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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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Suggested Citation:"Chapter 8: Supplemental Safety Findings." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report. Washington, DC: The National Academies Press. doi: 10.17226/26393.
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179 C H A P T E R 8 -SUPPLEMENTAL SAFETY FINDINGS Supplemental Safety Findings Introduction The literature review and agency interviews identified several research questions that would provide a means of assessing the safety performance of freeways that contain bus-on-shoulder (BOS) and part-time shoulder use (PTSU) facilities. These questions are identified in the following list.  Question 1: What is the overall effect of a proposed shoulder use design on total and severe crash frequency? This question considers both BOS and PTSU facilities.  Question 2a: What is the difference in safety performance when the shoulder is open or closed? This question relates to PTSU facilities only.  Question 2b: When the shoulder is closed, is there a difference in safety performance between a freeway with shoulder use and a freeway without shoulder use? This question relates to PTSU facilities only.  Question 3: What is the safety effect of converting shoulder use eligibility from bus-only to all vehicles?  Question 4: Are there differences in safety between using the left shoulder versus using the right shoulder? This question considers both BOS and PTSU facilities.  Question 5a: What is the safety effect of adding dynamic signs in replacement of static signs? This question relates to PTSU facilities only.  Question 5b: What is the safety effect of converting static operation to dynamic operation (i.e., static part-time shoulder use [S-PTSU] to dynamic part-time shoulder use [D-PTSU])? This question relates to PTSU facilities only.  Question 6: What is the safety effect of changing the width of the shoulder used for travel? This question considers both BOS and PTSU facilities.  Question 7: Are fatal and severe injury crashes over-represented during overnight hours like a typical urban freeway, or does shoulder use change this relationship? This question considers both BOS and PTSU facilities. This chapter describes the analysis undertaken to answer the questions identified in the previous list. Different statistical methods were used to answer these questions. Count regression models were used to answer Questions 1, 2a, 2b, 3, 4, 5a, and 6. Statistical analysis associated with these questions required the development of a regression model that was specifically tailored to the question. For some questions, only subsets of the full database were used to estimate the regression model. For these reasons, the regression coefficient for a given variable in a model developed to address one question may not be the same as that in a model developed for another question. The empirical Bayes (EB) before-after study framework was used to answer Question 5b. Binary logit models were used to answer research Question 7.

180 The remainder of this chapter is organized into 10 sections. The first section below provides an overview of the statistical methods used to answer the research questions. Each of the next eight sections addresses one research question. The last section summarizes the findings for each question. Overview of Statistical Modeling Approach Regression analysis was used to answer Questions 1, 2a, 2b, 3, 4, 5a, and 6. An overview of the analysis methods used to answer these questions is provided in the section titled Methological Background of Chapter 7. Additional details about these methods are offered in the section associated with each research question. The statistical analysis methods used to address Questions 5b and 7 are described in this section. Data were collected for three site types: freeway segment, ramp entrance speed-change lane site, and ramp exit speed-change lane site. To address some research questions using regression analysis, all site types were modeled together, with indicator variables to differentiate the site types. This approach was undertaken to increase the sample size used to estimate models and increase the likelihood of variables associated with specific research questions having statistical significance. Empirical Bayes Before-After Study Design For Question 5b, several facilities in the database were changed from S- PTSU operation to D-PTSU operation during the analysis period. This provided an opportunity to perform an observational before- after study of the operational change. For this evaluation, the EB before-after study design was applied (Hauer 1997). The basic steps of this study design are as follows:  Step 1: Develop safety performance functions (SPFs) to predict the safety performance of S-PTSU sites. The SPF was developed for a group of reference sites (i.e., S-PTSU sites that were never converted to D-PTSU).  Step 2: Compute the expected average crash frequency for the D-PTSU sites in the after period for the hypothetical case where they are not converted from S-PTSU to D-PTSU operation.  Step 3: Compare the expected and observed crash frequency to determine the safety effect of converting these sites from S-PTSU to D-PTSU operation. Each of these steps is described in more detail in the following sections. Step 1: Prediction of Safety Performance of a Reference Group In Step 1, a reference group is used to account for the effects of traffic volume changes and temporal effects on safety due to the variation of factors such as weather, demographics, and crash reporting. The reference group SPF is used for this purpose. It relates the frequency of crashes to traffic volume and other site-specific variables for the reference sites. In this case, the reference group consists of sites with S-PTSU operation that were never converted to D-PTSU. A fixed parameters model (Shankar et al. 1995) is used to estimate the SPF for this purpose. The general form of the regression model is shown in Equation 175 of Chapter 7. It is based on an assumed negative binomial distribution of the residual error. The variance for the negative binomial distribution is computed using the following equation: Equation 192 𝑉𝑎𝑟 𝜆 𝐸 𝜆 1 𝛼𝐸 𝜆

181 where Var(λi) is the variance of observed crashes occurring at site i; E(λi) is the predicted crash frequency at site i; and α is the overdispersion parameter. Equation 193 shows the general form of the regression model that was estimated for this application. This form is consistent with Equation 175. Equation 193 𝑁 , 𝐿 , 𝐴𝐴𝐷𝑇 exp 𝛽 𝑥 , 𝛽 where Np,I is the predicted average crash frequency for site I, crashes/year; Ls,I is the length of site I, miles; AADT,i is the annual average daily traffic volume for site I, veh/day; 0, …, n is the estimable regression coefficient for independent variable j, j = 1, …, n; and xi,j is the roadway or roadside side feature for site i and independent variable j. AADT in the context of the one-direction modeling conducted for this project is a directional AADT for the direction of the freeway being studied. Step 2: Expected Crash Frequency without Treatment using Empirical Bayes Adjustment The EB adjustment was applied to SPF predictions obtained from Equation 193 to incorporate the observed crash frequency in the prediction of crash frequency at each location. This adjustment is shown in Equation 194. Equation 194 𝑁 , 𝑤 𝑁 , 1 𝑤 𝑁 , where NEB,i is the expected crash frequency at location i based on EB adjustment, crashes/year; wi = adjustment weight for predicted crash frequency at site i; Np,i = predicted average crash frequency for site I, crashes/year; and Ni,obs = observed crash frequency at location I, crashes/year. The weight wi used for the EB adjustment for any location i is derived using Equation 195. Equation 195 𝑤 11 𝛼 ∑ 𝑁 , Thus, Equation 193 through Equation 195 were used to determine 𝑁 for the treatment sites in the before period. Specifically, these equations were applied to S-PTSU sites that were later converted to D- PTSU operation. Equation 193 was then used to calculate the predicted crash frequency 𝑁 for all treated sites in the after period. For this calculation, Equation 193 was applied to the same sites after the sites had been converted to D-PTSU. Finally, the expected crash frequency in the after period 𝑁 was calculated using Equation 196. The adjustment factor r was calculated using Equation 197. Equation 196 𝑁 𝑁 𝑟 with Equation 197 𝑟 ∑ 𝑁 ∑ 𝑁 where r is the adjustment factor that accounts for differences in duration and traffic volume between before and after periods, and, 𝑁 is the expected crash frequency during the after period. The value obtained from Equation 196 is the expected crash frequency if no treatment was applied. This value is then compared in Step 3 with the observed crash frequency after the treatment was applied to assess the safety effects of the treatment.

182 Step 3: Compare Predicted and Observed Safety Performance to Estimate Treatment Effectiveness An unbiased estimate of the safety effect θ of the treatment or countermeasure was obtained using Equation 198, where Equation 199 is used to compute the variance term needed in Equation 198. Equation 198 𝜃 𝑁 𝑁 1 𝑉𝑎𝑟 𝑁𝑁 with Equation 199 𝑉𝑎𝑟 𝑁 𝑟 1 𝑤 𝑁 where θ is the unbiased estimate of safety effect of the countermeasure, and 𝑁 is the observed crashes at the site during the after period. Finally, the standard error associated with this safety effect estimate was computed using Equation 200, where Equation 201 is used to compute the variance term needed in Equation 200. Equation 200 𝑆𝑡𝑑 𝐸𝑟𝑟𝑜𝑟 𝜃 ⎷ ⃓⃓⃓ ⃓⃓⃓ ⃓⃓⃓ ⃓⃓⃓ ⃓ 𝜃 ⎣ ⎢⎢ ⎢⎢ ⎢ ⎡ 𝑉𝑎𝑟 𝑁 𝑁 𝑉𝑎𝑟 𝑁 𝑁 1 𝑉𝑎𝑟 𝑁 𝑁 ⎦ ⎥⎥ ⎥⎥ ⎥ ⎤ with Equation 201 𝑉𝑎𝑟 𝑁 𝑁 Binary Logit Model For Question 7 in the list at the beginning of this chapter, sites were analyzed during different portions of the day. To determine if FI crashes are over-represented during overnight hours for BOS and PTSU facilities, a binary logit model was used. The KABCO injury scale was used to define severities in the BOS and PTSU observed crash data, except Hawaii. Hawaii defines only three severity categories (fatal, injury, and property-damage only) so it was excluded from analysis associated with Question 7. For this analysis, K (fatal), A (incapacitating injury), and B (non-incapacitating injury) crash severity categories were used to define the fatal-and-severe-injury category. B severity crashes were included to increase the sample size and the reliability of results because of the relatively rarity of K and A severity crashes. A brief overview of the modeling framework is described in the following paragraphs (Washington et al. 2010). Consider the following linear function to determine the severity outcome i for crash n: Equation 202 𝑠 𝛽 𝑋 𝜀 where Xin is a vector of explanatory variables used to determine the severity outcome i for a crash n; βi is a vector of estimated coefficients for severity outcome i; and εin is a random error term to account for the unobserved variables associated with severity outcome i and crash n. For the binary logit model, there are two severity outcomes, i = 1 or 0. The probability of crash n experiencing severity outcome i = 1, Pn(i

183 = 1), is shown in Equation 203, and the probability of crash n experiencing severity outcome i = 0, Pn(i = 0), is shown in Equation 204. Equation 203 𝑃 𝑖 1 𝑃 𝛽 𝑋 𝜀 0 𝑃 𝜀 𝛽 𝑋 exp 𝛽 𝑋1 exp 𝛽 𝑋 Equation 204 𝑃 𝑖 0 11 exp 𝛽 𝑋 For the models estimated to answer Question 7, severity outcome i = 1 was defined as KAB severities combined, while the C (possible injury) and O (property-damage-only) severity categories combined were defined as category i = 0. The independent variables considered in the models included traffic volume, roadway and roadside features, and crash characteristics. The statistical modeling process was guided by the principles described previously in this chapter in the section titled Count Regression Modeling. Question 1: Safety Effect of BOS and PTSU Question 1: What is the overall effect of a proposed shoulder use design on total and severe crash frequency? The response to Question 1 includes a section that addresses BOS facilities and a section that addresses PTSU facilities. Within each section, the data used to estimate the statistical models are summarized, the model is presented, and a response to the question is offered based on interpretation of the modeling results. BOS Facilities To estimate the relationship between BOS facilities and total crash frequency, a fixed s model was estimated. The general functional form of the model is shown in Equation 175 of Chapter 7. Data from Minnesota and Ohio were used for model estimation. The statistical modeling principles described in Chapter 7 were used to estimate the model. Empirical Setting The dataset used to answer this question included BOS sites and comparison sites on nearby freeways without BOS. BOS operation, when present, is on the left or right side of freeway sites in Ohio. In contrast, it is only on the right side of freeway sites in Minnesota. A total of 416 site observations were included in the database. Descriptive statistics for the data are shown in Table 73.

