Trip Length Distribution Under Multiplicative Spatial Models of Supply   and Demand: Theory and Sensitivity Analysis
  We propose new probabilistic models for the spatial distribution of supply and demand and use the models to determine how the trip length distribution is affected by the relative shortage or excess of supply, the spatial clustering of supply and demand, and the degree of attraction or repulsion between supply and demand at different spatial scales. The models have a multiplicative structure and in certain cases possess scale invariance properties. Using detailed population data in metropolitan US regions validates the demand model. The trip length distribution, evaluated under destination choice models of the intervening opportunities type, has quasi-analytic form.We take advantage of this feature to study the sensitivity of the trip length distribution to parameters of the demand, supply and destination choice models. We find that trip length is affected in important but different ways by the spatial density of potential destinations, the dependence among their attractiveness levels, and the correlation between supply and demand at different spatial scales. 
Daniele Veneziano and Marta C. Gonzalez
physics.data-an cs.SI physics.soc-ph