Hypernetworks and Supply-Demand Equilibrium Obtained with Disaggregate Demand Models

This paper presents a framework for discussing many transportation demand and supply-demand equilibrium problems. It regards the sequence of choices an individual faces when he or she is about to make a travel (or not-to-travel) decision as a case choice of a route on an abstract network (hypernetwork). Hypernetworks are intimately related to the multinomial probit (MNP) model of travel choice. For instance, the multivariate normal distribution underlying this model enables one to represent processes of travel choice as route choices on networks and to use the networks as visual aids in conceptualizing the specification of covariance matrices for MNP choice models. Hypernetworks enable us to carry out supply-demand equilibrium analyses with disaggregate demand models on a mathematically consistent basis (heuristic equilibration techniques based on feedback loops do not necessarily converge, as shown with a simple counterexample). This greatly enhances the potential of probabilistic discrete-choice disaggregate demand models, since it is now possible to avoid their mispredictions when applied to congested transportation systems.