184 Table 73. Descriptive statistics of BOS sites. Variable Mean Standard Deviation Minimum Maximum Total crashes (5 years) 16.28 23.39 0 167 Site length (miles) 0.22 0.19 0.02 1.20 Directional annual average daily traffic (veh/day) 44,882 17,598 15,370 95,106 Number of lanes per direction 2.75 0.83 2 5 Degree of curvature per mile 5.33 12.19 0.00 100.73 Lane width (feet) 11.88 0.34 11.20 14.40 Right shoulder width (feet)a 10.99 1.43 4.90 19.00 Left shoulder width (feet)a 7.74 3.68 2.40 21.40 Proportion of site with left-side (inside) rumble strips 0.36 0.47 0.00 1.00 Proportion of site with right-side (outside) rumble strips 0.33 0.45 0.00 1.00 Proportion of site with outside (roadside) barrier 0.27 0.35 0.00 1.00 Proportion of site with median (inside) barrier 0.81 0.37 0.00 1.00 Offset to median (inside) barrier (feet) 2.30 4.45 0.00 23.00 Width of unobstructed median (feet) 20.5 18.9 1.1 60.3 Distance to nearest downstream exit ramp (miles) 0.53 0.61 0.00 2.67 Distance to nearest upstream entrance ramp (miles) 0.55 0.61 0.00 2.55 Downstream exit ramp annual average daily traffic (veh/day) 7446 6387 455 32,622 Upstream entrance ramp annual average daily traffic (veh/day) 7452 6191 453 32,738 Indicator for freeway segment 0.68 0.47 0 1 Indicator for ramp entrance speed-change lane site 0.17 0.37 0 1 Indicator for ramp exit speed-change lane site 0.15 0.36 0 1 Indicator for Minnesota 0.59 0.49 0 1 Indicator for Ohio 0.41 0.49 0 1 Indicator for left-side BOS facility 0.18 0.38 0 1 Indicator for right-side BOS facility 0.49 0.50 0 1 Indicator for a lane drop in the segment 0.04 0.19 0 1 a Includes portion of the shoulder used for travel, if applicable. The variables shown in Table 73 were entered into the total crash frequency models in the form shown in Equation 175 of Chapter 7. In addition, new variables were created to either (a) account for combinations of elements within the same sites, or (b) create functional forms consistent with the Highway Safety Manual Supplement (HSM Supplement) (AASHTO 2014). These variables are characterized herein as “adjustment factors,” similar to the SPF adjustment factors in the HSM. They are described in the following equations: Equation 205 𝑓 min 𝑊 , 12 – 12 where flw is the factor for lane width; and Wl is the average width of all full-time travel lanes. The value of 12 is the baseline lane width. Equation 206 𝑓 𝑊 1 𝑃 𝑊 1 𝑃 where fsw is the factor for shoulder width; Wos is the outside shoulder width; Wis is the inside shoulder width; and Pir and Por are the proportion of the site length with inside and outside rumble strips, respectively. This factor produces a combined width for the left (inside) and right (outside) shoulders for the portion of the site’s length that does not have rumble strips.

185 Equation 207 𝑓 𝑃 𝑃 /2 where frs is the factor for rumble strips; Pir and Por are the proportion of the site length with inside and outside rumble strips, respectively. Equation 208 𝑓 𝐼 /𝑛 where fdrop is the factor for lane drop; Idrop is an indicator variable for lane drop presence (= 1.0 if lane drop is present; 0 otherwise); and nlanes is the number of through lanes in the segment, not including the lane that was dropped. Equation 209 𝑓 𝑊 1 – 𝑃 𝑊 𝑃 where fmw is the factor for median width; Wum is the non-shoulder part of the median width in feet, Pib is the proportion of the site length with a median barrier, and Wicb is offset to median barrier in feet for sections with median barrier. This factor represents the average width of the traversable median with no barrier and the median offset when barrier is present. If there was a discontinuous section of median barrier within a site that also has a continuous median barrier (such as a short barrier piece protecting a fixed object in front of the continuous barrier), then the following equation was used to compute Wicb: Equation 210 𝑊 𝑀𝑒𝑑𝑖𝑎𝑛𝑂𝑓𝑓𝑠𝑒𝑡 𝑝 𝑀𝑒𝑑𝑖𝑎𝑛𝐵𝑎𝑟𝐿𝑒𝑛𝐿 5280 𝑀𝑒𝑑𝑖𝑎𝑛𝐵𝑎𝑟𝑂𝑓𝑓𝑠𝑒𝑡 𝑀𝑒𝑑𝑖𝑎𝑛𝐵𝑎𝑟𝐿𝑒𝑛 𝐿 5280 where, Ls is the length of the site, miles; MedianBarLen is the length of the median barrier, feet; MedianBarOffset is the distance to the face of a discontinuous median barrier, feet; and MedianOffset is the distance to the face of a continuous median barrier, feet. If there was a discontinuous section of median barrier within a site that does not have a continuous median barrier, then Wicb is set equal to the offset to the (discontinuous) median barrier. Equation 211 𝑓 𝑃max 𝑊 , 0.75 where frb is the factor for roadside barrier; Pob is the proportion of the site length with an outside (roadside) barrier, and Wocb is the offset to the outside (roadside) barrier in feet. Crash Frequency Models Regression models were first developed with all 416 site observations. Then the research team examined the results to determine if there were any outliers. A total of 11 observations were found in the database that had a crash rate that exceeded the 99th-percentile value of crash rates in the data. Further examination of the data suggested these observations likely represented DOT data coding issues rather than the actual safety performance of these sites. These observations were removed from the database, and the model was re-estimated. The results are shown in Table 74 for total crash frequency and Table 75 for fatal-and-injury (FI) crash frequency, where FI crashes include the K, A, B, and C severity categories.

186 Table 74. Fixed parameters model of total crashes for BOS sites. Variable Coefficient Std. Error t-statistic p-value Constant −6.417 1.601 −4.01 <0.001 Natural logarithm of directional annual average daily traffic 0.867 0.152 5.71 <0.001 Indicator for presence of ramp entrance speed-change lane (1 if entrance speed-change lane site; 0 otherwise) −0.157 0.135 −1.18 0.238 Indicator for presence of ramp exit speed-change lane (1 if exit speed-change lane site; 0 otherwise) −0.253 0.217 −1.17 0.243 Indicator for BOS on left-side of freeway (1 if BOS is present along left-side of site; 0 otherwise) 0.235 0.169 1.39 0.165 Indicator for BOS on right-side of freeway (1 if BOS is present along right-side of site; 0 otherwise) −0.012 0.123 −0.10 0.920 Variable for median width (fmw) −0.019 0.004 −4.80 <0.001 Variable for shoulder width (fsw) −0.021 0.007 −3.17 0.002 Variable for lane drop (fdrop) 0.688 0.539 1.28 0.202 Variable for roadside barrier (frb) 0.180 0.214 0.84 0.398 Interaction between ramp exit speed-change lane and ramp volume/1000 (veh/day) 0.002 0.025 0.06 0.949 Overdispersion parameter (𝛼) 0.646 0.052 12.42 <0.001 Number of observations: 405 Log-likelihood: −1276.6285 McFadden Pseudo R2: 0.1380 In Table 74, the relative effect of a variable is computed as 100 𝑒 1 . For example, the relative effect of a site being a ramp entrance speed-change lane is −14.5% [ 100 𝑒 . 1 ]. In other words, a ramp entrance speed-change lane site has 14.5 percent fewer crashes than a freeway segment with other variables (volume, median width variable, etc.) being equal. The findings from the total crash model presented in Table 74 are summarized in the following list:  The presence of BOS on the left side of the freeway is associated with a 26.5 percent increase in total crashes. However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.165 that a coefficient value this large could be observed due to random variation when the true value equals 0.0.  The presence of BOS on the right side of the freeway is associated with a 1.2 percent decrease in total crashes. However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.920 that a coefficient value this large could be observed due to random variation when the true value equals 0.0.

187 Table 75. Fixed parameters model of FI crashes for BOS sites. Variable Coefficient Std. Error t-statistic p-value Constant −11.425 1.889 −6.05 <0.001 Natural logarithm of directional annual average daily traffic 1.199 0.178 6.74 <0.001 Indicator for presence of ramp entrance speed-change lane (1 if entrance speed-change lane site; 0 otherwise) −0.103 0.296 −0.35 0.728 Indicator for presence of ramp exit speed-change lane (1 if exit speed-change lane site; 0 otherwise) −0.311 0.192 −1.62 0.106 Indicator for BOS on left-side of freeway (1 if BOS is present along left-side of site; 0 otherwise) 0.071 0.188 0.38 0.704 Indicator for BOS on right-side of freeway (1 if BOS is present along right-side of site; 0 otherwise) 0.004 0.143 0.03 0.976 Variable for median width (fmw) −0.015 0.005 −2.88 0.004 Variable for shoulder width (fsw) −0.014 0.008 −1.85 0.064 Variable for lane drop (fdrop) 0.976 0.559 1.75 0.081 Variable for roadside barrier (frb) 0.304 0.230 1.32 0.186 Interaction between ramp exit speed-change lane and ramp volume/1,000 (veh/day) −0.036 0.041 −0.88 0.377 Overdispersion parameter (𝛼) 0.576 0.066 8.78 <0.001 Number of observations: 405 Log-likelihood: −1606.604 McFadden Pseudo R2: 0.1696 The findings from the FI safety prediction model presented in Table 75 are summarized below:  The presence of BOS operation on the left side of the freeway is associated with a 7.4 percent increase in FI crashes. However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.704 that a coefficient value this large could be observed due to random variation when the true value equals 0.0.  The presence of BOS operation on the right side of the freeway is associated with a 0.4 percent increase in FI crashes. However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.976 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. BOS Results For BOS presence on the right side of the freeway, both the total and FI model coefficients suggest that BOS presence is associated with a negligibly small change in crash frequency (from a practical perspective). Moreover, these coefficients are not statistically significant (at a significance level of 5 percent). Based on these findings, it is concluded that BOS presence on the right side of the freeway has neither a statistically significant nor a meaningful influence on crash frequency. For BOS presence on the left side of the freeway, both the total and FI model coefficients suggest that BOS presence is associated with a 7 to 26 percent increase in crash frequency. However, these coefficients are not statistically significant (at a significance level of 5 percent). The database only contained left-side BOS sites from one facility—I-71 in the Cincinnati area of Ohio. A second left-side BOS facility was initially believed to exist in the Cleveland, Ohio, area, but BOS operation has been discontinued. Minnesota does not have left-side BOS facilities. Furthermore, comparison sites for I-71 were selected from another freeway in the Cincinnati area rather than I-71 due to a lack of appropriate comparison sites on I-71. Thus, the indicator variable for BOS on the left side of the freeway is

188 effectively an indicator for the site being located on I-71 in Ohio. There is no means for determining whether the coefficient is reflecting “location on I-71” or “presence of left-side BOS.” Based on these findings, it is concluded that BOS presence on the left side of the freeway is unlikely to have a meaningful influence on crash frequency. However, data for additional sites are needed to be more conclusive on this issue. Based on the aforementioned findings, it is concluded that BOS presence—on either side of the freeway—is unlikely to have a meaningful influence on total or FI crash frequency. This conclusion is consistent with the findings of the literature review documented in Chapter 2, Literature Review. This review found that BOS presence was not associated with a meaningful influence on bus-involved crash frequency. PTSU Facilities An analysis (similar to the BOS analysis described in the previous section) was undertaken with the PTSU database. Initial findings indicated a statistically significant effect of PTSU presence on crash frequency, so effort was used to advance the model and its documentation to a level sufficient for inclusion in a future edition of the HSM. Consistent with the HSM Supplement (AASHTO 2014), one model was developed to predict the frequency of FI crashes, where FI crashes include K, A, B, and C severity levels. A second model was developed to predict the frequency of PDO crashes. The development of these two models is described in Chapter 5, HSM Predictive Model. The third model was developed to predict the distribution of fatal (K), incapacitating injury (A), and non-incapacitating injury (B), and possible injury (C) crashes within the frequency of FI crashes. It is referred to herein as a severity distribution function (SDF). The development of this model is described in Chapter 6, Crash Severity and Crash Type Distributions. Information presented in this section summarizes aspects of the three models most relevant to answering Question 1, as applied to PTSU operation. Empirical Setting The database used to develop the predictive models identified in the previous section includes data for 728 study sites, collectively representing 14 freeway facilities in the states of Georgia, Hawaii, Minnesota, Ohio, and Virginia. The sites have a total length of 164.8 miles. About 25 percent of the total mileage consists of freeway facilities with PTSU operation during 1 or more hours of the day; the remainder of sites are non-PTSU “comparison” sites. Additional information about the study sites is provided in Chapter 4, Project Database. The data for all five states were used to develop the crash prediction model. The data for Hawaii were not used to develop the SDF because Hawaii’s crash records did not distinguish between the A, B, and C severity levels. Table 76 summarizes key geometric and traffic characteristics of the sites in the database. The sites are located in urban areas and have lane counts that range from 2 to 7 in the subject direction of travel. The variables listed are those used in the examination of Question 1. Additional variables are included in the database; they are described in Chapter 5. The facilities with PTSU operation collectively operate between 1 and 11 hours of the average day of year. These hours of operation are reflected in the “proportion of time the PTSU operates” variable shown in the table. These hours of operation are shown in the table as a proportion of the 24-hour day. The “proportion of AADT during high volume hours” is used in Chapter 18 of the HSM Supplement (AASHTO 2014). Guidance for computing its value is provided in Section 18.4 of the HSM. It is used in the SDF to estimate the FI crash severity distribution. The proportion of K, A, and B severity crashes is predicted to decrease with an increase in the proportion of annual average daily traffic (AADT) during high volume hours.

