Discussion-piece #4

Ridership and User Benefits from Variable Trip Tables

Federal Transit Administration

June 6, 2006

1.  [Motivations.]{.underline} FTA has long required that project
    sponsors maintain fixed person-trip tables in the development of
    ridership forecasts for baseline and build alternatives that FTA
    will use to evaluate proposed New Starts projects. Historically,
    this requirement has reflected both the absence of methods to
    predict changes in trip tables caused by major transit projects and
    the need to avoid yet another source of potential over-estimates of
    transit ridership on New Starts projects. One consequence of this
    policy is that it precludes the estimation of project-specific
    mobility benefits associated with changes in travel patterns caused
    by major new transit facilities. Over the past several years,
    however, the problem of overestimates may have moderated and methods
    to predict transit-caused changes in trip tables have become more
    common. Therefore, given FTA's ongoing efforts to credit proposed
    projects with their full range of likely benefits, a reconsideration
    of the fixed-trip-table policy may be in order.

2.  [Variable trip-tables in travel models]{.underline}. Trip
    distribution models predict the attraction locations of the trips
    produced in each zone. These models have historically adopted the
    "gravity" formulation and have used highway travel time as the
    measure of separation between zones producing and attracting trips.
    Often, these models have been "doubly constrained" with iterative
    methods that adjust the predicted trip tables to ensure that the
    total number of trips attracted to each zone matches the number of
    trip-attractions predicted (in trip generation) for that zone. Over
    the past several years, an increasing number of models have added
    transit service levels to the measures of separation between zones.
    This trend has been most evident in new trip distribution models
    that use logit formulations. Consequently, some current model sets
    produce person-trip tables that, at least for some trip purposes,
    are sensitive to transit service levels. Forecasts for an
    alternative that introduces a major transit facility will include
    person-trip tables that have more travel in the zone-to-zone cells
    well served by the new facility than in the baseline alternative --
    and will yield higher overall transit ridership, more riders on the
    new facility, and more mobility benefits compared to a
    fixed-trip-table forecast.

3.  [User benefits from variable trip-tables.]{.underline} FTA's current
    measure of user benefits is derived from the denominator of the
    (logit or nested-logit) mode choice model. The denominator captures
    all attributes of all modes considered by the model, and is
    therefore an ideal descriptor of the overall mobility -- and changes
    in the overall mobility -- of travelers. A similar measure can be
    computed from the denominator of (logit) trip distribution (or
    "destination choice") models. In the easiest computational case, the
    destination choice model will employ a logsum term from the mode
    choice model as the measure of separation between zones:

    exp(C~ls~ x logsum~ij~) x size~j~

    \(1\) Probability of travel from i to all possible j =
    \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

    sum~j~\[exp(C~ls~ x logsum~ij~) x size~j~\]

    where i and j are the production and attraction locations, logsum is
    the natural logarithm of the denominator of the logit mode choice
    model, C~ls~ is the coefficient on the logsum variable, and size~j~
    is some measure of the size or attractiveness of j. The logsum
    variable extracted from the mode choice model for use in this
    destination choice equation is exactly the same measure from mode
    choice used in FTA's current calculation of user benefits. The
    denominator of this destination choice model measures the total
    mobility of travelers producing trips from zone i, choosing among
    all of the zones in the region as possible destinations. This
    structure provides for the easiest user-benefits computations
    because it effectively combines the mode- and destination-choice
    models into a large nested-logit model that is internally consistent
    and precise in its accounting of the effects of changes in any
    attribute of any mode. The denominator converts easily into a
    generalized price of travel to possible destinations through its
    natural logarithm, divided by the mode-choice coefficient on
    in-vehicle time scaled by the logsum coefficient:

    ln{sum~j~\[exp(C~ls~ x logsum~ij~) x size\]}

    \(2\) Price of travel from i to all possible j =
    \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

    Civt x Cls

    This calculation is exactly analogous to the calculation of the
    price of travel from i to each j (using the logsum~ij~) that is done
    in the current FTA user benefits computations. The change in price
    caused by a major transit investment will appear in both its
    mode-choice component and this more inclusive destination-choice
    component. User benefits derived from both mode-choice and
    destination-choice effects are simply the product of this more
    inclusive price change times the number of travelers producing trips
    from zone i. Consequently, with local models structured along the
    lines sketched above, an internally consistent way is available for
    computation of user benefits that include the benefits derived from
    changes in travel patterns in response to transit investments.

4.  [An example.]{.underline} The attached Excel file illustrates the
    approach with home-based-work-trip models structured as those
    sketched above. The first worksheet provides a map of the 10-zone
    system for which the models are applied. The second worksheet
    summarizes the model parameters (highlighted in green), productions
    and attractions, and zone-to-zone impedances for highway and transit
    travel; it also provides entry locations (highlighted in yellow)
    that can be used to change these zone-to-zone impedances to
    represent highway and/or transit improvements or changes in
    development patterns. The third worksheet computes transit shares
    for both the baseline and build alternatives, and computes the
    logsum terms from the denominators of these logit calculations.

    The fourth worksheet applies the destination-choice model for both
    alternatives. It first uses the logsum terms from the mode choice
    worksheet to compute the singly constrained results, and then
    adjusts the "attractiveness" terms for each destination zone j to
    iterate the model to a doubly constrained result. The differences
    between the two results are evident in the deltas they produce. The
    singly constrained model produces a baseline trip table whose column
    sums do not match the predicted trip attractions in each zone. More
    importantly for this example, the column sums change between the
    baseline and build alternatives. In contrast, the doubly constrained
    model (after three iterations) matches the column sums to the trip
    attractions; it therefore has identical column sums for both
    baseline and build.

