Validation of Urban Freeway Models (2014)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

4Context One of key objectives of the SHRP 2 Reliability program research is to develop methods for researchers and practitioners to evaluate the causal factors of travel time unreliability. The Federal Highway Administration (FHWA) defined three types of sources that contribute to congestion and travel time vari- ability: (1) traffic-influencing events, like incidents, work zones, and weather; (2) traffic demand, either through day-to-day variability or special events; and (3) physical highway features, like traffic control devices (such as ramp meters) and physical bottlenecks (1). Various projects within the SHRP 2 Reliability program have investigated various pieces of how to under- stand the relationship between these sources and travel time variability. These efforts include how the source data can be measured and processed (SHRP 2 L02), how simulation models can incorporate nonrecurrent congestion sources to generate travel time distributions (SHRP 2 L04), how nonrecurrent congestion impacts on travel time reliability can be incorpo- rated into the Highway Capacity Manual (SHRP 2 L08), and how the reliability improvements of various interventions can be predicted (SHRP 2 L03). The SHRP 2 L03 project collected traffic, incident, and weather data on urban freeway sections from around the United States and used it to develop cross-sectional statisti- cal models to predict various moments of the travel time distribution based on the explanatory variables. To accom- modate the needs of model users with varying quantities of data available to them, the L03 team developed two types of models: • Data-poor models, in which travel time reliability is a func- tion of the mean travel time; and • Data-rich models, in which travel time reliability is a function of some combination of incident lane hours lost, hours of rainfall, and the demand-to-capacity ratio. These L03 models were calibrated in sites around the country and validated using data collected in the Seattle metropolitan area. The models were also adapted and implemented in the SHRP 2 L07 project within a spreadsheet tool to evaluate the cost-effectiveness of highway design features. The SHRP 2 L33 project, Validation of Urban Freeway Models, had three specific goals: (1) perform further validation of the data-rich and data-poor predictive urban freeway travel time reliability models developed in the SHRP 2 L03 project; (2) enhance the models to improve their prediction of the reliability impacts of various reliability improvement strate- gies; and (3) validate the enhanced models to promote their acceptance and use among researchers and practitioners. In conducting research on travel time reliability, it should be noted that, while it is relatively straightforward to calculate reliability using measured data, it is a challenging task to predict reliability at the individual route level using a model. This is because people make route choice decisions dynamically in the real world, especially with the recent trends of traffic and incident information made available in real time to the traveling public. L03 Review This section summarizes the L03 predictive model work to provide a framing for the work done in L33. More information on L03 can be found in this report in Appendix A. Modeling Approach For the predictive models, the L03 project team collected traffic, incident, work zone, and weather data in eight metropolitan areas: Houston, Texas; Minneapolis, Minnesota; Los Angeles, San Francisco, and San Diego, California; Atlanta, Georgia; Jacksonville, Florida; and Seattle, Washington. Data were C h a p T E R 1 Background

5 Following initial investigation of the relationships between the assembled variables and the calculated reliability metrics, the L03 team proposed two model forms: 1. “A detailed deterministic model that uses all of the data being collected to a maximum degree (data-rich model)” 2. “A simpler model based on the fact that many of the applica- tions [Highway Capacity Manual (HCM) and travel demand forecasting models] work in an environment with limited data (data-poor model)” Each of these models is described in further detail below. Data-Rich Models The data-rich models were calibrated to predict reliability measures within four different time periods: • Peak hour: 60-min period during which the space mean speed is less than 45 mph collected on a total of 81 urban freeway study sections, which shared the following characteristics: • Relatively homogeneous in terms of traffic and geometric conditions • Represent portions of trips taken by travelers • No midsection