189 Table 76. Descriptive statistics of PTSU sites. Variablea Mean Minimum Maximum Freeway Segment Variables Directional AADT volume of segment, AADTfs (veh/day) 60,010 15,370 147,210 Proportion of AADT during hours where volume > 1,000 veh/h/lane 0.17 0.0 0.42 Proportion of time PTSU operates (for sites with PTSU)b 0.20 0.057 0.455 Cross Section Variables Number of lanes (in subject travel direction), n 3.3 2 7 Inside PTSU lane width (left side), Wil,ptsu (ft) 11.7 3.5c 14.0 Lane width (excluding PTSU lane), Wl (ft) 11.9 10.5 14.4 Outside PTSU lane width (right side), Wl,ptsu (ft) 11.2 5.0c 16.8 Barrier Variables Proportion of site length with barrier present in the median, Pib 0.88 0.0 1.0 Proportion of site length with barrier present on the outside (roadside), Pob 0.43 0.0 1.0 Turnout Variables Number of sites with turnout beyond the shoulder 37 n.a. n.a. Length of turnout (from start of taper to end of taper), Ltout (ft) 520 75 1,500 n.a. = not applicable. a Variable names and definitions are consistent with those in Chapter 18 of the HSM Supplement (AASHTO 2014). b Proportion of time PTSU operates = (weekday hours × 5/7 + weekend hours × 2/7)/24. c PTSU tapers from full width to zero width over segment; table value is an average width over length of segment. A study period was established for each facility in each of the five states. At those facilities with PTSU operation, the study period was defined to bracket the years during which PTSU was operating. The study period duration ranged from 1 to 5 years for the set of sites, with an average of 4.8 years per site. The crash data for the study sites are summarized in Table 77. As shown in the last row of this table, the sites are collectively associated with 4,807 FI crashes and 11,937 PDO crashes. These counts are combined with the exposure value in the fourth column to obtain the corresponding crash rates shown in the last two columns of the table. The overall crash rate (shown in the last row of the table) is 0.28 FI crashes per million vehicle miles (crashes/mvm) and 0.70 PDO crashes/mvm. Table 77. Summary of crash data by site type. PTSU Operation Site Type Exposure (mvm) Observed Crashes Crash Rate (cr/mvm) FI PDO FI PDO Yes Freeway segment 5,071 1,833 4,030 0.36 0.79 Ramp ent. speed-change lane 427 125 259 0.29 0.61 Ramp exit speed-change lane 303 130 346 0.43 1.14 Total: 5,801 2,088 4,635 0.36 0.80 No Freeway segment 9,674 2,350 6,276 0.24 0.65 Ramp ent. speed-change lane 1,035 203 590 0.20 0.57 Ramp exit speed-change lane 586 166 436 0.28 0.74 Total: 11,295 2,719 7,302 0.24 0.65 All Sites Combined Total: 17,096 4,807 11,937 0.28 0.70 mvm = million vehicle miles; n.a. = not applicable The data presented in Table 77 indicate that the sites without PTSU operation have a lower crash rate than those with PTSU operation. The ratio of the FI crash rates ratio is 1.50 (= 0.36/0.24). This ratio suggests that PTSU operation may be associated with a 50 percent increase in FI crashes.

190 FI and PDO Crash Frequency Models Two crash frequency prediction models were developed for the purpose of evaluating the effect of a proposed PTSU design on total and severe crash frequency. One model predicts the frequency of FI crashes. A second model predicts the frequency of PDO crashes. Total crash frequency is computed as the sum of the FI and PDO crash frequencies. Both models are described in Chapter 5. Each model includes variables that describe the traffic demand characteristics, geometric elements, and PTSU operational features. The variables related to PTSU design and operation are provided in the following list.  Proportion of time that PTSU operates.  PTSU lane width.  Proportion of site length with PTSU transition zone present between, upstream of, or downstream of a PTSU lane.  Number of through lanes within site (including managed lanes but not including auxiliary lanes or PTSU lanes).  Proportion of segment length with turnout present.  Turnout spacing. The first four variables in the aforementioned list are incorporated in a PTSU operation adjustment factor (AF). An AF is analogous in its interpretation to a crash modification factor (CMF) in Part C of the HSM (AASHTO 2010). The values are shown in the top one-third of Table 78 are from the PTSU operation AF for various combinations of PTSU lane width, proportion time PTSU operating, and number of lanes. The PTSU operation AF is also applicable to sites that are between, upstream of, or downstream of a site with a PTSU lane. These sites are considered to include a PTSU transition zone where vehicles in the main lanes interact with those vehicles preparing to enter (or having just exited) the PTSU lane. The values are shown in the bottom one-third of Table 78 are from the PTSU operation AF for a 0.27-mile segment with various combinations of proportion time PTSU operating. The last three variables in the aforementioned list are incorporated in the turnout presence AF. This AF is combined with (i.e., multiplied by) the PTSU operation AF to produce the values shown in the middle one-third of Table 78. The values shown are based on a turnout spacing of 0.5 miles. The AF values in each of the upper two portions of Table 78 are shown to increase with an increase in the proportion time the PTSU is operating, a reduction in PTSU lane width, and an increase in number of lanes. The values decrease when turnouts are provided. The AF value listed in the table for the case where the proportion time PTSU operating equals 0.0 corresponds to the case where the width of the PTSU lane is effectively serving as additional shoulder width. Typical values for the variables identified in Table 78 include 0.5-mile turnout spacing, a proportion time PTSU operating of 0.2, and an 11-foot PTSU lane width, and four lanes. For these values, the AF value is 1.41. This AF value suggests that PTSU operation can increase the annual FI crash frequency by 41 percent for typical conditions. This value is consistent with that found in the crash rates listed in Table 77. A similar table of AF values was prepared for the PTSU-related AFs included in the PDO crash prediction model. The AF values for the PDO model follow the same trends as those for FI crashes but tend to be about 10 percent larger in value (i.e., AFPDO ≈ 1.1 × AFFI).

191 Table 78. Estimated PTSU operation AF for FI crashes. PTSU Type PTSU Lane Width (ft) Proportion Time PTSU Operatinga AF Value by Number of Lanes 2 4 6 PTSU lane (no turnouts) 11 0.0 0.80 0.89 0.93 0.1 1.11 1.19 1.22 0.2 1.42 1.49 1.52 0.3 1.73 1.79 1.82 0.4 2.04 2.09 2.11 12 0.0 0.78 0.88 0.92 0.1 1.08 1.17 1.20 0.2 1.37 1.45 1.48 0.3 1.67 1.74 1.77 0.4 1.96 2.03 2.05 PTSU lane (turn-out every 0.5 miles) 11 0.0 0.72 0.85 0.89 0.1 1.00 1.13 1.18 0.2 1.28 1.41 1.46 0.3 1.56 1.70 1.75 0.4 1.84 1.98 2.04 12 0.0 0.71 0.84 0.89 0.1 0.97 1.11 1.16 0.2 1.24 1.38 1.43 0.3 1.51 1.65 1.70 0.4 1.77 1.92 1.97 PTSU transition zoneb Any 0.0 1.00 1.00 1.00 0.1 1.11 1.11 1.11 0.2 1.22 1.22 1.22 0.3 1.33 1.33 1.33 0.4 1.43 1.43 1.43 a Proportion time PTSU operating = (weekday hours × 5/7 + weekend hours × 2/7)/24 b Segment length is 0.27 miles. Severity Distribution Function An SDF was developed to be used with the FI crash prediction model to provide the means for estimating the frequency of crashes by severity level K, A, B, or C. This model is described in Chapter 6. It includes the variable “proportion of time that PTSU operates,” which is relevant to the question of the safety effect of PTSU operation. Table 79 lists the predicted severity distribution for freeway segments as a function of proportion time that the PTSU operates, proportion AADT during high volume hours, and proportion of site adjacent to barrier. The proportions shown indicate that the proportion of K, A, and B crashes decrease (while the proportion of C crashes increase) with an increase in the proportion of site adjacent to barrier. The proportions shown in the table also indicate that an increase in the proportion AADT during high volume hours corresponds to a decrease in the proportion of K, A, and B crashes. Finally, the proportions shown indicate that an increase in the proportion of time that PTSU operates corresponds to a decrease in K and A crashes (while the proportion of B crashes increases and the proportion of C crashes stays about the same).

192 Table 79. Comparison of predicted severity distribution for freeway segments. Proportion Time PTSU Operates Proportion AADT in High Volume Hours Proportion Segment Adjacent to Barrier Crash Proportion by Severity K A B C 0.0 0.05 0.1 0.005 0.056 0.417 0.521 0.5 0.005 0.051 0.378 0.567 0.9 0.004 0.046 0.339 0.611 0.25 0.1 0.005 0.051 0.375 0.570 0.5 0.004 0.045 0.336 0.615 0.9 0.004 0.040 0.299 0.657 0.45 0.1 0.004 0.045 0.333 0.618 0.5 0.004 0.040 0.296 0.660 0.9 0.003 0.035 0.261 0.700 0.5 0.05 0.1 0.001 0.039 0.439 0.521 0.5 0.001 0.036 0.397 0.567 0.9 0.000 0.032 0.357 0.611 0.25 0.1 0.001 0.035 0.394 0.570 0.5 0.000 0.032 0.353 0.615 0.9 0.000 0.028 0.314 0.657 0.45 0.1 0.000 0.031 0.350 0.618 0.5 0.000 0.028 0.311 0.660 0.9 0.000 0.025 0.275 0.700 PTSU Results Based on the results described in the previous sections, urban freeway segments with PTSU operation are typically associated with a larger crash frequency than those segments without PTSU operation. Specifically, the AF for PTSU operation in the crash prediction models indicates that FI and PDO crash frequency increases with an increase in the number of hours that PTSU operates during the average day. The provision of turnouts can mitigate this increase. The trends in Table 78 suggest that the provision of turnouts at 0.5-mile spacing can reduce the PTSU operation AF value by 5 to 10 percent. The predicted severity distribution from the SDF indicates that an increase in the proportion of time that PTSU operates corresponds to a decrease in the most severe crashes (i.e., K and A). Thus, the increase in FI crash frequency with PTSU operation is partially offset by a shift in the severity distribution away from the most severe crashes. The two trends identified in the preceding paragraphs were examined in combination using a crash cost analysis. To facilitate this examination, one direction of a hypothetical freeway section was evaluated. The section has two 12-ft through traffic lanes in the subject travel direction. The freeway experiences an average of one FI crash for every two PDO crashes. The directional AADT volume is 31,500 veh/day. The base condition for this examination is a freeway without PTSU operation. The PTSU operation, turnout presence, and outside shoulder width AFs were used to compute the AF values shown in columns 3 and 4 of Table 80. The SDF was used to compute the severity distribution shown in columns 5 to 8. The relative cost per crash was computed using the equation described in the table footnote. This cost is relative to the number of crashes predicted for the base condition (which has a cost of $31,118). The relative crash cost tends to increase with an increase in the “proportion time PTSU operating” due to the associated increase in crash frequency relative to the base condition. The relative cost is shown to be smaller than the base condition cost when the “proportion time PTSU operating” is small. This trend results because the width of the PTSU lane is effectively serving as additional shoulder width when PTSU operation is not allowed.

