Abstract
Spatial interaction—the flows of people, goods, or other entities from place to place—can be conceptualized as occurring in a scalar field of influences, both of external origin (that is, travel costs) and of internal origin (that is, temporal correlations between flows). Conventional spatial interaction models, however, incorporate into their cost functions only the exogenous effects. This omission is addressed. The presence of significant positive and negative correlations between flows would be indicative of a ‘frustrated’ system of interactions, one in which all tendencies cannot be simultaneously respected. Cost (energy) minimization (a generalization of the classical problem of transportation) that can be pursued by means of simulated annealing, reduces these stresses. Enhancement of the tensions, on the other hand, leads to an equivalence with the quadratic transportation problem of Dorigo and Tobler, and suggests that the eigenvalues of the matrix of correlations between flows, are estimates of travel cost for a set of ‘eigenflows’.
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