An approach to estimating and updating origin-destination matrices based upon traffic counts preserving the prior structure of a survey matrix

The scope of this paper is eminently practical. It addresses the problem of estimating and updating observed O-D matrices based upon available link flow information by means of the non-linear programming approach corresponding to the Augmented Lagrangian Function (ALM). In this way, one can estimate O-D matrices in a way which uses an efficient algorithm that minimizes the amount of stored information required for solving large-sized problems. A solution algorithm is provided, which has been completely developed and designed to be used within commercial assignment codes. The limitations and the features of these programmes have, in a natural way, conditioned the solution adopted for the model proposed. The case of updating a trip matrix, from a home-based survey, of a real problem corresponding to an existing city is analysed. For this application case two methodologies are reviewed; the first one does not incorporate constraints related to the total number of trips, the zonal productions and attractions, or individual O-D pairs; the second one does take them into account. The results obtained from the application of the proposed method to a prior O-D trip matrix, show huge differences with respect to the results yielded when the adjustment process does not limit the variations of the single terms (O-D pairs) with upper or lower boundaries. This comparison is carried out and based upon the wide spread Spiess's Gradient Algorithm. The graphical results depict the drastic contrasts observed, related to the distortion experienced by the information contained in the O-D trip matrix of a home-based survey, when using this methodology and the one proposed here.