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

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253 A p p e n d i x H The original equations that predicted the percentiles of the Travel Time Index (TTI) as a function of the mean TTI used a power function. This form fit the data extremely well when the mean TTI was less than 2.0. This is where the majority of the data points were distributed. However, especially for planning applications, mean TTIs well over 2.0 (i.e., average annual speeds less than 30 mph for the section) are possible. It was observed that the relationship flattened at the upper end of the data, and this flattening was more pronounced for the higher percentiles. Therefore, a natural log relationship was chosen as a more appropriate model form: Y a x= + ∗ ( )1 1ln ( . )H The original power (exponential) relationship for the stan- dard deviation as a function of the mean was verified, but the coefficients were reestimated using an expanded data set. The original functional form for the prediction of the per- centage of trips on-time at different speed thresholds was also assumed to be a power fit, but further investigation revealed that a negative exponential form fit the on-time measures for 50 and 45 mph: Y a x= ∗ −[ ]( )exp ( . )1 2H A sigmoidal function fit the on-time measure for 30 mph extremely well: Y a b a w x x = + − + ∗ −[ ]( )1 0 3exp ( . )H Note that MeanTTI in the predictive equations is the over- all annual average TTI, which includes the effect of demand fluctuations and disruptions. If analysts only have an estimate of the recurring-only average TTI, it should be adjusted upward using the original L03 equation: MeanTTI RecurringMeanTTI H1.2204= ∗1 0274 4. ( . ) More work remains to be done to make this adjustment more sensitive to the effect of disruptions. Revised section-level equations are as follows: 95 1 3 6700 5th percentile TTI MeanTTI H= + ∗ ( ). ln ( . ) 90 1 2 7809 6th percentile TTI MeanTTI H= + ∗ ( ). ln ( . ) 80 1 2 1406 7th percentile TTI MeanTTI H= + ∗ ( ). ln ( . ) StdDevTTI MeanTTI H= ∗ −( )0 71 1 8056. ( . ). PctTripsOnTime50mph MeanTTI= − ∗ −[ ]( )e 2 0570 1. (H. )9 PctTripsOnTime45mph MeanTTI= − ∗ −[ ]( )e 1 5115 1. (H. )10 PctTripsOnTime30mph Me= + + ∗0 333 0 672 1 50366. . .e anTTI H −[ ]( )( )[ ]1 8256 11 . ( . ) Revised Data-Poor Equations

254 Figure H.1. Relationship between mean TTI and 95th percentile TTI: predicted model superimposed on the data. Figure H.2. Relationship between mean TTI and standard deviation of TTI: predicted model superimposed on the data.

255 Figure H.3. Relationship between mean TTI and percentage of trips with travel speeds >–50 mph: predicted model superimposed on the data. Figure H.4. Relationship between mean TTI and percentage of trips with travel speeds >–45 mph: predicted model superimposed on the data.

256 Figure H.5. Relationship between mean TTI and percentage of trips with travel speeds >–30 mph: predicted model superimposed on the data.