Identification and Evaluation of the Cost-Effectiveness of Highway Design Features to Reduce Nonrecurrent Congestion (2014)

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40 The objective of the safety analysis was to estimate, in quan- titative terms, the safety effectiveness for each treatment of interest. Design treatments to reduce nonrecurrent conges- tion have two potential effects on safety for the highway facili- ties on which they are implemented: • Design treatments may have a direct effect on crash fre- quency or severity if they affect the speeds or lateral positions of vehicles. Effects on crash frequency may result from treat- ments that change lane width, shoulder width, or other geo- metric features related to the base capacity of the facility, as indicated by Highway Capacity Manual (HCM) procedures (2). Crash severity may be affected by design treatments that change the roadside design of the facility. • Design treatments may have an indirect effect on crash fre- quency if they reduce congestion on the highway facility. The relationship between congestion and crash frequency is documented in this section. Although the direct effects of design treatments on crash frequency for freeways have not been fully documented, they have recently been investigated in NCHRP Project 17-45 for inclusion in the Highway Safety Manual (5). This research has documented the effect on safety of changing the inside and outside shoulder width on freeways. The direct effect of design treatments on roadside crash severity can be estimated with the Roadside Safety Analysis Program (6). The relation- ship between congestion and safety has been determined in Project L07 and included in the assessment of design treatments. Direct effects of Design treatments on Safety A new safety prediction methodology for freeways has been developed in NCHRP Project 17-45 (4). This methodology is currently in the approval process for inclusion in the Highway Safety Manual (5). The only variables in the safety prediction methodology that appear to relate directly to the assessment of design treatments are outside shoulder width and inside shoulder width. The effect of outside shoulder width on safety on a tangent roadway section is represented by the following crash modifi- cation factor (CMF), as given by Equation 5.1: [ ]( ) ( )−CMF = exp 10 5.1osa W where Wos = outside shoulder width on freeway section (ft; range, 4 to 14 ft); and a = regression coefficient (-0.0647 for fatal-and-injury [FI] crashes and 0.0000 for property-damage-only [PDO] crashes). The percentage change in crashes resulting from a change in outside shoulder width can be determined from the CMFs in Table 5.1 and as shown by Equation 5.2: ( ) ( )= − ×Percentage change in crashes CMF 1 100 5.2 Thus, a CMF of 1.03 corresponds to a 3% increase in crash frequency, and a CMF of 0.97 corresponds to a 3% decrease in crash frequency. The effect of inside shoulder width on safety is given by Equation 5.3: [ ]( ) ( )= −CMF exp 6 5.3isa W where Wis = inside shoulder width on freeway section (ft; range, 2 to 12 ft); and a = regression coefficient (-0.0172 for FI crashes and -0.0153 for PDO crashes). Table 5.2 shows CMFs for the effect on safety of changing inside shoulder width. C h a p t e r 5 Safety Assessment of Design Treatments

41 Tables 5.1 and 5.2 can be used by users of the Analysis Tool to determine the direct effects of changing outside or inside shoulder width on safety. The design treatments to which these effects potentially apply are as follows: • Accessible shoulder 44 Inside shoulder width 44 Outside shoulder width • Drivable shoulder 44 Inside shoulder width 44 Outside shoulder width • Alternating shoulder 44 Inside shoulder width 44 Outside shoulder width Development of Congestion– Safety relationship The reduction of congestion through application of design treatments or intelligent transportation system improvements has been widely thought to have a positive effect on safety, but this relationship has not been well quantified in previous research. Congestion may result in stalled or slowed traffic, and the situation in which high-speed vehicles approach the rear of an unexpected traffic queue clearly presents a substan- tial risk of collision. There is also a clear potential for colli- sion within queues of stop-and-go traffic. The frequency of both of these conditions can be ameliorated by treatments to reduce nonrecurrent congestion. However, collision severity is clearly a function of speed, so the lower speeds on road- ways during congested periods may reduce overall collision severity. This trade-off between crash frequency and severity in congested versus uncongested conditions had never been satisfactorily quantified. Research on this issue for freeway facilities has been conducted by Zhou and Sisiopiku (7) and Hall and Pendleton (8). In particular, Zhou and Sisiopiku suggest that different crash types respond in different ways to volume-to-capacity ratios based on hourly volumes. The research results presented below illustrate why a difference between crash types appears reasonable. To determine a relationship between safety and congestion for use in evaluating design treatments, relationships between crash rates and level of service (LOS) were developed that were based on 3 years (2005 to 2007) of data obtained from freeways in two metropolitan areas: Seattle, Washington, and Minneapolis–St. Paul, Minnesota. The selection of the two metropolitan areas was based on the availability of relevant data; the sites in Minneapolis–St. Paul included two to five