**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

**Suggested Citation:**"Appendix E - Probability of Passing Across the Opposing Lanes (THREOL)." National Academies of Sciences, Engineering, and Medicine. 2022.

*Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers*. Washington, DC: The National Academies Press. doi: 10.17226/26679.

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E-1Â Â A P P E N D I X E Probability of Passing Across the Opposing Lanes (THREOL) CONTENTS Chapter 1 Introduction Chapter 2 Model Considerations Avoiding Measuring the Same Variable Twice Method Chapter 3 Data Used for Modeling Chapter 4 Model Development Chapter 5 Application of Modeling Results References

E-2 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Traffic volume in the opposing direction is thought to affect the probability of a cross- median crash, P(CMC). Given that an errant vehicleâs trajectory extends to the other side of the median, determining the probability it will become a cross-median crash, P(CMC), is the focus of this appendix. P(CMC) is assumed to be a function of both a vehicle fully crossing the median and a second vehicle being present in the opposing travel way. Therefore, the P(CMC) is a function of another vehicle being present. THREOL is the conditional probability of passing through the opposing traffic given that a vehicle reaches the opposing traffic. THREOL is therefore 1âP(CMC). CHAPTER 1 INTRODUCTION

Probability of Passing Across the Opposing Lanes (THREOL) E-3Â Â The conditional probability of a cross-median crash (CMC) given that a cross-median event (CME) has occurred, P(CMC|CME), is defined by the relationship: In other words, the probability of both a CMC and CME, , compared with the P(CME) determines the conditional probability of a CMC. This modeling technique is founded on the assumption that P(CME) is greater than zero, a reasonable assumption considering the many observed CMCs and the definitions used to establish these variables. The consideration of how frequently or why vehicles enter the median is not the focus of this appendix. Likewise, the median and vehicle characteristics that influence P(CME) are not the focus of this appendix. The focus of this appendix is to calculate the probability that a vehicle that crosses the median will strike or be struck by a vehicle in the opposing lanes (CMC). For these reasons, it was important to remove and/or account for as many confounding factors as possible. AVOIDING MEASURING THE SAME VARIABLE TWICE One focus of other ongoing efforts is to understand the influence of terrain on rollover and barrier performance; therefore, it was desirable to remove the consideration of slopes and terrain from this model to the extent possible to allow for use of the results of the more focused and extensive terrain research efforts to be capitalized upon. In other words, this model of the probability of CMC already assumes the vehicle has crossed the median (CME). The effect of median width was captured elsewhere; thus, care should be taken to not measure the effect of median width again. It was desirable, therefore, to model what happens when a vehicle reaches the far edge of the median absent the influence of median width and median terrain. This was accomplished here by considering cross-over-the-centerline crashes (CO) on undivided roadways. For modeling, an undivided roadway is assumed to equal a divided roadway with a median width equal to the distance between the double yellow lines (i.e., typically one foot) and no median terrain. Head-on and sideswipe crashes that occurred on undivided roadways were used to develop the data set on which these efforts are based to remove the influence of the median width and median terrain confounders. For roadways with a median width equal to zero, P(CME) = P(MRE) because, by definition, all left encroachments cross both yellow lines at the center of the roadways at the start of the encroachment event. The conditional probability of CMC given CME established above can be rewritten as follows: CHAPTER 2 MODEL CONSIDERATIONS

