Further Development of the Safety and Congestion Relationship for Urban Freeways (2014)

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15 This chapter addresses interpreting the state-by-state results presented in Chapter 2. Comparison of the Safety- Congestion Relationships Between States Chapter 2 presented the safety-congestion relationships developed in both the original Phase 2 research and in the new Task IV-5 research. As noted in the background discus- sion in Chapter 1, the original safety-congestion relationships developed in Phase 2 for Seattle and Minneapolis–St. Paul freeways both showed a U-shaped curve with the lowest crash rates in the middle of the traffic density range, at about LOS C. Crash rates at lower densities (i.e., better LOS) are slightly higher than the minimum crash rate, due primarily to single-vehicle crashes. Crash rates at higher densities (i.e., poorer LOS) are substantially higher than the minimum crash rate, due to multiple-vehicle crashes. This U-shaped relationship is quite pronounced for the Seattle data in Fig- ure 2.1 and is clearly present in Minneapolis–St. Paul, though confounded by a secondary peak in the middle traffic density range (approximately LOS D), as shown in Figure 2.2. The data for Sacramento freeways, shown in Figure 2.3, largely confirm the Seattle and Minneapolis–St. Paul results, showing a U-shaped relationship with minimum crash rates at about LOS C, slightly higher crash rates at lower densities (i.e., better LOS), and substantially higher crash rates at higher densities (i.e., poorer LOS). The data for freeways in the Kansas portion of the Kansas City metropolitan area (see Figure 2.4) show little variation in crash rate over the range of traffic density, although crash rates were substantially higher in the lowest traffic density category (LOS A+) and slightly higher in the highest traffic density category (LOS F+). Review of the data shows that the Kansas freeways experienced a substantially lower portion of LOS F conditions than the other metropolitan areas and, therefore, did not have much opportunity to show higher crash rates at higher traffic densities. The data for freeways in the Missouri portion of the Kansas City metropolitan area (see Figure 2.5) show very similar results to those in the Kansas portion, although the crash rate for the highest traffic density category (LOS F+) was not any higher than the crash rates at medium crash densities (LOS C and D). The most appropriate interpretation of these results is that the Seattle, Minneapolis–St. Paul, and Sacramento results show similar shapes for the safety-congestion relationships. The results for the Kansas City metropolitan area are not nec- essarily inconsistent with the other metropolitan areas but may not include sufficient congestion to show higher crash rates at the highest crash densities. Combined Safety-Congestion Relationship The research team’s assessment was that the most appropriate method to obtain an overall safety-congestion relation- ship was to combine the Seattle, Minneapolis–St. Paul, and Sacramento results into a single relationship. Graphs of the data from these three metropolitan areas all show relation- ships between safety and congestion with similar shapes. The Kansas City data were not included because they did not show higher crash rates at higher traffic densities. It should be recognized that the available data for the Kansas City area are not necessarily inconsistent with the relationships found for Seattle, Minneapolis–St. Paul, and Sacramento; especially for the Kansas portion of the Kansas City metropolitan area, the lack of definitive results for sites with high traffic densities was due primarily to the sparsity of data for high congestion levels and does not necessarily represent any fundamental difference in the safety-congestion relationship from the other areas. It should also be noted that the shape of the over- all safety-congestion relationship would not have been very C h a p t e R 3 Interpretation of Results

16 crash rate for the three metropolitan areas and then averaging the individual data points. With this translation completed, the results are representative of a freeway system with a total crash rate of 1.86 crashes per MVMT, a fatal-and-injury crash rate of 0.42 crashes per MVMT, and a property-damage- only crash rate of 0.82 crashes per MVMT, which represents the average freeway crash rate for Seattle, Minneapolis– St. Paul, and Sacramento, giving equal weight to each metro- politan area. The portion of the safety-congestion relationship that is most relevant to the objectives of Project L07 is the range from LOS C to LOS F, which shows that freeway crash rates can be reduced by decreasing congestion. As in the original Phase 2 research, the best fit to the safety-congestion relation- ship in this range was found to