freeway-to-freeway interchanges From this data set, the L03 team calculated a number of explanatory variables to test for inclusion in the models. Illustrative examples of these variables, as well as the reliability metrics computed as potential dependent variables, are shown in Table 1.1. It is important to note that the reliability metrics shown in this table and used in the modeling are calculated as the volume-weighted average of all of the 5-min-level Travel Time Indices in the given time period over a year. This is a critical piece of the analysis chain, as it means that the ultimate travel time distributions and results are weighted toward the time periods that are the most heavily traveled. This is in contrast to a facility-level perspective, which treats each measurement equally regardless of how many vehicles experienced it. Table 1.1. L03 Modeling Analysis Data Set Category Sample Measures Dependent Variables Reliability Metrics • Mean, standard deviation, median, mode, minimum, and percentile travel times and TTIs • Buffer indices, planning time index, skew statistics, and misery index • On-time percentages Independent Variables Area Operations Characteristics • Number of service patrol trucks • Service patrol trucks per mile • Quick Clearance Law? • Number of ramp meters, dynamic message signs, and closed circuit television (CCTV) cameras Service Patrols • Number of service patrol trucks covering section • Percentage of time periods when trucks are active Capacity and Volume Characteristics • Start and end times of peak hour and peak period • Calculated and imputed vehicle miles traveled • Average of demand-to-capacity ratio on all section links • Highest demand-to-capacity ratio of all links on the section Incident Characteristics • Number of incidents • Incident rate per 100 million vehicle miles • Incident lane-hours lost • Incident shoulder hours lost • Mean, standard deviation, and 95th percentile of incident duration Event Characteristics • Number of work zones • Work zone lane-hours lost • Work zone shoulder hours lost • Mean, standard deviation, and 95th percentile of work zone duration Weather Characteristics • Number of hours with precipitation amounts exceeding various thresholds • Number of hours with measurable snow • Number of hours with frozen precipitation • Number of hours with fog

6• Peak period: period of at least 75 min during which is the space mean speed is less than 45 mph • Midday: 11:00 a.m.–2:00 p.m., Monday–Friday • Weekday: All day, Monday–Friday The team selected a natural logarithmic form for the regres- sion model, because it is able to predict a TTI of 1 when the independent variables are 0. Root mean square error (RMSE) was used as the goodness-of-fit measure to compare between models with different combinations of independent variables. Variables were allowed to stay in the model equation with an alpha level of 0.1. After evaluating the potential independent variables, the L03 team ultimately selected the following to predict reliability within the defined time periods: • Incident lane-hours lost (ILHL) • Hours of precipitation exceeding 0.05 in. (RainHrs) • Critical demand-to-capacity ratio (dccrit) • Average demand-to-capacity ratio (dcaverage) Note that demand cannot be directly measured, and methods to calculate this and other independent variables are given in detail in Appendix C. Table 1.2 shows the explanatory variables that were used to predict different moments of the travel time index dis- tribution (column names) within the defined time periods (row names). Below the explanatory variables, it also displays the RMSE for each model measured during the calibration process. Data-Poor Models The data-poor model was first envisioned to take advan- tage of commonly available independent variables (such as annual collisions per million, vehicle miles traveled, speed limit, and yearly demand profiles). However, exploratory analysis showed promising relationships between the mean travel time and all selected reliability metrics. Because the mean travel time is a ready output from planning and oper- ational tools such as travel demand and simulation models, this relationship became the focus of the data-poor model development. Unlike the data-rich models, the data-poor models were not calibrated for specific time periods. The original set of data-poor equations developed in L03 and presented in the L03 final report use an exponential form to relate the mean TTI with measures of reliability. The data-poor models were developed to predict some reliability metrics not directly pulled from the travel time distribution. The definitions for these are • PctTripsOnTimeX: The percentage of on-time