Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies (2012)

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124 C h a p t e r 7 potential Model Forms Background The primary goal of the statistical analysis was to produce a highly practical set of relationships that could be used to pre- dict reliability, especially within the contexts of existing techni- cal applications such as travel demand forecasting models and simulation models. The Phase 1 report proposed two model forms to be investigated: (a) a detailed deterministic model that uses all the data being collected to the maximum degree (data-rich model) and (b) a simpler model reflecting the fact that many of the applications (e.g., Highway Capacity Manual [HCM] and travel demand forecasting models) work in an environment with limited data (data-poor model). The first model will reveal a deep understanding of reliability and its causal factors; the second makes the relationships operational for many applications. It should be pointed out that the model forms are aimed at predicting reliability, which is based on summarizing travel times that occur over the course of a year. So, every observa- tion in the analysis data set represents summarized conditions for a study section for a year. The statistical models are not designed to predict what a specific travel time will be given a set of conditions (e.g., volume, weather, and incident charac- teristics). Such prediction can be done with a variety of other analytic methods, such as microsimulation. Prediction or the probability of a specific travel time occurring is related to reli- ability, but predicting reliability metrics is not the purpose of this research. However, the microscale analysis done for the congestion by source analysis (Chapter 5) does get down to this level. Data-Rich Model The data-rich model structure is mechanistic in nature; the factors (the mechanisms) that cause unreliable travel times were postulated based on the research team’s past experience. It also is a tiered model in which the independent variables at lower levels (left side of the model chain) become dependent variables at higher levels. The key feature of this model struc- ture is that improvements can be traced to a relatively small number of factors, which reduces the need to observe reli- ability changes in before-and-after experiments. As discussed earlier, to conduct before-and-after tests of all improvements would be cost prohibitive. The structure of the data-rich deterministic (tiered) model is outlined in Figure 7.1 and explained below. The data-rich model structure can be explained as a series of causal mechanisms that influence each other. Each tier is constructed so that the most immediate and direct influences (independent variables) are used to explain the effect of the dependent variable. For example, for the effects of incidents, it is postulated that incident-related reliability is most directly affected by the capacity hours lost (a combination of lane hours and shoulder hours lost because of blockages) due to incidents. The capacity hours lost attributable to incidents are directly affected (i.e., caused) by incident duration, the usability of shoulders, the incident rate, and so on. In Figure 7.1, Reliability is equal to f{demand-to-capacity (d/c) ratio, distance to downstream bottleneck, number of lanes, primary incident capacity hours lost, secondary crash capacity hours lost, opposite direction incident hours (rubber- necking of incidents in the opposite direction by motorists in the study direction), work zone capacity hours lost, weather factors, traffic fluctuation, active control type}. Note that capacity hours lost is a way to combine lane hours lost and shoulder hours lost for incidents, as well as an approximation for the additional hours lost because of work-zone visual effects. This is not the measured capacity loss, but the straight translation of lanes and shoulders lost to HCM-based (theo- retical) capacity. Measured capacity loss due to incidents will be greater. Reliability is measured by one of the metrics in Chapter 2; for d/c ratio, demand is measured as the average for the time Cross-Sectional Statistical Analysis of Reliability

125 Notes: 1) “ ” means “...is a function of...” 2) Primary Incident and Secondary Crash hours lost are modeled similarly. Figure 7.1. Variables and tiered structure for the mechanistic (data-rich) model.

126 slice under study, and capacity is physical (HCM) capacity. The d/c ratio should be estimated as the average for the study section or, alternatively, the critical (highest) d/c ratio for the links on the study section. An explanation of the some of the other factors in Fig- ure 7.1 follows: • Incident capacity hours lost = f{incident duration, primary incident rate, shoulder usability}. Lane hours lost may be used instead of capacity hours lost because it can be mea- sured directly; capacity is a transformed measure as it requires using analytic methods to calculate. 44 Duration = f{equipment, incident management policies, truck percentage}. Truck percentage is used as a surro- gate to capture the different types of incidents that can occur (lateral locations, blockages). 44 Primary incident rate = f{primary crash rate break- downs}. It was not the research team’s intent to conduct a detailed safety analysis yielding a predictive relationship for accident (crash) rate. Crash reduction factors recently compiled by FHWA can be used to trace the impacts of safety-related geometric improvements through to changes in reliability (1). 44 Shoulder usability is the presence of a shoulder wide enough to store vehicles involved in a minor crash or breakdown. • Opposite direction incident hours = f{incident duration, incident rate} (for the opposite direction of travel). 44 Duration = f{equipment, incident management policies, truck percentage}. 44 Primary incident rate = f{primary crash rate, break- downs}. • Work zone capacity hours lost = f{work zone type, work zone duration}. 44 Work zone duration = f{work zone management policies}. • Weather factors = f{precipitation type, precipitation inten- sity, temperature, fog}. Data-Poor Model Originally, a model form using a combination of easily obtained data items was envisioned (Table 7.1). This simpler form would be compatible with many user applications for which detailed data are not available. However, during the course of the research, the team decided on a different strat- egy for the data-poor model. As discussed in the following section, it became apparent that all of the reliability metrics could be predicted as a function of mean travel time. This feature greatly simplifies the construction of the data-poor model and makes it compatible with most existing analytic methods. relationship Between Mean travel time and reliability Metrics Link Level: Urban Freeways Exploratory Research All travel demand models and traffic operations models can predict mean speeds of traffic and, therefore, mean travel time rates. With the mean travel time rate (minutes per mile) and the predicted 95% travel time rate, one then can compute the Buffer Index. An analysis was undertaken with a small data set to develop equations for predicting the 95% travel time rate as a function of the mean travel time rate. The equations were developed for the weekday peak peri- ods for two freeway corridors: 1. San Mateo SR 101 freeway between I-280 in San Fran- cisco and SR 114 in Palo Alto, California, a distance of 27 miles; and 2. Alameda I-238 and I-580 freeways between I-238 in San Leandro and I-205 in Tracy, California, a distance of 33 miles. Nineteen days of toll tag vehicle travel time data were col- lected for San Mateo SR 101 during the hours of 6:00 to 10:00 a.m. and 2:30 to 7:30 p.m. each weekday (excluding holidays) between January 5 and January 31, 2009, for four directional segments ranging from 10.8 to 15.9 miles in length. Sample sizes ranged between 8,500 and 19,200 toll tag–equipped vehicles for each direction for each peak period. Table 7.1. Original Independent Variables for the Data-Poor Model Weather Variables Same as for data-rich model form Incident Variables Annual collisions per million vehicle miles traveled Proportion of fatal or injury collisions Incident duration Design and Control Variables Design capacity Speed limit Average signal delay (if applicable) Traffic management activities (e.g., ramp metering, freeway service patrol) Demand Variables Hourly, weekly, seasonal demand profile over course of year

127 Eight data points on reliability were obtained. A data point consisted of mean, standard deviation, and 95th percentile travel time measurements for each direction of travel on each segment for each peak period. The data for San Mateo SR 101 are given in Table 7.2. Figure 7.2 shows the regression curves fitted to the data. Sixteen days of toll tag vehicle travel time data were collected for Alameda I-238 and I-580 during the hours of 5:00 to 9:00 a.m. and 2:30 to 7:30 p.m. each weekday (excluding holidays) between May 2 and May 23, 2008, for six directional segments ranging from 2 to 21 miles in length. Twelve data points on reliability were obtained. The data for Alameda I-238 and I-580 are given in Table 7.3. Figure 7.3 shows the regression curves fitted to the data. Figure 7.4 shows the combined Alameda and San Mateo freeway reliability relationships. The results for this exploratory research were very encour- aging. They implied that prediction of the reliability metrics could be based on the mean travel time. This led the team to Table 7.2. San Mateo SR 101 Reliability Data Segment Stretch Length (mi) Peak Period Mean (min) Standard Deviation (min) 95th Percentile Buffer Index (%) Sample Size SR 101 northbound Palo Alto (SR 114) to SR 92 10.75 6:00 to 10:00 a.m. 38.4 31.2 132.2 244 8,598 SR 101 northbound Palo Alto (SR 114) to SR 92 10.75 2:30 to 7:30 p.m. 27.8 15.2 73.5 164 19,145 SR 101 southbound SR 92 to Palo Alto (SR 114) 10.75 6:00 to 10:00 a.m. 36.3 29.4 124.6 243 17,321 SR 101 southbound SR 92 to Palo Alto (SR 114) 10.75 2:30 to 7:30 p.m. 26.0 18.9 82.8 219 9,864 SR 101 northbound SR 92 to I-280 15.85 6:00 to 10:00 a.m. 46.5 29.8 136.0 193 9,395 SR 101 northbound SR 92 to I-280 15.85 2:30 to 7:30 p.m. 33.5 24.6 107.2 220 10,696 SR 101 southbound I-280 to SR 92 15.85 6:00 to 10:00 a.m. 48.9 34.5 152.5 212 17,679 SR 101 southbound I-280 to SR 92 15.85 2:30 to 7:30 p.m. 44.6 22.8 113.1 154 13,108 Figure 7.2. Reliability relationships for San Mateo SR 101 for weekday a.m. and p.m. peak periods, January 5 to January 31, 2010.