directional lanes of travel, and those in Seattle included two to four directional lanes of travel. Each station for which traf- fic volume and speed data were available included detectors in each lane across one direction of travel on a freeway. For Table 5.2. CMFs for Changing Inside Shoulder Width on Freeways (4) Inside Shoulder Width (ft) (before) Inside Shoulder Width (ft) (after) 2 4 6 8 10 12 Fatal-and-Injury Crashes 2 1.00 0.97 0.93 0.90 0.87 0.84 4 1.03 1.00 0.97 0.93 0.90 0.87 6 1.07 1.03 1.00 0.97 0.93 0.90 8 1.11 1.07 1.03 1.00 0.97 0.93 10 1.15 1.11 1.07 1.03 1.00 0.97 12 1.19 1.15 1.11 1.07 1.03 1.00 Property-Damage-Only Crashes 2 1.00 0.97 0.94 0.91 0.88 0.86 4 1.03 1.00 0.97 0.94 0.91 0.88 6 1.06 1.03 1.00 0.97 0.94 0.91 8 1.10 1.06 1.03 1.00 0.97 0.94 10 1.13 1.10 1.06 1.03 1.00 0.97 12 1.17 1.13 1.10 1.06 1.03 1.00 Table 5.1. CMFs for Changing Outside Shoulder Width on Freeways (4) Outside Shoulder Width (ft) (before) Outside Shoulder Width (ft) (after) 4 6 8 10 12 14 Fatal-and-Injury Crashes 4 1.00 0.88 0.77 0.68 0.60 0.52 6 1.14 1.00 0.88 0.77 0.68 0.60 8 1.30 1.14 1.00 0.88 0.77 0.68 10 1.47 1.30 1.14 1.00 0.88 0.77 12 1.68 1.47 1.30 1.14 1.00 0.88 14 1.91 1.68 1.47 1.30 1.14 1.00 Property-Damage-Only Crashes 4 1.00 1.00 1.00 1.00 1.00 1.00 6 1.00 1.00 1.00 1.00 1.00 1.00 8 1.00 1.00 1.00 1.00 1.00 1.00 10 1.00 1.00 1.00 1.00 1.00 1.00 12 1.00 1.00 1.00 1.00 1.00 1.00 14 1.00 1.00 1.00 1.00 1.00 1.00

42 analysis purposes, the freeway system was divided into direc- tional segments, usually extending from one interchange to the next. The sections were selected so that a given detector would be representative of the traffic conditions for all crashes within that section. The most appropriate station was selected for each directional segment; whenever possible, a station near the center of a segment was selected. Table 5.3, which summa- rizes the available site data, shows that there were 145 roadway sections representing 200 mi of directional freeway segments in Seattle and 419 roadway sections representing 410 mi of directional freeway segments in Minneapolis–St. Paul. Database Development The original detector data collected at each station on the freeways consisted of 5-min volume and average speed data for each travel lane; speeds or volumes were missing for some 5-min intervals on one or more lanes. Most missing data were attributed to detector malfunctions. As no set of loop detec- tors will function across all freeway lanes all the time, some missing volume and speed data are inevitable. A detector that malfunctions is usually out of service for a substantial time period; however, there is no reason to believe that missing data due to a malfunctioning detector leads to a bias in the remaining data set. Missing traffic volume data could not be estimated and were treated as missing. Missing speed data were estimated as the average of the speeds for the adjacent lanes on both sides of the missing lane, as long as the two speeds being averaged were within 5 mph of one another. Speed data were estimated only when volume data were avail- able. If the difference between the speeds in the lanes adjacent to the missing lane was greater than 5 mph, traffic conditions were considered to be too nonhomogeneous to estimate the missing speed. The percentage of time periods with missing data was approximately 19% of the 3-year study period for Seattle and 16% for Minneapolis–St. Paul. In addition, a deci- sion was reached to exclude from the study all data in the Minneapolis–St. Paul area after the I-35W bridge collapse on August 1, 2007, which resulted in unusual flow conditions. Although this period might have been interesting (because volumes changed dramatically on many freeway segments), the changed driving conditions were new to many drivers, and the Minnesota Department of Transportation (DOT) made many modifications to specific roadways to increase base capacity; complete documentation of all these changes and their geometrics are not readily available. Flow rates in vehicles per hour per lane were computed from the data for each station both for each lane and for all lanes combined based on the available 5-min volume data. These flow rates included some large fluctuations. The speed and volume data were aggregated into 15-min intervals, which provided much more stable data. Once processed, the vol- ume and speed data were used to determine the LOS for each 15-min interval (discussed later in this section). Crash data for each directional freeway segment were com- piled for the same 15-min periods as the traffic volume and speed detector data on the basis of the reported crash date and time. The crash data, which were obtained through the Highway Safety Information System, included all mainline freeway crashes that occurred within the limits of each road- way section of interest during the study period. Crash severity levels considered in the evaluation were as follows: • Total crashes (i.e., all crash severity levels combined) • FI crashes • PDO crashes Table 5.3. Site Distribution Characteristics for Directional Freeway Segments in Seattle and Minneapolis–St. Paul Metropolitan Area No. of Directional Lanesa No. of Sites Length (mi) No. of 15-min Recordsb Seattle, Washington 2 66 93.8 6,937,920 3 56 81.9 5,886,720 4 23 24.1 2,417,760 All lanes 145 199.8 15,242,400 Minneapolis–St. Paul, Minnesota 2 151 146.0 15,780,000 3 185 184.8 19,412,448 4 73 67.6 7,673,760 5 10 11.7 1,051,200 All lanes 419 410.1 43,917,408 a Not including high-occupancy vehicle lanes. b Includes records with missing volume or speed values.

