Simultaneous estimation of the origin-destination matrices and the parameters of a nested logit model in a combined network equilibrium model

This paper deals with the inverse problem of a type of traffic equilibrium models with combined modes. This problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model. The inputs for the model are an origin-destination (O-D) trip matrix for the various alternatives that have been considered, and a set of parameters for a nested logit model used as a demand model. This model has been formulated by using a new approach called the calibration and demand adjustment model (CDAM) based on bilevel programming which simultaneously estimates an O-D matrix and the parameters for the nested logit model. In this paper, the CDAM properties are studied and it is proved the CDAM solution exists. This paper develops a heuristic column (paths/hyperpaths) generation algorithm for the CDAM. This algorithm iterates between the network equilibrium problem and that which is used to obtain a set of paths when equilibrium is attained, and the CDAM is restricted to the set of previously generated columns (the so-called restricted CDAM). The restricted CDAM is formulated as a single level model under certain hypotheses and it furnishes a solution upon which to base a new estimation of the O-D matrix and the vector of parameters. The computational tests on the algorithm have been carried out using data from a multi-modal network in Madrid.