128 examine both link-level and section-level predictive models using more complete data sets. Final Link-Level Reliability Predictive Models Data from 164 detector locations on the Atlanta study sec- tions were analyzed. A detector is considered to represent conditions on a link, and a link on a freeway is between inter- changes. The Travel Time Index (TTI) was computed separately for the peak and midday time periods and combined into a single data set to get data over a wide range of congestion conditions (see Appendix G for an explanation of how the TTI was calculated and interpreted). Figures 7.5 and 7.6 show the relationships between the mean and 95th percentile TTI and 80th percentile TTI, respectively, for the Atlanta study links. Linear, exponential, and logarithmic regression models were fit to these data; the exponential form was found to pro- vide the best fit. The models were fit without an intercept Table 7.3. Reliability Data for Alameda I-238 and I-580 Segment Stretch Length (mi) Peak Period Mean (min) Standard Deviation (min) 95% Percentile Buffer Index (%) I-238 westbound I-580 to I-880 2 5:00 to 9:00 a.m. 4.3 0.8 6.6 55 I-238 westbound I-580 to I-880 2 2:30 to 7:30 p.m. 4.4 2.4 11.7 164 I-238 eastbound I-880 to I-580 2 5:00 to 9:00 a.m. 2.2 0.1 2.7 19 I-238 eastbound I-880 to I-580 2 2:30 to 7:30 p.m. 3.2 10.0 33.0 947 I-580 eastbound I-238 to I-680 10 5:00 to 9:00 a.m. 9.7 0.4 10.9 12 I-580 eastbound I-238 to I-680 10 2:30 to 7:30 p.m. 11.2 2.9 19.8 77 I-580 westbound I-680 to I-238 10 5:00 to 9:00 a.m. 10.1 1.3 14.1 40 I-580 westbound I-680 to I-238 10 2:30 to 7:30 p.m. 9.3 0.5 10.7 15 I-580 eastbound I-680 to I-205 21 5:00 to 9:00 a.m. 20.5 0.5 21.9 7 I-580 eastbound I-680 to I-205 21 2:30 to 7:30 p.m. 27.3 4.4 40.5 48 I-580 westbound I-205 to I-680 21 5:00 to 9:00 a.m. 29.4 6.2 48.0 63 I-580 westbound I-205 to I-680 21 2:30 to 7:30 p.m. 21.4 0.6 23.3 9 Figure 7.3. Reliability relationships for Alameda I-238 and I-580 for weekday a.m. and p.m. peak periods, May 2 to May 23, 2008.

129 good measure of how accurately a model predicts the response, and is the most important criterion for fit if the main purpose of the model is prediction, which is the aim here. The predictive equations are 95 16 3 th percentile TTI mean TTI RMSE 1.6954 = = . %; alpha level of coefficient <( )0 0001 7 1. ( . ) term so that when the mean TTI is 1.0, the percentile values also will be 1.0. The lack of an intercept term means that the calculated R2 values were not meaningful. Instead, root mean square error (RMSE) was used as the goodness-of-fit mea- sure. RMSE is the square root of the variance of the residuals. It indicates the absolute fit of the model to the data (i.e., how close the observed data points are to the model’s predicted values). Lower values of RMSE indicate better fit. RMSE is a Figure 7.4. Combined travel time reliability data relationships (exploratory) for SR 101, I-238, and I-580. Figure 7.5. 95th percentile TTI versus mean TTI for Atlanta study links.

130 80 7 4 th percentile TTI mean TTI RMSE 1.3162 = = . %; alpha level of coefficient <( )0 0001 7 2. ( . ) standard deviation mean TTI RMSE = −( ) = 1 6 05231. 0 0 0001 7%; . ( .alpha level of coefficient <( ) 3) It is extremely important to note that in the data used to develop these equations, mean TTI is the grand (overall) mean; because it was developed from continuous detector data, it includes all of the possible influences on congestion (e.g., incidents and inclement weather). Almost all applications and models that predict mean travel time and speeds only consider recur- ring congestion. Therefore, an adjustment must be made to the recurring-only travel time so that it corresponds to the grand mean shown in Equations 6 through 8. Data from the Atlanta and Seattle study sections were used to develop the recurring-only adjustment factor. For the peak period time slice, a simple assignment was made for each sec- tion: if either an incident or weather occurred on a particular day, the resulting TTI was considered to be nonrecurring. Otherwise it was assigned as recurring. The analysis showed that the nonrecurring TTI was 26.4% higher than the recur- ring TTI in Atlanta and 28.7% higher in Seattle. Table 7.4 presents the section-by-section data for Seattle and also dem- onstrates that, even though travel time variability (as mea- sured by the standard deviation) is lower for disruption-free conditions, there still is a substantial amount of variability associated with recurring-only congestion. The ratio of the overall mean to the recurring mean was also computed for the peak period; in Atlanta the overall mean TTI was 12.1% higher than the recurring-only TTI, and in Seattle it was 13.0% higher. Seattle data were also used to develop recurring-to-nonrecurring ratios for the midday and weekend time periods (Table 7.5). However, as noted in Chapter 5, the amount of nonrecurring delay depends very much on the base level or recurring delay, so applying per- centages can be misleading. Therefore, the peak period, mid- day, and weekend and holiday results were pooled and a regression equation was developed: overall mean TTI recurringmean TTI1=1 0274. p .2204 alpha level of coefficientsR2 0 910= . ; =( = ) 0 001 167 7 . ( . and 0.0001, respectively; n 4) where overall mean TTI is the mean TTI in the predictive equations, and recurring mean TTI is the mean TTI that con- siders recurring sources only. Section Level: Urban Freeways Data from urban freeway study sections in Atlanta, Minne- apolis, Jacksonville, Los Angeles, Houston, and San Diego were used to develop relationships between a wider set of reli- ability metrics and mean TTI. The peak period and midday measurements were again combined to obtain a data set that had both congested and uncongested observations. The rela- tionships for selected travel time metrics appear in Figures 7.7 through 7.14. Equations 10 through 20 below are the predic- tive equations. Note that the parameters necessary to com- pute the Buffer Index and skew statistic are estimated. Figure 7.6. 80th percentile TTI versus mean TTI for Atlanta study links.

131 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods Section Time of Peak Congestion Type TTI Mean Standard Deviation I-405 Bellevue northbound a.m. Nonrecurring 1.418 0.422 Recurring 1.215 0.252 Total 1.281 0.252 I-405 Bellevue northbound p.m. Nonrecurring 1.672 0.800 Recurring 1.206 0.274 Total 1.346 0.274 I-405 Kennydale northbound a.m. Nonrecurring 4.405 1.699 Recurring 3.198 1.480 Total 3.657 1.480 I-405 Kennydale northbound p.m. Nonrecurring 1.347 0.517 Recurring 1.130 0.212 Total 1.186 0.212 I-405 Kennydale southbound a.m. Nonrecurring 1.915 0.686 Recurring 1.427 0.395 Total 1.539 0.395 I-405 Kennydale southbound p.m. Nonrecurring 2.200 0.975 Recurring 1.730 0.579 Total 1.898 0.579 I-405 Kirkland northbound a.m. Nonrecurring 1.017 0.055 Recurring 1.009 0.016 Total 1.011 0.016 I-405 Kirkland northbound p.m. Nonrecurring 2.120 0.788 Recurring 1.712 0.677 Total 1.995 0.677 I-405 Kirkland southbound a.m. Nonrecurring 1.917 0.535 Recurring 1.574 0.450 Total 1.766 0.450 I-405 Kirkland southbound p.m. Nonrecurring 1.161 0.303 Recurring 1.032 0.097 Total 1.104 0.097 I-405 North northbound a.m. Nonrecurring 1.065 0.095 Recurring 1.039 0.082 Total 1.045 0.082 I-405 North northbound p.m. Nonrecurring 1.687 0.454 Recurring 1.550 0.414 Total 1.609 0.414 (continued on next page)