43 15-min volume during a particular hour, as is commonly used in HCM procedures. As specified in the HCM, six LOS categories are assigned by traffic density ranges as follows: • LOS A: 0 to 11 passenger cars per mile per lane (pc/mi/ lane) • LOS B: 11 to 18 pc/mi/lane • LOS C: 18 to 26 pc/mi/lane • LOS D: 26 to 35 pc/mi/lane • LOS E: 35 to 45 pc/mi/lane • LOS F: 45+ pc/mi/lane As the LOS categories are quite broad, a more refined LOS categorization was used to better capture the relation- ship between density and crash rates. The 18 LOS categories selected are shown in Table 5.5. Table 5.4 summarizes the crash data (number and percent- age) by collision type and severity separately for Seattle and Minneapolis–St. Paul over the 3-year period. Level of Service Calculations LOS was computed for each 15-min record by using the oper- ational analysis procedure presented in HCM, Chapter 23 (2). Components in the LOS calculations included directional volume, directional speed, flow rates, traffic mix adjustment factor to determine flow rates in passenger cars per hour per lane (i.e., heavy-vehicle adjustment factor), and traffic density. Truck percentages for each roadway section were obtained from maps and other data published by the state DOT or the relevant metropolitan planning organization. The operational measure used to define LOS for freeways is the traffic density in passenger cars per hour per mile. The traffic density for a 15-min period was computed from the available speed and volume data, as shown by Equation 5.4: ( )= 4 5.415 15 HV 15 D V f S where D15 = traffic density for a 15-min period; V15 = traffic volume (number of vehicles) for the 15-min period summed across all lanes; fHV = heavy-vehicle adjustment factor from HCM, Equa- tion 23-3 (assuming site-specific truck percentage and zero recreational vehicles); and S15 = average spot speed across all lanes (weighted by lane volumes) (mph). Equation 5.4 does not include the peak hour factor; that is, D15 is based on the actual 15-min volume, not the highest Table 5.4. Crash Distribution by Collision Type and Crash Severity for Freeway Sections in Minneapolis–St. Paul and Seattle Collision Type No. (%) of Crashes by Crash Severity Fatal A Injury B Injury C Injury PDO Minneapolis–St. Paul Single vehicle 5 (35.7) 12 (37.5) 127 (41.0) 297 (21.7) 939 (20.7) Multiple vehicle 9 (64.3) 20 (62.5) 183 (59.0) 1,070 (78.3) 3,594 (79.3) All 14 (100) 32 (100) 310 (100) 1,367 (100) 4,533 (100) Seattle Single vehicle 17 (68.0) 32 (36.0) 214 (31.8) 639 (14.6) 1,449 (15.0) Multiple vehicle 8 (32.0) 57 (64.0) 459 (68.2) 3,745 (85.4) 8,220 (85.0) All 25 (100) 89 (100) 673 (100) 4,384 (100) 9,669 (100) Table 5.5. LOS Categories Used in the Study LOS Traffic Density Range (pc/mi/lane) LOS Traffic Density Range (pc/mi/lane) A+ 0 to 3 D+ 26 to 29 A 3 to 7 D 29 to 32 A- 7 to 11 D- 32 to 35 B+ 11 to 13 E+ 35 to 38 B 13 to 15 E 38 to 41 B- 15 to 18 E- 41 to 45 C+ 18 to 20 F+ 45 to 50 C 20 to 23 F 50 to 55 C- 23 to 26 F- 55+

44 within each of the 18 LOS categories for each metropolitan area. The resulting pairs of data points are plotted by severity level and metropolitan area in Figures 5.1 and 5.2. Figure 5.1 shows the variation of crash rate per MVMT with traffic density for freeway sections in the Seattle metro- politan area. Each point represents the crash rate for all 15-min periods of the 3-year period that fell in a particular Development of LOS–Crash Rate Relationships Based on the 15-min crash rate and traffic density data, aver- age crash rates (expressed in crashes per million vehicle miles of travel [MVMT]) were calculated within each of the 18 LOS categories, separately for each severity level and each metro- politan area. Similarly, average densities were calculated (a) (b) (c) Figure 5.1. Freeway traffic density versus (a) total, (b) FI, and (c) PDO crash rates in the Seattle area.