E-4 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers In other words, the probability of both a crossover crash (CO) and MRE compared with the P(MRE) is a surrogate for the conditional probability of a CMC that controls for median width and terrain. P(MRE) is equal to the frequency of left-encroaching vehicles compared with the AADT of the segment of interest, , while the is equal to the frequency of a CO crash and left-encroaching vehicle compared with the AADT of the segment of interest, . The above relationship can then be further simplified as follows: The frequency of left-encroaching vehicles is known. The frequency of crossover crashes when a left encroachment over the centerline has occurred is not known. The focus of model development is to determine the frequency of crossover crashes. The FREQCO model itself must control for the remaining confounding factors. METHOD The state of the practice for modeling count data such as highway crashes is to fit a negative binomial model, usually with a Poisson-gamma mixture distribution. âIn statistics, count data refer to observations that have only nonnegative integer values ranging from zero to some greater undetermined value.â (Hilbe 2011) In highway safety, zero counts of crashes are particularly important and represent areas where crashes were not observed (i.e., more safe areas). One approach to tracking zero counts as well as the non-zero counts is to track crashes by highway segment. This approach has the added benefit of allowing the consideration of the influence of segment characteristics on crash frequency. The crash counts are the response variable, and the segment characteristics such as AADT, percentage of trucks (PT), highway geometrics, and area type become the explanatory variables that explain the occurrence of the crashes. Each segment is associated with each of the predictor variables and the number of crashes that occur on that segment during the study period. The characteristics of the segment are used to explain why each segment experiences more or fewer crashes than other segments. Ideally, all possible predictor variables would be known. This ideal situation remains unrealized. However, it is common to consider the known predictor variables when developing a model to ensure the effect of the predictor variable of interest is not misrepresented. Roadway characteristics that may also modify the P(CMC) such as PT, highway geometrics, and area type (i.e., urban and rural) are recognized confounding factors but are accounted for elsewhere in the encroachment probability model. Ensuring that the final representation of P(CMC), when implemented in the encroachment probability model, does not double-count the effect of these confounders is equally important to controlling for their effect. Controlling for these confounders was attempted using two different approaches: (1) explicitly modeling control variables, and (2) limiting the data set to segments where the confounders contained measurements within the base conditions of the previously developed models. The latter is ultimately recommended, as discussed below. Under both approaches, a negative binomial regression model of crossover crashes was estimated using the COUNT package available in R. (Hilbe 2016; R 2017) The model relates the

Probability of Passing Across the Opposing Lanes (THREOL) E-5Â Â explanatory variables to the response variable using the method of maximum likelihood to quantify the magnitude of each predictor relationships. Along with each model, the fit statistics are presented. The p-value is a measure of how probable the result observed may have occurred by chance. A low p-value indicates the results are statistically significant and were unlikely to have occurred by chance (e.g., p < 0.05). A higher p-value only indicates that the results have not proven the null hypothesis false, not that the null hypothesis is true. The p-value cannot be relied on alone. The pseudo-R2 statistic was determined for each model. The pseudo- R2 is not interpreted the same way as the coefficient of determination is for an ordinary least squares regression. A low value of the pseudo-R2 can indicate lack of fit while higher values carry no such indication. There is no definition of a low value. The Akaike Information Criterion (AIC) fit statistic provides comparative information, with lower values indicating a better fitting model than the model it is compared with. Bayesian Information Criterion (BIC) is interpreted the same way. Both are calculated from the likelihood function. (Hilbe 2014) Negative binomial model parameters are estimated using maximum likelihood, where the parameters of the probability distribution that characterize the data are estimated. The log of the likelihood function is used to determine which parameters make the model most likely to be the case when the data is considered. Through an iterative process, the derivative of the log likelihood function is taken and set to zero to estimate the parameters. When the difference between iterative values is less than a specified tolerance (i.e., 10â6), the iterations stop and the values are at the maximum likelihood estimated values. The log likelihood (LL) is also reported with the models; however, is only useful when calculating other fit statistics (e.g., AIC and BIC). Any measurement has uncertainty, which should be communicated. This uncertainty in statistical analysis can be conveyed by noting the standard error or the confidence interval along with the measurements. The standard error is a measure of how much the estimate could change within the model. The 95% confidence interval is essentially the same type of statistic as standard error; the 95% confidence interval limits indicate that the analyst is 95% confident the true value of the coefficient is within the stated range. It is important to note the 95% confidence interval is equal to twice the standard error for normally distributed error. Negative binomial models are assumed to have normally distributed errors. The original intent of this project was to use the models developed under NCHRP Report 794: Median Cross-Section Design for Rural Divided Highways. (Graham 2014) Unfortunately, there appears to be a typographical error in the model printed in NCHRP Report 794, as both the CMC+CME and CMC models shown are identical. It was decided to use a previously obtained Highway Safety Information System data set of Ohio and Washington highway crashes that could be linked to highway segment information such as AADT, PT, segment length, area type, speed limit, number of lanes, lane width, and vehicle type. This database was requested for Ohio from 2002 through 2010 and for Washington from 2002 through 2007 under the NCHRP Project 17-54 research effort. (Carrigan 2018) The NCHRP Project 17-54 data set of homogenous segments were merged with CO and opposite direction sideswipe crashes (i.e., ACCTYPE field codes â1â and â4â). The crashes were counted by crash severity and vehicle type and assigned to the appropriate homogenous segment CHAPTER 3 DATA USED FOR MODELING

