A Network Model for Dynamic Traffic Assignment

Models for predicting traffic congestion over time on a road network have been formulated as non-linear optimization problems. In this paper, we construct a new dynamic flow model represented as an optimization problem on a time-space network. In this model, there is a one-to-one correspondence between any directed path on the time-space network and a travel actually taken by a user of the road network. This is an advantage over conventional dynamic flow models in which a travel by a user may correspond to multiple paths in the underlying time-space network. The proposed network model involves arc capacity constraints that depend on the amount of flows of relevant arcs. Since those capacity constraints prevent this model from being treated as network flow problem, we adopt a penalty function techinique to transfer them into the objective function, thereby obtaining a standard non-linear minimum cost flow problem. We report some numerical results to show the validity of the proposed model.