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

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250 A p p e n d i x G introduction The key principle for constructing reliability metrics for use in Project L03 was that the metrics had to be based on the measurement of travel times over an appreciable amount of time and meaningful highway distances. Travel times are eas- ily relatable to nontechnical audiences, and once measured they can be transformed into a wide variety of additional metrics. The Travel Time Index (TTI) was used as the pri- mary congestion metric in Project L03 for various reliability estimation and prediction models. Three reasons exist for this choice. First, because study sec- tions vary in length, using raw travel times is misleading, and the travel times must be normalized for distance. As a unitless index, the TTI is normalized. Second, the TTI is already in wide- spread use in congestion performance monitoring. Third, the moments and derivative measures derived from the TTI turn out to be identical to those of the travel time distribution for a particular road section and time slice. An alternative metric to the TTI is the travel rate (the inverse of space mean speed, in minutes per mile). For the statistical modeling, moments from the distribu- tion of TTIs were used as the dependent variables (e.g., the 80th percentile TTI). As shown below, these can be easily con- verted to travel times, and these travel times can be used to create additional performance metrics (e.g., delay). Calculation of Travel Time index The starting point for the research was to transform field data into travel time–based metrics. The first step in this process was to define highway sections over which travel time statis- tics would be calculated. The following principles were used in defining sections: • Sections should be relatively homogenous in terms of traf- fic and geometric conditions. Multiple interchanges are allowed as long as they do not provide for major drops or additions in traffic volumes along the section; • Sections should represent portions of trips taken by trav- elers. Typical distances for urban freeway sections are 3 to 6 miles; and • Major bottlenecks, defined as major freeway-to-freeway interchanges, can be present at the downstream end of the section, but never in midsection. The majority of data that were available came from urban freeway surveillance systems, specifically, point detection of volumes and speeds from closely spaced equipment. These point measurements were converted to travel times over fixed highway distances with a method in widespread use by researchers and practitioners: it is assumed that the point speed measures the travel time over a distance half the dis- tance to the nearest upstream and downstream detectors. This assumption works well if detector spacing is close (i.e., 0.5-mile spacing or less). Figure G.1 shows the process for computing section travel times from individual detectors; this was done at a 5-minute time interval level. For each detector zone, vehicle miles traveled (VMT) and vehicle hours traveled (VHT) were computed: VMT VOLUME DetectorZoneLength G.=  ( )1 VHT VMT Min FreeFlowSpeed Speed G.= ( )( ), ( )2 When aggregating to the section level, at least half of the detectors had to report valid data for each of the 5-minute periods; otherwise the data were set to missing. If less than half of the detector data was missing, VMT and VHT were factored up based on the ratio of total section length to the sum of the lengths of the individual detector zones. For every 5-minute interval in the year, total VMT and VHT were computed. From these, key performance measures were computed: Computation of Travel Time Metrics

251 of the study was to measure congestion, not high speeds. If speeds were not capped, the resulting statistics would be biased because of the credit given to high speeds. However, the original data have been preserved for future examination by researchers who may wish to remove this restriction. The congestion metrics were computed for each 5-minute period in a day over the course of a year. For any given analysis time slice (e.g., peak hour, peak period), a TTI distribution and its moments were computed as the VMT-weighted average of all the 5-minute TTIs in that time slice for the entire year. The various moments of the TTI distributions (e.g., 95th percen- tile TTI) were then used in the statistical modeling. SpaceMeanSpeed VMT VHT G.= ( )3 TravelRate 1 SpaceMeanSpeed G.= ( )4 TTI MAX 1 TravelRate FreeFlowSpeed G= ( )[ ]( ). , (0 1 .5) Because the bases for the measures were total VMT and VHT, the process was self-weighting. For urban freeways, FreeFlow- Speed was fixed at 60 mph. Note that TTI was not allowed to be lower than 1.0; that is, speeds higher than 60 mph were set to 60 mph. This adjustment was made because the purpose Figure G.1. Converting spot speeds to section travel times. Source: Turner, S., R. Margiotta, and T. Lomax, Monitoring Urban Freeways in 2003: Current Conditions and Trends from Archived Operations Data. Report No. FHWA-HOP-05-018. December 2004. http://mobility.tamu.edu/mmp/FHWA-HOP-05-018/.

252 Converting predicted TTi percentiles to Other Metrics TTI percentiles can be thought of as a ratio comparing the travel time for a given percentile with the travel time under free-flow conditions. For example, a 95th percentile TTI of 1.8 means that the 95th percentile travel time is 80% higher than the free-flow travel time. Therefore, the travel time asso- ciated with any percentile can be computed as TravelTime TTI TravelTime G.ffn n=  ( )6 where n is the percentile and TravelTimeff is the travel time under free-flow conditions. Travel times can be combined with other data to compute other congestion-related metrics such as vehicle hours of delay: SpaceMeanSpeed SectionLength TravelTime G.= ( )7 Delay SectionLength SpaceMeanSpeed Sec =     − tionLength FreeFlowSpeed Volume          ( )G.8 Percentiles for the various travel times can also be used to compute the Buffer Index and Skew Index: Buffer Index 95th percentile travel time mean t = − ravel time mean travel time G.   ( )9 SkewIndex 90th percentile travel time mediantr = − avel time median travel time 10th percent   − ile time G.  ( )10 As an example, consider the data in Table G.1, which were derived from a few Atlanta study sections for 2007. Both the travel time and TTI distributions were developed by follow- ing the procedure discussed above. Applying Equation 6 for the 95th percentile for Section 2, 95th percentile travel time 95th percentile= TTI free-flow travel time = = 1 837 5 840 10 . . .728 which matches the actual 95th percentile travel time devel- oped straight from the data (accounting for slight round-off error). Note also that the Buffer and Skew Indices can be computed either from the travel times or TTIs. Again for Section 2, the Buffer Index using the TTI distribution is 1 837 1 337 1 337 0 374. . . .−( ) = And with the pure travel times is 10 727 7 805 7 805 0 374. . . . .−( ) = Table G.1. Travel Time and TTI Distributions for A.M. Peak Hour, Selected Atlanta Study Sections Travel Time (min) TTI Section Free-Flow 10th Percentile Median Mean 95th Percentile 10th Percentile Median Mean 95th Percentile 1 5.510 5.510 5.523 5.562 5.629 1.000 1.002 1.009 1.022 2 5.840 5.846 7.601 7.805 10.727 1.001 1.302 1.337 1.837 3 4.970 5.091 7.548 7.580 10.996 1.024 1.519 1.525 2.213 4 4.550 4.560 5.081 5.411 7.342 1.002 1.117 1.189 1.614 5 6.860 6.883 10.113 10.013 13.152 1.003 1.474 1.460 1.917 Note: Section 1 is a radial freeway leading away from the I-285 Beltway; its peak is in the afternoon.