193 Table 80. Change in crash frequency, severity, and cost associated with PTSU operation. PTSU Type Proportion Time PTSU Operatinga AF Value by Severityb Severity Distributionc Relative Crash Cost ($)d,e Proportion Change in Costg FI PDO K A B C PTSU lane (no turnouts Base cond.f 1.00 1.00 0.004 0.042 0.313 0.641 31,118 0.05 1.10 1.17 0.004 0.042 0.313 0.641 33,255 1.07 0.1 1.27 1.39 0.003 0.039 0.317 0.641 37,594 1.21 0.2 1.62 1.83 0.002 0.037 0.320 0.642 46,078 1.48 0.3 1.97 2.27 0.001 0.034 0.323 0.642 54,486 1.75 0.4 2.31 2.71 0.001 0.032 0.326 0.641 62,925 2.02 PTSU lane (turnout every 0.5 miles) Base cond. f 1.00 1.00 0.004 0.042 0.313 0.641 31,118 0.05 0.99 1.02 0.004 0.042 0.313 0.641 29,842 0.96 0.1 1.15 1.21 0.003 0.039 0.317 0.641 33,726 1.08 0.2 1.46 1.60 0.002 0.037 0.320 0.642 41,319 1.33 0.3 1.77 1.98 0.001 0.034 0.323 0.642 48,843 1.57 0.4 2.09 2.36 0.001 0.032 0.326 0.641 56,395 1.81 a Proportion time PTSU operating = (weekday hours × 5/7 + weekend hours × 2/7)/24 b Product of PTSU operation, turnout presence, and outside shoulder width AFs. PTSU design conditions include two through lanes, PTSU lane width of 12 feet, paved outside shoulder width of 2 feet. PTSU operation AF values for FI crashes obtained from Table 78. AF values for PDO crashes from Table 43 of Chapter 5. Outside shoulder width AF values from Equation 66 and Equation 90 in Chapter 5. c Proportions from SDF described in Chapter 6. Proportion of AADT volume in high volume hours is 0.40. It is computed using default value equation provided in Section 18.4 of Chapter 18 in the HSM Supplement (AASHTO 2014). “AADT per lane” used in this equation is 15,750 veh/day/lane, which is typical for sites in database. The proportion of site adjacent to barrier is 0.43, which is typical for sites in the database. d Crash cost is computed as: CC = (Pk × ck + PA × cA+ PB × cB + PC × cC) × AFFI + cPDO × AFPDO × RPDO/FI ; where CC = crash cost ($/crash); Pj = probability of a FI crash being described as severity j (j = K, A, B, C); cj = societal crash cost for crash described as severity j; AFFI = value for FI crashes from PTSU operation AF and turnout presence AF (as shown in the table); AFPDO = value for PDO crashes from PTSU operation AF and turnout presence AF (as shown in the table); and RPDO/FI = ratio of PDO crashes to FI crashes = 2 (i.e., 2 PDO crashes for each FI crash). e Societal crash costs from Table 7-1 of the HSM (AASHTO 2010). cK = $4,008,900; cA = $216,000; cB = $79,000; cC = $44,900; and cPDO = $7,400. f Base condition: no PTSU lane; no PTSU operation; no turnout; 10-foot outside shoulder width. g Proportion change in crash cost equals the crash cost for the subject row divided by the crash cost for the base condition. The proportion change in crash cost is shown in the last column of Table 80. This proportion can be compared with the AF values shown in columns 3 and 4. For a given row (i.e., value of proportion time PTSU operating), the proportion change in cost value is less than or equal to the FI AF and PDO AF values. This trend reflects the reduction in the proportion of very severe crashes associated with PTSU operation. In fact, when a turnout is provided every 0.5 miles and the proportion time PTSU operating is 0.06 or less (e.g., ≤ 2 h/day during the week days and 0 h/day during the weekends), the change in crash cost is less than 1.0 and there is a safety benefit associated with PTSU operation.

194 Questions 2a and 2b: Safety Effect of PTSU Presence Question 2a: What is the difference in safety performance when the shoulder is open or closed? Question 2b: When the shoulder is closed, is there a difference in safety performance between a freeway with shoulder use and a freeway without shoulder use? These two questions focus on PTSU facilities only. This section includes information about the empirical setting, followed by interpretation of the model coefficients that were used to answer the questions. Empirical Setting Data collected at all sites were used to answer Questions 2a and 2b. Sites with and without PTSU were used in the analysis in order to answer Question 2b, which compares safety performance of freeway sites with and without PTSU facilities. The site types considered include: freeway segments, ramp entrance speed-change lane sites, and ramp exit speed-change lane sites. In addition, hourly volume estimates were obtained for the PTSU and comparison sites in order to estimate the predicted total crash frequency for each weekday and weekend hour. Table 81 summarizes the data used to answer the questions. There are a total of 14,976 observations in the database, which represent 312 unique sites in Georgia, Hawaii, Minnesota, and Virginia. There are 48 observations available for each site—one representing each hour of weekdays and weekend days.

195 Table 81. Descriptive statistics of PTSU sites and comparison sites. Variable Mean Standard Deviation Minimum Maximum Total crashes (in a specific hour over analysis period) 0.6648 2.083 0 44 Site length (miles) 0.239 0.207 0.015 1.232 Directional annual average daily traffic (veh/day) 80,170 19,590 31,401 147,207 Number of lanes per direction 3.997 0.709 3 7 Degree of curvature per mile 3.534 8.424 0 75.103 Lane width (feet) 11.95 0.43 10.5 14.1 Right shoulder width (feet) 11.53 4.37 0.2 28.7 Left shoulder width (feet) 10.20 4.43 1.3 23.5 Proportion of site length with left-side (inside) rumble strips 0.341 0.456 0.0 1.0 Proportion of site length with right-side (outside) rumble strips 0.144 0.338 0.0 1.0 Proportion of site length with outside (roadside) barrier 0.624 0.351 1.0 1.0 Proportion of site length with median (inside) barrier 1.0 0.0 1.0 1.0 Offset to median (inside) barrier (feet) 9.369 4.593 0.0 26.9 Offset to outside (roadside) barrier (feet) 3.321 4.379 0.0 20.6 Width of unobstructed median (feet) 12.300 16.139 1.5 96.4 Variable Proportion in Database Proportion of freeway segments 0.75 Proportion of ramp entrance speed-change lane sites 0.13 Proportion of ramp exit speed-change lane sites 0.12 Proportion of Minnesota sites 0.05 Proportion of Georgia sites 0.20 Proportion of Virginia sites 0.58 Proportion of Hawaii sites 0.17 Proportion of left-side PTSU sites 0.09 Proportion of right-side PTSU sites 0.33 Crash Frequency Models Regression analysis was used to estimate a model for predicting the total crash frequency of the PTSU sites. The general form of the model is shown in Equation 212: Equation 212 𝑁 , , 𝑒 𝐿 , 𝑦 𝑝 , 𝐴𝐴𝐷𝑇 exp 𝑏 𝑃 , 𝑥 , 𝑏 where, Np,i,k = predicted average crash frequency for site i during hour k (k = 1, …, 48) (crashes); Ls,i = length of site i (miles); AADT,i = annual average daily traffic volume for site i (veh/day); y = number of years; pik = proportion of traffic at site i for hour k; Popen,k = proportion of the time during hour k that the PTSU facility is open;  b0, …, bn = estimable regression coefficient for independent variable j, j = 1, …, n; and xi,j = roadway or roadside side feature for site i and independent variable j. The total number of crashes on each site was used as the dependent variable in the model. The AADT, horizontal curvature, presence of speed-change lanes, presence of PTSU lanes, cross section dimensions (e.g., lane, shoulder, and median width), rumble strip presence, and other site-specific features were considered as candidate independent variables for inclusion in the model and do not vary hourly. In

196 addition, state indicator variables were included in the model to control for differences in crash reporting among the agencies represented in the database. The site length was assumed to be directly proportional to the number of total crashes and was included as an offset variable in the model. Additionally, since the number of crashes observed at each location was for some predefined time period (e.g., between 3 to 5 years), the amount of time that crash data were available at each location was also included as an offset variable to ensure that the model accurately predicted annual average crash frequency. In the model specification shown in Equation 212, the proportion of the AADT during each hour of the day, which was separated based on weekday and weekend periods, was multiplied by the AADT to estimate the hourly traffic volume at each site. An indicator variable was developed to account for whether the PTSU lane was opened or closed—it took on a value between 0 and 1 in the model, where 0 indicated the PTSU lane was closed for the entire hour for every day in the study period, while 1 indicated the PTSU lane was open for the entire hour for every day in the study period. If the lane was open for a fraction of an hour, the indicator was equal to the proportion of the hour (e.g., an average of 30 minutes during the study period was set equal to 0.5). The resulting model is shown in Table 82. The candidate independent variables shown in this table were entered into the model in the form shown in Equation 213. In addition, new variables (like those described in Equation 205 to Equation 211) were created to either (a) account for combinations of elements within the same sites, or (b) create functional forms more consistent with the HSM Supplement (AASHTO 2014). Equation 213 ln 𝑁 ln 𝑦 ln 𝐿 𝑏 𝑏 ln 𝑝 𝐴𝐴𝐷𝑇 𝑏 𝐼 𝑏 𝐼 𝑏 𝑃 , , 𝑏 𝑓 𝑏 𝑓 𝑏 𝑊 𝑏 𝑊 𝑏 𝑃 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 where, Np = predicted average crash frequency for site (crashes); y = number of years (years); Ls = site length (miles); pk = proportion of traffic at site for hour k; AADT = annual average daily traffic volume (veh/day); IENSCL = indicator variable for sites that are ramp entrance speed-change lanes; IEXSCL = indicator variable for sites that are ramp exit speed-change lanes; PPTSU,open,k = proportion of the time during hour k that the PTSU facility is open; fmw = median width factor; frb = roadside barrier factor; Wls = width of left shoulder (feet); Wrs = width of right shoulder (feet); Por = proportion of outside (right) shoulder with rumble strips; IPTSU = indicator variable for PTSU presence on a segment; IWeekend = indicator variable for hours during a weekend day; IVA = indicator variable for sites in Virginia; IGA = indicator variable for sites in Georgia; IHI = indicator variable for sites in Hawaii; and b0, …, bn = estimable regression coefficients for independent variables at site. The model in Table 82 has a coefficient (i.e., b11) that suggests that weekend hours have 34.6 percent of the predicted crash frequency associated with weekday hours. This result was expected because there are fewer weekend days than week days (i.e., 0.40 = 2 weekend days / 5 week days). The fact that the coefficient is associated with 0.346 (and not 0.40) reflects the influence of other attributes of weekends that are contributing to crash risk, such as different congestion levels or different driver populations.

197 Table 82. Fixed parameters model of total crashes per hour for PTSU sites. Variable Coefficient Std. Error t-statistic p-value b0: Constant −7.574 0.247 −30.719 <0.001 b1: Natural logarithm of directional hourly volume 0.964 0.028 34.086 <0.001 b2: Indicator for presence of ramp entrance speed-change lane (1 if entrance speed-change lane site; 0 otherwise) −0.044 0.060 −0.742 0.458 b3: Indicator for presence of ramp exit speed-change lane (1 if exit speed-change lane site; 0 otherwise) 0.427 0.061 6.958 <0.001 b4: Proportion of time during an hour that the PTSU is open (number of minutes per hour that the lane is open divided by 60, ranges from 0 to 1) 0.865 0.057 15.180 <0.001 b5: Variable for median width (fmw) −0.018 0.006 −2.894 0.004 b6: Variable for roadside barrier (frb) 0.456 0.051 8.887 <0.001 b7: Total right shoulder width (feet) −0.011 0.005 −2.445 0.015 b8: Total left shoulder width (feet) −0.016 0.006 −2.711 0.007 b9: Proportion of site with right-side (outside) rumble strips −0.400 0.062 −6.446 <0.001 b10: Indicator for PTSU facility presence (1 if PTSU facility is present; 0 otherwise) 0.044 0.041 1.086 0.278 b11: Indicator for weekend operation (1 if hour is in a weekend; 0 otherwise) −1.061 0.037 −28.877 <0.001 b12: Indicator for Virginia (1 if site is located in Virginia; 0 otherwise) −0.116 0.079 −1.471 0.141 b13: Indicator for Georgia (1 if site is located in Georgia; 0 otherwise) −0.483 0.090 −5.362 <0.001 b14: Indicator for Hawaii (1 if site is located in Hawaii; 0 otherwise) −1.418 0.091 −15.628 <0.001 Overdispersion parameter (𝛼) 1.168 0.042 28.015 <0.001 Number of observations: 14,976 2 × Log-likelihood: −24551.343 McFadden Pseudo R2: 0.180 Results This section discusses the results for Questions 2a and 2b. The results for each question are provided in a separate subsection. Question 2a Results The coefficient for the “proportion of time during an hour that the PTSU lane is open” variable (i.e., b4) can be used to estimate the difference in safety performance of a PTSU site when the lane is open versus closed. The value of this variable ranges from 0 to 1, where 0 is equivalent to a lane being closed for the full hour, while 1 is equivalent to the lane being open for a full hour. In the model presented in Table 82, the coefficient b4 of 0.865 is associated with the variable for “proportion of time during an hour that the PTSU lane is open.” The null hypothesis that this value equals 0.0 can be rejected at a 5 percent significance level. The probability of computing a value this large because of random variation (when the true value equals 0.0) is less than 0.001. Based on these results, opening a PTSU lane for an entire hour (compared to having the PTSU lane closed for the entire hour) is associated with a 137 percent increase in total crashes. Opening the PTSU lane for half of an hour (compared to having the PTSU lane closed for the entire hour), is associated with a 54.1 percent increase in total crash frequency.