45 (a) (b) (c) Figure 5.2. Freeway traffic density versus (a) total, (b) FI, and (c) PDO crash rates in the Minneapolis–St. Paul area.

46 upward). The data suggest that the three curves start at the same density (corresponding to minimum crash rate) and have similar shapes. In modeling, it was assumed that the relationships applied would be used only in the range from the minimum observed crash rate to the highest observed density. Predicting changes in crash rate with traffic density under free-flow conditions is not relevant to the assessment of design treatments for nonrecurrent congestion. Predict- ing changes in crash rate substantially above the observed data for the highest density is not reliable. Regression models were obtained only for total and FI crashes; a model for PDO crashes was obtained by subtraction. The best fit to the data was found to be a third-order poly- nomial with respect to density, as shown by Equation 5.5: a a a a Crash rate Density Density Density 5.5 0 1 2 2 3 3 ( ) = + × + × + × The regression results, based on 18 data points each for total and FI crash rates, are summarized in Table 5.7. All coef- ficients were statistically significant at the 0.0001 level. The total and FI curves reach a local minimum at a density around 20 pc/mi/lane; this value was selected as the density below which the data would not be modeled. At the high end of the density range, the curves were ended at a density of 78 pc/mi/lane. The two right-hand columns in Table 5.7 pre- sent the crash rates for each severity level at the ends of the fitted curve (20 and 78 pc/mi/lane). Figure 5.4 illustrates the observed and predicted crash rates as a function of traffic density. The final relationships are shown in Equations 5.6 through 5.8. D D D Total crashes per MVMT 2.636 0.2143 0.00708 4.80 10 5.62 5 3 ( ) = − × + × − × ×− D D D FI crashes per MVMT 1.022 0.0842 0.00264 1.79 10 5.72 5 3 ( ) = − × + × − × ×− D D D PDO crashes per MVMT 1.614 0.1301 0.00444 3.01 10 5.82 5 3 ( ) = − × + × − × ×− The crash rate–traffic density relationships shown in Figure 5.4 and Equations 5.6 through 5.8 are used in two ways in the analysis of the effectiveness of design treatments for nonrecurrent congestion. The primary application is to estimate the percentage reduction in crashes expected from the reduction in congestion resulting from the imple- mentation of any of the design treatments of interest. A secondary application is to allocate crashes between hours of the day on the basis of the congestion levels present. The LOS category (see Table 5.5) and the midpoint of traffic density for that LOS category. The plots generally show a U-shaped curve with the lowest crash rates in the middle of the crash rate range at about LOS C. Crash rates at lower den- sities (i.e., better LOS) are slightly higher than the minimum crash rate. Crash rates at higher densities (i.e., poorer LOS) are substantially higher than the minimum crash rate. The relationships implied by Figure 5.1 appear promising to evaluate the safety effects of design treatments intended to reduce nonrecurrent congestion. For example, if a particu- lar treatment shortens the duration of several incidents and results in 5 h per year with traffic operations in LOS C rather than LOS F, the relationships implied by Figure 5.1 should help to quantify that safety benefit as a specific number of crashes reduced. Figure 5.2 shows a plot of crash rate and traffic density data for the Minneapolis–St. Paul area analogous to that shown for the Seattle area in Figure 5.1. The Minneapolis– St. Paul data show a relationship similar to Seattle, but the U-shaped curve is not as pronounced and is complicated by highly variable data in the traffic density range from 30 to 40 pc/mi/lane (i.e., LOS D through E+). However, regres- sion modeling confirmed the U-shaped nature of the crash rate–traffic density relationship. There is no obvious expla- nation for this secondary peak, which is not present in the Seattle data and may be a quirk of the data for Minneapolis– St. Paul. The