132 I-405 North southbound a.m. Nonrecurring 3.534 1.879 Recurring 2.254 1.320 Total 2.820 1.320 I-405 North southbound p.m. Nonrecurring 1.239 0.558 Recurring 1.084 0.220 Total 1.123 0.220 I-405 South northbound a.m. Nonrecurring 1.320 0.526 Recurring 1.222 0.210 Total 1.241 0.210 I-405 South northbound p.m. Nonrecurring 2.810 1.008 Recurring 2.420 0.719 Total 2.578 0.719 I-405 South southbound a.m. Nonrecurring 1.566 0.736 Recurring 1.425 0.433 Total 1.446 0.433 I-405 South southbound p.m. Nonrecurring 1.807 0.981 Recurring 1.447 0.497 Total 1.522 0.497 I-5 Everett northbound a.m. Nonrecurring 1.053 0.344 Recurring 1.015 0.090 Total 1.026 0.090 I-5 Everett northbound p.m. Nonrecurring 2.253 1.337 Recurring 1.483 0.895 Total 1.872 0.895 I-5 Everett southbound a.m. Nonrecurring 1.306 0.734 Recurring 1.072 0.280 Total 1.152 0.280 I-5 Everett southbound p.m. Nonrecurring 1.167 0.416 Recurring 1.069 0.192 Total 1.105 0.192 I-5 Lynnwood northbound a.m. Nonrecurring 1.811 1.412 Recurring 1.303 0.680 Total 1.443 0.680 I-5 Lynnwood northbound p.m. Nonrecurring 1.483 0.717 Recurring 1.171 0.345 Total 1.312 0.345 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods (continued) Section Time of Peak Congestion Type TTI Mean Standard Deviation (continued on next page)

133 I-5 Lynnwood southbound a.m. Nonrecurring 2.238 1.151 Recurring 1.572 0.641 Total 1.898 0.641 I-5 Lynnwood southbound p.m. Nonrecurring 1.246 0.719 Recurring 1.069 0.118 Total 1.117 0.118 I-5 North King northbound a.m. Nonrecurring 1.002 0.012 Recurring 1.001 0.010 Total 1.001 0.010 I-5 North King northbound p.m. Nonrecurring 1.935 0.543 Recurring 1.572 0.541 Total 1.791 0.541 I-5 North King southbound a.m. Nonrecurring 2.547 1.068 Recurring 1.856 0.669 Total 2.068 0.669 I-5 North King southbound p.m. Nonrecurring 1.749 1.327 Recurring 1.089 0.401 Total 1.345 0.401 I-5 Seattle CBD northbound a.m. Nonrecurring 2.036 0.775 Recurring 1.328 0.358 Total 1.913 0.358 I-5 Seattle CBD northbound p.m. Nonrecurring 2.110 0.845 Recurring 1.365 0.409 Total 1.961 0.409 I-5 Seattle CBD southbound a.m. Nonrecurring 1.181 0.307 Recurring 1.070 0.094 Total 1.127 0.094 I-5 Seattle CBD southbound p.m. Nonrecurring 1.852 0.487 Recurring 1.420 0.349 Total 1.721 0.349 I-5 Seattle North northbound a.m. Nonrecurring 1.020 0.041 Recurring 1.016 0.037 Total 1.017 0.037 I-5 Seattle North northbound p.m. Nonrecurring 1.913 0.843 Recurring 1.525 0.905 Total 1.741 0.905 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods (continued) Section Time of Peak Congestion Type TTI Mean Standard Deviation (continued on next page)

134 I-5 Seattle North southbound a.m. Nonrecurring 2.721 1.611 Recurring 1.484 0.812 Total 2.157 0.812 I-5 Seattle North southbound p.m. Nonrecurring 3.044 1.654 Recurring 1.385 0.749 Total 2.560 0.749 I-5 South northbound a.m. Nonrecurring 2.008 0.771 Recurring 1.554 0.577 Total 1.764 0.577 I-5 South northbound p.m. Nonrecurring 1.020 0.111 Recurring 1.005 0.049 Total 1.014 0.049 I-5 South southbound a.m. Nonrecurring 1.005 0.043 Recurring 1.003 0.047 Total 1.004 0.047 I-5 South southbound p.m. Nonrecurring 2.038 0.780 Recurring 1.426 0.522 Total 1.761 0.522 I-5 Tukwila northbound a.m. Nonrecurring 1.826 0.765 Recurring 1.213 0.235 Total 1.502 0.235 I-5 Tukwila northbound p.m. Nonrecurring 1.243 0.425 Recurring 1.017 0.031 Total 1.082 0.031 I-5 Tukwila southbound a.m. Nonrecurring 1.077 0.338 Recurring 1.034 0.195 Total 1.042 0.195 I-5 Tukwila southbound p.m. Nonrecurring 1.353 0.487 Recurring 1.116 0.273 Total 1.205 0.273 I-90 Bellevue eastbound a.m. Nonrecurring 1.003 0.024 Recurring 1.008 0.051 Total 1.007 0.051 I-90 Bellevue eastbound p.m. Nonrecurring 1.221 0.598 Recurring 1.097 0.211 Total 1.117 0.211 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods (continued) Section Time of Peak Congestion Type TTI Mean Standard Deviation (continued on next page)

135 I-90 Bellevue westbound a.m. Nonrecurring 1.570 0.601 Recurring 1.216 0.241 Total 1.307 0.241 I-90 Bellevue westbound p.m. Nonrecurring 1.509 1.058 Recurring 1.026 0.214 Total 1.305 0.214 I-90 Bridge eastbound a.m. Nonrecurring 1.208 0.366 Recurring 1.138 0.255 Total 1.190 0.255 I-90 Bridge eastbound p.m. Nonrecurring 1.592 0.624 Recurring 1.143 0.280 Total 1.414 0.280 I-90 Bridge westbound a.m. Nonrecurring 1.373 0.435 Recurring 1.116 0.238 Total 1.159 0.238 I-90 Bridge westbound p.m. Nonrecurring 2.233 1.022 Recurring 1.551 0.748 Total 1.739 0.748 I-90 Issaquah eastbound a.m. Nonrecurring 1.000 0.008 Recurring 1.001 0.017 Total 1.001 0.017 I-90 Issaquah eastbound p.m. Nonrecurring 1.049 0.121 Recurring 1.016 0.052 Total 1.023 0.052 I-90 Issaquah westbound a.m. Nonrecurring 2.005 0.863 Recurring 1.380 0.485 Total 1.476 0.485 I-90 Issaquah westbound p.m. Nonrecurring 1.010 0.025 Recurring 1.016 0.038 Total 1.015 0.038 I-90 Seattle eastbound a.m. Nonrecurring 2.582 1.495 Recurring 1.824 1.124 Total 1.957 1.124 I-90 Seattle eastbound p.m. Nonrecurring 2.185 1.610 Recurring 1.294 0.760 Total 1.432 0.760 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods (continued) Section Time of Peak Congestion Type TTI Mean Standard Deviation (continued on next page)

136 I-90 Seattle westbound a.m. Nonrecurring 1.423 0.527 Recurring 1.095 0.288 Total 1.210 0.288 I-90 Seattle westbound p.m. Nonrecurring 1.192 0.199 Recurring 1.118 0.132 Total 1.140 0.132 SR 167 Auburn northbound a.m. Nonrecurring 1.893 0.622 Recurring 1.627 0.573 Total 1.685 0.573 SR 167 Auburn northbound p.m. Nonrecurring 1.094 0.181 Recurring 1.058 0.058 Total 1.067 0.058 SR 167 Auburn southbound a.m. Nonrecurring 1.148 0.731 Recurring 1.060 0.299 Total 1.072 0.299 SR 167 Auburn southbound p.m. Nonrecurring 2.487 1.280 Recurring 1.739 0.878 Total 1.961 0.878 SR 167 Renton northbound a.m. Nonrecurring 1.802 1.124 Recurring 1.325 0.356 Total 1.624 0.356 SR 167 Renton northbound p.m. Nonrecurring 1.244 0.465 Recurring 1.032 0.106 Total 1.172 0.106 SR 167 Renton southbound a.m. Nonrecurring 1.060 0.063 Recurring 1.055 0.064 Total 1.056 0.064 SR 167 Renton southbound p.m. Nonrecurring 2.163 1.054 Recurring 1.423 0.541 Total 1.637 0.541 SR 520 Redmond eastbound a.m. Nonrecurring 1.017 0.053 Recurring 1.010 0.014 Total 1.011 0.014 SR 520 Redmond eastbound p.m. Nonrecurring 2.148 0.951 Recurring 1.595 0.483 Total 1.869 0.483 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods (continued) Section Time of Peak Congestion Type TTI Mean Standard Deviation (continued on next page)