198 Question 2b Results The “proportion of time during an hour that the PTSU lane is open” variable was set to zero using the model shown in Table 82. The indicator for “PTSU facility presence” variable was then used to compare the safety performance of site with a PTSU lane that is closed to a site without a PTSU lane. In the model presented in this table, the coefficient b10 of 0.044 is associated with the indicator for “PTSU facility presence.” However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.278 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. The coefficient indicates that PTSU facility presence is associated with 4.5 percent larger total crash frequency. The model used to answer Question 1 predicts PTSU sites as having more total crashes than non-PTSU sites. The hourly analysis described here for answering Questions 2a and 2b found this increase total in crashes is associated with PTSU being active (i.e., open to traffic) rather than simply present (i.e., closed or open). This finding is consistent with the trends shown previously in Table 78. This table shows a relatively large increase in the value of the PTSU operation adjustment factor with an increase in the percent of time in the day PTSU is open. Based on these results, it is concluded that PTSU facility presence when the shoulder is closed may be associated with a nominally small increase in total crash frequency. However, data for additional sites are needed to confirm whether PTSU facility presence (when the shoulder is closed) truly increases total crash frequency in all conditions and by what amount. Question 3: Safety Effect of Converting BOS to PTSU Question 3: What is the safety effect of converting shoulder use eligibility from bus-only to all vehicles? As discussed previously in the Question 1 section of this chapter, the analysis of crash data indicated that the presence of BOS is unlikely to have a meaningful influence on total or FI crash frequency. Therefore, the safety effect of converting a BOS facility to a PTSU facility is expected to be the same as converting a typical freeway with no shoulder use to a PTSU facility. None of the PTSU facilities studied was converted from BOS during the study period, so it was not possible to conduct a before-after study. The discussion in the Question 1 section and in Chapters 5 and 6 provides additional information on the safety effects of converting typical freeways to PTSU facilities. Question 4: Safety Effect of Left versus Right Shoulder Question 4: Are there differences in safety between using the left shoulder versus using the right shoulder? This question is applicable to both BOS and PTSU facilities. However, as discussed in the Question 1 section, the analysis of crash data indicated that BOS operation is unlikely to have a meaningful influence on total or FI crash frequency. Hence, the question of whether a change in shoulder width has an effect on the safety of a freeway with BOS operation is addressed in Question 1 (i.e., shoulder width has unlikely to have a meaningful influence). This section addresses the question of whether there are differences in safety between left-side PTSU versus right-side PTSU.

199 Empirical Setting A database containing PTSU sites was developed to answer Question 4. The database included all PTSU sites and PTSU comparison sites. The site types considered include: freeway segments, ramp entrance speed-change lane sites, and ramp exit speed-change lane sites. A summary of the pertinent features of these data is shown in Table 83. There are a total of 312 site observations in the database. Table 83. Descriptive statistics of PTSU sites and PTSU comparison sites. Variable Mean Standard Deviation Minimum Maximum Total crashes (5 years) 31.95 46.28 0 298 Site length (miles) 0.239 0.207 0.015 1.232 Directional annual average daily traffic (veh/day) 80,170 19,621 31,401 147,207 Number of lanes per direction 3.997 0.709 3 7 Degree of curvature per mile 3.534 8.424 0 75.103 Lane width (feet) 11.95 0.43 10.5 14.1 Right shoulder width (feet) 11.53 4.37 0.2 28.7 Left shoulder width (feet) 10.20 4.43 1.3 23.5 Proportion of site length with left-side (inside) rumble strips 0.341 0.456 0.0 1.0 Proportion of site length with right-side (outside) rumble strips 0.144 0.338 0.0 1.0 Proportion of site length with outside (roadside) barrier 0.624 0.351 1.0 1.0 Proportion of site length with median (inside) barrier 1.0 0.0 1.0 1.0 Offset to median (inside) barrier (feet) 9.369 4.593 0.0 26.9 Offset to outside (roadside) barrier (feet) 3.321 4.379 0.0 20.6 Width of unobstructed median (feet) 12.300 16.139 1.5 96.4 Variable Proportion in Database Proportion of freeway segments 0.75 Proportion of ramp entrance speed-change lane sites 0.13 Proportion of ramp exit speed-change lane sites 0.12 Proportion of Minnesota sites 0.05 Proportion of Georgia sites 0.20 Proportion of Virginia sites 0.58 Proportion of Hawaii sites 0.17 Proportion of left-side PTSU facility sites 0.09 Proportion of right-side PTSU facility sites 0.33 This project’s dataset only included 34 left-side PTSU sites. Additional left-side PTSU sites exist in the United States, but they could not be studied for this project because they were (a) new and did not have sufficient crash history or (b) were located in states with insufficient crash data quality for statistical analysis. Crash Frequency Models The total number of crashes at each site was used as the dependent variable in the model. The AADT on the freeway, horizontal curvature, presence of speed-change lanes, presence of PTSU lanes, cross section dimensions (e.g., lane, shoulder, and median width), rumble strip presence, and other site-specific features were considered as candidate independent variables for inclusion in the model. In addition, state indicator variables were included in the model to control for differences in crash reporting among the agencies represented in the database.

200 The site length was assumed to be directly proportional to the number of total crashes and was included as an offset variable in the model. Additionally, since the number of crashes observed at each location was for some predefined time period (e.g., between 3 to 5 years), the amount of time that crash data were available at each location was also included as an offset variable to ensure that the model accurately predicted the annual average crash frequency. Indicator variables for the presence of left-side and right- side PTSU were specifically included in the model to provide a basis for answering Question 4. The resulting model for PTSU sites is shown in Table 84. The candidate independent variables shown in Table 83 were entered into the model in the form shown in Equation 214. In addition, new variables (like those described in Equation 205 to Equation 211) were created to either (a) account for combinations of elements within the same sites, or (b) create functional forms more consistent with the HSM Supplement (AASHTO 2014). Equation 214 ln 𝑁 ln 𝑦 ln 𝐿 𝑏 𝑏 ln 𝐴𝐴𝐷𝑇 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 𝑏 𝑓 𝑏 𝑓 𝑏 𝑊 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 𝑏 𝐼 where, Np = predicted average crash frequency for site (crashes); y = number of years (years); Ls = site length (miles); pk = proportion of traffic at site for hour k; AADT = annual average daily traffic volume (veh/day); IENSCL = indicator variable for sites that are ramp entrance speed-change lanes; IEXSCL = indicator variable for sites that are ramp exit speed-change lanes; IDS = indicator variable for dynamic signs; ISS = indicator variable for static signs; fmw = median width factor; frb = roadside barrier factor; Wrs = width of right shoulder (feet); ILPTSU = indicator for left-side PTSU presence on a site; IRPTSU = indicator for right-side PTSU presence on a site; IVA = indicator variable for sites in Virginia; IGA = indicator variable for sites in Georgia; IHI = indicator variable for sites in Hawaii; and b0, …, bn = estimable regression coefficients for independent variables at site.

201 Table 84. Fixed parameters model of total crashes for PTSU sites. Variable Coefficient Std. Error t-statistic p-value b0: Constant −17.266 2.361 −7.312 <0.001 b1: Natural logarithm of directional annual average daily traffic 1.875 0.209 8.965 <0.001 b2: Indicator for presence of ramp entrance speed-change lane (1 if entrance speed-change lane site; 0 otherwise) −0.076 0.144 −0.525 0.599 b3: Indicator for presence of ramp exit speed-change lane (1 if exit speed-change lane site; 0 otherwise) 0.562 0.150 3.752 <0.001 b4: Indicator for dynamic sign presence in the site (1 if dynamic signs are present in site; 0 otherwise) 0.248 0.161 1.536 0.125 b5: Indicator for static sign presence in the site (1 if static signs are present in site; 0 otherwise) 0.230 0.200 1.150 0.250 b6: Variable for median width (fmw) −0.017 0.011 −1.511 0.131 b7: Variable for roadside barrier (frb) 0.330 0.134 2.465 0.014 b8: Total right shoulder width (feet) −0.015 0.012 −1.187 0.235 b9: Indicator for PTSU facility on left-side of freeway (1 if PTSU facility on left-side of freeway; 0 otherwise) −0.182 0.206 −0.881 0.378 b10: Indicator for PTSU facility on right-side of freeway (1 if PTSU facility on right-side of freeway; 0 otherwise) 0.219 0.155 1.413 0.158 b11: Indicator for Virginia (1 if site is located in Virginia; 0 otherwise) −0.347 0.227 −1.529 0.126 b12: Indicator for Georgia (1 if site is located in Georgia; 0 otherwise) −0.897 0.267 −3.353 <0.001 b13: Indicator for Hawaii (1 if site is located in Hawaii; 0 otherwise) −1.658 0.263 −6.308 <0.001 Overdispersion parameter (𝛼) 0.527 0.042 12.491 <0.001 Number of observations: 312 2 × Log-likelihood: −2470.116 McFadden Pseudo R2: 0.111 Results The effect of PTSU presence is captured in four variables. These variables include the two variables associated with the b4 and b5 coefficients related to sign type, and the two variables associated with the b9 and b10 coefficients indicating which shoulder is used for PTSU. All facilities with static or dynamic signs are PTSU facilities (as defined for this project’s database). Therefore, a site with PTSU has one of the following conditions:  Right-side PTSU with static signing  Right-side PTSU with dynamic signing  Left-side PTSU with static signing  Left-side PTSU with dynamic signing Given the characteristics described in the previous paragraph, the indicators for right-side PTSU and left-side PTSU in the model in Table 84 cannot be used by themselves to assess the safety of PTSU presence (on the right or the left side) versus a comparison facility without PTSU. However, these indicators can be used to infer the safety effect of changing PTSU from one side of the freeway to the other. If right-side PTSU is assumed as a base condition, sites with left-side PTSU are estimated to have 33 percent fewer crashes {= 100×[exp(−0.182 − 0.219) −1]}. The standard error associated with this difference is estimated as 0.258 (= [0.2062 + 0.1552]0.5) and the p-value is 0.120. Based on these statistics,

202 the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.120 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. The results described in the previous paragraph are obtained from a fixed parameters model of total crash frequency. A random parameters model was developed for FI crash frequency using the same database. Indicators for both left-side PTSU and right-side PTSU were included in the model. This model is described in Chapter 7, Advanced Predictive Models. If right-side PTSU is assumed as a base condition, sites with left-side PTSU are estimated to have 16 percent fewer crashes {= 100×[exp(0.024 − 0.203) −1]}. The standard error associated with this difference is estimated as 0.146 (= [0.1172 + 0.0872]0.5), and the p-value is 0.220. Based on these statistics, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.220 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. Other research conducted for this project provides a secondary means of assessing the safety effect of left-side versus right-side PTSU operation. Specifically, an analysis of sites with static PTSU operation (discussed in the Question 5b section below) found that left-side PTSU was associated with 39 percent fewer total crashes compared to right-side PTSU. The null hypothesis that this value equals 0.0 can be rejected at a 5 percent significance level. The probability the observed coefficient value is this large because of random variation (when the true value equals 0.0) is only 0.020. Collectively, these results indicate that left-side PTSU is generally associated with fewer crashes than right-side PTSU. The evidence is strongest for sites with static PTSU operation. However, the magnitude of the inferred effect of changing from right-side to left-side PTSU is larger than expected and not supported by other research. Therefore, additional research is needed to confirm that this effect is (a) truly a result of the side on which the PTSU operates (and not a result of other unobserved variables) and (b) consistent for all sites at which PTSU operation is shifted from the right to the left side (and not limited to sites with static PTSU operation). Question 5a: Safety Effect of Dynamic Signage Question 5a: What is the safety effect of using dynamic signs as opposed to static signs? Dynamic signs are electronic and change their display when the shoulder is open or closed. Typically, a dynamic sign uses a green arrow to indicate the shoulder is open and a red X to indicate the shoulder is closed. Static signs are metal and list the days and hours in which the shoulder is open. Empirical Setting and Crash Frequency Models An observational before-after study would be the preferred method to answer Question 5a. However, no facilities were identified that underwent this conversion. As a result, the analysis for this question employed a with-without comparison study using a cross-sectional data. The data summarized in Table 83, along with the regression model shown in Table 84, was used to compare the safety performance of facilities with static signs to those PTSU facilities with dynamic signs. Results The effect of PTSU presence is captured in four variables. These variables include the two variables associated with the b4 and b5 coefficients related to sign type, and the two variables associated with the b9 and b10 coefficients indicating which shoulder is used for PTSU. All facilities with static or dynamic signs are PTSU facilities. Therefore, a site with PTSU will have one of the following conditions:

