Curbing the computational difficulty of the logit equilibrium assignment model

In the past, research in traffic assignment modeling has been directed primarily towards improving the deterministic model. Alternative, more behavioral principles were thought to be too demanding computationally. This paper presents two mathematical contributions that enable one to solve a logit assignment model with flow-dependent travel times at a reduced cost. First, a convergence test for Fisk’s minimization program is introduced, based on a duality gap principle. Second, a new definition of Dial’s STOCH fixed-time logit assignment procedure is given, in which the set of available paths is defined only once and the computations are re-interpreted. A numerical experiment indicates that these tools make the logit assignment model very competitive compared with the procedures conventionally used for solving the deterministic model.