137 SR 520 Redmond westbound a.m. Nonrecurring 1.088 0.271 Recurring 1.022 0.119 Total 1.037 0.119 SR 520 Redmond westbound p.m. Nonrecurring 1.764 1.307 Recurring 1.163 0.628 Total 1.498 0.628 SR 520 Seattle eastbound a.m. Nonrecurring 1.967 0.687 Recurring 1.555 0.526 Total 1.695 0.526 SR 520 Seattle eastbound p.m. Nonrecurring 1.632 0.595 Recurring 1.370 0.378 Total 1.483 0.378 SR 520 Seattle westbound a.m. Nonrecurring 1.843 0.780 Recurring 1.353 0.487 Total 1.509 0.487 SR 520 Seattle westbound p.m. Nonrecurring 3.004 1.003 Recurring 2.370 0.994 Total 2.722 0.994 I-405 Bellevue southbound a.m. Nonrecurring 1.311 0.545 Recurring 1.130 0.587 Total 1.169 0.587 I-405 Bellevue southbound p.m. Nonrecurring 4.163 1.562 Recurring 2.006 0.975 Total 3.731 0.975 I-405 Eastgate northbound a.m. Nonrecurring 1.798 0.445 Recurring 1.616 0.456 Total 1.667 0.456 I-405 Eastgate northbound p.m. Nonrecurring 1.104 0.283 Recurring 1.042 0.124 Total 1.058 0.124 I-405 Eastgate southbound a.m. Nonrecurring 1.228 0.901 Recurring 1.035 0.189 Total 1.064 0.189 I-405 Eastgate southbound p.m. Nonrecurring 3.048 1.265 Recurring 2.581 0.786 Total 2.728 0.786 Total Nonrecurring 1.733 Total Recurring 1.347 Overall Total 1.522 Table 7.4. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections During Peak Periods (continued) Section Time of Peak Congestion Type TTI Mean Standard Deviation

138 95 15 7 th percentile TTI mean TTI RMSE 1.8834 = = . %; alpha level of coefficient <( )0 0001 7 5. ( . ) 90 9 4 th percentile TTI mean TTI RMSE 1.6424 = = . %; alpha level of coefficient <( )0 0001 7 6. ( . ) 80 4 5 th percentile TTI mean TTI RMSE a 1.365 = = . %; lpha level of coefficient <( )0 0001 7 7. ( . ) median TTI mean TTI RMSE alpha le 0.8601 = = 6 3. %; vel of coefficient <( )0 0001 7 8. ( . ) 10th percentile TTI mean TTI RMSE 0.1524 = = 5 4. %; alpha level of coefficient <( )0 0001 7 9. ( . ) PctTripsOnTime10 mean TTI= − −[ ]1 0 4396 1 0436. .p 1 8 4 7 10 ( ) =( )RMSE . % ( . ) where PctTripsOnTime10 is the percentage of trips that occur below the threshold of 1.1 * median TTI. PctTripsOnTime25 mean TTI= − −[ ]1 0 2861 1 0525. .p 1 7 5 7 11 ( ) =( )RMSE . % ( . ) where PctTripsOnTime25 is the percentage of trips that occur below the threshold of 1.25 * median TTI. PctTripsOnTime50mph mean TTI= − −[ ]1 0 8985 1 0. .p 6387 18 0 7 12 ( ) =( )RMSE . % ( . ) where PctTripsOnTime50mph is the percentage of trips that occur at space mean speeds above the threshold of 50 mph. PctTripsOnTime45mph mean TTI= − −[ ]1 0 8203 1 0. .p 7692 14 0 7 13 ( ) =( )RMSE . % ( . ) where PctTripsOnTime45mph is the percentage of trips that occur at space mean speeds above the threshold of 45 mph. PctTripsOnTime30mph mean TTI= − −[ ]1 0 4139 1 1. .p 5527 4 4 7 14 ( ) =( )RMSE . % ( . ) Table 7.5. Recurring, Nonrecurring, and Total TTIs for Seattle Study Sections on Midday Periods and Weekends and Holidays Time Period Congestion Type TTI Midday Recurring 1.121 Nonrecurring 1.227 Total 1.153 Weekend and Holiday Recurring 1.034 Nonrecurring 1.142 Total 1.058 Note: Midday was defined in the Seattle analysis as from 9:00 a.m. to 3:00 p.m. Weekend and holiday excludes midnight to 4:00 a.m. Figure 7.7. Section-level relationship for mean and 10th percentile TTI.

139 where PctTripsOnTime30mph is the percentage of trips that occur at space mean speeds above the threshold of 30 mph. standard deviation mean TTI= −( )0 6182 1 0540. .p 4 2 781 0 0R = <. ; .alpha levels of coefficients 001 7 15( ) ( . ) As with the link level, if the recurring-only mean TTI is avail- able, it must be factored with Equation 3. Appendix H presents a revised set of section-level equa- tions for the prediction of the 80th, 95th, and 99th percentile TTIs, standard deviation, and on-time metrics. These were fit to the same data described in this section, but different model forms were selected. Signalized Arterials The predictive equations for reliability metrics as a function of the mean for signalized arterials were obtained from the Figure 7.8. Section-level relationship for mean and median TTI. Figure 7.9. Section-level relationship for mean TTI and 80th percentile.

140 six Orlando study sections. Unlike urban freeways, on the sig- nalized arterials there was no apparent relationship between mean TTI and the on-time reliability metrics. 99 12 7 th percentile TTI mean TTI RMSE 2.2120 = = . %; alpha level of coefficient <( )0 0001 7 16. ( . ) 97 5 10 2 . . th percentile TTI mean TTI RMSE 2.0845 = = %; . ( .alpha level of coefficient <( )0 0001 7 17) 95 7 1 th percentile TTI mean TTI RMSE 1.9125 = = . %; alpha level of coefficient <( )0 0001 7 18. ( . ) 80 2 1 th percentile TTI mean TTI RMSE 1.4067 = = . %; alpha level of coefficient <( )0 0001 7 19. ( . ) median TTI mean TTI RMSE alpha le 0.9149 = =1 9. %; vel of coefficient <( )0 0001 7 20. ( . ) Figure 7.10. Section-level relationship for mean TTI and 95th percentile. Figure 7.11. Section-level relationship for mean TTI and on-time at median plus 10%.

141 10th percentile TTI mean TTI RMSE 0.2689 = = 4 0. %; alpha level of coefficient <( )0 0001 7 21. ( . ) Rural Freeways The predictive equations for reliability metrics as a function of mean TTI for rural freeways were derived using data from I-45 in Texas and I-95 in South Carolina. Four sections were used, two routes in each direction. The travel times used were for the entire segment (and, therefore, are long) and were derived using the vehicle trajectory method. These sections are not influenced by major urban areas or bottlenecks; exam- ination of long-distance trips that pass through or otherwise touch urban areas is likely to reveal different patterns. An additional metric, the 97.5th percentile, was added because of the extreme skew in the travel time distributions for long-distance rural trips. Note that the 10th percentile TTI Figure 7.12. Section-level relationship for mean TTI and on-time at 45 mph threshold. Figure 7.13. Section-level relationship for mean TTI and on-time at 30 mph threshold.

142 was found to be 1.0, which is to be expected under routinely uncongested conditions. It also is worth noting that for these rural sections, mean TTI ranged from 1.025 to 1.045, extremely low values compared with the urban sections studied. 99th percentile TTI mean TTI RMSE 4.2584 = = 4 2. %; alpha level of coefficient =( )0 0052 7 22. ( . ) 97.5th percentile TTI mean TTI RMSE 2.6723 = = 0 3. %; . ( .alpha level of coefficient <( )0 0001 7 23) 95th percentile TTI mean TTI RMSE 2.1365 = = 0 4. %; alpha level of coefficient <( )0 0001 7 24. ( . ) 80th percentile TTI mean TTI RMSE 1.4923 = = 0 1. %; alpha level of coefficient <( )0 0001 7 25. ( . ) median TTI mean TTI RMSE alpha le 0.8763 = = 0 1. %; vel of coefficient <( )0 0001 7 26. ( . ) 10th percentile TTI =1 0 7 27. ( . ) Statistical Modeling of reliability The research team followed the modeling approach for the data-rich model form as closely as possible (see further dis- cussion at the beginning of this chapter). The concept was to build a chain of relationships that are deterministic in nature rather than merely searching for a single predictive equation from the large set of independent variables available. Several observations should be made about the data set that have implications for applications of the models: • The study sections routinely experience relatively high lev- els of congestion. • Operations activities, particularly incident management, were well developed in the areas studied. Although it would have been interesting to study locations without such advanced activities, such locations in all likelihood would not have the data available for the research. • The study sections had wide cross-sections, three or more lanes per direction, and number of lanes generally influ- ences the impact of lane closures. (The average number of lanes on the study sections was 3.6.) However, number of lanes in the statistical models was not shown to be statisti- cally significant. This may be a function of the reduced sample sizes in each number of lanes category. • Minneapolis–St. Paul was the only location with any substan- tial winter weather conditions. For this reason, frozen pre- cipitation was not used as a potential predictor of reliability. Even in Minneapolis–St. Paul, the number of days with snowfall or icing was relatively limited throughout the course of a year, making it difficult for frozen precipitation to show up as statistically significant. Further, on days when snow or ice is forecast, it is likely that demand will be dramatically lowered: travelers seek other modes or decide not to travel. For these reasons, the reliability measures explored in this research are not useful descriptors of winter weather impacts. Figure 7.14. Predicting peak period d/c ratio.