203  Right-side PTSU with static signing  Right-side PTSU with dynamic signing  Left-side PTSU with static signing  Left-side PTSU with dynamic signing Given the characteristics described in the previous paragraph, the indicators for static signs and dynamic signs in the model in Table 84 cannot be used by themselves to assess the safety of PTSU presence (with static or dynamic signs) versus a comparison facility without PTSU. However, these indicators can be used to infer the safety effect of changing sign type on a PTSU facility from static to dynamic. If the static sign is assumed to be the base condition, sites with dynamic signs are estimated to have 2 percent more crashes {= 100×[exp(0.248 − 0.230) −1]}. The standard error associated with this difference is estimated as 0.257 (= [0.1612 + 0.2002]0.5), and the p-value is 0.944. Based on these statistics, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.944 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. Based on the results of this analysis, it is concluded that there is no meaningful difference between the total crash frequency of sites with static signs and those with dynamic signs, all other variables being the same. It is unlikely that the conversion from static signs to dynamic signs on a PTSU site will have a meaningful effect on total crash frequency. Question 5b: Safety Effect of Dynamic PTSU Questions 5b: What is the safety effect of converting static operation to dynamic operation? This question relates to PTSU facilities only. D-PTSU operation has variable hours of operation such that the days and times at which the shoulder is open can vary. By definition, D-PTSU facilities must have dynamic signs. S-PTSU operation has fixed hours of operation. Some S-PTSU facilities have dynamic signs, and others have static signs. The EB before-after study design was used to answer this question. This study design is described previously in this chapter in the Overview of Statistical Modeling Approach section. The empirical setting and results of the evaluation are described in this section. Empirical Setting and Crash Frequency Models The first step of the EB before-after study design requires the development of an SPF using a group of reference sites which, in this case, were the sites associated with S-PTSU facilities. These facilities were never converted to D-PTSU operation. The general form of the SPF is shown in Equation 215. Equation 215 𝑁 , 𝐿 , 𝐴𝐴𝐷𝑇𝑖𝑏𝐴𝐴𝐷𝑇 exp 𝑏 𝑥 , 𝑏 where Np,i = the predicted average crash frequency for site i (crashes/year); Ls,i = length of site i (miles); AADT,i = annual average daily traffic volume for site i (veh/day);  b0, …, bn = estimable regression coefficients for independent variable j, j = 1, …, n; and xi,j = roadway or roadside side feature for site i and independent variable j. The data collected for S-PTSU sites were used to estimate the reference group SPF. The site types considered include: freeway segments, ramp entrance speed-change lane sites, and ramp exit speed- change lane sites. Comparison sites were not used. Sites that were converted from S-PTSU to D-PTSU

204 were not included in the estimation data. There are a total of 123 site observations in the database. A summary of these data is shown in Table 85. Table 85. Descriptive statistics of sites with static PTSU. Variable Mean Standard Deviation Minimum Maximum Total crashes (5 years) 39.76 50.37 0 298 Site length (miles) 0.26 0.20 0.02 0.93 Directional annual average daily traffic (veh/day) 83,052 16,573 44,214 147,163 Number of lanes per direction 3.84 0.68 3 6 Degree of curvature per mile 0.37 0.66 0 2.91 Lane width (feet) 11.76 0.36 10.90 13.00 Total right shoulder width (feet) 13.15 4.82 0.26 28.76 Total left shoulder width (feet) 9.16 3.49 1.52 18.19 Proportion of site length with left-side (inside) rumble strips 0.34 0.47 0 1 Proportion of site length with right-side (outside) rumble strips 0 0 0 0 Proportion of site length with outside (roadside) barrier 0.43 0.38 0 1 Proportion of site length with median (inside) barrier 0.98 0.13 1 1 Variable Proportion in Database Proportion of freeway segments 0.80 Proportion of ramp entrance speed-change lane sites 0.10 Proportion of ramp exit speed-change lane sites 0.11 Proportion of Minnesota sites 0.00 Proportion of Virginia sites 0.56 Proportion of Hawaii sites 0.22 Proportion of Georgia sites 0.22 Proportion of left-side PTSU facility sites 0.15 Proportion of right-side PTSU facility sites 0.85 The total number of crashes on the S-PTSU sites was used as the dependent variable in the SPF. The AADT, horizontal curvature, presence of speed-change lanes, presence of right-side PTSU operation, presence of left-side PTSU operation, cross section dimensions (e.g., lane, shoulder, and median width), rumble strips presence, and other site-specific features were considered as candidate independent variables for inclusion in the model. The site length was assumed to be directly proportional to the number of total crashes and was included as an offset variable in the model. Additionally, since the number of crashes observed at each location was for some predefined time period (e.g., between 3 to 5 years), the amount of time that crash data were available at each location was also included as an offset variable to ensure that the model accurately predicted annual average crash frequency. Results The reference group SPF is shown in Table 86. This SPF was used to estimate crash frequency on the set of sites that were converted from S-PTSU to D-PTSU. These sites are located on I-66 in Virginia and I-85 in Georgia. On I-66, S-PTSU to D-PTSU conversion included the replacement of cantilever structures over the shoulder with gantries spanning the entire roadway that provide lane control signals for all lanes for incident management purposes. The D-PTSU system on I-66, while appearing different to drivers than the S-PTSU system, is similar to other D-PTSU systems opened in recent years. On I-85, S-

205 PTSU to D-PTSU conversion was undertaken with no infrastructure changes. Both sites had dynamic signs during the S-PTSU operational period. Table 86. Fixed parameters model of total crashes for sites with static PTSU. Variable Coefficient Std. Error t-statistic p-value b0: Constant −19.789 4.544 −4.355 < 0.001 b1: Natural logarithm of directional annual average daily traffic 2.082 0.401 5.189 < 0.001 b2: Indicator for presence of ramp entrance speed-change lane (1 if entrance speed-change lane site; 0 otherwise) −0.064 0.228 −0.279 0.780 b3: Indicator for presence of ramp exit speed-change lane (1 if exit speed-change lane site; 0 otherwise) 0.509 0.219 2.320 0.020 b4: Indicator for presence of PTSU operation on the left- hand side (1 if PTSU is on the left-hand side; 0 otherwise) −0.487 0.209 −2.330 0.020 b5: Indicator for site in Georgia (1 if true; 0 otherwise) −0.458 0.170 −2.694 0.007 b6: Indicator for site in Hawaii (1 if true; 0 otherwise) −0.916 0.200 −4.570 < 0.001 Overdispersion parameter (𝛼) 0.470 0.056 8.393 < 0.001 Number of observations: 123 2 × Log-likelihood: −1037.139 McFadden Pseudo R2: 0.101 An EB-adjusted estimate of the “expected crash frequency if no treatment (i.e., conversion to D-PTSU) had been applied” was then computed using Equation 194 through Equation 197. Then, using Equation 198, this estimate was compared with the observed crash frequency after the treatment was applied to assess the safety effect conversion from static to dynamic operation. The results are provided in Table 87. Table 87. Total crash frequency CMF for converting PTSU site from static to dynamic operation. Observed Crash Count in After Period EB Estimate of Total Crash Count in After Period CMF Standard Error 2,652 2,858 0.927 0.0243 The results shown in Table 87 show that converting a PTSU site from static to dynamic operation is associated with a CMF value of 0.927. This value corresponds to a 7.3 percent reduction in total crash frequency. The null hypothesis that this value equals 1.0 can be rejected at a 5 percent significance level. The probability the observed CMF value is this small because of random variation (when the true value equals 1.0) is only 0.004. Based on the results of this analysis, it is concluded that converting from S-PTSU to D-PTSU operation decreases total crash frequency by about 7.3 percent. Question 6: Safety Effect of Shoulder Width Questions 6: What is the safety effect of changing the width of the shoulder used for travel? This question is applicable to both BOS and PTSU facilities. However, as discussed earlier in this chapter in the Question 1 section, the analysis of crash data indicated that BOS operation is unlikely to have a meaningful influence on total or FI crash frequency. Hence, an answer to the question of whether a

206 change in the width of the shoulder used for BOS travel has an effect on freeway safety is considered to be of no practical value. Therefore, this section addresses the question of whether a change in the width of the shoulder used for PTSU travel has an effect on freeway safety. Empirical Setting Data collected for freeway facilities with PTSU operation were used to answer this question. Comparison sites were not used. For the purposes of answering this question, “shoulder width” was defined to include both the portion of the shoulder used for PTSU travel, as well as the portion of the shoulder beyond this (i.e., beyond the second edge line) that is never used for travel. The dataset included three site types. The site types considered include: freeway segments, ramp entrance speed-change lane sites, and ramp exit speed-change lane sites. A summary of the pertinent features of these data is shown in Table 88. There are a total of 153 site observations in the database. Table 88. Descriptive statistics of sites with PTSU. Variable Mean Standard Deviation Minimum Maximum Total crashes (5 years) 40.24 50.21 0 298 Site length (miles) 0.272 0.207 0.023 0.929 Directional annual average daily traffic (veh/day) 82,294 11,336 44,214 102,093 Number of lanes per direction 3.48 0.60 3 5 Degree of curvature per mile 1.98 7.48 0 75.10 Lane width (feet) 11.81 0.37 10.9 12.9 Total right shoulder width (feet) 13.61 5.30 1.7 28.8 Total left shoulder width (feet) 9.39 3.21 1.5 18.3 Proportion of site length with left-side (inside) rumble strips 0.20 0.40 0.0 1.0 Proportion of site length with right-side (outside) rumble strips 0 0 0 0 Proportion of site length with outside (roadside) barrier 0.65 0.32 0.0 1.0 Proportion of site length with median (inside) barrier 1.0 0.0 1.0 1.0 Variable Proportion in Database Proportion of freeway segments 0.75 Proportion of ramp entrance speed-change lane sites 0.11 Proportion of ramp exit speed-change lane sites 0.14 Proportion of Minnesota sites 0.03 Proportion of Virginia sites 0.78 Proportion of Hawaii sites 0.09 Proportion of Georgia sites 0.10 Proportion of left-side PTSU facility sites 0.12 Proportion of right-side PTSU facility sites 0.88 Crash Frequency Models Regression analysis was used to estimate a model for predicting total crash frequency for the PTSU sites. The total number of crashes at the PTSU sites was used as the dependent variable in the model. The AADT, horizontal curvature, presence of speed-change lanes, presence of right-side PTSU operation, presence of left-side PTSU operation, cross section dimensions (e.g., lane, shoulder, and median width),

207 rumble strips presence, and other site-specific features were considered as candidate independent variables for inclusion in the model. The site length was assumed to be directly proportional to the number of total crashes and was included as an offset variable in the model. Additionally, since the number of crashes observed at each location was for some predefined time period (e.g., between 3 to 5 years), the amount of time that crash data were available at each location was also included as an offset variable to ensure that the model accurately predicted annual average crash frequency. The estimated model for PTSU sites is shown in Table 89. The candidate independent variables shown in Table 88 were entered into the model in the form shown in Equation 216. In addition, new variables (like those described in Equation 205 to Equation 211) were created to either (a) account for combinations of elements within the same sites, or (b) create functional forms consistent with the HSM Supplement (AASHTO 2014). Equation 216 ln 𝑁 ln 𝑦 ln 𝐿 𝑏 𝑏 ln 𝐴𝐴𝐷𝑇 𝑏 𝐼 𝑏 𝐼 𝑏 𝑓 𝑏 𝑊 1 𝑃𝑇𝑆𝑈 𝑏 𝑊 𝑃𝑇𝑆𝑈 where, Np = predicted average crash frequency for site (crashes); y = number of years (years); Ls = site length (miles); AADT = annual average daily traffic volume (veh/day); IENSCL = indicator variable for sites that are ramp entrance speed-change lanes; IEXSCL = indicator variable for sites that are ramp exit speed-change lanes; frb = roadside barrier factor; Wrs = width of right shoulder (feet); PTSURIGHT = indicator for right-side PTSU presence on a site; IVA = indicator variable for sites in Virginia; IGA = indicator variable for sites in Georgia; IHI = indicator variable for sites in Hawaii; and b0, …, bn = estimable regression coefficients for independent variables at site. Table 89. Fixed parameters model of total crashes for PTSU sites. Variable Coefficient Std. Error t-statistic p-value b0: Constant −10.605 4.433 −2.393 0.017 b1: Natural logarithm of directional annual average daily traffic 1.263 0.391 3.231 0.001 b2: Indicator for presence of ramp entrance speed-change lane (1 if entrance speed-change lane site; 0 otherwise) −0.105 0.207 −0.506 0.613 b3: Indicator for presence of ramp exit speed-change lane (1 if exit speed-change lane site; 0 otherwise) 0.387 0.195 1.979 0.048 b4: Variable for roadside barrier (frb) 0.680 0.178 3.819 < 0.001 b5: Right shoulder width for sites without PTSU operation on the right-hand side −0.032 0.028 −1.131 0.258 b6: Right shoulder width for sites with PTSU operation on the right-hand side −0.023 0.013 −1.835 0.064 Overdispersion parameter (𝛼) 0.478 0.051 9.373 < 0.001 Number of observations: 153 2 × Log-likelihood: −1306.249 McFadden Pseudo R2: 0.093