E-6 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers using the recorded route and milepost of each crash. The resulting data set included a list of segments. Each segment had a field for AADT, PT, SegL, area type, SPD_LIMT, NO_LANES, and LANEWID. Each segment also contained a field for the count of crashes occurring on the segment by each crash severity and vehicle type (e.g., passenger car fatal crash = PC_K; heavy vehicle serious crash = HV_A, etc.). The data set includes 1,204,084 segments. In some instances, the segments included fields where the information was not available (NA) or the field contained a nonsense value (e.g., AADT=0). The data set was filtered to remove these segments from consideration, as shown here, before any modeling. The remaining segments are noted in parentheses. â¢ Consider only segments where the area type is known (1,202,105). â¢ Consider only segments where the length in miles is 0.1 â¤ L â¥ 2 (404,620). â¢ Consider only segments where ADT > 0 (403,666). â¢ Consider only segments where the PT is known (242,862). â¢ Consider only segments where the value of the number of lanes = 2 (221,171). â¢ Consider only segments where the posted speed limit > 0mph (220,975). This filtering of the data set resulted in 220,975 segments being included in the modeling. The descriptive statistics for this data set are shown in Table E-1. This table includes shorthand for the categorical variable names to allow the information to be displayed in table format. PSL=50 is for the posted speed limit equal to 50 mph. LW=10 is for lane width of 10 feet. Each number after the equal sign represents the value of that variable associated with that indicator variable.

Probability of Passing Across the Opposing Lanes (THREOL) E-7Â Â Table E-1 Descriptive Statistics for P(CMC) Data Set Continuous Variables Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.13 0.19 0.31 0.35 2 AADT 10 1,110 2,280 3,611 4,760 68,336 PT 0.0 3.8 5.7 7.00 8.6 67 Lane Width 7 10 10 10.97 12 41 Shoulder Width 0 2 3 3.59 4 30 DOC 0 0 0 0.52 0 76 PG 0 0 0 1.52 0 20 PC_KABCOU 0 0 0 0.0345 0 6 HV_KABCOU 0 0 0 0.0075 0 3 MC_KABCOU 0 0 0 0.0008 0 2 KABCOU 0 0 0 0.0445 0 7 Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) PSL=20 68 PSL=40 5,528 PSL=60 1,764 PSL=25 5,783 PSL=45 20,958 PSL=65 229 PSL=30 392 PSL=50 6,868 Rural 185,414 PSL=35 30,921 PSL=55 149,064 Urban 35,561

E-8 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Recall the number of crashes per year was tabulated in the data set. A negative binomial model was fit to the dataset of head-on crashes and the log of the segment length in miles was included as an offset to allow for the frequency of head-on crashes to be evaluated per year per mile. As this research progressed, the encroachment frequency model was changed to include an offset of MVMT, not segment length. These results were not used in this research effort, as explained below. The resulting parameter estimates are shown in Table E-2 for the crossover model with control variables which takes this form: Where: FREQCO = Frequency of crossover crashes per year per mile. AADT = Annual Average Daily Traffic (vpd). Ai = Control variable values for each segment under consideration. Bi = Regression coefficients. N = Total number of control variables considered per segment. CHAPTER 4 MODEL DEVELOPMENT

