Validation of Urban Freeway Models (2014)

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10 Sites The L33 team calibrated and validated its models using urban freeway data collected in the following metropolitan areas: • San Diego; • San Francisco; • Sacramento, California; • Los Angeles; • Minneapolis–Saint Paul, Minnesota; • Spokane, Washington; and • Salt Lake City, Utah. Details about the study segments and data sets are pro- vided in the L33 validation plan included in Appendix B. The San Diego, San Francisco Bay Area, Sacramento, and Los Angeles metropolitan regions (grouped together into a California data set), Salt Lake City, and Spokane data were collected from the 3-year period between January 1, 2010, and December 31, 2012. The Minnesota data were collected from the 3-year period between June 1, 2009, and May 31, 2012. The L33 team selected these sites in part because their agen- cies collect and archive continuous, high quality traffic data. These characteristics are also critical for L33 validation and enhancement activities. As such, this project used data col- lected in many of the same locations as L03. The L33 project team ensured that the model validation performed in L33 does not use the same data collected during the same time frame on the same freeways segments as was used to calibrate or validate the models in L03. Because this is a critical requirement, the L33 team conducted a thorough review of the data set. The roadway sections that were studied within each of these regions were selected in accordance with the application guide- lines of the L03 data-rich and data-poor models through the following criteria: • Length of around 5 mi (range from 2 to 10 mi) • Good data quality over a year • Monitored by point detectors with no more than an aver- age spacing of ¾ mi, or monitored by automated vehicle identification (AVI) technologies at the section origin and destination • No midsection freeway-to-freeway interchanges or bottle- necks • Relative homogeneity in terms of traffic and geometric conditions Processing This section briefly describes the data processing that was performed to generate the dependent and independent vari- ables for the validation of the data-rich and data-poor models. Further detail on these steps is provided in the L33 validation plan included in Appendix B. Traffic Data For the validation, traffic data is needed to calculate (1) the dependent TTI reliability measures; (2) the mean TTI inde- pendent variable for the data-poor models; (3) the demand- to-capacity ratios used as independent variables for some of the data-rich models; and (4) the peak hour and peak period time slice definitions. Raw traffic data were extracted from the Performance Measurement System (PeMS) deployment databases for each study location. The raw data consisted of 5-min traffic flow, occupancy, and speed for each detector station along a roadway section. The following steps were taken to turn the raw data points into section-level TTI reliability statistics over a year: 1. Calculate 5-min vehicle miles traveled (VMT) and vehicle hours traveled (VHT) at each detector station (link) using the link’s volume, speed, and length (the distance halfway to the nearest neighboring stations in the upstream and downstream directions) C h a P t e r 2 Data

11 year is the 99th-percentile D/C ratio over all midday periods in the year. The average D/C ratio over the year is the mean of all the midday D/C ratios over the year. Incident Lane-Hours Lost The number of incident lane-hours lost on a roadway section over the year is an independent variable in some of the data- rich models. Estimating this number for a roadway section requires two key pieces of information from each incident: (1) the number of lanes it blocked and (2) its duration. In data- sets for which one or both of these variables were unavailable, they were estimated from the L03 final report equations based on the agency incident clearance policies and the presence of shoulders. Hours of Precipitation Exceeding 0.05 in. The number of hours of precipitation exceeding 0.05 in. on a roadway section over a year is an independent variable in some of the data-rich models. Hourly weather data from the National Weather Service (NWS) was used to compute the number of hours that had precipitation exceeding defined thresholds (ultimately, the number of hours where rainfall exceeded 0.05 in. was included in the data-rich model). Characteristics Data-Rich Independent Variables This section describes and evaluates the independence of the data-rich independent variables that were input into each model in order to predict travel time reliability. Peak Hour The distributions of the critical demand-to-capacity ratio, incident lane-hours lost, and hours of rainfall exceeding 0.05 in., as well as some basic summary statistics for these variables, are shown in Figure 2.1. There is a fairly wide dis- tribution of all of these variables, though no notable outliers. Table 2.1 shows the correlation coefficients between the independent variables, and Figure 2.2 shows scatterplots illus- trating these relationships. The critical demand-to-capacity ratio and the number of incident lane-hours lost exhibit the strongest, though still weak, linear relationship. Peak Period The distributions of the critical demand-to-capacity ratio, incident lane-hours lost, and hours of rainfall exceeding 0.05 in., as well as some basic summary statistics for these 2. Aggregate the link-level data to section-level 5-min VMT, VHT, space mean speed, TTI, and travel time 3. Exclude 5-min data points collected when fewer than 50% of the section’s detectors were not working 4. Group the 5-min section-level data into the peak hour, peak period, midday, and weekday time slices over an entire year, and calculate for each section-year-time slice combination the • Mean TTI • Percentile TTIs (10th, 50th, 80th, 95th, and 99th) • On-time statistics [percentage of trips (VMT) made within 1.1x the median travel time and within 1.25x the median travel time] • Failure statistics [percentage of trips (VMT)] with speeds less than 50 mph, 45 mph, and 30 mph The peak hour and peak period time slices used in Step 4 were calculated from the outputs of Step 3 as follows: • Peak Hour: Identify the 60-min period on non-holiday weekdays with the lowest average speed. Each consecutive section speed must be less than or equal to 45 mph. • Peak Period: Identify non-holiday, weekday time periods of at least 75 min during which the average section speeds are less than or equal to 45 mph. Demand-to-Capacity Ratios The following two forms of the demand-to-capacity (D/C) ratio were used as independent variables in the data-rich models: • Critical demand-to-capacity ratio: The critical demand of a section is calculated as the highest 99th-percentile demand measured on a link on the segment during the given time period (peak hour or peak period) over a year. • Average demand-to-capacity ratio: The average demand is calculated as the average demand measured on all links on the segment during the given time period (peak hour or peak period) over a year. The capacity used in both ratios is the hourly capacity according to National Cooperative Highway Research Pro- gram (NCHRP 387) methodologies. The demand is summed up over all 5-min periods in the time slice over a single day. Since only volume, not demand, can be directly measured by loop detectors, demand was computed using the methodology developed in L03 and summarized in Appendix B. To give an example of this process, for a single day, the D/C ratio during the midday period is equal to the sum of all of the 5-min demands over the 3-hour midday period divided by the hourly capacity. The 99th-percentile D/C ratio over the

