Editing Trip distribution (section)

== History ==

Over the years, modelers have used several different formulations of trip distribution. The first was the Fratar or Growth model (which did not differentiate trips by purpose). This structure extrapolated a base year trip table to the future based on growth, but took no account of changing spatial accessibility due to increased supply or changes in travel patterns and congestion. (Simple Growth factor model, Furness Model and Detroit model are models developed at the same time period)

The next models developed were the gravity model and the intervening opportunities model. The most widely used formulation is still the gravity model.

While studying traffic in [[Baltimore, Maryland]],  [[Alan Voorhees]] developed a mathematical formula to predict traffic patterns based on land use. This formula has been instrumental in the design of numerous transportation and public works projects around the world. He wrote "A General Theory of Traffic Movement," (Voorhees, 1956) which applied the gravity model to trip distribution, which translates [[trip generation|trips generated]] in an area to a matrix that identifies the number of trips from each origin to each destination, which can then be loaded onto the network.

Evaluation of several model forms in the 1960s concluded that "the gravity model and intervening opportunity model proved of about equal reliability and utility in simulating the 1948 and 1955 trip distribution for Washington, D.C." (Heanue and Pyers 1966). The Fratar model was shown to have weakness in areas experiencing land use changes. As comparisons between the models showed that either could be calibrated equally well to match observed conditions, because of computational ease, gravity models became more widely spread than intervening opportunities models. Some theoretical problems with the intervening opportunities model were discussed by Whitaker and West (1968) concerning its inability to account for all trips generated in a zone which makes it more difficult to calibrate, although techniques for dealing with the limitations have been developed by Ruiter (1967).

With the development of [[logit]] and other discrete choice techniques, new, demographically disaggregate approaches to travel demand were attempted. By including variables other than travel time in determining the probability of making a trip, it is expected to have a better prediction of travel behavior. The [[Logistic regression|logit model]] and gravity model have been shown by Wilson (1967) to be of essentially the same form as used in statistical mechanics, the entropy maximization model. The application of these models differs in concept in that the gravity model uses impedance by travel time, perhaps stratified by socioeconomic variables, in determining the probability of trip making, while a discrete choice approach brings those variables inside the utility or impedance function. Discrete choice models require more information to estimate and more computational time.

Ben-Akiva and Lerman (1985) have developed combination destination choice and [[transport mode|mode]] choice models using a logit formulation for work and non-work trips.  Because of computational intensity, these formulations tended to aggregate traffic zones into larger districts or rings in estimation.  In current application, some models, including for instance the transportation planning model used in Portland, Oregon, use a logit formulation for destination choice. Allen (1984) used utilities from a logit based mode choice model in determining composite impedance for trip distribution.  However, that approach, using mode choice log-sums implies that destination choice depends on the same variables  as mode choice.  Levinson and Kumar (1995) employ mode choice probabilities as a weighting factor and develop a specific impedance function or “f-curve” for each mode for work and non-work trip purposes.