Probability of Passing Across the Opposing Lanes (THREOL) E-9Â Â Table E-2 Negative Binomial Model for Cross-Over Crashes Coefficients: Parameter Estimate Standard Error P-Value 95% Confidence Interval (Intercept) -9.3993 0.49 < 2e-16 -10.4910 -8.5228 log(AADT) 0.9025 0.02 < 2e-16 0.8690 0.9363 log(PT) 0.0235 0.00 1.32e-15 0.0178 0.0293 Urban 0.1343 0.03 6.69e-06 0.0758 0.1928 Rural 1.0000 --- --- --- --- PSL.20 1.0000 --- --- --- --- PSL.25 0.4377 0.47 0.353 -0.3989 1.5042 PSL.30 0.5085 0.50 0.309 -0.3970 1.6172 PSL.35 0.1129 0.47 0.810 -0.7197 1.1770 PSL.40 0.0043 0.47 0.993 -0.8350 1.0725 PSL.45 -0.0708 0.47 0.880 -0.9059 0.9948 PSL.50 -0.3035 0.47 0.521 -1.1438 0.7653 PSL.55 -0.2767 0.47 0.556 -1.1104 0.7880 PSL.60 -0.7111 0.51 0.162 -1.6382 0.4095 PSL.65 -0.6755 0.73 0.357 -2.1498 0.7372 LANEWID 0.0215 0.00 1.13e-06 0.0127 0.0301 DOC 0.0454 0.01 2.73e-14 0.0326 0.0569 PG 0.0454 0.01 1.39e-08 0.0187 0.0386 SHLDR_PRE -0.0517 0.00 < 2e-16 -0.0606 -0.0429 AIC 68,272 BIC 68,447 Dispersion Parameter (Î±) 1.099 Standard Error 0.0730 LL (full) -34,119 Pseudo-R2 0.15 Recall that the initial data set was filtered to remove segments with missing or nonsense values, which resulted in a data set of 220,975 segments that were used in the model developed with included control variables. A different approach will be taken in this section. The approach taken here is to further limit the data set to include segments that meet the base conditions of the complementary encroachment probability model for which this P(CMC|CME) model is being explored such that this P(CMC|CME) model does not account for variation in highway characteristics which are already accounted for elsewhere in the encroachment probability model. The 220,975-segment data set was further limited for this analysis as shown here, with the remaining segments noted in parentheses: â¢ Consider only segments where the area type is rural (185,414). â¢ Consider only segments where the PT â¥ 10 (36,038). â¢ Consider only segments where the posted speed limit â¥ 45mph (32,069). â¢ Consider only segments where 10 feet â¤ LANEWID â¥ 12 feet (24,690).

E-10 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers â¢ Consider only segments where the DOC = 0 (21,918). â¢ Consider only segments where -2% â¤ PG â¥ +2% (17,443). This limited data set resulted in 17,443 segments being included in this analysis. The descriptive statistics for this limited data set are shown in Table E-3 using the same shorthand for the categorical variables previously discussed for Table E-1. Table E-3 Descriptive Statistics for Limited P(CMC) Data Set Continuous Variables Min. 1st Qu. Median Mean 3rd Qu. Max. SegL 0.1 0.17 0.32 0.4879 0.65 2 AADT 40 1594 2850 3604 5110 20260 PC_KABCOU 0 0 0 0.0308 0 3 HV_KABCOU 0 0 0 0.0170 0 3 MC_KABCOU 0 0 0 0.0007 0 1 KABCOU 0 0 0 0.0501 0 5 Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) PSL=45 1143 PSL=55 15510 PSL=65 107 PSL=50 562 PSL=60 121 Again, a negative binomial model was fit to the dataset of head-on crashes and the log of the segment length in miles was included as an offset to allow for the frequency of head-on crashes to be evaluated per year per mile. As noted above, the encroachment frequency model was changed as this research progressed to include an offset of MVMT, not segment length. These results were not used in this research effort, as explained below. The resulting parameter estimates are shown in Table E-4 for the crossover model with explicitly limits confounders and takes this form: Where: FREQCO = Frequency of crossover crashes per year per mile. AADT = Annual Average Daily Traffic (vpd). Bi = Regression coefficients.

Probability of Passing Across the Opposing Lanes (THREOL) E-11Â Â Table E-4 Negative Binomial Model for Cross-Over Crashes Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -11.3901 0.49 < 2e-16 -12.3625 -10.4393 log(AADT) 1.1050 0.06 < 2e-16 0.9928 1.2193 AIC 6142 BIC 6158 Dispersion parameter (Î±) 1.296 Standard Error 0.339 LL (full) -3069.25 Pseudo-R2 0.12 The limited data set described above that results in 17,443 segments was used to fit a negative binomial model of head-on crashes with an offset of log(MVMT) to allow for the crash rate of head-on crashes to be directly compared with the reconsidered Cooper encroachment rate model. These results were ultimately implemented in this research effort. The resulting parameter estimates are shown in Table E-5 for the crossover model that explicitly limits confounders and takes this form: Where: FREQCO = Frequency of crossover crashes/MVMT. AADT = Bi-directional Annual Average Daily Traffic (vpd). Bi = Regression coefficients. MVMT = Million vehicle miles traveled (AADTÂ·365Â·L)/1,000,000. Table E-5 Negative Binomial Model for Cross-Over Crashes Offset MVMT Coefficients: Parameter Estimate Standard Error P-Value 95% Confidence Interval (Intercept) -3.4744 0.49 1.36e-12 -4.4469 -2.5237 log(AADT) 0.1050 0.06 0.0689 -0.0072 0.2193 AIC 6,142 BIC 6,158 Dispersion Parameter (Î±) 1.296 Standard Error 0.339 LL (full) -3,069.25 Pseudo-R2 0.12 Recall that a FREQCO model that controls for highway characteristics is desired and that this model is presumed to be a function of AADT. The severity of these crashes is understood through a different model and need not be considered here; rather, this model should consider all observed crashes to allow for the conversion from a frequency model to a probability model.