U-shaped relationship between crash rate and traffic density has a clear interpretation. At low traffic densities, there are few vehicle–vehicle interactions, and inattentive or fatigued drivers are likely to depart from their lane or leave the road- way. This trend ameliorates as traffic densities increase to the middle range. At high traffic densities, vehicle–vehicle inter- actions increase to the point that rear-end or sideswipe (i.e., lane-changing) crashes become more frequent. Table 5.6 con- firms that single-vehicle crashes predominate at lower traffic densities, and multiple-vehicle crashes predominate at higher traffic densities. The crash rates were generally lower in the Minneapolis– St. Paul metropolitan area than in the Seattle metropolitan area. However, for the planned application to safety–congestion relationships, the similar shape of the two crash rate–traffic density relationships is most important. To best represent this shape, the data from the Seattle and Minneapolis–St. Paul metro politan areas were combined, separately for each sever- ity level, giving each area equal weight. The resulting data are shown in Figure 5.3. The figure shows separate data for total crashes, FI crashes, and PDO crashes. Curves were fit to these data by using ordi- nary least squares regression analysis for the LOS range for which design treatments are of greatest interest to reduce nonrecurrent congestion (i.e., from the minimum density

47 Table 5.6. Crash Type Distribution for Seattle and Minneapolis–St. Paul Freeways by LOS Category Level of Servicea A B C D E F Crash Type Collision Type No. of Crashes (% of total) Seattle Single vehicle Run-off-road Fixed object Animal Overturn Pedestrian Other 56 502 17 50 5 62 (4.3) (38.4) (1.3) (3.8) (0.4) (4.7) 26 249 4 31 0 34 (2.4) (22.9) (0.4) (2.8) (0.0) (3.1) 26 233 6 36 3 34 (1.5) (13.9) (0.4) (2.1) (0.2) (2.0) 17 157 3 20 1 27 (1.0) (9.1) (0.2) (1.2) (0.1) (1.6) 6 66 0 6 0 7 (0.4) (4.4) (0.0) (0.4) (0.0) (0.5) 7 66 0 14 1 15 (0.2) (1.8) (0.0) (0.4) (0) (0.4) Subtotal 692 (52.9) 344 (31.6) 338 (20.1) 225 (13.1) 85 (5.6) 103 (2.8) Multiple vehicle Rear end Same-direction sideswipe Opposite-direction sideswipe Head-on Angle Other 355 95 88 3 62 12 (27.2) (7.3) (6.7) (0.2) (4.7) (0.9) 456 96 117 3 53 20 (41.9) (8.8) (10.7) (0.3) (4.9) (1.8) 915 179 154 0 63 29 (54.5) (10.7) (9.2) (0.0) (3.8) (1.7) 1102 192 134 2 45 24 (63.9) (11.1) (7.8) (0.1) (2.6) (1.4) 1179 135 76 1 20 11 (78.2) (9.0) (5.0) (0.1) (1.3) (0.7) 3115 276 141 1 37 16 (84.4) (7.5) (3.8) (0.0) (1.0) (0.4) Subtotal 615 (47.1) 745 (68.4) 1,340 (79.9) 1,499 (86.9) 1,422 (94.4) 3,586 (97.2) Total 1,307 (100.0) 1,089 (100.0) 1,678 (100.0) 1,724 (100.0) 1,507 (100.0) 3,689 (100.0) Minneapolis–St. Paul Single vehicle Run-off-road Fixed object Animal Railroad train Parked motor vehicle Overturn Pedestrian Other 304 33 9 2 2 1 1 175 (24.4) (2.6) (0.7) (0.2) (0.2) (0.1) (0.1) (14.0) 136 16 6 0 0 0 0 101 (10.9) (1.3) (0.5) (0.0) (0.0) (0.0) (0.0) (8.1) 81 5 3 2 0 1 0 58 (7.5) (0.5) (0.3) (0.2) (0.0) (0.1) (0.0) (5.4) 35 4 1 0 0 0 0 24 (5.6) (0.6) (0.2) (0.0) (0.0) (0.0) (0.0) (3.8) 11 1 0 0 0 0 0 4 (6.0) (0.5) (0.0) (0.0) (0.0) (0.0) (0.0) (2.2) 14 3 2 1 0 0 0 14 (4.9) (1.0) (0.7) (0.3) (0.0) (0.0) (0.0) (4.9) Subtotal 527 (42.3) 259 (20.8) 150 (13.9) 64 (10.3) 16 (8.8) 34 (11.8) Multiple vehicle Rear end Same-direction sideswipe Opposite-direction sideswipe Head-on Angle Other 327 191 6 17 39 139 (26.2) (15.3) (0.5) (1.4) (3.1) (11.2) 576 207 2 13 36 151 (46.3) (16.6) (0.2) (1.0) (2.9) (12.1) 640 142 4 8 22 113 (59.3) (13.2) (0.4) (0.7) (2.0) (10.5) 423 60 2 1 9 65 (67.8) (9.6) (0.3) (0.2) (1.4) (10.4) 114 22 1 0 6 23 (62.6) (12.1) (0.5) (0.0) (3.3) (12.6) 193 25 0 0 2 33 (67.2) (8.7) (0.0) (0.0) (0.7) (11.5) Subtotal 719 (57.7) 985 (79.2) 929 (86.1) 560 (89.7) 166 (91.2) 253 (88.2) Total 1,246 (100.0) 1,244 (100.0) 1,079 (100.0) 624 (100.0) 182 (100.0) 287 (100.0) a LOS was assigned to each crash on the basis of the freeway segment and the traffic conditions for the 15-min period in which the crash occurred.