trips made with respect to X times the median TTI • PctTripsOnTimeXmph: The percentage of on-time trips made with respect to a speed threshold of X mph The functional form and calibration RMSEs for these models are shown in Tables 1.3 and 1.4. These original data-poor models were revised with new model forms or updated with new coefficients following the finalization of the L03 final report and were included in an appendix to the final report. No calibration errors were presented for these revised equations. The new functional forms are shown in Tables 1.3 and 1.4. The revised models for the TTI moment predictions were validated and explored for enhancement in the L33 project. Validation The L03 final report shows validation results for a select set of the data-rich and original data-poor models using data Table 1.2. L03 Data-Rich Explanatory Variables and RMSE by Model Period 10th Mean 50th 80th 95th 99th Peak Hour Variable dccrit, ILHL, RainHrs dccrit, ILHL dccrit, ILHL dccrit, ILHL dccrit, ILHL, RainHrs dccrit, ILHL RMSE 10–20% 20–30% 20–30% 30–40% 30–40% >40% Peak Period Variable dccrit, ILHL, RainHrs dccrit, ILHL dccrit, ILHL dccrit, ILHL, RainHrs dccrit, ILHL, RainHrs dccrit, ILHL, RainHrs RMSE <10% 10–20% 20–30% 20–30% 30–40% 30–40% Midday Variable dccrit dccrit dccrit dccrit dccrit dccrit RMSE <10% <10% 20–30% <10% 20–30% 30–40% Weekday Variable dcaverage dcaverage, ILHL dcaverage dcaverage, ILHL dcaverage, ILHL dcaverage, ILHL RMSE <10% 20–30% <10% 10–20% 30–40% >40%

7 collected on 26 freeway segments in the Seattle metropolitan area. Table 1.5 shows the validation error (the percentage dif- ference between the measured and the predicted values) for each roadway section for each validated model. Positive errors indicate that the model overpredicted the TTI (thus predict- ing that the segment is less reliable than it actually is) and negative errors indicate that the model underpredicted the TTI (thus predicting that the segment is more reliable than it actually is). The L03 team noted that the models tend to underpredict the weekday TTIs in the Seattle region and speculated that it may be due to the lack of a rain variable in the weekday mod- els, which raises errors in regions like Seattle that experience a lot of rainfall. The data-poor model exhibits the same under prediction trend, particularly with the 95th-percentile equation. The L03 project team recommended further vali- dation of the models to address these high errors. Research Questions To evaluate and enhance the L03 predictive models described above, the L33 project was guided by the following research questions: • What are the right explanatory variables to use to predict travel time reliability? • Is it possible to have single models that can be applied in all regions? • What are the most useful measures for the predictive models to output? • What is the right functional form for the reliability models? Final Report Structure Following this background chapter, the remainder of this final report is structured as follows: • Chapter 2: Data describes the data sets used in the L03 model validation and L33 model enhancement and validation stages of this project • Chapter 3: Existing Model Validation presents the validation results for the L03 data-rich and data-poor models • Chapter 4: Enhanced Models and Application Guidelines presents the recalibration and new model results for the data-rich and data-poor models and discusses recommen- dations for applying the models This report also contains the following five appendices, each of which contains one of the work products of the L33 project. • Appendix A: Review of L03 and Related Models is a techni- cal memorandum discussing the work performed in the SHRP 2 L03 project and other SHRP 2 Reliability projects that developed predictive models. Table 1.4. Data-Poor Functional Form and RMSE by Model, Part 2 PctTrips OnTime10mph PctTrips OnTime25mph PctTrips OnTime50mph PctTrips OnTime45mph PctTrips OnTime30mph Original Models Form exponential exponential exponential exponential exponential RMSE <10% <10% 10–20% 10–20% <10% Revised Models Form NA NA exponential exponential sigmoidal RMSE na na na na na Note: No calibration errors were presented for the L03 revised data-poor models; NA = not available; na = not applicable. Table 1.3. Data-Poor Functional Form and RMSE by Model, Part 1 10th Median 80th 90th 95th Original Models Form exponential exponential exponential exponential exponential RMSE <10% <10% <10% <10% 10–20% Revised Models Form natural log natural log natural log natural log natural log RMSE na na na na na Note: No calibration errors were presented for the L03 revised data-poor models; na = not applicable.