E-12 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Further, this model must be offset by MVMT for use with the Cooper data model. The simpler model where the confounders are explicitly controlled through limiting segments considered, as documented in Table E-4, is preferred because (1) the AIC and BIC values are lower, (2) the model makes better engineering sense, and (3) the simpler model best satisfies the principals of parsimony (i.e., Occamâs razor). The model shown in Table E-5 has these same qualities but also has an offset of MVMT, and therefore, it is implemented in this research. The frequency of CO crashes when a left encroachment over the centerline has occurred is estimated to be: It was previously derived that . The frequency of right-encroaching vehicles on four-lane divided highways by MVMT is represented by the model of Cooper data shown in Table E-6. (Ray 2012)

Probability of Passing Across the Opposing Lanes (THREOL) E-13Â Â Table E-6 Primary Right Base Encroachments per MVMT for Four-Lane Divided Highways (Ray 2012) Divided Highways Up to this point, the model considered the frequency of crossover crashes from both directions. This model must be divided by two to allow for consideration of each direction of travel as the encroachment model shown in Table E-6 estimates a single encroachment direction. The encroachment model shown in Table E-6 must be multiplied by the EAFLR for encroachment side to represent the left encroachments. Since the Miaou-Cooper model in Table E-6 is limited to AADT â¤ 46,000 veh/day, only the adjustment for AADT â¤ 67,000 veh/day was 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0 20,000 40,000 60,000 80,000 100,000 E nc ro ac hm en ts /M V M T f or O ne E nc ro ac hm en t D ir ec ti on Average Daily Traffic (vpd)

E-14 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers used. The result for an estimate of the encroachment rate from one left-side encroachment on a four-lane divided highway is, therefore, as follows: Finally, half the frequency of CO/MVMT is then divided by the left-encroachment frequency to determine the probability of a CMC given a CME has occurred P(CMC|CME). The solid line in Figure E-1 shows the curve based on this statistical model. Figure E-1 Probability of a cross-median crash given a cross-median event occurs. P(CMC|CME) is the probability that a vehicle will collide with a vehicle in the opposing lanes given that the encroaching vehicle has crossed the median and entered the opposing lanes. The Cooper-Miaou data used above to develop the statistical model is limited to traffic volumes below 46,000 veh/day for four-lane divided roadways and 6,000 veh/day for undivided two-lane roadways. The portions of the curves for higher AADT, therefore, are extrapolations that are not based on any observed data. Predicting P(CMC|CME) for high traffic volumes is also important, so another approach was necessary for the high-volume portion of the figure. A traffic engineering volume-capacity approach was used to supplement the statistical data. The Highway Capacity Manual (HCM) assumes lane capacities between 2,250 and 2400 passenger cars (pc)/ln/h for freeways depending on the land use (i.e., downtown, urban, suburban, or rural) and free-flow speed (i.e., between 55 and 70 mi/h associated with the previous land-use categories).(Margiotta 2017; HCM 2016) If a highway operated at a capacity of 2,200 pc/ln/h for 24 h a day, 365 days a year, it would be equivalent to a bi-directional AADT of 2,200Â·24 = 52,800 veh/day/ln. At capacity, the lanes are full of vehicles operating with minimal headway. The chance of a cross-median crash (CMC) given an encroachment into the opposing lanes (CME) operating at maximum capacity is 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 - 10,000 20,000 30,000 40,000 50,000 60,000 P (C M C | C M E ) Inside Opposing Lane Volume (veh/day) Statistical Model Logistic Extrapolation

Probability of Passing Across the Opposing Lanes (THREOL) E-15Â Â assumed to be one. In other words, a vehicle entering an opposing lane operating at these extreme conditions is virtually guaranteed to be struck by another vehicle. A simple model of this would be a straight line between zero AADT corresponding to P(CMC|CME) = 0 and an AADT of 52,800 veh/day corresponding to P(CMC|CME) = 1.0, certainty of a CMC. A linear model, however, is not realistic at the very lowest and highest volumes. A linear model would require an instantaneous change in slope at AADTs of zero and 52,800 veh/day. A more physically compelling model that provides smooth slopes transitions throughout is provided by the following logistic function: This logistic function closely replicates the lower half of the curve derived above from the statistical model and provides a reasonable extrapolation for the upper half of the curve. The two curves are coincident at an AADT of 23,00 veh/day, so the statistical model is used for AADT less than 23,000 veh/day, and the logistic model based on traffic capacity is used for AADT greater than 23,000 veh/day as shown in Figure E-1.