48 Figure 5.3. Crash rate versus density for combined Seattle and Minneapolis–St. Paul areas. Table 5.7. Regression Results for FI and Total Crash Rates versus Density Severity Level Regression Coefficient Model Fit Crash Rate (crashes/MVMT) at Specified Density a0 a1 a2 a3 RMSE R2 (%) 20 pc/mi/lane 78 pc/mi/lane Total 2.636 -0.2143 0.00708 -4.80 × 10-5 0.183 98.5 0.80 6.22 FI 1.022 -0.0842 0.00264 -1.79 × 10-5 0.072 98.0 0.25 2.04 PDO 1.614 -0.1301 0.00444 -3.01 × 10-5 NA NA 0.54 4.17 Note: For PDO crashes, regression coefficients and crash rates for 20 and 78 pc/mi/lane were obtained by subtraction (total - FI). RMSE = root mean square error. Figure 5.4. Observed and predicted total, FI, and PDO crash rates versus traffic density.

49 known because it is, by definition, equal to 1.00. As shown in Figure 5.5, these five percentile values can be plotted to esti- mate the cumulative TTI curve. To estimate the average density from this TTI curve, the data are divided into five subsets. Each subset represents a proportion of all the vehicles using the freeway section during the specific hour under consideration (e.g., 8:00 to 9:00 a.m.). These proportions are termed the “weight” of each subset, and are as follows: • Subset 1 (TTI0 - TTI10): Weight1 = 10% • Subset 2 (TTI10 - TTI50): Weight2 = 40% • Subset 3 (TTI50 - TTI80): Weight3 = 30% • Subset 4 (TTI80 - TTI95): Weight4 = 15% • Subset 5 (TTI95 - TTI99): Weight5 = 5% Subset 5 is given a weight of 5%, even though the differ- ence between 95% and 99% is only 4%. This assumption is equivalent to estimating that TTI100 ≈ TTI99. Each subset has an average TTI value representing the travel time for all the vehicles in the subset. This average TTI value is calculated for each subset by using Equation 5.12: ( ) ( )= +TTI TTI TTI 2 5.12subset lower upper i where TTIsubset i = average TTI value for subset i; TTIlower = lowest TTI value for the subset; and TTIupper = highest TTI value for the subset. For example, for subset 1 (TTI0 - TTI10), TTIlower = TTI0, and TTIupper = TTI10. By using these values, the average travel time can be cal- culated for each subset. This value represents the amount of time that one vehicle would spend on the freeway section if relationships shown in Figure 5.4 and Equations 5.6 through 5.8 are applied only in the traffic density range from 20 to 78 pc/mi/lane. Above and below this crash density range, the crash rate is assumed to be constant at the end-point values shown in the two right-hand columns of Table 5.7. The full crash rate–traffic density relationship incorpo- rated in the assessment methodology is shown by Equa- tions 5.9, 5.10, and 5.11: D D D Total crashes per MVMT 0.80 if Density 20 pc/mi/lane 2.636 0.2143 0.00708 4.80 10 6.22 if Density 78 pc/mi/lane 5.9 2 5 3 ( )= < − × + × − × × >      − D D D FI crashes per MVMT 0.25 if Density 20 pc/mi/lane 1.022 0.0842 0.00264 1.79 10 2.04 if Density 78 pc/mi/lane 5.10 2 5 3 ( )= < − × + × − × × >      − D D D PDO crashes per MVMT 0.54 if Density 20 pc/mi/lane 1.614 0.1301 0.00444 3.01 10 4.17 if Density 78 pc/mi/lane 5.11 2 5 3 ( )= < − × + × − × × >      − The two applications in which the crash rate–traffic density relationships are used in the assessment tool are described in more detail below. prediction of Crash reduction Due to Congestion reduction resulting from Design treatments For each design treatment evaluated in Project L07, an untreated travel time index (TTI) curve and a treated TTI curve were predicted for each hour of the day. The Project L07 research team devised a methodology to convert a TTI curve into an equivalent traffic density distribution that could use the safety–density relationship to predict untreated and treated crash rates. This methodology is described in the following paragraphs. Project L03 provided equations to predict the 10th, 50th, 80th, 95th, and 99th percentile values of the cumulative TTI distribution. The lowest or zero percentile value of TTI is also Figure 5.5. Example of cumulative TTI distribution approximated from five percentile values.