143 • The above discussion points out an issue with statistical modeling of reliability. Rare events that cause extreme dis- ruptions are difficult to relate to the percentiles of an annual travel time distribution; the more common occurrences (e.g., bottleneck congestion, incidents, rainfall) tend to pro- duce the statistically significant results. Further, diversion of demand during extreme disruptions will lessen the observed travel time impacts below what they would have been in the face of full demand. The dependent variables used in the statistical analysis were derived from the distributions of the TTI for each analysis section. TTI was chosen because, as a unitless index, it is nor- malized for different section lengths. An alternative would have been to use the travel rate (measured in minutes per mile). Since TTI is computed as the actual travel rate divided by the ideal travel rate (i.e., the travel rate at the free-flow speed), the two measures are related. Several dependent vari- ables based on the key moments of the TTI distributions were used: mean TTI, as well as the 10th, 50th (median), 80th, 95th, and 99th percentile TTIs. From these statistics, both the Buffer Index and skew statistic were computed (see the formulas in Table 4.4). Note that no adjustment for recurring-only conditions was necessary because the mean TTI predicted here includes both recurring and nonrecur- ring sources. The first stage of this model form is to link reliability mea- sures to lane hours lost due to incidents and work zones, d/c ratio, and weather conditions. During initial investigations, the project team noticed that including only incident lane hours lost as opposed to the sum of incidents and work zones produced more reliable models. This observation spurred a review of the original data used in the analysis. Members of the team talked with personnel at the Atlanta traffic management center (TMC), as well as with personnel from Traffic.com. Both groups admitted that work zone data are currently difficult to obtain and to code with accuracy. In Atlanta’s case, the work zone units sometimes report their activities to the TMC; at other times, the TMC enters work zone data they had not been notified of by viewing it through their closed-circuit cameras. Further complicating matters is that the lane-blocking characteristics of a work zone usu- ally change over time, but the work zone units report only a single number representing the general condition. TMC per- sonnel try to compensate by visually observing the work zone periodically, but this means that the work zone infor- mation was not updated frequently, resulting in coded dura- tions that were longer than the actual ones. Finally, in the highly congested sections used in the analysis, lane closures during peak times are avoided whenever possible. In the case of Traffic.com, the number of reported work zones was extremely low. For these reasons, the team chose to include only incident lane hours lost in the statistical models as the major event— or disruption-related variable. In the case of Atlanta, if an active work zone with lane closures occurred during the time period of interest (e.g., the peak period), that day was excluded when compiling the final analysis data set. In apply- ing the models, it was expected that lane hours lost due to short-term work zones would have roughly the same impact as incidents. Long-term work zones will usually affect demand and result in shifts to other routes, modes, and times of travel. A variety of equation forms were tried, including natural logarithmic, Cobb–Douglas (multiplicative with exponents), and polynomials. The natural logarithmic form was selected because it has the feature of predicting a TTI of 1.0 when the independent variables are zero. As with the simple models, RMSE was used as the primary goodness-of-fit measure. Because the models were fit with no intercept term, to ensure continuity at the zero point, R2 values could not be calculated. For the significance of the coefficients, a gener- ous alpha level of 0.1 was used to allow variables to stay in the equations. First-Stage Models A large combination of independent variables was tested, with a focus on capturing the factors hypothesized to influ- ence reliability (Figure 7.1), where reliability is measured over the course of a year. The results for the first-stage equations, the most important because they established that reliability can be predicted from congestion-causing conditions, appear below. Separate equations were fit for the peak hour, peak period, midday, and weekday time periods. Summary statistics for the base data appear in Table 7.6. Peak Period mean TTI dc ILHLcrit= + +e 0 09677 0 00862 0 0090. . .p p 4 7 28pRain05Hrs( ) ( . ) RMSE = 18.8%; alpha level of coefficients: <0.0001, <0.0001, 0.0189 (in order of appearance in the equations). 99th percentile TTI dccrit= +e 0 33477 0 012350. .p pILHL Rain05Hrs+( )0 025315 7 29. ( . )p RMSE = 39.8%; alpha level of coefficients: <0.0001, 0.0002, 0.0022. 95th percentile TTI dc Icrit= +e 0 23233 0 01222. .p p LHL Rain05Hrs+( )0 01777 7 30. ( . )p RMSE = 32.3%; alpha level of coefficients: <0.0001, <0.0001, 0.0078.

144 80th percentile TTI dccrit= +e 0 13992 0 01118. .p pILHL Rain05Hrs+( )0 01271 7 31. ( . )p RMSE = 25.8%; alpha level of coefficients: <0.0001, <0.0001, 0.0163. 50th percentile TTI dccrit= +e 0 09335 0 00932. .p pILHL( ) ( . )7 32 RMSE = 20.5%; alpha level of coefficients: <0.0001, <0.0001. 10th percentile TTI dccrit= +e 0 01180 0 00145. .p pILHL( ) ( . )7 33 RMSE = 6.7%; alpha level of coefficients: 0.0169, 0.0060. Peak Hour mean TTI dc ILHLcrit= + +e 0 27886 0 01089 0 0293. . .p p 5 7 34pRain05Hrs( ) ( . ) RMSE = 26.4%; alpha level of coefficients: 0.0008, 0.0094, 0.0838. 99th percentile TTI dccrit= +e 1 13062 0 01242. .p pILHL( ) ( . )7 35 RMSE = 41.3%; alpha level of coefficients: <0.0001, 0.0477. 95th percentile TTI dccrit= +e 0 63071 0 01219. .p pILHL Rain05Hrs+( )0 04744 7 36. ( . )p RMSE = 38.3%; alpha level of coefficients: <0.0001, 0.0436, 0.0553. 80th percentile TTI dccrit= +e 0 52013 0 01544. .p pILHL( ) ( . )7 37 RMSE = 34.1%; alpha level of coefficients: <0.0001, 0.0031. 50th percentile TTI dccrit= +e 0 29097 0 01380. .p pILHL( ) ( . )7 38 RMSE = 28.3%; alpha level of coefficients: <0.0001, 0.0015. 10th percentile TTI dccrit= +e 0 07643 0 00405. .p pILHL( ) ( . )7 39 RMSE = 15.2%; alpha level of coefficients: 0.0081, 0.0748. Midday (11:00 a.m. to 2:00 p.m., Weekdays) mean TTI dccrit= ( )e 0 02599 7 40. ( . )p RMSE = 7.5%; alpha level of coefficient: <0.0001. 99th percentile TTI dccrit= ( )e 0 19167 7 41. ( . )p RMSE = 33.4%; alpha level of coefficient: <0.0001. 95th percentile TTI dccrit= ( )e 0 07812 7 42. ( . )p RMSE = 21.8%; alpha level of coefficient: <0.0001. 80th percentile TTI dccrit= ( )e 0 02612 7 43. ( . )p RMSE = 9.2%; alpha level of coefficient: <0.0001. 50th percentile TTI dccrit= ( )e 0 01134 7 44. ( . )p RMSE = 21.8%; alpha level of coefficient: <0.0001. 10th percentile TTI dccrit= ( )e 0 00389 7 45. ( . )p RMSE = 5.1%; alpha level of coefficient: <0.0016. Weekday mean TTI dc ILHLaverage = +( )e 0 00949 0 00067 7. . (p p . )46 RMSE = 29.3%; alpha level of coefficients: <0.0001, 0.0051. 99th percentile TTI dcaverage = + e 0 07028 0 002. .p 22 7 47 pILHL( ) ( . ) RMSE = 38.9%; alpha level of coefficients: <0.0001, 0.0261. 95th percentile TTI dcaverage = + e 0 03632 0 002. .p 82 7 48 pILHL( ) ( . ) RMSE = 31.8%; alpha level of coefficients: <0.0001, 0.0007. 80th percentile TTI dcaverage = + e 0 00842 0 001. .p 17 7 49 pILHL( ) ( . ) RMSE = 14.7%; alpha level of coefficients: 0.0004, 0.0023. Table 7.6. Summary Statistics for the Statistical Analysis Time Slice Section Years No. of Observations Mean dccrit Annual Incident Lane Hours Lost TTI Average 95th Percentile Peak period 85 1.98 18.11 1.53 2.41 Peak hour 70 0.86 5.69 1.62 2.50 Midday 91 2.13 13.15 1.06 1.21 Weekday 89 11.98 67.91 1.16 1.84 Note: midday = 11:00 a.m. to 2:00 p.m., weekdays.

