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A hierarchical optimization problem: Estimating traffic flow using Gamma random variables in a Bayesian context
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DOI：10.1016/j.cor.2012.04.011.png)
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Abstract
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In this paper a hierarchical optimization problem generated by a Bayesian method to estimate origin-destination matrices, based on Gamma models, is given. The problem can be considered as a system of equations in which three of them are optimization problems: (1) a Wardrop minimum variance (WMV) assignment model, which is used to derive the route choice probabilities, (2) a least squares problem, used to obtain the OD sample data, and (3) a maximum likelihood problem to estimate the posterior modes. A multi-level iterative approach is proposed to solve the multi-objective problem that converges in a few iterations. Finally, two examples of applications are used to illustrate the proposed methods and procedures, a simple and the medium size Ciudad Real networks. A comparison with existing techniques, which provide similar flows, seems to validate the proposed methods. (C) 2012 Elsevier Ltd. All rights reserved.
Keywords:
Gamma distribution
Conjugate priors
Evidence propagation
Parameter estimation
Prior assessment of hyperparameters
Origin-destination
Link flow estimation
Multi-level technique
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