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We propose new probabilistic models for the spatial distribution of supplyand demand and use the models to determine how the trip length distribution isaffected by the relative shortage or excess of supply, the spatial clusteringof supply and demand, and the degree of attraction or repulsion between supplyand demand at different spatial scales. The models have a multiplicativestructure and in certain cases possess scale invariance properties. Usingdetailed population data in metropolitan US regions validates the demand model.The trip length distribution, evaluated under destination choice models of theintervening opportunities type, has quasi-analytic form.We take advantage ofthis feature to study the sensitivity of the trip length distribution toparameters of the demand, supply and destination choice models. We find thattrip length is affected in important but different ways by the spatial densityof potential destinations, the dependence among their attractiveness levels,and the correlation between supply and demand at different spatial scales.

Trip Length Distribution Under Multiplicative Spatial Models of Supply and Demand: Theory and Sensitivity Analysis