145 50th percentile TTI dcaverage = ( )e 0 0021 7 50. ( .p ) RMSE = 4.7%; alpha level of coefficients: <0.0001. 10th percentile TTI dcaverage = ( )e 0 00047 7 5. ( .p 1) RMSE = 2.0%; alpha level of coefficients: 0.0121. where dccrit = critical demand-to-capacity ratio on the study section (i.e., highest d/c ratio for all links on the section), dcaverage = average d/c ratio on the study section (i.e., the mean of the d/c ratio for all the links on the section), ILHL = annual lane hours lost due to incidents that occur within the time slice of interest (e.g., the peak period), and Rain05Hrs = hours in the year during which rainfall is ≥0.05 inches that occur within the time slice of interest. Several interaction terms involving volume or d/c ratio with event characteristics were also tried, but they failed to be significant in the regressions. It was expected that these terms would be important determinants of reliability, especially given the results of the exploratory research showing the strong effect of volume. However, it must be remembered that the models do not attempt to predict congestion on any given day, when these interactions are very likely to be significant. Rather, over the course of a year (over which reliability is determined), the interaction affects appear to be negligible. Similarly, there were not enough cases of extreme or rare weather events (e.g., fog, snow) in the data to influence the annual summary metrics in a statistical sense. In the case of winter weather, unless the precipitation is unexpected, demand is likely to be lower as travelers forego trips or seek transit service. On an individual day, however, there is no denying that such events exert a strong influence on conges- tion. The predictive equations balance these variations by relying on a relatively common weather event, hourly rain- fall ≥0.05 inches, to explain weather effects on annual reliability. For reasons discussed above, the lane hours lost factor was limited to those related to incidents. The study sections were all located on high-volume, multilane roadways with signifi- cant congestion. Work zones during peak times were very likely not to involve lane closures, as it is common practice to keep all lanes open during the peak periods and to close them during off-peak times. Also, the coding of work zones, espe- cially changes in lane closures over their duration, was found to be inconsistent in the data sets. Work zones are also rare events in general; some sections will have little or no work activity during a year, but incidents happen continuously. Finally, long-term work zones involving continuous lane clo- sures will shift demand away from the facility. For these rea- sons, making a statistical connection with work zone–related lane closures proved difficult. However, the team still believes that lane closures due to short-term work zones are roughly equal to incidents in their effect on traffic. For this reason, it is recommended that if short-term work zones close lanes during peak periods, then an estimate of the annual lane hours lost due to them should be made and added to the ILHL factor used in the equations. Table 7.7 presents several analysis of variance statistics from the model development. It is revealing that the midday models do not include the effect of either incidents or rain. Midday periods typically show reduced demand and little overall congestion. The fact that events do not show up as statistically relevant may indi- cate that demand (volume) is low enough that there is enough buffer to absorb the effect of most events. The importance of demand and capacity to predicting reliability measures cannot be overstated. Examination of the Type I (sequential) and Type III (marginal) sums of squares for the peak models reveals the relative contribution of the independent variables. Type I sums of squares esti- mate the contribution of adding the variables in sequence. Type III sums of squares show the additional contribution of a variable given that the other variables are already in the model. Higher values indicate greater contribution to the model’s explanatory power. For the 80th, 95th, and 99th per- centile TTIs, the Type III sums of squares all show that the marginal contribution of the d/c ratio is higher than the other factors. Second-Stage Models Estimating D/C Ratio The demand used in developing the models was the volume that occurred for the entire length of the study period, adjusted for any potential queuing affects as discussed in Chapter 4. Because the data were continuously collected for an entire year, the 99th percentile demand volume was selected. This was done to correspond to the usual way that traffic data are developed for highway capacity analysis, as follows. For the peak hour, the 99th percentile demand vol- ume is close to the volume determined by the traditional K-factor, the 30th-highest hour of the year. Table 7.8 shows a comparison of these values for detectors (stations) in Atlanta for 2008. Note that the 99th percentile hourly volume was taken from a distribution of the actual peak hour volumes (nonholiday weekdays) for the year; that is, it was developed from all weekdays. The 30th-highest hourly volumes (K-factor volumes) are derived in the usual way by rank ordering all hours in the year.

146 The lengths of the time periods differ: the peak hour is 1 hour long, the midday period is 3 hours long (11:00 a.m. to 2:00 p.m.), and the peak period is variable as defined in Chapter 4. To develop demand volume, users should rely on local data to the extent possible, using the guidance above. In the absence of local data, the following default procedure is offered, based on the assumption that the 99th percentile of the peak hour volumes is equivalent to the K-factor volumes. Figure 7.15 shows the relationship between peak period d/c and the product of peak hour d/c times the length of the peak period assembled from the urban freeway study sections. A linear regression was performed on the data and produced the following equation: d c d c peak period length pp ph ( ) = ( ){ }p p 0 01648. (7 52. ) where (d/c)pp = peak period d/c, (d/c)ph = peak hour d/c, (d/c)ph = peak hour volume to capacity (usually developed from travel demand fore- casting models or by applying K- and D-factors to AADT), and peak period length = length of peak period (min; see Chap- ter 4). The maximum peak period length in the data was 200 min- utes. Therefore, it is recommended that this equation be used only for peak period lengths up to 200 minutes. The peak hour volume-to-capacity (v/c) ratio is computed either from empirical (factored daily traffic) data or model Table 7.7. Analysis of Variance Statistics for Peak Models Model Dependent Variable Independent Variable Type I SS Type III SS Peak period Mean TTI d/c 13.16 0.97 ILHL 1.40 1.18 HrsRain05 0.20 0.20 Median TTI d/c 9.54 1.66 ILHL 1.47 1.47 80th Percentile TTI d/c 25.51 2.02 ILHL 2.39 1.99 HrsRain05 0.40 0.40 95th Percentile TTI d/c 53.54 5.58 ILHL 2.97 2.38 HrsRain05 0.78 0.78 99th Percentile TTI d/c 96.56 11.59 ILHL 3.27 2.42 HrsRain05 1.58 1.58 Peak hour Mean TTI d/c 14.22 0.86 ILHL 0.65 0.50 HrsRain05 0.21 0.21 Median TTI d/c 11.66 2.46 ILHL 0.87 0.87 80th Percentile TTI d/c 29.17 7.87 ILHL 1.09 1.09 95th Percentile TTI d/c 49.60 4.37 ILHL 0.89 0.62 HrsRain05 0.56 0.56 99th Percentile TTI d/c 102.60 37.17 ILHL 0.71 0.71 Note: SS = sums of squares.

147 Station ID Hourly Volume 99th Percentile 30th Highest Ratio 200511 8,558 7,756 0.91 200512 6,115 5,698 0.93 200516 8,067 7,697 0.95 200517 8,095 7,600 0.94 200520 2,524 2,986 1.18 750502 11,931 11,278 0.95 750503 14,848 14,385 0.97 750505 11,377 11,631 1.02 750506 11,210 11,612 1.04 750508 12,119 11,987 0.99 750509 11,795 11,955 1.01 750510 8,939 9,542 1.07 750511 9,325 10,020 1.07 750512 8,613 8,907 1.03 750513 9,298 9,435 1.01 750515 8,446 8,730 1.03 750516 8,548 8,833 1.03 750517 6,791 6,342 0.93 750518 9,904 9,864 1.00 750519 10,012 10,001 1.00 750520 10,457 10,188 0.97 750521 10,081 10,037 1.00 750522 9,582 9,296 0.97 750523 7,846 7,490 0.95 750524 9,882 9,646 0.98 750526 6,930 6,968 1.01 751472 5,706 6,439 1.13 751473 5,872 6,073 1.03 751475 8,458 8,209 0.97 751476 8,176 8,184 1.00 751477 8,327 8,181 0.98 751479 9,380 9,805 1.05 751480 10,096 9,510 0.94 751481 9,000 9,669 1.07 751482 9,390 9,476 1.01 751484 9,750 10,185 1.04 751486 9,880 9,926 1.00 751487 9,775 10,075 1.03 751488 9,873 9,648 0.98 751491 12,394 12,369 1.00 751495 14,396 14,027 0.97 751496 12,494 12,551 1.00 2850002 4,110 3,880 0.94 2850003 8,028 7,945 0.99 2850004 12,823 12,634 0.99 2850005 10,688 10,585 0.99 2850008 9,552 9,129 0.96 2850009 9,649 9,290 0.96 2850010 10,308 10,094 0.98 2850011 10,270 10,069 0.98 2850012 10,063 9,935 0.99 2850013 10,112 10,015 0.99 2850014 12,370 12,046 0.97 2850015 10,309 10,048 0.97 2850016 10,345 10,077 0.97 2850017 8,897 8,684 0.98 2850020 6,813 6,880 1.01 2850021 8,399 9,692 1.15 2850023 9,529 9,257 0.97 2850024 7,736 8,314 1.07 2850025 8,307 8,589 1.03 2850026 9,402 9,820 1.04 2850028 7,930 9,056 1.14 2850029 7,911 8,384 1.06 2850031 8,020 8,707 1.09 2850032 7,935 8,503 1.07 2850033 8,256 8,748 1.06 2850034 8,233 8,960 1.09 2850035 8,786 9,633 1.10 2850036 9,130 9,348 1.02 2850042 3,705 3,983 1.08 2851004 4,457 4,796 1.08 2851005 5,204 5,330 1.02 2851006 8,343 8,027 0.96 2851007 11,484 11,980 1.04 2851008 13,046 13,553 1.04 Station ID Hourly Volume 99th Percentile 30th Highest Ratio Table 7.8. Comparison of 99th Percentile Hourly Volumes and K-Factor Volumes (continued on next page)

