A commutation flow model and the effect of workers decentralization using the joint distribution of home and workplace locations

The objective of this paper is to show the theoretical relationship between spatial distribution of urban workers and commuting or business-trip distances, using the Vaughan's joint distribution of home and workplace locations. First, we describe macroscopic relationship of the locations between home and workplace, which is based on Vaughan's quadvariate normal distribution whose marginal distributions are according to Sherratt's bivariate normal distribution, by introducing intensive parameters, i.e. jobs-housing balance and spatial correlations. Then we derive the analytical expression of commuting distance or business-trip distance by using those parameters. We find out the optimal workplace distribution that minimizes the weighted sum of average commute travel distance and average business-trip distance. Commuting distance has a minimum value with respect to jobs-housing balance, when spatial correlation is constant. The decentralization of jobs is reasonable policy when the spatial correlation is sufficiently large and the weight of business-trip is low. Thus, jobs-housing balance and spatial correlation of home and workplaces play important roles in identifying travel distance, and also in determining optimal spatial distribution of urban workers.