    The fifth worksheet "UBfromMC(1)" computes user benefits from the
    mode choice prices (using the current FTA approach) for the
    [singly]{.underline} constrained trip distribution model. In each
    zone-to-zone cell, the worksheet converts changes in the mode-choice
    logsum term between the alternatives into price changes and
    multiplies them by the (fixed baseline) number of trips. The sixth
    worksheet "UBfromMC(2)" attempts to compute user benefits from the
    same mode choice prices but bases the calculations on the different
    person-trip tables for the baseline and build alternatives that
    emerge from the [doubly]{.underline} constrained trip distribution
    model. This worksheet uses the price and trips in each cell to
    compute travel "expenditures" in the cell, and computes user
    benefits as the differences in these expenditures.

    The sixth worksheet "UBfromTD" computes user benefits from the
    trip-distribution model itself using equation (2) above to calculate
    trip-distribution prices and price changes, for both the singly and
    doubly constrained trip distribution models. For the build
    alternative included in the example, the results for the singly
    constrained model are 113 hours at the trip distribution, 2.5 hours
    more than from the standard approach using mode choice alone.
    Consequently, the standard FTA approach with fixed trip tables
    captures 98 percent of the benefits. The results for the doubly
    constrained model are more complex. While the net benefits at the
    trip distribution level are the same as for the singly constrained
    model, both benefits and disbenefits occur for individual production
    zones. Benefits for trips produced in zone 2 increase to 138 hours
    -- 25 hours and 23 percent more than the zone 2 benefits in the
    singly constrained model. This increase is the direct result of the
    iterations in the doubly constrained model: they increased the
    number of trips from zone 2 to zone 1, the cell with the 20-minute
    improvement -- as part of the effort to reconcile the shortfall of
    in the zone-1 column-sum in the singly constrained model. This
    increase is exactly offset, however, by the disbenefits incurred by
    travelers from all other zones. These disbenefits occur because the
    iterations in the doubly constrained model decreased the relative
    attractiveness of zones 2 through 10 to shift some trips produced in
    all zones to zone-1 destinations. Consequently, the iterations make
    the effective price of travel increase to zones 2 through 10, and
    travel to those zones incurs negative user benefits. A real-world
    interpretation is that the improved mobility from zone 2 to zone 1
    increases the competitiveness of residents of zone 2 in the
    competition for jobs in zone 1. Because there are a fixed number of
    jobs in zone 1 (in the models, anyway), some residents of other
    zones lose out, and have to take jobs in second-best locations. The
    reverse effect happens with a decrease in travel time to a zone that
    has a surplus in its column sum compared to its trip attractions in
    the singly constrained model (zone 9, for example): the iterations
    increase the attractiveness of zones 1-8 and 10, so the secondary
    user benefits to these zones would be positive.

    An important insight is evident in the result that the TD-level
    benefits are smaller that the computed MC-level benefits for the
    doubly constrained model. This outcome demonstrates the
    infeasibility of computing benefits from changes in trip tables with
    mode-choice-level prices of travel. The computation is infeasible
    because the mode choice model is entirely unaware of the adjustments
    made to the attractiveness of each destination j during the
    iterations to doubly constrain the distribution results. This
    inconsistency confounds the calculation of trip-distribution effects
    with mode-choice-level information.

    The last worksheet applies the same mode-choice and
    trip-distribution models to a very simple problem with one
    production zone, two attraction zones, and two travel modes.

5.  [Potential problems.]{.underline} While it appears that plausible
    user benefits can be computed for trip-distribution effects under
    ideal conditions, a number of barriers remain to the implementation
    of this idea nationally. Probably no model set in the United States
    employs trip distribution and mode choice models precisely
    consistent with the structure above for all trip purposes,
    socio-economic markets, and times of day. Some use the above
    structure for work travel or for travel generated by car-less
    households, but rely on highway travel time alone to represent
    impedance in for other purposes and markets. Some models use a
    harmonic mean formula to compute composite highway-and-transit
    impedances weighted by mode shares from the mode choice model; that
    formulation might support workable user benefits calculations based
    on the trip distribution model in spite of inconsistencies between
    the composite impedance measures in mode choice and trip
    distribution. Most models partition zones by walk-accessibility and
    apply the mode choice model separately for the individual markets;
    but no trip distribution models recognize the different levels of
    mobility that result for the various walk-access markets. More
    significantly, of course, is the reality that most model sets
    continue to use highway travel time alone to represent impedance in
    trip distribution -- and therefore provide no basis for computing
    transit-caused user benefits from trip distribution.

6.  [Conclusions.]{.underline} At least one way exists in conventional
    practice to compute user benefits that include the effects of
    variable trip tables in addition to the mode-choice-level benefits
    currently recognized by FTA from fixed-trip-table calculations.
    However, relatively few model sets in the United States have the
    properties necessary to support these calculations. Further, the
    level of effort to maintain such model sets is higher -- perhaps
    significantly higher -- than to maintain models that use
    highway-only impedances in trip distribution and thereby ignore
    transit influences on overall travel patterns. Finally, experiments
    with the attached spreadsheet suggest that the additional benefits
    from variable trip tables are small -- apparently well less than 10
    percent. Given the absence of a ready basis nationally for
    computation of these benefits and their apparently modest size, FTA
    continues to view the project-specific computation of
    variable-trip-table benefits as a low priority. FTA has no current
    plans to expand the user benefits measure to capture these benefits
    and will, instead, continue to rely on the allowances for missing
    benefits (outlined in discussion-piece #1) to cover their absence.