208 Results The model shown in Table 89 is used to answer the question about the safety effect of changing shoulder width. The right-side shoulder width variable for “sites without PTSU operation on the right side” has a coefficient value of −0.032. However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.258 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. The right-side shoulder width variable for “sites with right side PTSU” has a coefficient value of −0.023. However, the null hypothesis that this value equals 0.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.064 that a coefficient value this large could be observed due to random variation when the true value equals 0.0. The coefficients associated with these variables can be interpreted using the following equations: Right shoulder without PTSU: 𝑒 . Right shoulder with PTSU: 𝑒 . Both equations indicate that sites with wide right shoulders are associated with fewer total crashes than sites with narrow right shoulders, all other factors being the same. For sites without PTSU, a site with a shoulder that is 1 foot wider than another site is predicted to have 3.1 percent fewer crashes. For sites with PTSU, a site with a shoulder that is 1 foot wider than another site is predicted to have 2.3 percent fewer crashes. The crash prediction model for PTSU sites described in Chapter 5 includes an AF for PTSU lane width. The shoulder width used in this AF is defined as the width of the portion of the shoulder used for travel; it does not distinguish between right-side and left-side PTSU. The computed AF value exhibits a trend that is very similar to that described in the previous paragraph and, as shown in Chapter 5, is very similar to the AFs reported in the HSM Supplement (AASHTO 2014). Based on these results, it is concluded that changing the width of the right shoulder on right-side PTSU facilities is associated with a change in crash frequency. An increase in 1 foot of right shoulder width is associated with a 2.3 percent reduction in crash frequency, all other factors being the same. This magnitude of the change is consistent with that reported in the HSM Supplement (AASHTO 2014). It should be noted that regression models were also developed to explore the relationship between left side shoulder width and crash frequency. However, given the small number of sites with left-side PTSU, the results were neither statistically significant nor practically meaningful. Question 7: Safety Effect of PTSU on Severity Question 7: Are fatal and severe injury crashes over-represented during overnight hours like a typical urban freeway, or does shoulder use change this relationship? To answer this question, separate BOS and PTSU crash severity data files were developed. Site characteristics were appended to each crash event that was observed on BOS and PTSU facilities during the analysis period. As such, the unit of analysis is the severity outcome for each observed crash. The general methodological framework developed to answer this question is as follows:  Step 1: Develop a statistical model of the likelihood that a specific crash results in a fatal or severe injury outcome for BOS or PTSU facilities, which include an indicator for nighttime travel periods, as well as traffic volume and other site-specific characteristics.  Step 2: Repeat Step 1 for BOS and PTSU comparison sites, which are assumed to be typical urban freeways.

209  Step 3: Compare the ratio of the nighttime indicators results from Steps 1 and 2 to determine if there is difference in nighttime crash severities among BOS or PTSU facilities and comparable non-BOS or non-PTSU facilities. For this analysis, crashes that were reported between 10:00 PM and 4:59 AM were defined as nighttime events, while crashes that were reported between 8:00 AM and 3:59 PM were defined as daytime period crashes. Because data from several states were included in the analysis, these time periods were chosen so that daytime and nighttime periods were defined the same across different latitudes and seasons of the year. Crashes that were reported outside of these time periods were not included in this analysis. Binary logistic regression was used to estimate the severity models described in Steps 1 and 2. With one exception, the KABCO severity scale was used to define severities in all states represented in the database. The exception was Hawaii. This state defines only three severity categories (fatal, injury, and property-damage only). For this analysis, K (fatal), A (incapacitating injury), and B (non-incapacitating injury) crash severity categories were used to define the fatal-and-severe-injury category. Hawaii data were not used to answer Question 7. An overview of the analysis methodology is described in the Overview of Statistical Modeling Approach section earlier in this chapter. Empirical Setting Two databases were developed for answering Question 7. One database was developed for the PTSU analysis, and a second database was developed for the BOS analysis. A summary of the data used for the PTSU analysis is provided in Table 90. There are 9,521 crashes in the PTSU database (excluding Hawaii). Approximately 20 percent of the crashes were classified as K, A, or B severity. Approximately 20.6 percent of the crashes occurred during nighttime periods defined for this analysis, while approximately 35.7 percent were reported during the daytime hours defined for this analysis.

210 Table 90. Summary of PTSU crash severity data. Variable Mean Standard Deviation Minimum Maximum Directional annual average daily traffic (veh/day) 88,453 24,007 31,401 147,207 Number of lanes per direction 4.07 1.03 3 7 Lane width (feet) 11.93 0.40 11.26 14.15 Right shoulder width (feet) 7.23 4.57 0.25 21.13 Left shoulder width (feet) 9.49 4.26 1.24 23.52 Right shoulder to PTSU lane (feet) 4.68 5.59 0.0 15.47 Left shoulder to PTSU lane (feet) 0.88 3.25 0.0 14.01 Proportion of site length with left-side (inside) rumble strips 0.24 0.41 0.0 1.00 Proportion of site length with right-side (outside) rumble strips 0.11 0.30 0.0 1.00 Proportion of site length with outside (roadside) barrier 0.68 0.31 0.0 1.00 Proportion of site length with median (inside) barrier 0.91 0.26 0.0 1.00 Offset to median (inside) barrier (feet) 0.13 0.37 0.0 2.11 Offset to outside (roadside) barrier (feet) 2.63 3.50 0.0 20.58 Width of unobstructed median (feet) 14.60 20.06 1.51 96.41 Variable Proportion in Database Fatal Crashes 0.0011 A-injury Crashes 0.0241 B-injury Crashes 0.1772 C-injury Crashes 0.0938 Property-damage Only 0.7039 Nighttime Crashes 0.2062 Daytime Crashes 0.3574 Multi-vehicle Crashes 0.9039 Single-vehicle Crashes 0.0961 Proportion of freeway segments 0.8694 Proportion of ramp entrance speed-change lane sites 0.0631 Proportion of ramp exit speed-change lane sites 0.0674 Proportion of sites with a lane drop 0.0665 A summary of the data used for the BOS analysis is shown in Table 91. There are 6,776 crashes in the BOS database. Nearly 11 percent of the crashes were classified as K, A, or B severity. Approximately 34.0 percent of the crashes occurred during nighttime periods defined for this analysis, while approximately 32.1 percent were reported during the daytime hours defined for this analysis.

211 Table 91. Summary of BOS crash severity data. Variable Mean Standard Deviation Minimum Maximum Directional annual average daily traffic (veh/day) 53,456 16,726 15,370 95,106 Number of lanes per direction 3.23 0.79 2 5 Degree of curvature per mile 2.66 7.10 0 72.60 Lane width (feet) 11.88 0.32 11.18 14.39 Right shoulder width (feet) 11.04 1.50 4.90 18.95 Left shoulder width (feet) 9.65 3.64 2.41 21.36 Proportion of site length with left-side (inside) rumble strips 0.50 0.48 0.0 1.0 Proportion of site length with right-side (outside) rumble strips 0.51 0.48 0.0 1.0 Proportion of site length with outside (roadside) barrier 0.33 0.31 0.0 1.0 Proportion of site length with median (inside) barrier 0.90 0.25 0.0 1.0 Offset to median (inside) barrier (feet) 1.50 3.38 0.0 22.98 Offset to outside (roadside) barrier (feet) 2.94 4.33 0.0 22.90 Width of unobstructed median (feet) 14.04 13.47 1.17 60.29 Variable Proportion in Database Fatal Crashes 0.0021 A-injury Crashes 0.0096 B-injury Crashes 0.0978 C-injury Crashes 0.1434 Property-damage Only 0.7469 Nighttime Crashes 0.3396 Daytime Crashes 0.3214 Multi-vehicle Crashes 0.7450 Single-vehicle Crashes 0.2550 Proportion of freeway segments 0.8590 Proportion of ramp entrance speed-change lane sites 0.0790 Proportion of ramp exit speed-change lane sites 0.0620 Proportion of sites with a lane drop 0.0530 The variables shown in Table 90 and Table 91 were entered into the severity model in the form shown in Equation 203. In addition, new variables were created to either (a) account for combinations of elements within the same sites, or (b) create functional forms consistent with the HSM Supplement (AASHTO 2014). Some of these new variables are in Equation 205 to Equation 211. Two additional variables are summarized in the following equations: Equation 217 𝑓 𝑊 1 𝑃 where frsw is the factor for right shoulder width; Wos is the outside shoulder width and Por is the proportion of the site length with outside rumble strips. Equation 218 𝑓 𝑊 1 𝑃 where flsw is the factor for left shoulder width; Wis is the inside shoulder width and Pir is the proportion of the site length with inside rumble strips. PTSU Severity Prediction Models The fatal-and-severe-injury severity models for PTSU sites and comparison sites are described in this section. The odds ratio for each model variable is computed as odds ratio = exp(bi). An odds ratio greater

212 than 1.0 indicates that the odds of a crash being a fatal or severe crash increases as the value of the independent variable increases (or changes from zero to unity for an indicator variable). An odds ratio less than 1.0 indicates that the odds of a crash being a fatal or severe crash decreases as the value of the independent variable decreases (of changes from unity to zero for an indicator variable). The model in Table 92 was estimated using only freeway segments on PTSU facilities. Only crashes that occurred during the daytime and nighttime periods were considered in the model. A total of 1,827 total crashes were included in the database used to estimate the model. Table 92. Fatal-and-severe-injury crash severity model for PTSU freeway segments. Variable Odds Ratio Std. Error t-statistic p-value Constant 0.285 0.175 −2.05 0.041 Directional annual average daily traffic (veh/day) 1.000 0.000001 −1.91 0.056 Nighttime indicator (1 if crash occurred at night; 0 if crash occurred during the daytime) 0.879 0.139 −0.82 0.414 Variable for right shoulder width (frsw) 1.075 0.018 4.29 <0.001 Variable for left shoulder width (flsw) 0.993 0.014 −0.48 0.630 Number of observations: 1,827 Log-likelihood at convergence: −910.53 McFadden Pseudo R2: 0.0167 The model in Table 93 was estimated using only freeway segments on comparison facilities. Only crashes that occurred during the daytime and nighttime periods were considered in the model. A total of 1,249 crashes were included in the database used to estimate the model. The model specification that was used to estimate the model shown in Table 92 was also used to estimate the comparison segment model. Table 93. Fatal-and-severe-injury crash severity model for comparison freeway segments. Variable Odds Ratio Std. Error t-statistic p-value Constant 0.857 0.254 −0.52 0.601 Directional annual average daily traffic (veh/day) 1.000 0.00003 −4.01 <0.001 Nighttime indicator (1 if crash occurred at night; 0 if crash occurred during the daytime) 0.822 0.144 −1.12 0.264 Variable for right shoulder width (frsw) 1.006 0.024 0.25 0.800 Variable for left shoulder width (flsw) 0.984 0.019 −0.81 0.418 Number of observations: 1,249 Log-likelihood at convergence: −650.61 McFadden Pseudo R2: 0.0156 In addition to the “independent” models shown in Table 92 and Table 93, another PTSU severity model was also estimated by “matching” segments where crashes were observed. This matching approach was used to control for differences in traffic volume, roadway geometry, and roadside geometry along segments. As such, the only differences at the segment were the time of day and the presence of a PTSU facility. The time of day (nighttime versus daytime) and the site type (PTSU versus comparison) were included in a binary logit model as an interaction term. The resulting model is shown in Table 94.

