Basic Operations of the Mittrans Model11

The MIT-TRANS model represents an extreme form of test for the feasibility and validity of the spatial aggregation methodology, because it treats an entire urban area as a single zone. The model is based on the application of Monte Carlo simulation, as the main numerical integration technique, to forecast trip generation, trip distribution, and modal split, with a system of disaggregate travel demand models. There are seven disaggregate models for both work and nonwork trips linked together (outputs from one model become inputs to lower-hierarchy models). Examples of predictions are the number of trips made, mode shares, person-miles of travel, vehicle-miles, and average vehicle occupancy rates for both work and nonwork trips, number of automobiles per family, and so on. These predictions are policy-sensitive, as reflected by the fact that they embody elastic travel demand models for the choices of workplace, auto ownership, mode to work, nonwork travel frequency, destination, and mode.

It should be noted that the MIT-TRANS model in its present form represents only the demand component of an overall policy evaluation package which must also include a supply component and evaluation procedures. Future extensions of the MIT-TRANS model include the development of network abstract transportation supply and traffic assignment models and the integration of these models and the aggregation procedure into an equilibrium framework. (In lieu of a complete supply-demand equilibrium framework, a set of level-of-service relationships describing a spatial distribution of the equilibrium conditions of an existing transportation system with externally specified parameters is being used in the current MIT-TRANS model.)

11. A detailed description of this model is given in Watanatada and Ben-Akiva (1977).

The operations of the MIT-TRANS model are summarized schematically in figure 8.3. It accepts three sets of inputs: (1) the aggregate city geometry and land use distribution parameters, (2) the urbanized area's socioeconomic characteristics, and (3) the specifications of a transportation policy alternative. These policy specifications are used to modify the level-of-service relationships which have been calibrated for the base conditions. The Monte Carlo aggregation procedure—a numerical integration procedure—operates on these inputs, the disaggregate choice models, and the (modified) level-of-service relationships to produce aggregate travel demand forecasts for the urbanized area. The forecasts can be disaggregated by market segments such as by income group.

Figure 8.3

Basic operations of MIT-TRANS model

Figure 8.3

Basic operations of MIT-TRANS model

The urbanized area is modeled as a quasi-circular shape with the origins (home ends of trips) and destinations (nonhome ends) defined by sets of coordinates (R, X) and (r, <£), or (L, 9 | R, X), respectively, as depicted in figure 8.4. For each of three income classes the household density function such as negative exponential is assumed (figure 8.5). The spatial alternatives—jobs, shopping destinations, and social recreational facilities—are also represented by employment density functions (negative exponential) and other functions describing locational attributes. The parameters of these density functions can be easily estimated from total counts of population and employment for a central city and its entire metropolitan area.

Figure 8.4

City geometry and system of coordinates

Figure 8.4

City geometry and system of coordinates

Household density per square mile (by income class)

Household density per square mile (by income class)

city center (miles)

Figure 8.5

Negative exponential distribution of households city center (miles)

Figure 8.5

Negative exponential distribution of households

The transportation level-of-service functions by mode and time of day are expressed in terms of trip geometry variables, which are in turn functions of the coordinates of the trip ends.

MIT-TRANS also includes a procedure, similar to the one used by Duguay et al. (1976), to obtain the distribution of socioeconomic characteristics of the urban area population by generating a sample of households from available data. The procedure can operate on samples of disaggregate observations from the census public use sample, or any other household survey, and available aggregate data from surveys or published sources for the past years, from forecasts, or from explicit future scenarios.

The operations of the Monte Carlo aggregation procedure, summarized in figure 8.6, include the following basic steps:

Figure 8.6

Monte Carlo aggregation procedure

Figure 8.6

Monte Carlo aggregation procedure

1. Determine household sample size.

2. Generate sample of households for forecast year, characterizing each household by (R, À) location and a set of socioeconomic attributes.

3. Determine sample size of spatial alternatives by purpose.

4. Generate sample of spatial alternatives by purpose for each household in the sample, defining each destination by (L, 6) coordinates.

5. Modify appropriate attributes of the alternatives for policy analysis.

6. Apply linked demand models for each household in the sample.

7. Expand sample forecasts to population market segments.

8. Compare forecasts against base case for policy analysis.

The Monte Carlo approach was selected to circumvent the extreme complexity of setting the bounds of the integrals for L and 0 and to allow the use of alternative parametric distributions. The flexibility of the technique is demonstrated for an integral taken from a continuous logit model for an individual at (R, A), which for simplicity is written as where the origin of the coordinates (L, 6) is at (R, A).

The most simple technique is to draw points (L, 6)„ uniformly over the area j and obtain the following unbiased estimator :

where A} is the area of zone j and Nj the number of points drawn in zone J.

Alternatively, since the input distribution of spatial alternatives is given in terms of (r, 0), it is possible, for example, to draw directly from the negative exponential distributions shown in fig. 8.5. (It involves drawing from a gamma distribution.) In this case i

However, with regard to shopping trips most destinations are expected to be 4 to 5 miles from the trip maker's home. Uniform sampling or sampling from an urbanized area employment distribution generate many locations outside the potential destination area with a very low value of K(L, 6). Therefore a more efficient sampling technique based on the knowledge of the entire integrand is also employed. The basic principle of importance sampling is to find a probability density function fj(L, 6), such that

varys as little as possible (Hammersley and Handscomb 1965). Drawing from f/L, 9) results in

It is necessary, however, to find /¡(L, 9) that is simple enough to allow locations (L, 8)„ to be drawn conveniently. The featureless plane example presented earlier suggests for the entire urbanized area the gamma distribution with a parameter which can be calculated from generally available information on average trip lengths. In the implementation of this procedure some efficiency was lost because locations were sampled from a gamma distribution over an infinite space and therefore some fell outside the urbanized area.

The MIT-TRANS model was programmed in Fortran for an IBM 370/168 computer. It required about 0.6 CPU minutes per policy run with a standard error of about 1 percent of predicted average passenger miles of travel.

The model was calibrated for the 1968 metropolitan Washington, D.C., area and then used to forecast 1975 conditions as a validation test. Between 1968 and 1975 there were substantial changes in the metropolitan Washington area. The major changes in travel behavior include increased auto ownership, increased vehicle miles of travel per household, and decreased transit patronage. All the forecasted changes agree with these trends.

Apart from Washington, D.C., the model was also calibrated for the Minneapolis-St. Paul area, which has two central business districts. The elasticities produced by the model for both the Washington, D.C., and the Twin Cities are comparable to before-and-after empirical evidence and forecasts obtained from other more detailed studies.

Several Monte Carlo sampling experiments were conducted to investigate the statistical properties of the model. It was found empirically that a small number of sampled destinations would result in minimal bias and optimal efficiency.

The empirical results have led to the basic conclusion with respect to the applicability of disaggregate travel demand models and Monte Carlo techniques for aggregate sketch-planning predictions. The travel demand-forecasting methodology proposed operates with readily available aggregate input data, while still maintaining the full degree of policy sensitivity available in recently developed systems of disaggregate models. The most important future extensions of the methodology are the incorporation of supply and traffic assignment models and the development of a version of MIT-TRANS for multiple zones of varying sizes.

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