E-16 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers If a vehicle enters opposing lanes but does not have a crash with opposing traffic, the vehicle occupants will not experience any harm associated with entering opposing lanes. The proportion of the vehicles passing through, rather than having a crash must therefore be tabulated (i.e., THREOL). The values of THREOL are found by subtracting the estimates shown graphically in Figure E-1 from unity and have been tabulated in Table E-7. The values in Table E-7 have been tabulated by lane volume in vehicles per day in the opposing lane adjacent to the median. If the lane volume is not known, the bi-directional AADT may be divided by the number of lanes. Table E-7 Proportion of Vehicles Passing Across the Opposing Lane Without Striking an Opposing Vehicle Given a Vehicle Enters the Opposing Lanes (THREOL) Opposing Lane Volume (veh/day) THRUEOL Opposing Lane Volume (veh/day) THRUEOL Opposing Lane Volume (veh/day) THRUEOL Opposing Lane Volume (veh/day) THRUEOL 500 0.8893 12,000 0.7859 24,000 0.4502 36,000 0.0691 1,000 0.8893 13,000 0.7694 25,000 0.4013 37,000 0.0573 2,000 0.8878 14,000 0.7514 26,000 0.3543 38,000 0.0474 3,000 0.8830 15,000 0.7318 27,000 0.3100 39,000 0.0392 4,000 0.8765 16,000 0.7106 28,000 0.2689 40,000 0.0323 5,000 0.8689 17,000 0.6876 29,000 0.2315 41,000 0.0266 6,000 0.8602 18,000 0.6627 30,000 0.1978 42,000 0.0219 7,000 0.8505 19,000 0.6356 31,000 0.1680 43,000 0.0180 8,000 0.8398 20,000 0.6063 32,000 0.1419 44,000 0.0148 9,000 0.8280 21,000 0.5745 33,000 0.1192 45,000 0.0121 10,000 0.8152 22,000 0.5401 34,000 0.0998 50,000 0.0045 11,000 0.8012 23,000 0.5027 35,000 0.0832 60,000 0.0006 CHAPTER 5 APPLICATION OF MODELING RESULTS

Probability of Passing Across the Opposing Lanes (THREOL) E-17Â Â REFERENCES Carrigan, Christine E. and Malcolm H. Ray, NCHRP Project 17-54, "Consideration of Roadside Features in the Highway Safety Manual," Transportation Research Board, Washington, DC, 2018. Graham, Jerry L., Douglas W. Harwood, Karen R. Richard, Mitchell K. O'Laughlin, Eric T. Donnell, and Sean N. Brennan, NCHRP Report 794: Median Cross- Section Design for Rural Divided Highways, Transportation Research Board, Washington, DC, 2014. Highway Capacity Manual, 6th Edition: A Guide for Multimodal Mobility Analysis, Transportation Research Board, Washington, DC, 2016. Hilbe, J. M., "COUNT: functions, data and code for count data," R package version, Vol. 1, No. 4, 2016. Hilbe, Joseph M., Modeling count data, Cambridge University Press, 2014. Hilbe, Joseph M., Negative Binomial Regression, Cambridge University Press, Cambridge, 2011. Margiotta, Richard and Scott Washburn, "Simplified Highway Capacity Calculation Method for the Highway Performance Monitoring System," Cambridge Systematics Incorporated, Federal Highway Administration, Cambridge, Massachusetts, 2017. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org Ray, Malcolm H., Christine E. Carrigan, and C. A. Plaxico, NCHRP Project 22-27, "Roadside Safety Analysis Program (RSAP) Update, Appendix B: Engineer's Manual RSAP," Transportation Research Board, Washington, DC, 2012.

Abbreviations and acronyms used without denitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACIâNA Airports Council InternationalâNorth America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing Americaâs Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration GHSA Governors Highway Safety Association HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TDC Transit Development Corporation TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S. DOT United States Department of Transportation

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