213 Table 94. Fatal-and-severe-injury crash severity model for matched PTSU freeway segments. Variable Odds Ratio Std. Error t-statistic p-value Constant 0.146 0.156 −1.80 0.072 PTSU comparison-nighttime Interaction 0.922 0.174 −0.43 0.668 PTSU-daytime Interaction 1.155 0.245 0.68 0.498 PTSU-nighttime Interaction 1.904 0.459 2.67 0.008 PTSU comparison-daytime Interaction -- -- -- -- Number of observations: 2,978 Log-likelihood at convergence: −1,473.9 McFadden Pseudo R2: 0.0567 While this analysis controls for traffic volume, roadway design, and roadside features, there are sites that experience either no nighttime or no daytime crashes, so these sites are not included in model. As such, their nighttime and daytime crashes are not considered in model estimation. PTSU Results The odds ratios provided in the previous section are evaluated in this section. Specifically, they are used to determine if fatal-and-severe-injury crashes are over-represented during nighttime hours on freeways with PTSU. The results of this evaluation are described in the following three subsections. Independent Crash Severity Models In the model shown in Table 93, the odds of a fatal or severe crash outcome are 17.8 percent lower at night than they are in the daytime on comparison segments. This percentage is based on the odds ratio of 0.822. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.264 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. In the model shown in Table 92, the odds of a fatal or severe crash outcome are 12.1 percent lower at night than they are in the daytime on PTSU segments. This percentage is based on the odds ratio of 0.879. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.414 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. Matched Crash Severity Models In the model shown in Table 94, the baseline is a comparison segment-daytime interaction. The comparison-nighttime interaction odds ratio is 0.922. This value indicates that the odds of a fatal or severe injury outcome are lower at night at comparison segments related to the daytime period. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.668 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. The PTSU-daytime interaction odds ratio is 1.155. This value indicates that the odds of a fatal or severe crash outcome are higher at PTSU segments during the daytime than it is at comparison segments during the daytime. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.498 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. The PTSU-nighttime interaction odds ratio is 1.904. This value indicates that the odds of a fatal or severe injury crash are higher for this scenario relative to the comparison segment daytime scenario. The

214 null hypothesis that this value equals 1.0 can be rejected at a 5 percent significance level. The probability the odds ratio is this large because of random variation (when the true value equals 1.0) is only 0.008. These last two odds ratios can be compared to determine the odds of a fatal or severe crash outcome at night relative to the daytime on PTSU segments. This comparison is based on the ratio of these two odds ratios. This ratio is 1.65 (= 1.904/1.155). Its standard error is computed as 0.529 (= 1.904/1.155 ×[(0.459/1.904)2 + (0.245/1.155)2]0.5), and its p-value is computed as 0.120. The null hypothesis that the value of 1.65 equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.12 that a ratio this large could be observed due to random variation when the true value equals 1.0. Summary Based on the results of this analysis, fatal-and-severe-injury crashes are underrepresented at the comparison segments based on their proportion of daily crashes. The computed odds ratios suggest that the odds of a fatal or severe injury outcome at night are between 82.2 and 92.2 percent of that for a daytime crash. However, it is noted that neither odds ratio is statistically significant at a 5 percent significance level. The results of the analysis are not as consistent the PTSU segments as they are for the comparison segments. For PTSU segments, the computed odds ratios suggest that the odds of a fatal or severe injury outcome at night is between 87.9 and 165 percent of that for a daytime crash. Neither odds ratio is statistically significant at a 5 percent significance level. Given the wide range in values obtained from this analysis, additional research is needed to determine whether PTSU presence has an effect on the distribution of crash severity by time of day. BOS Severity Prediction Models The fatal-and-severe-injury severity models for BOS sites and comparison sites are described in this section. The odds ratio for each model variable is computed as odds ratio = exp(i). An odds ratio greater than 1.0 indicates that the odds of a crash being a fatal or severe crash increases as the value of the independent variable increases (or changes from zero to unity for an indicator variable). An odds ratio less than 1.0 indicates that the odds of a crash being a fatal or severe crash decreases as the value of the independent variable decreases (of changes from unity to zero for an indicator variable). The model in Table 95 was estimated using only freeway segments on BOS facilities. Only crashes that occurred during the daytime and nighttime periods were considered in the model. A total of 2,984 total crashes were included in the database used to estimate the model. Table 95. Fatal-and-severe-injury crash severity model for BOS freeway segments. Variable Odds Ratio Std. Error t-statistic p-value Constant 0.232 0.068 −4.97 <0.001 Directional annual average daily traffic (veh/day) 1.000 0.000001 −0.15 0.879 Nighttime indicator (1 if crash occurred at night; 0 if crash occurred during the daytime) 1.060 0.131 0.48 0.634 Multi-vehicle crash indicator (1 if crash involved more than one vehicle; 0 if crash was a single-vehicle collision) 0.679 0.088 −2.98 0.003 Variable for right shoulder width 0.967 0.018 −1.87 0.061 Variable for left shoulder width 0.946 0.021 −2.52 0.012 Number of observations: 2,984 Log-likelihood at convergence: −1,061.51 McFadden Pseudo R2: 0.0214

215 The model in Table 96 was estimated using only freeway segments on comparison facilities. Only crashes that occurred during the daytime and nighttime periods were considered in the model. A total of 897 crashes were included in the database used to estimate the model. The model specification that was used to estimate the model shown in Table 95 was also used to estimate the comparison segment model. Table 96. Fatal-and-severe-injury crash severity model for comparison freeway segments. Variable Odds Ratio Std. Error t-statistic p-value Constant 0.231 0.125 −2.71 0.007 Directional annual average daily traffic (veh/day) 1.000 0.00001 −1.05 0.292 Nighttime indicator (1 if crash occurred at night; 0 if crash occurred during the daytime) 1.084 0.222 0.39 0.694 Multi-vehicle crash indicator (1 if crash involved more than one vehicle; 0 if crash was a single-vehicle collision) 0.774 0.157 −1.26 0.207 Variable for right shoulder width 0.953 0.056 −0.83 0.405 Variable for left shoulder width 1.118 0.070 1.78 0.076 Number of observations: 897 Log-likelihood at convergence: −358.34 McFadden Pseudo R2: 0.0156 In addition to the “independent” models shown in Table 95 and Table 96, another BOS severity model was also estimated by “matching” segments where crashes were observed. This matching approach was used to control for differences in traffic volume, roadway geometry, and roadside features along segments. As such, the only differences at the segment were the time of day and the presence of a BOS facility. The time of day (nighttime versus daytime) and the site type (BOS versus comparison) were included in a binary logit model as an interaction term. The resulting model is shown in Table 97. Table 97. Fatal-and-severe-injury crash severity model for matched BOS freeway segments. Variable Odds Ratio Std. Error t-statistic p-value Constant 0.279 0.101 −3.54 <0.001 BOS Comparison-Nighttime Interaction 0.837 0.191 −0.78 0.436 BOS-Daytime Interaction 0.559 0.221 −1.47 0.141 BOS-Nighttime Interaction 0.553 0.214 −1.53 0.125 BOS Comparison-Daytime Interaction -- -- -- -- Number of observations: 3,478 Log-likelihood at convergence: −1,278.2 McFadden Pseudo R2: 0.0782 BOS Results The odds ratios provided in the previous section are evaluated in this section. Specifically, they are used to determine if fatal-and-severe-injury crashes are over-represented during nighttime hours on freeways with BOS. The results of this evaluation are described in the following three subsections. Independent Crash Severity Models In the model shown in Table 96, the odds of a fatal or severe crash outcome are 8.4 percent higher at night than they are in the daytime on comparison segments. This percentage is based on the odds ratio of

216 1.084. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.694 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. Additionally, the odds of a fatal or severe crash outcome on comparison facilities are lower when multiple vehicles are involved in the crash relative to single- vehicle collisions. In the model shown in Table 95, the odds of a fatal or severe crash outcome are 6 percent higher at night than they are in the daytime on BOS segments. This percentage is based on the odds ratio of 1.060. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.634 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. Additionally, the odds of a fatal or severe crash outcome on BOS sites are lower when multiple vehicles are involved in the crash relative to single-vehicle collisions. Matched Crash Severity Models In the model shown in Table 97, the baseline is a comparison segment-daytime interaction. The comparison-nighttime interaction odds ratio is 0.837. This value indicates that the odds of a fatal or severe injury outcome are lower at night at comparison segments related to the daytime period. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.436 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. The BOS-daytime interaction odds ratio is 0.559. This value indicates that the odds of a fatal or severe crash outcome are lower at BOS segments during the daytime than it is at comparison segments during the daytime. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.141 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. The BOS-nighttime interaction odds ratio is 0.553. This value indicates that the odds of a fatal or severe injury crash are lower for this scenario relative to the comparison segment daytime scenario. However, the null hypothesis that this value equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.125 that an odds ratio this large could be observed due to random variation when the true value equals 1.0. These last two odds ratios can be compared to determine the odds of a fatal or severe crash outcome at night relative to the daytime on BOS segments. This comparison is based on the ratio of these two odds ratios. This ratio is 0.989 (= 0.553/0.559). Its standard error is computed as 0.547 (= 0.553/0.559 ×[(0.214/0.553)2 + (0.221/0.559)2]0.5), and its p-value is computed as 0.984. The null hypothesis that the value of 0.989 equals 1.0 cannot be rejected at a 5 percent significance level. There is a probability of 0.984 that a ratio this large could be observed due to random variation when the true value equals 1.0. Summary For comparison segments, the computed odds ratios suggest that the odds of a fatal or severe injury outcome at night are between 83.7 and 108 percent of that for a daytime crash. Neither odds ratio is statistically significant at a 5 percent significance level. For BOS segments, the computed odds ratios suggest that the odds of a fatal or severe injury outcome at night are between 98.9 and 106 percent of that for a daytime crash. Neither odds ratio is statistically significant at a 5 percent significance level. Based on these results, it is concluded that fatal-and-severe- injury crashes are not over-represented by a meaningful amount during nighttime hours.

217 Summary of Findings This chapter presented analysis used to answer research questions related to the safety performance of PTSU and BOS. Table 98 summarizes the findings related to each question. Table 98. Summary of Findings Question Findingsa, b 1. What is the overall effect of a proposed shoulder use design on total and severe crash frequency?  Adding BOS operation on the right shoulder has neither a statistically significant nor a meaningful influence on total or FI crash frequency.  Adding BOS operation on the left shoulder was not found to have a statistically significant effect on crash frequency. There is some evidence that FI crash frequency increases by about 7%; however, additional data are needed to be more conclusive on this point.  Adding PTSU operation is typically associated with a statistically significant and meaningful increase in FI and PDO crash frequency, although there is a reduction in the proportion of severe crashes. However, when a turnout is provided every 0.5 miles and PTSU operates 2 hour/day or less during the weekdays and 0 hour/day during the weekends, there is a safety benefit associated with PTSU operation. 2a. What is the difference in safety performance when the shoulder is open or closed?  Opening a PTSU lane for a full hour is associated with a 137% increase crash frequency for the site during that hour compared to leaving the PTSU lane closed. The predicted change is statistically significant. 2b. When the shoulder is closed, is there a difference in safety performance between a freeway with shoulder use and a freeway without shoulder use?  When the shoulder is closed on a PTSU facility, there may be a nominally small (i.e., about 4.5%) increase in total crash frequency. However, this outcome is not statistically significant. Data for additional sites are needed to confirm whether PTSU facility presence (when the shoulder is closed) truly increases total crash frequency in all conditions and by what amount. 3. What is the safety effect of converting shoulder use eligibility from bus-only to all vehicles?  None of the study sites was converted from BOS to PTSU during the study period. Based on the findings from Question 1, the conversion from BOS to PTSU is likely to be similar to adding PTSU operation. 4. Are there differences in safety between using the left shoulder versus using the right shoulder?  Left-side PTSU is generally associated with fewer crashes than right-side PTSU at the sites studied. The evidence is strongest for sites with static PTSU operation. The magnitude of the inferred effect of changing from right-side to left-side PTSU is not statistically significant. Moreover, it is larger than expected and not supported by other research. Therefore, additional research is needed to confirm that this effect is (a) truly a result of the side on which the PTSU operates (and not a result of other unobserved variables) and (b) consistent for all sites at which PTSU operation is shifted from the right to the left side (and not limited to sites with static PTSU operation). 5a. What is the safety effect of adding dynamic signs in replacement of static signs?  The difference between the total crash frequency of sites with static signs and those with dynamic signs is neither statistically significant nor meaningfully significant, all other variables being the same. It is unlikely that the conversion from static signs to dynamic signs on a PTSU site will have a meaningful effect on total crash frequency. 5b. What is the safety effect of converting static operation to dynamic operation?  A before-after study of two facilities converted from S-PTSU to D-PTSU operation found a 7.3% decrease in total crash frequency. This result is statistically significant and meaningfully significant. 6. What is the safety effect of changing the width of the shoulder used for travel?  Changing the width of the right shoulder on right-side PTSU facilities is associated with a change in crash frequency. An increase in 1 foot of right shoulder width is associated with a 2.3% reduction in crash frequency, all other factors being the same. This effect was not found to be statistically significant; however, the magnitude of the change is consistent with that reported in the HSM Supplement (AASHTO 2014). 7. Are fatal and severe injury crashes over-represented during overnight hours like a typical urban freeway, or does shoulder use change this relationship?  For PTSU facilities, the odds of a fatal or severe injury outcome at night are between 87.9 and 165% of that for a daytime crash. Neither value is statistically significant. Given the wide range in values, additional research is needed to determine whether PTSU presence has an effect on the distribution of crash severity by time of day.  For BOS segments, the odds of a fatal or severe injury outcome at night are between 98.9 and 106% of that for a daytime crash. Neither value is statistically significant. It is concluded that fatal-and-severe-injury crashes are not over-represented by a meaningful amount during nighttime hours. a “Statistically significant” refers to a significance level of 5 percent (i.e., 95% level of confidence). b A factor has a meaningful influence on safety when the magnitude of its estimated effect is considered sufficiently large as to influence infrastructure investment decisions.

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Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report Get This Book
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Part-time shoulder use is a congestion relief strategy that allows use of the left or right shoulders as travel lanes during some, but not all, hours of the day.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 309: Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report describes the development of crash prediction models for freeways with PTSU operation.

Supplemental to the document is a Freeway Analysis Tool, which includes BOS Data, S D PTSU Data, and a Prediction Tool, as well as NCHRP Web-Only Document 309: Safety Performance of Part-Time Shoulder Use on Freeways, Volume 1: Informational Guide and Safety Evaluation Guidelines.

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