148 output. Using the HCM to calculate hourly capacity, a typical way to compute the v/c ratio from empirical data is v c AADT -factor -factor hourly capacity= ( )p pK D (7 53. ) where AADT = annual average daily traffic, K-factor = 30th-highest hour of traffic in a year, and D-factor = directional split of traffic in the 30th highest hour. The weekday and midday (11:00 a.m. to 2:00 p.m.) time periods also use the 99th percentile demand volume. Local values for these are preferred, but if these are not available, then the following factors developed from the Atlanta study sections can be used: 99th percentile weekday demand AADT= p1 251 7. ( .54) 99th percentile midday demand AADT= p 0 234 7 5. ( . 5) Capacity in the d/c ratio was defined in the analysis as the hourly capacity determined according to HCM methods. Capacity should include the effect of weaving sections and merge areas, as appropriate. Estimating Lane Hours Lost Total (annual) lane hours lost is the sum of lane hours lost due to incidents (ILHL) and work zones. Work zone lane hours lost must be estimated with local knowledge of the extent and characteristics of planned work zones. Incident lane hours lost are calculated as follows: ILHL number incidents lanes blocked inciden= p p t duration ( . )7 56 ILHL incident rate VMT= p ( . )7 57 where number incidents = number of annual incidents (incident rate and VMT should be computed for the particular time slice under study, e.g., the peak period); lanes blocked = number of lanes blocked per incident; incident duration = average incident duration (hours), defined as the time between when the incident started and when the last lane or shoulder is cleared; and VMT = vehicle miles traveled. If incident rate is unavailable locally, it can be estimated by multiplying the crash rate by 4.545, which assumes that crashes are 22% of all incidents; this factor was developed from analyzing the incident data in the analysis data set. If lanes blocked per incident is unavailable locally, it can be estimated using the following factors, developed from 2 years of incident data from Atlanta: • 0.476 if a usable shoulder is present and it is local policy to move lane-blocking incidents to the shoulder as rapidly as possible. A usable shoulder is capable of safely storing the disabled vehicle and emergency vehicles (this is the policy in Atlanta); Station ID Hourly Volume 99th Percentile 30th Highest Ratio 2851009 9,424 9,916 1.05 2851010 8,815 8,831 1.00 2851011 11,198 11,305 1.01 2851012 11,023 11,141 1.01 2851013 11,389 10,942 0.96 2851014 10,371 10,352 1.00 2851015 11,536 10,472 0.91 2851016 10,581 10,564 1.00 2851018 12,597 12,155 0.96 2851020 10,428 10,278 0.99 2851021 9,930 9,743 0.98 2851022 11,255 11,096 0.99 2851023 9,545 8,975 0.94 2851026 12,935 13,354 1.03 2851027 8,847 10,051 1.14 2851028 9,190 9,746 1.06 2851029 9,879 10,410 1.05 2851030 9,842 9,817 1.00 2851031 9,131 9,647 1.06 2851033 8,118 7,999 0.99 2851034 10,065 10,960 1.09 2851035 9,107 9,673 1.06 2851036 8,440 8,899 1.05 2851037 8,451 8,925 1.06 2851038 8,441 9,101 1.08 2851039 9,017 9,402 1.04 2851041 9,123 8,579 0.94 2851043 3,687 3,815 1.03 Average 1.01 Table 7.8. Comparison of 99th Percentile Hourly Volumes and K-Factor Volumes (continued)

149 • 0.580 if lane-blocking incidents are not moved to the shoulder. This factor was developed by considering lane- blocking incidents that were moved to the shoulder, and reassigning them back to lane-blocking status; and • 1.140 if usable shoulders are unavailable. Average incident duration is largely a function of incident management policies and actions. However, a statistical rela- tionship from the data available proved elusive. The team had originally hoped to use Traffic Incident Management Self- Assessment scores as a way of quantitatively capturing the myriad of factors that comprise incident management pro- grams, but these scores were available for only a few of the locations. As a means of guidance to practitioners, Table 7.9 provides peak period incident characteristics of the study locations. Estimating Hours of Rainfall ≥0.05 Inches The National Weather Service maintains hourly records of weather conditions that should be used to calculate this factor. Graphical Display of Equations Figures 7.16 through 7.18 graphically show the behavior of selected equations for predicting the 95th percentile TTI. Figure 7.15. Predicting peak period d/c ratio. Table 7.9. Peak Period Incident Characteristics for Study Locations Urban Area Average Incident Durationa (min) Quick- Clearance Law PDO-Move- to-Shoulder Law Fatality Removal Without Medical Examiner Atlanta 43.5 Yes Yes Yes Houston 43.2 Yes Yes Yes Jacksonville 32.1b Yes Yes Yes Los Angeles 51.5 No Yes No Minneapolis 47.3 No No No San Diego 52.0 No Yes No Note: PDO = property damage only. a Average incident duration is defined as the time between when the incident started and when the last lane or shoulder is cleared. b End time is defined as when the lane is cleared (incident may still be active on shoulder).

150 congestion is high (e.g., mean TTIs greater than 2.5). Low congestion during the peak period was rare in the data on which the models were fit, so a recommendation for their application would be to apply the peak period models only in situations in which at least a modest amount of congestion exists. (The rainfall factor was set to 4 hours for peak hour and 8 hours for the peak period.) For weekdays (all 24 hours), the models tended to under- predict Seattle conditions, especially the 95th percentile TTIs. This may be due to the lack of a weather or rain variable in the weekday models, which proved to be insignificant for the model data set, but rain was shown in Chapter 5 to be an Validation of Statistical Models Data from the Seattle area, which were used in the congestion by source analysis in Chapter 5, were used to validate the sta- tistical models. Travel time metrics and lane hours lost infor- mation were compiled directly from Seattle detector data and the Seattle incident data base, respectively. Data on demand and capacity were compiled from Highway Performance Monitoring System data for the Seattle study sections. The results appear in Tables 7.10 and 7.11. For peak peri- ods, the models tend to overpredict the key metrics when actual congestion is fairly low and underpredict when actual 95th percentile TTI = e(0.63071*dccrit + 0.01219*ILHL + 0.04744*Rain05Hrs) Figure 7.16. Effect of incident lane hours lost, peak hour equations. 95th percentile TTI = e(0.23233*dccrit + 0.01222*ILHL + 0.01777*Rain05Hrs) Figure 7.17. Effect of incident lane hours lost, peak period equations.

151 Table 7.10. Peak Period Model Validation for Seattle Section Mean TTI 80th Percentile TTI 95th Percentile TTI Actual Predicted Error (%) Actual Predicted Error (%) Actual Predicted Error (%) I-405 Bellevue northbound 1.346 1.810 34.5 1.507 2.301 52.7 2.314 3.369 45.6 I-405 Eastgate northbound 1.667 1.835 10.0 1.981 2.372 19.7 2.720 3.740 37.5 I-405 Eastgate southbound 2.728 1.955 -28.4 3.227 2.575 -20.2 4.209 4.091 -2.8 I-405 Kennydale southbound 1.898 1.677 -11.6 2.313 2.077 -10.2 3.376 2.958 -12.4 I-405 Kirkland northbound 1.995 2.019 1.2 2.408 2.640 9.6 3.132 3.827 22.2 I-405 Kirkland southbound 1.766 1.748 -1.0 2.147 2.189 2.0 2.673 3.119 16.7 I-405 North northbound 1.609 1.654 2.8 1.876 2.031 8.3 2.236 2.822 26.2 I-405 North southbound 2.820 1.792 -36.4 4.090 2.254 -44.9 6.272 3.161 -49.6 I-405 South northbound 2.578 1.609 -37.6 3.080 1.960 -36.4 3.756 2.707 -27.9 I-405 South southbound 1.522 1.607 5.6 1.797 1.957 8.9 2.406 2.703 12.3 I-5 Everett northbound 1.872 1.976 5.5 2.777 2.570 -7.5 4.294 3.740 -12.9 I-5 Everett southbound 1.520 1.843 21.2 1.850 2.348 26.9 2.590 3.387 30.8 I-5 Lynnwood northbound 1.443 1.722 19.4 1.667 2.163 29.8 3.539 3.198 -9.6 I-5 Lynnwood southbound 1.898 1.829 -3.6 2.448 2.338 -4.5 3.968 3.481 -12.3 I-5 South northbound 1.764 2.084 18.2 2.313 2.782 20.3 3.184 4.318 35.6 I-5 South southbound 1.762 1.964 11.5 2.350 2.576 9.6 3.251 3.969 22.1 I-5 Tukwila northbound 1.502 1.819 21.1 1.811 2.054 13.4 2.582 2.840 10.0 I-5 Tukwila southbound 1.205 1.858 54.2 1.265 2.111 66.8 1.933 2.926 51.3 I-90 Bellevue westbound 1.307 1.609 23.1 1.453 1.961 35.0 1.998 2.716 35.9 I-90 Bridge eastbound 1.414 1.636 15.7 1.868 2.008 7.5 2.622 2.832 8.0 (continued on next page) 95th percentile TTI = e(0.03632*dcaverage + 0.00282*ILHL) Figure 7.18. Effect of incident lane hours lost, weekday equations.

