# Guide for Highway Capacity and Operations Analysis of Active Transportation and Demand Management Strategies Appendix E: Measures of Effectiveness

This Appendix provides details on the computations of the annual facility performance measures for evaluating ATDM investments. Note that throughout this Guide, the terms “measures of effectiveness” and “performance measures” have been used interchangeably.

## Computation of Annual VMT

There are two measures of vehicle-miles traveled (VMT) that are evaluated. The demand VMT is the input demand to the traffic operations tool. The VMT served is the amount of the demand that the traffic operations tool predicts can be served by the facility within the selected study period. These two values of VMT are accumulated for the year by multiplying the VMT input and output by the tool for each scenario by the number of days per year represented by the scenario. The number of days represented by the scenario is determined by multiplying its probability of occurrence by the total number of days in the reliability space being evaluated.

Equation 7

Where:

AVMT = Annual total vehicle miles traveled
N = Number of days within the reliability analysis space.
VMT(s) = VMT estimate for scenario “s.”
P(s) = Probability of scenario “s.”

The difference between the input demand VMT and the served VMT predicted by the traffic operations analysis tool is the “unserved VMT demand” for the facility.

## Computation of Annual VHT

In cases where the estimated queues spill over the temporal and/or spatial limits of the operations analysis tool then the best solution is to expand the limits of the tool and rerun the analysis. The limits should be revised if the spillover is frequent, occurring in many scenarios with cumulative probability of greater than 10%.

However, if the cumulative probability of those scenarios with spillovers is less than 10%, then the analyst may consider whether resource constraints, the low probabilities of such extreme scenarios, and cost-effectiveness considerations, may limit the ability to expand the limits. In such situations, it is necessary for the analyst to work with the study stakeholders to:

1. Assess the probability (and therefore the significance) of the scenarios causing the overflow,
2. Assess the degree to which not accurately modeling the overflows will introduce bias that would significantly affect the decisions regarding ATDM investments, and, if significant,
1. Determine if a reasonable increase in the study limits will adequately capture the overflows, and if not,
2. Approximately account for the congestion spill over outside of the operations analysis tool limits as described below.

The annual vehicle hours traveled (VHT) should include delays to vehicles waiting (or denied entry) to the facility during the study period, plus the time spent traveling or stopped within the facility. The reported VHT may also need to be adjusted for residual queues remaining within the facility or at its entry segments according to the following equation.

Equation 8

Where:

VHT’(s) = Adjusted vehicle-hours traveled for scenario “s” veh-hrs).
VHT(s) = Vehicle hours traveled reported by analysis tool for scenario “s” (veh-hrs).
DAP = Duration of analysis period, for HCM it is typically 15 minutes (min).
VDE(a) = Number of vehicles denied entry to facility at end of analysis period “a” (veh).
Q(j,s) = Number of vehicles remaining in queue on entry segments “j” at end of last analysis period for scenario “s” (veh).
c(j) = Capacity of facility entry segment “j” (veh/hr).

Adjustment for Vehicles Denied Entry (does not apply to all analysis tools): Some operations analysis tools do not accumulate and report the delay for vehicles denied entry to the facility. In such cases the analyst will need to manually accumulate the delays to these vehicles for each analysis period and add them to the VHT reported by the traffic operations analysis tool for the scenario (see second term in Equation 8).

Adjustments for Temporal Spill Over of Queues (Queues remaining at end of last analysis period): In cases where the queuing persists through the last analysis period, the analyst should manually compute the time necessary to clear the queue remaining at the end of the last analysis period assuming no new demand arrives. This added time is divided by two (to get the average delay per vehicle) and multiplied by the number of vehicles in the queue to obtain the residual delay (see third term in Equation 8).

The capacity for each entry segment with a residual queue (see third term in Equation 8) will be the discharge rate for that segment during the last analysis period within the study period.

## Computation of Annual VHD

The annual vehicle hours of delay (VHD) are computed by subtracting the estimated vehicle-hours traveled if all travel demand were at free-flow speed from the adjusted VHT.

## Computation of Annual Delay per VMT

The annual average delay (in seconds) per vehicle-mile traveled (VMT) is computed by dividing the annual VHD by the Annual Demand VMT and multiplying the result by 3,600 seconds per hour. If average delay per trip is desired, the annual delay per VMT is divided by the average trip length on the facility. If the majority of trips on the facility are through trips (traveling end to end on the facility), then the average trip length will be somewhat less than the length of the facility.

## Computation of Annual Average Speed

The annual average speed for the facility is the VMT demand divided by the adjusted VHT.

## Computation of Reliability Statistic

The mean travel time indices (TTI) for each scenario are sorted from lowest to highest and the probabilities of each scenario accumulated to obtain the cumulative percentiles. The analyst then interpolates from the table the desired percentile TTI results. The 95th percentile TTI is the Planning Time Index. In the example shown in Table 45, the Planning Time Index is approximately 1.69. A similar procedure is used to compute the 80th Percentile TTI as 1.238.

Table 45: Example Computation of PTI
Sorted Mean TTI for each scenario Scenario Probability Cumulative Probability
1.058 0.06% 0.06%
1.060 1.14% 1.20%
1.060 5.72% 6.92%
1.061 0.02% 6.95%
1.062 0.00% 6.95%
1.063 0.01% 6.96%
1.073 8.58% 15.54%
1.075 0.57% 16.11%
1.076 0.11% 16.22%
1.149 4.29% 20.51%
1.150 8.58% 29.09%
1.164 17.16% 46.25%
1.170 0.69% 46.94%
1.171 0.41% 47.34%
1.185 17.16% 64.50%
1.196 0.03% 64.54%
1.197 0.01% 64.54%
1.211 0.23% 64.77%
1.224 5.72% 70.49%
1.239 10.21% 80.71%
1.257 0.20% 80.91%
1.281 0.61% 81.52%
1.354 1.14% 82.67%
1.420 8.58% 91.25%
1.462 2.06% 93.30%
1.505 0.12% 93.43%
1.604 0.41% 93.84%
1.682 0.41% 94.24%
1.715 5.72% 99.96%
1.796 0.04% 100.00%

Note: 95th% = (0.9500-0.9424)/(0.9996-0.9424) * (1.715-1.682) + 1.682 = 1.686

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 United States Department of Transportation - Federal Highway Administration