Efficient population behavior and the simultaneous choices of origins, destinations and routes

In this paper we derive a new model for the simultaneous choices of origins, destinations and routes, i.e. the combined distribution and assignment problem. The new model--the Continuous Dispersed Equilibrium model (CDE)--is obtained as the optimal solution of a certain optimization problem. The objective function of the optimization problem contains two terms: entropy and cost function. Furthermore, it is shown how this optimization problem can be obtained as the continuous formulation of the corresponding discrete problem of deriving the most probable flow pattern under efficient population behavior. Hence, the CDE model represents the most probable flows under efficient behavior. We also discuss the relationship of the CDE model to the classical Combined Distribution and Assignment model (CDA). The model can be used for predicting flow patterns and total system cost for a metropolitan area.