12 variables, are shown in Figure 2.3. As with the peak hour, each of the variables exhibits a wide distribution. This makes sense because the duration of the peak period varies from section to section, and as the peak period duration increases, the D/C ratio is certain to increase and the incident and rain terms are likely to increase. D/C_crit ILHL Rain Figure 2.1. Independent variables summary, peak hour. Table 2.1. Correlation Coefficients between Independent Variables, Peak Hour D/Ccrit ILHL Rain D/Ccrit 1 0.272 -0.14 ILHL 0.272 1 -0.21 Rain -0.14 -0.21 1 Table 2.2 shows the correlation coefficients between the independent variables, and Figure 2.4 shows scatterplots illustrating these relationships. The relationships between variables in the peak period are much stronger than they are for the peak hour. The relationship between the critical-demand- to-capacity ratio and the incident lane-hours lost is particularly strong. Midday The distribution of the only independent variable in the midday models—the critical demand-to-capacity ratio—is shown in Figure 2.5. Most of the ratios are between 1 and 3. Weekday The distributions of the average demand-to-capacity ratio and the incident lane-hours lost, as well as some basic summary

13 Figure 2.2. Relationships between independent variables, peak hour.

14 D/C_crit ILHL Rain Figure 2.3. Independent variables summary, peak period. Table 2.2. Correlation Coefficients between Independent Variables, Peak Period D/Ccrit ILHL Rain D/Ccrit 1 0.917 0.637 ILHL 0.917 1 0.505 Rain 0.637 0.506 1 statistics for these variables, are shown in Figure 2.6. There are some potential outliers noticeable (in the incident lanes-hours lost distribution), which are around three times as high as the next-highest values. These were collected on a few of the Minneapolis roadway sections. Figure 2.7 shows the scatterplot of the incident lane-hours lost against the average demand-to-capacity ratio. The linear relationship here is weak, with a correlation coefficient of 0.2. Summary Table 2.3 contains a summary of the correlation coefficients of the three independent variables for three time periods.

15 Figure 2.4. Relationships between independent variables, peak hour. D/C_crit Figure 2.5. Independent variable summary, midday.

16 D/C_avg ILHL Figure 2.6. Independent variables summary, weekday.

17 Figure 2.7. Relationship between independent variables, weekday. Table 2.3. Correlation Coefficients of Independent Variables D/C ILHL Rain Hour Period Weekday Hour Period Weekday Hour Period D/C Hour 1 0.27 -0.14 Period 1 0.92 0.64 Weekday 1 0.20 ILHL Hour 0.28 1 -0.21 Period 0.92 1 0.51 Weekday 0.20 1 Rain Hour -0.14 -0.21 1 Period 0.64 0.51 1