50 where PDOCRsubset i is the PDO crash rate (crashes/MVMT) for subset i. To estimate the crash frequencies from the crash rates, the annual travel must be determined, which is calculated as shown by Equation 5.18: ( )= × ×AMVMT Demand Length 1,000,000 5.18tot daysN where AMVMTtot = total annual million vehicle miles traveled (MVMT/year); Demand = hourly volume for the freeway segment dur- ing an hour time-slice (vehicles/h); Length = length of freeway segment (mi); and Ndays = number of days in yearly study period. As explained in Chapter 4 under Model Variables, the usual days considered in the yearly study period are nonholiday weekdays, so that Ndays is 250 days. The annual travel for each subset is then calculated as given by Equation 5.19: ( )=AMVMT (AMVMT )(Weight ) 5.19subset tot subseti i where AMVMTsubset i equals the annual million vehicle miles traveled for subset i (MVMT/year), and Weightsubset i is the pro- portion of all vehicles using the freeway section during the hour. The total predicted number of crashes can then be cal- culated for the freeway segment by summing the predicted number of crashes in each subset. The number of predicted FI and PDO crashes are calculated as given by Equations 5.20 and 5.21, respectively: i i i NFI (FICR )(AMVMT ) 5.20tot subset subset 1 5 ∑ ( )= = where NFItot is the total predicted number of FI crashes per year. i i i NPDO (PDOCR )(AMVMT ) 5.21tot subset subset 1 5 ∑ ( )= = where NPDOtot is the total predicted number of PDO crashes per year. The final values for the predicted number of FI and PDO crashes per year are calculated and recorded first for the untreated TTI curve on the basis of the five TTI percentiles. Next, this series of calculations is completed using the five percentile values for the treated TTI curve. With these values, the reductions in FI and PDO crashes can be estimated as shown by Equations 5.22 and 5.23, respectively: that vehicle had a TTI equal to the average TTI for the subset, as shown by Equation 5.13: ( )= ×TT Length TTI FFS 5.13subset subset i i where TTsubset i = average travel time for subset i (h); Length = length of freeway segment (mi); TTIsubset i = average TTI value for the subset; and FFS = free-flow speed for the freeway segment (mph). The free-flow speed is determined by using HCM, Chap- ter 23 (3) procedures (see Equation 5.26). The average speed for each subset is then calculated as shown by Equation 5.14: ( )= =Speed Length TT FFS TTI 5.14subset subset subset i i i where Speedsubset i = average speed for subset i (mph); Length = length of freeway segment (mi); and TTsubset i = average travel time for the subset (h). Next, the density is calculated for each subset as shown by Equation 5.15. Because the safety–density relationship is only valid for densities between 20 and 78 pc/mi/lane, calculated densities below or above this range are limited at 20 and 78, respectively. i i i Density 225 1 Speed FFS 225 1 1 TTI 5.15 subset subset subset ( )( ) ( ) ( ) = − = −     where Densitysubset i is the average traffic density (pc/mi/lane) for subset i, and Speedsubset i is the average speed (mph) for the subset. The FI crash rate and PDO crash rate for each subset are estimated by using the safety–density relationship, as shown by Equations 5.16 and 5.17, respectively: i i i i FICR 1.022 0.0842 Density 0.00264 Density 0.0000179 Density 5.16 subset subset subset 2 subset 3 ( ) ( ) ( ) ( ) = − + − where FICRsubset i is the FI crash rate (crashes/MVMT) for subset i. i i i i PDOCR 1.614 0.1301 Density 0.00444 Density 0.0000179 Density 5.17 subset subset subset 2 subset 3 ( ) ( ) ( ) ( ) = − + −

