Trip Distribution Models

Taxonomy

The long history of trip distribution models has resulted in different methodological modeling frameworks. Thus, trip distribution models can be [Page 1616]considered as probabilistic in relation to deterministic, aggregated vis-à-vis disaggregated, and static vis-à-vis dynamic models.

Deterministic trip distribution models have been developed as optimization formulations in mathematical programming (for example, as minimum cost models subject to origin, destination, entropy, and cost constraints). Such formulations are adequate to describe overall origin-destination travel patterns when cost or time minimization is the dominant behavioral consideration (for example, among morning commuters going to work).

Additional deterministic formulations have been proposed within the classical microeconomic paradigm of utility-maximizing choice behavior subject to budget constraints. Under various forms of utility functions, the resulting demand function takes the form of a gravity model. Other such efforts have introduced interaction costs (for example, travel time) directly into the utility function. Such approaches require strong assumptions about individual choice behavior and are difficult to test in practice.

More generally, however, traveling from place to place involves a multitude of individual decisions that defy any attempt at deterministic description, to say nothing of prediction. As a result, various probabilistic frameworks have been developed.

One of the earliest models proposed in this regard is Stouffer's “intervening opportunities model,” which has been shown to be a special case of a gravity model. Alternative probabilistic approaches employed Luce's theory of individual choice behavior. Additional efforts applied McFadden's multinomial logit model, which can be shown to yield gravity models with exponential deterrence functions—for example, of the form

Another type of random utility approach used Simon's satisficing principle in which individual decisions to interact in space (for example, travel) are modeled by a probabilistic threshold variable depending on relevant measures of spatial separation (for example, travel distance, travel time, etc.).

Probabilistic theories based on statistical equilibrium concepts have been proposed. The essence of the approach is that the most probable state of microspatial interactions can lead to very regular patterns of macro interaction behavior that are exactly representable by exponential gravity models. It is interesting to note that most trip-distribution models developed are static, implying a shift from one stationary (or equilibrium) state to another. In dynamic contexts, gravity models have been used to describe state transitions in Markov processes.

Disaggregate trip distribution models, also referred to as destination choice models, can be developed as individual choice models (for example, logit models, probit models, etc.) to predict the probability that an individual will choose to travel to a particular destination as a function of individual and destination characteristics.

One of the main issues in this regard is the definition of destination alternatives in the relevant choice sets. This task is more feasible with particular types of trips (for example, shopping trips where a store or a class of stores can be identified). For other types of trips (for example, recreational trips, nonwork trips, etc.), such alternatives may not be easy to identify. In those cases, it may be possible to further disaggregate trip purposes to more elemental dimensions.

...