access points in a given row is based on the ratio found in the database assembled for model estimation. The access point density for the non-traversable median is based on the assumption that 20 percent of the access points on the traversable median segment would be consolidated. This assumption was intended to reflect the type of consolidation that often occurs when the median is converted from traversable to non-traversable. Columns 4 and 9 of Table 194 list the predicted truck-related average crash frequency for the traversable and non-traversable median types, respectively. A row-by-row comparison of the predicted values shows that the truck-related crash frequency is higher for the non-traversable median than it is for the traversable median. This trend is likely due to the increase in total pavement surface width provided by the traversable median. A traversable median can be used by drivers to provide greater separation between the truck and the vehicles in adjacent lanes. With a traversable median, drivers in an inside lane that desire to pass a truck in the outside lane can shift closer to the far edge line (perhaps even encroach on the paved median) to avoid a possible sideswipe collision. This benefit was discussed previously for the transit vehicle in the text associated with Figure 64. A similar safety benefit was found for the presence of a wide outside shoulder, as shown previously in Figure 60.

367 Columns 5 and 10 of Table 194 list the predicted overall traffic stream average crash frequency for the traversable and non-traversable median types, respectively. These estimates were obtained using the safety prediction methodology in Chapter 12 of the HSM (AASHTO, 2010). A row-by-row comparison of the predicted values shows that the overall traffic stream crash frequency is lower for the non- traversable median than it is for the traversable median. This trend reflects the fact that the non- traversable median provides significant safety benefit to passenger cars, which represent a majority of the vehicles using urban arterial streets. It is a reminder that the “overall” safety of the street should always be considered in the decision-making process. Pavement Width Alternatives. The lane width CMF and the shoulder width CMF were used to compute the CMF value for alternative lane and shoulder width combinations. The objective of this comparison is to illustrate the use of the predictive method to explore alternative allocations of cross section width. In this regard, the calculations were repeated for a range of lane and shoulder widths for a given pavement width. The findings from this analysis are listed in Table 195. Table 195. Comparison of alternative lane and shoulder width combinations, truck-vehicle safety – TWLTL vs. non-traversable median. Width of Four Lanes and Shoulder1, ft Average Lane Width, ft Average Shoulder Width, ft Lane Width CMF Shoulder Width CMF Product of Lane and Shoulder CMFs 49 10 4.5 1.131 0.752 0.850 10.5 3.5 1.096 0.827 0.906 11 2.5 1.063 0.909 0.967 11.5 1.5 1.031 1.000 1.031 51 10 5.5 1.131 0.684 0.773 10.5 4.5 1.096 0.752 0.824 11 3.5 1.063 0.827 0.879 11.5 2.5 1.031 0.909 0.938 12 1.5 1.000 1.000 1.000 12.5 0.5 0.970 1.100 1.067 Note: 1 - Total lane plus shoulder width shown is based on the presence of four through lanes and no bike lanes. The last column of Table 195 lists the CMF value computed by multiplying the lane width CMF and the shoulder width CMF. A combined CMF value of 1.0 is computed for the base lane width (12 ft) and base shoulder width (1.5 ft). CMF values less than 1.0 correspond to conditions that produce a reduction in crash frequency, relative to base conditions. Similarly, CMF values larger than 1.0 correspond to conditions that produce an increase in crash frequency. The values in the last column of the table are less than 1.0 when the shoulder width exceeds 1.5 feet. This trend suggests that a wider shoulder has a larger overall safety benefit for trucks than a wider lane, for the same pavement width. This trend is in contrast to that for transit vehicles. The trends in CMF values for transit vehicles (shown in Table 191) indicated that transit vehicles benefit primarily from wider lanes.

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