152 Table 7.11. Weekday Model Validation for Seattle Section Mean TTI 80th Percentile TTI 95th Percentile TTI Actual Predicted Error (%) Actual Predicted Error (%) Actual Predicted Error (%) I-405 Bellevue northbound 1.186 1.130 -4.7 1.285 1.127 -12.3 1.865 1.606 -13.9 I-405 Eastgate northbound 1.177 1.177 0.0 1.232 1.158 -6.0 1.964 1.867 -4.9 I-405 Eastgate southbound 1.369 1.190 -13.1 1.399 1.181 -15.5 2.432 1.959 -19.4 I-405 Kennydale southbound 1.357 1.119 -17.5 1.642 1.113 -32.2 2.491 1.544 -38.0 I-405 Kirkland northbound 1.196 1.133 -5.3 1.123 1.146 2.1 2.227 1.633 -26.7 I-405 Kirkland southbound 1.162 1.123 -3.3 1.133 1.128 -0.4 2.000 1.572 -21.4 I-405 North northbound 1.135 1.124 -0.9 1.137 1.116 -1.9 1.784 1.568 -12.1 I-405 North southbound 1.105 1.136 2.8 1.318 1.137 -13.8 2.121 1.640 -22.7 I-405 South northbound 1.476 1.121 -24.1 1.933 1.110 -42.6 2.967 1.549 -47.8 I-405 South southbound 1.270 1.122 -11.6 1.446 1.112 -23.1 1.904 1.556 -18.3 I-5 Everett northbound 1.192 1.119 -6.1 1.031 1.129 9.5 2.514 1.553 -38.2 I-5 Everett southbound 1.054 1.122 6.4 1.012 1.134 12.1 1.216 1.570 29.1 I-5 Lynnwood northbound 1.134 1.112 -2.0 1.085 1.106 1.9 1.730 1.504 -13.1 I-5 Lynnwood southbound 1.165 1.116 -4.2 1.100 1.113 1.2 1.978 1.528 -22.7 I-5 South northbound 1.117 1.142 2.3 1.033 1.155 11.8 1.859 1.684 -9.4 I-5 South southbound 1.154 1.127 -2.3 1.061 1.129 6.3 2.123 1.592 -25.0 I-5 Tukwila northbound 1.111 1.117 0.6 1.066 1.118 4.8 1.680 1.536 -8.5 I-5 Tukwila southbound 1.060 1.114 5.1 1.043 1.112 6.6 1.207 1.517 25.7 I-90 Bellevue westbound 1.101 1.076 -2.2 1.000 1.076 7.6 1.516 1.330 -12.3 I-90 Bridge eastbound 1.118 1.078 -3.6 1.075 1.074 -0.1 1.876 1.335 -28.8 I-90 Bridge westbound 1.161 1.080 -7.0 1.053 1.078 2.4 1.547 1.346 -13.0 I-90 Issaquah westbound 1.077 1.062 -1.4 1.043 1.056 1.3 1.454 1.260 -13.4 SR 167 Auburn northbound 1.168 1.084 -7.2 1.248 1.078 -13.6 1.759 1.363 -22.5 SR 167 Auburn southbound 1.189 1.084 -8.8 1.265 1.078 -14.7 1.954 1.365 -30.1 SR 167 Renton northbound 1.201 1.093 -9.0 1.213 1.087 -10.4 1.916 1.406 -26.6 SR 167 Renton southbound 1.123 1.090 -3.0 1.144 1.083 -5.4 1.581 1.392 -12.0 Average error (%) -4.6 -4.8 -17.2 I-90 Bridge westbound 1.739 1.687 -3.0 2.608 2.091 -19.8 3.483 2.960 -15.0 I-90 Issaquah westbound 1.476 1.679 13.8 1.880 2.090 11.2 2.635 3.051 15.8 SR 167 Auburn northbound 1.685 1.615 -4.2 2.057 1.976 -3.9 2.567 2.795 8.9 SR 167 Auburn southbound 1.961 1.681 -14.3 2.693 2.082 -22.7 4.162 2.958 -28.9 SR 167 Renton northbound 1.623 1.689 4.0 1.744 2.100 20.4 3.361 3.026 -10.0 SR 167 Renton southbound 1.637 1.675 2.3 2.029 2.078 2.4 3.357 2.991 -10.9 Average error (%) 4.8 6.7 7.2 Table 7.10. Peak Period Model Validation for Seattle (continued) Section Mean TTI 80th Percentile TTI 95th Percentile TTI Actual Predicted Error (%) Actual Predicted Error (%) Actual Predicted Error (%)

153 95th percentile TTIs in Seattle are so much higher compared with their means, but this indicates that further validation of the models with data from other cities is warranted. reference 1. Bahar, G., M. Masliah, R. Wolff, and P. Park. Desktop Reference for Crash Reduction Factors. Report No. FHWA-SA-07-015. Office of Safety, Federal Highway Administration, U.S. Department of Trans- portation, September 2007. extremely important factor in Seattle congestion. Without testing another city, it is not known if Seattle is an exception or if rainfall has a universal influence on total weekday conges- tion. The problem may lie in the fact that Seattle weekday 95th percentile TTIs do not behave in the same way as those of the other cities. Table 7.12 shows the prediction of the 95th percentile TTI from the mean TTI using the data-poor model. The predicted 95th percentiles are consistently lower than the actual ones, yet the data-poor relationship had an excellent goodness-of-fit. The team is not sure why the Table 7.12. Application of Data-Poor Model to Seattle Weekday Data Section Mean TTI 80th Percentile TTI 95th Percentile TTI Actual Predicted Error (%) Actual Predicted Error (%) I-405 Bellevue northbound 1.186 1.285 1.262 -1.8 1.865 1.379 -26.0 I-405 Eastgate northbound 1.177 1.232 1.249 1.4 1.964 1.358 -30.8 I-405 Eastgate southbound 1.369 1.399 1.536 9.8 2.432 1.807 -25.7 I-405 Kennydale southbound 1.357 1.642 1.516 -7.7 2.491 1.776 -28.7 I-405 Kirkland northbound 1.196 1.123 1.277 13.8 2.227 1.402 -37.1 I-405 Kirkland southbound 1.162 1.133 1.228 8.4 2.000 1.327 -33.6 I-405 North northbound 1.135 1.137 1.188 4.5 1.784 1.269 -28.9 I-405 North southbound 1.105 1.318 1.146 -13.0 2.121 1.207 -43.1 I-405 South northbound 1.476 1.933 1.702 -11.9 2.967 2.083 -29.8 I-405 South southbound 1.270 1.446 1.385 -4.2 1.904 1.568 -17.7 I-5 Everett northbound 1.192 1.031 1.271 23.3 2.514 1.393 -44.6 I-5 Everett southbound 1.054 1.012 1.075 6.2 1.216 1.105 -9.1 I-5 Lynnwood northbound 1.134 1.085 1.188 9.5 1.730 1.268 -26.7 I-5 Lynnwood southbound 1.165 1.100 1.232 12.1 1.978 1.334 -32.5 I-5 South northbound 1.117 1.033 1.163 12.6 1.859 1.232 -33.7 I-5 South southbound 1.154 1.061 1.217 14.6 2.123 1.311 -38.3 I-5 Tukwila northbound 1.111 1.066 1.154 8.2 1.680 1.218 -27.5 I-5 Tukwila southbound 1.060 1.043 1.083 3.8 1.207 1.116 -7.6 I-90 Bellevue westbound 1.101 1.000 1.140 14.0 1.516 1.199 -20.9 I-90 Bridge eastbound 1.118 1.075 1.164 8.3 1.876 1.233 -34.3 I-90 Bridge westbound 1.161 1.053 1.226 16.4 1.547 1.324 -14.4 I-90 Issaquah westbound 1.077 1.043 1.107 6.1 1.454 1.150 -20.9 SR 167 Auburn northbound 1.168 1.248 1.236 -1.0 1.759 1.339 -23.9 SR 167 Auburn southbound 1.189 1.265 1.267 0.1 1.954 1.385 -29.1 SR 167 Renton northbound 1.201 1.213 1.284 5.9 1.916 1.412 -26.3 SR 167 Renton southbound 1.123 1.144 1.172 2.4 1.581 1.244 -21.3 Average error (%) 5.5 -27.4