be a cubic functional form. Figure 3.1 illustrates the combined safety-congestion rela- tionship by crash severity levels. The coefficients of these cubic relationships are presented in Table 3.1. The curves shown in Figure 3.1 can be represented math- ematically as follows in Equations 3.1–3.3: Total crashes per MVMT 2.190 0.1979 0.00728 5.34 10 (3.1)2 5 3 D D D = − × + × − × ×− FI crashes per MVMT 0.831 0.0718 0.00246 1.76 10 (3.2)2 5 3 D D D = − × + × − × ×− PDO crashes per MVMT 1.359 0.1261 0.00482 3.58 10 (3.3)2 5 3 D D D = − × + × − × ×− different even if the Kansas City data were included, because the average crash rate for Kansas City freeways was very close to the average crash rate for the other three metropolitan areas; the lack of data for higher traffic densities in Kansas City means that inclusion of the Kansas City data would have had only a small influence on that end of the curve. Table 2.7 shows that volume and/or speed data are missing for 18.5% of the 15-min periods in the Seattle metropolitan area and 16.1% of the 15-min periods in the Minneapolis– St. Paul metropolitan area. These missing data were due pri- marily to random events such as detector outages and should not represent any systematic bias in the data. Therefore, the presence of these missing data does not raise a concern about using the remaining data for the Seattle and Minneapolis– St. Paul metropolitan areas in modeling the safety-congestion relationship. The Sacramento metropolitan area had the least missing data among the metropolitan areas studied (only about 1% of the available 15-min periods) because the Caltrans PeMS includes estimates for speed and volume when actual data are not available. The research team reviewed the data, and most of the estimated values appeared to be during nighttime peri- ods when the traffic operational conditions were unquestion- ably at LOS A. Since the analysis conducted focused on the level of service range from LOS C to LOS F, the inclusion of some estimated speed and volume data for low-volume con- ditions at LOS A did not appear to bias the study results in any way. A combined safety-congestion relationship for the Seattle, Minneapolis–St. Paul, and Sacramento metropolitan areas was developed by translating the curves to the average freeway Crash type FI observed FI predicted PDO observed PDO predicted Total observed Total predicted Cr a s he s pe r M VM T 0 1 2 3 4 5 6 Traffic density (pc/mi/ln) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Figure 3.1. Observed and predicted FI, PDO, and total crash rates versus traffic density (Seattle, Minneapolis–St. Paul, and Sacramento areas combined).

17 Over the entire traffic density range, crash rates are expressed as follows in Equations 3.4 through 3.6, based on Table 3.1: Total crashes per MVMT 0.72 if Density 20 pc mi ln 2.190 0.1979 0.00728 5.34 10 5.77 if Density 76 pc mi ln (3.4)2 5 3D D D = < − × + × − × × >      − FI crashes per MVMT 0.24 if Density 20 pc mi ln 0.831 0.0718 0.00246 1.76 10 1.86 if Density 76 pc mi ln (3.5)2 5 3D D D = < − × + × − × × >      − PDO crashes per MVMT 0.48 if Density 20 pc mi ln 1.359 0.1261 0.00482 3.58 10 3.91 if Density 76 pc mi ln (3.6)2 5 3D D D = < − × + × − × × >      − Figure 3.2 compares the curves developed from the Seattle, Minneapolis–St. Paul, and Sacramento data (black lines) to the original curves developed from the Seattle and Minneapolis– St. Paul data only (gray lines). The figure shows that the revised relationships differ only slightly from the original relationships. The safety-congestion relationships shown in Figure 3.1 and Equations 3.4 through 3.6 are appropriate for use in the Proj- ect L07 Analysis Tool in place of the original relationships shown in Figure 1.1, and the tool will be updated accordingly. Table 3.1. Regression Results for Total, FI, and PDO Crash Rates Versus Traffic Density (Seattle, Minneapolis–St. Paul, and Sacramento Areas Combined) Severity Level Regression Coefficients Model Fit Crash Rate (Crashes per MVMT) at Specified Density a0 a1 a2 a3 RMSEa R2 (%) 20 pc/mi/ln 76 pc/mi/ln Total 2.190 -0.1979 0.00728 -5.34 × 10−5 0.145 99.1 0.72 5.77 FI 0.831 -0.0718 0.00246 -1.76 × 10−5 0.060 98.4 0.24 1.86 PDOb 1.359 -0.1261 0.00482 -3.58 × 10−5 NA NA 0.48 3.91 a Root mean square error. b Regression coefficients and crash rates for 20 and 76 pc/mi/ln obtained by subtraction (Total - FI). Crash type FI predicted (1) FI predicted (2) PDO predicted (1) PDO predicted (2) Total predicted (1) Total predicted (2) Cr a s he s pe r M VM T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Traffic density (pc/mi/ln) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Figure 3.2. Predicted FI, PDO, and total crash rates versus traffic density (1  Seattle and Minneapolis–St. Paul areas combined; 2  Seattle, Minneapolis–St. Paul, and Sacramento, areas combined).

