Gravity Models

Development

Early 20th-century gravity models were developed by analogy with the physical sciences. By mid-20th century the intervening opportunities model was proposed to derive a model of flows from a different premise. The model assumed (1) that each traveler examines destinations sequentially starting with those closest to him/her and proceeding outward and (2) that each destination is chosen in proportion to the number of opportunities in it by someone who has not already accepted a closer destination. Later research showed that the intervening opportunities model is a special case of the form Tij = AiBjFij above.

In the 1950s and 1960s the gravitational analogy for the gravity model was challenged and a number of changes to the algebraic form of the function Fcij were proposed, for example,

During that time, particularly in transportation studies, the separation measure, cij, was changed from distance to travel time, and since travel time is usually more sensitive to transportation system improvements, it also facilitated examination of the impacts of such improvements. Another frequently used measure is generalized cost, which is a linear combination of travel time and travel cost.

In the 1960s the gravity model was derived using entropy maximization, and Alan Wilson in his seminal work derived the model

The entropy maximization approach assumed that (a) all microstates (lists of individual trips from all origins to all destinations) are equally probable and (b) the most probable meso-state (an origin–destination trip table) is the one given by the largest number of microstates. Wilson's model is equivalent to the generalized gravity model Tij = AiBjFij above by

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