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.
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- Shihsien, Liu & Fricker, Jon D., 1996. "Estimation of a trip table and the [Theta] parameter in a stochastic network," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(4), pages 287-305, July.
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- D E Boyce, 1986. "Integration of Supply and Demand Models in Transportation and Location: Problem Formulations and Research Questions," Environment and Planning A, SAGE Publishing, vol. 18(4), pages 485-489, April.
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- Cascetta, Ennio & Nguyen, Sang, 1988. "A unified framework for estimating or updating origin/destination matrices from traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 22(6), pages 437-455, December.
- Codina, Esteve & Garcia, Ricardo & Marin, Angel, 2006. "New algorithmic alternatives for the O-D matrix adjustment problem on traffic networks," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1484-1500, December.
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