8Table 1.5. L03 Validation Errors Roadway Section Peak Period Weekday Data-Poor Mean 80th 95th Mean 80th 95th 80th 95th I-405 Bellevue northbound +30 to 40% Over +40% Over +40% Under +10% +10 to 20% +10 to 20% Under +10% +20 to 30% I-405 Eastgate northbound +10 to 20% +10 to 20% +30 to 40% NA Under +10% Under +10% Under +10% +30 to 40% I-405 Eastgate southbound -10 to 20% -10 to 20% Under -10% -10 to 20% -10 to 20% -10 to 20% Under +10% -20 to 30% I-405 Kennydale southbound -10 to 20% -10 to 20% -10 to 20% -10 to 20% -30 to 40% -30 to 40% Under -10% -20 to 30% I-405 Kirkland northbound Under +10% Under +10% +20 to 30% Under +10% Under +10% +20 to 30% +10 to 20% +30 to 40% I-405 Kirkland southbound Under -10% Under +10% +10 to 20% Under -10% Under +10% +20 to 30% Under +10% +30 to 40% I-405 North northbound Under +10% Under +10% +20 to 30% Under +10% Under +10% +10 to 20% Under +10% +20 to 30% I-405 North southbound -30 to 40% Over -40% Over -40% Under +10% -10 to 20% -20 to 30% -10 to 20% Over -40% I-405 South northbound -30 to 40% -30 to 40% -20 to 30% -20 to 30% Over -40% Over -40% -10 to 20% -20 to 30% I-405 South southbound Under +10% Under +10% +10 to 20% +10 to 20% +20 to 30% +10 to 20% Under +10% +10 to 20% I-5 Everett northbound Under +10% Under -10% -10 to 20% Under +10% Under +10% -30 to 40% +20 to 30% Over -40% I-5 Everett southbound +20 to 30% +20 to 30% +30 to 40% Under +10% +10 to 20% +20 to 30% Under +10% Under +10% I-5 Lynnwood northbound +10 to 20% +20 to 30% Under -10% Under +10% Under +10% -10 to 20% Under +10% +20 to 30% I-5 Lynnwood southbound Under -10% Under -10% -10 to 20% Under -10% Under +10% -20 to 30% +10 to 20% -30 to 40% I-5 South northbound +10 to 20% +20 to 30% +30 to 40% Under +10% +10 to 20% Under +10% +10 to 20% +30 to 40% I-5 South southbound +10 to 20% Under +10% +20 to 30% Under +10% Under +10% +20 to 30% +10 to 20% +30 to 40% I-5 Tukwila northbound +20 to 30% +10 to 20% +10 to 20% Under +10% Under +10% Under +10% Under +10% +20 to 30% I-5 Tukwila southbound Over +40% Over +40% Over +40% Under +10% Under +10% +20 to 30% Under +10% Under +10% I-90 Bellevue westbound +20 to 30% +30 to 40% +30 to 40% Under +10% Under +10% +10 to 20% +10 to 20% +20 to 30% I-90 Bridge eastbound +10 to 20% Under +10% Under +10% Under +10% Under +10% +20 to 30% Under +10% +30 to 40% I-90 Bridge westbound Under -10% -10 to 20% -10 to 20% Under -10% Under +10% -10 to 20% +10 to 20% -10 to 20% I-90 Issaquah westbound +10 to 20% +10 to 20% +10 to 20% Under +10% Under +10% +10 to 20% Under +10% +20 to 30% SR 167 Auburn northbound Under -10% Under -10% Under +10% Under -10% -10 to 20% +20 to 30% Under -10% -20 to 30% SR 167 Auburn southbound -10 to 20% -20 to 30% -20 to 30% Under -10% -10 to 20% -30 to 40% Under +10% -20 to 30% SR 167 Renton northbound Under +10% +20 to 30% -10 to 20% Under +10% +10 to 20% -20 to 30% Under +10% +20 to 30% SR 167 Renton southbound Under +10% Under +10% -10 to 20% Under +10% Under +10% -10 to 20% Under +10% +20 to 30% Note: NA = not available.

9 • Appendix B: Validation Plan is a technical report outlining the data collection and analysis strategy for validating the L03 data-rich and data-poor models. • Appendix C: Data-Rich Validation is a technical memoran- dum containing detailed validation results for the data-rich models. • Appendix D: Data-Poor Validation is a technical memo- randum containing detailed validation results for the data- poor models. • Appendix E: Model Enhancements is a technical memo- randum showing the results of the data-poor model reca- libration and enhancement. Reference 1. Federal Highway Administration, U.S. Department of Transpor- tation. Traffic Congestion and Reliability: Trends and Advanced Strategies for Congestion Mitigation. http://www.ops.fhwa.dot .gov/congestion_report/chapter2.htm. Accessed on January 9, 2014.