18 Safety-Congestion Relationships for Specific Nonrecurrent Congestion Scenarios The results shown in Figures 3.1 and 3.2 incorporate the effects of both recurrent and nonrecurrent congestion as well as many periods of uncongested flow. Since the focus of Project L07 is on nonrecurrent congestion, a further analysis was conducted to check whether the results shown in Figures 3.1 and 3.2 are representative of nonrecurrent congestion. This investigation was conducted with the data for Sacramento freeways. The investigation of nonrecurrent congestion required the development of criteria to distinguish recurrent and non­ recurrent congestion. This was accomplished as follows: • First, periods when medium­ or long­term work zones were present on the study sites were identified. This was accom­ plished by plotting the time sequence of mean 15­min traffic speeds for off­peak periods (separately for daytime and nighttime periods). Periods with medium­ or long­term work zones that constitute nonrecurrent congestion were easily identified by noting periods of reduced traffic speeds that lasted for a defined time period (often weeks or months) and then returned to normal levels. Some work zones were daytime­only work zones, some were nighttime­only work zones, and some were under way during both daytime and nighttime hours. Work­zone periods with reduced speeds were classified as nonrecurrent congestion regardless of the actual traffic flow levels in the work zone (i.e., a work zone in place with reduced speeds 24 h per day was classified as non­ recurrent congestion for 24 h per day). • Second, other periods of nonrecurrent congestion (not in work zones) were identified by application of a set of rules. These rules were based on experience in other projects and a review of a sample of the Sacramento data. For each 15­min time slice, for each day of the week at each site (e.g., 1:00 p.m. to 1:15 p.m. for all Mondays during the 3­year study period), the mean and standard deviation of the daily 15­min speeds were determined based on data for all periods when medium­ to long­term work zones were not present (see above). The rules for identifying nonrecurrent congestion periods other than work­zone periods were as follows: 44 If the standard deviation of speed for a site, day of week, and time of day (15­min period) time slice is greater than or equal to 6 mph, then the 15­min periods for every day in that time slice are not classified as nonrecurrent con­ gestion (i.e., they represent either recurrent congestion or normal uncongested flow). 44 If the speed for an individual 15­min period is less than the mean speed for the time slice minus 1.5 times the stan­ dard deviation of speed for the time slice and the speed for that individual 15­min period is more than 8 mph less than the mean speed for the time slice, then that individual 15­min period is classified as nonrecurrent congestion. Application of the preceding criteria to 26,960,918 individual site­periods (a 15­min period at a given site) for which volume and speed data are available for Sacramento freeways resulted in 5,636,666 site­periods (21%) classified as nonrecurrent conges­ tion and 21,324,252 site­periods (79%) classified as recurrent congestion or normal uncongested flow. Figure 3.3 presents crash rate versus traffic density for the nonrecurrent congestion periods, and Figure 3.4 presents comparable data for the recurrent congestion and normal uncongested flow. Both plots show the same U­shaped rela­ tionship between crash rate and traffic density found for the Severity level FI PDO Total Cr as he s pe r M VM T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Traffic density (pc/mi/ln) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Figure 3.3. Crash rate versus traffic density for nonrecurrent congestion periods in Sacramento.

