Computation of Equilibrium Over Transportation Networks: The Case of Disaggregate Demand Models

The transportation planning forecasting process has been traditionally performed on a sequential, disconnected, heuristic basis, using different methodologies for each one of the stages. In an attempt to improve this situation, a first step toward developing a unified transportation forecasting methodology is described in this paper. This is done by showing how many, seemingly different, problems can be cast as analogous route choice problems on abstract networks and studied with the same methodology. As a consequence of this analogy, it is possible to perform equilibrium analyses and to study several problems simultaneously, by choosing an adequate topology for the abstract network. The bulk of this paper is devoted to presenting an algorithm within which many of these transportation equilibrium analyses can be carried out. The conditions of equilibrium are identified and defined, and an efficient algorithm for the solution of the equilibration problem is introduced. The solution method, which uses the multinomial probit model for allocation of flow to routes, can increase the accuracy and reduce the cost of many transportation equilibrium analyses.