51 estimation of Crash Distributions by hour of Day Chapter 23 of the 2000 Highway Capacity Manual provides a methodology for estimating freeway operating speed (3). To determine the operating speed, the free-flow speed of the freeway segment is first calculated using Equation 5.26, which is based on HCM Equation 23-1: ( )= − − − −FFS BFFS 5.26LW LC IDf f f fN where FFS = free-flow speed (mph); BFFS = base FFS (70 mph, urban; 75 mph, rural); fLW = adjustment for lane width from HCM Exhibit 23-4 (mph); fLC = adjustment for right-shoulder lateral clearance from HCM Exhibit 23-5 (mph); fN = adjustment for number of lanes from HCM Exhibit 23-6 (mph); and fID = adjustment for interchange density from HCM Exhibit 23-7 (mph). Operating speed for 70 < FFS ≤ 75 and a flow rate of (3,400 - 30FFS) < vp ≤ 2,400 is given by Equation 5.27: S vp FFS FFS 160 3 30FFS 3,400 30FFS 1,000 5.27 2.6( ) ( )= − − + − −         where S is operating speed (mph), and vp is the 15-min passen- ger car–equivalent flow rate (passenger cars per hour per lane [pcphpl]). For 55 < FFS ≤ 70 and (3,400 - 30FFS) < vp ≤ (1,700 + 10FFS), S is given by Equation 5.28: S vp FFS 1 9 7FFS 340 30FFS 3,400 40FFS 1,700 5.28 2.6 ( ) ( )= − − + − −         For 55 ≤ FFS ≤ 75 and vp ≤ (3,400 - 30FFS), operating speed equals free-flow speed, as shown by Equation 5.29: ( )= FFS 5.29S The average density can then be estimated by dividing operating speed S by the hourly demand volume, as shown by Equation 5.30: Density Demand hour hour i i S = ( )5 30. where Densityhour i is the average traffic density for hour i (pc/mi/lane), and Demandhour i is the hourly demand volume for hour i (pc/h). ( )= −   ∗%Reduction 1 NFI NFI 100 5.22FI tot tr tot unt where %ReductionFI = estimated percentage reduction in fatal- and-injury crashes due to the congestion- mitigation effect of a design treatment; NFItot unt = untreated total predicted number of fatal and major-injury crashes per year; and NFItot tr = treated total predicted number of fatal and major-injury crashes per year. ( )= −   ∗%Reduction 1 NPDO NPDO 100 5.23PDO tot tr tot unt where %ReductionPDO = estimated percentage reduction in PDO crashes due to the congestion-mitiga- tion effect of a design treatment; NPDOtot unt = untreated total predicted number of PDO crashes per year; and NPDOtot tr = treated total predicted number of PDO crashes per year. Finally, the percentage reduction values for each crash type are multiplied by the number of expected crashes for the roadway segment to determine the expected number of crashes reduced, as shown for FI and PDO crashes, respec- tively, in Equations 5.24 and 5.25: ( )( ) ( )=NReduction %Reduction100 Nexp 5.24FI FI FI where NReductionFI is the predicted number of fatal-and-injury crashes per year to be reduced by the congestion-mitigation effect of a design treatment, and NexpFI is the number of expected fatal and major-injury crashes per year without treatment. ( )( ) ( )=NReduction %Reduction100 Nexp 5.25PDO PDO PDO where NReductionPDO is the predicted number of PDO crashes per year to be reduced by the congestion-mitigation effect of a design treatment, and NexpPDO is the number of expected PDO crashes per year without treatment. The estimated number of FI and PDO crashes reduced per year by a particular design treatment at a particular site can then be used in a life-cycle benefit–cost analysis to quan- tify the value of the annual safety benefit expected from the design treatment. The life-cycle benefit–cost analysis meth- odology is presented in Chapter 6 of this report.

52 where NChour i is the predicted total number of crashes for hour i (crashes/year), and Length is the length of the freeway segment (mi). Finally, the estimated number of crashes for each hour is summed across all 24 hourly time-slices to determine the total number of predicted crashes for the year. Each hour’s predicted number of crashes is then divided by the total number of predicted crashes to determine the rela- tive probability of a crash occurring during that hour, as described by Equation 5.33: ∑ ( )= = CrashProb NC NC 5.33hour hour hour1 24i i ii where CrashProbhour i is the relative probability of a crash during hour i. Using this traffic density estimate, the crash rate– traffic density relationship developed in Project L07 pre- dicts the crash rate for each hourly time-slice by using Equation 5.31: ( ) ( ) ( ) ( ) = − + − CR 2.636 0.2143 Density 0.00708 Density 0.000048 Density 5.31 hour hour hour 2 hour 3 i i i i where CRhour i is the total crash rate for hour i (crashes/MVMT). The total predicted number of crashes for each hourly time-slice is then estimated as shown by Equation 5.32: ( )=NC (Demand )(Length)(250)(CR ) 1,000,000 5.32hour hour hour i i i