19 overall data set (see Figure 2.3). This provides strong evidence that the general relationship between crash rate and traffic density shown in Figure 3.1 is applicable to both recurrent and nonrecurrent congestion. A further investigation was undertaken to examine the role of various sources of nonrecurrent congestion. The 5,636,666 site-periods of nonrecurrent congestion on Sacramento free- ways were broken down as follows: • 5,631,097 site-periods related to work zones; • 59 site-periods related to crashes; and • 5,510 site-periods related to other sources of nonrecurrent congestion. The work-zone periods were identified as previously described. These periods constituted the vast majority of the periods identified as nonrecurrent congestion. Figure 3.5 illus- trates the relationship between crash rate and traffic density for work-zone periods. This plot is virtually identical to the plot in Figure 3.3 and displays the same U-shaped relation- ship shown previously. Figure 3.5 includes congestion related to crashes that occurred in work zones. Cr a s he s pe r M VM T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Traffic density (pc/mi/ln) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Severity level FI PDO Total Figure 3.4. Crash rate versus traffic density for recurrent congestion and normal uncongested flow (non-work-zone periods) in Sacramento. Figure 3.5. Crash rate versus traffic density for work-zone periods in Sacramento. Severity level FI PDO Total Cr as he s pe r M VM T 0 1 2 3 4 5 6 Traffic density (pc/mi/ln) 50 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

20 Nonrecurrent congestion related to crashes was identified by matching all periods of nonrecurrent congestion identi- fied according to the rules presented above with the locations and times of crashes. Any nonrecurrent congestion was iden- tified as crash-influenced if it occurred • In the same 15-min period as a crash or in one of the three subsequent 15-min periods; and • In the same freeway section as a crash or in any freeway section within 2 mi upstream of the freeway section where the crash occurred. This process identified only 59 site-periods with nonrecurrent congestion related to crashes (not including crashes in the work zones). There were so few crash-related periods of nonrecurrent congestion that it was not meaningful to plot them. However, all of the crash-related periods of nonrecurrent congestion resulted in traffic densities in the range from LOS C to LOS D. There were no periods of extremely high traffic density (i.e., LOS E or F) related to crashes. The other 5,510 site-periods of nonrecurrent congestion relate to other congestion sources; these include vehicle break- downs, short-term work zones, and weather events. There were no crashes during these 5,510 site-periods because, by defini- tion, all periods with crashes (or influenced by crashes) were included in one of the other nonrecurrent congestion catego- ries. Therefore, it is not feasible to plot crash rate versus traffic density for these periods. Interpretation of Results Figure 3.1 presents the best overall illustration of the relation- ship between safety and congestion found in the research. The relationships shown in Figure 3.1 are represented analytically in Table 3.1 and Equations 3.1 through 3.6. Variation of Crash Severity with Increasing Congestion Levels The authors’ original expectation was that, while crash fre- quency might increase at higher congestion levels, crash severity might not increase, or might even decrease, because traffic speeds would be lower at high congestion levels. The research results, as illustrated in Figure 3.1, contradict this original expectation. The research results in Figure 3.1 show that both fatal-and-injury and property-damage-only crashes increase as the traffic density increases. The increase in fatal- and-injury crashes is not as large as the increase in property- damage-only crashes, but the frequency of more severe crashes does increase as congestion increases. Using the Safety-Versus-Congestion Results to Estimate Crash Reduction due to Congestion Reduction Resulting from Design Treatments The full algorithm developed in Reliability Project L07 for assessing the cost-effectiveness of design treatments for reduc- ing nonrecurrent congestion is presented in the Project L07 final report (1). This section discusses how the results pre- sented in this chapter’s Combined Safety-Congestion Rela- tionship section are used in that algorithm to estimate the safety effect of congestion reduction. To understand the full context of this procedure, as applied in the Project L07 Analysis Tool, refer to the Project L07 final report (1). As an example, suppose that a design treatment was under consideration for implementation on an urban freeway and application of the procedures in the Project L07 final report indicated that, for the traffic conditions present in one particu- lar hour of a typical day, implementation of the design treat- ment would reduce congestion such that the traffic density would be reduced by that treatment from 65 to 55 pc/mi/ln. Computations with Equation 3.5 indicate that such a change in density would, on average, reduce fatal-and-injury crashes by 19% (from 1.72 to 1.40 crashes per MVMT). Similarly, computations with Equation 3.6 indicate that the change in density would, on average, reduce property-damage-only crashes by 18% (from 3.70 to 3.05 crashes per MVMT). It is therefore reasonable to expect that the expected crash fre- quency on the candidate treatment site during the hour in question (or during a 1-h time slice representing that par- ticular hour over course of the entire year) would be reduced by 19% for fatal-and-injury crashes and 18% for property- damage-only crashes. To determine the overall annual crash reduction, this calculation would need to be repeated for each of the 24 h of the day. The Analysis Tool developed in Project L07 (1) automates this computation to eliminate the need for repeti tive manual calculations.