The Development of a New Gravity—Opportunity Model for Trip Distribution

Abstract

In this paper the development of a new gravity—opportunity model for trip distribution is presented. Wilson's formalism to obtain the gravity model, and Schneider's intervening-opportunities model are used as the basis for deducing the new model. The notational difficulties associated with the amalgamation of the gravity and opportunity models are circunvented via the definition of an intervening-opportunity matrix. The conventional gravity model is shown to be a particular case of the new gravity—opportunity model. The calibration of the new model is reached by using Furness's matrix calibration procedure together with Hooke and Jeeves's nonlinear optimizing method. Finally, a practical application of the model for estimating intermunicipal passenger flows by public transport, in Southern Brazil, is reported.

Areas, nodes and networks: Some analytical considerations

“…As shown by Gonçalves and Ulysséa-Neto (1993) and Roy (1993), it is possible to integrate the gravity and intervening opportunities models. This allows the traditional distance-deterrence effect to be combined with the influence of the opportunities intervening between the origin and final destination.…”

“…This path-based approach will extend the combined gravity/intervening opportunities model introduced by Gonçalves and Ulysséa-Neto (1993) and somewhat refined in Roy (1993). After all, the opportunities are physically located along the actual paths of the network, rather than along the single abstract path generally assumed in spatial interaction models.…”

Competing destinations and intervening opportunities interaction models of inter-city telecommunication flows

“…In general, destination masses are divided by a power of the distance between the CD/IO destination and either i (IO) or j (CD). This power is often exogenously specified, but may also be iteratively estimated (Fotheringham, 1983a), or may be set equal to zero (Stouffer, 1940(Stouffer, , 1960Conçalves and Ulysséa-Neto, 1993).…”

“…Another approach involves the use of an intervening opportunities (IO) factor, based on the ideas developed by Stouffer (1940Stouffer ( , 1960, who argued that the observed attenuating effects of distance represent the absorbing effects of those opportunities located between the origin and the ex post destination. IO factors have been used, among others, by Barber and Milne (1988) in modeling internal migration in Kenya, by Fik and Mulligan (1990) and Fik et al (1992), together with CD factors, and by Conçalves and Ulysséa-Neto (1993) in modeling public transportation flows.…”

A Procedure of Global Optimization and its Application to Estimate Parameters in Interaction Spatial Models

“…From the amalgamation of the gravitational models and intervening opportunities models, the hybrid models appeared, also called of gravity-opportunity models (Baxter [3], Wills [35], Gonçalves [16] and Gonçalves [17]). …”