Formulation of Traffic Estimation Models by Observed Link Flows and Comparative Study of Their Accuracy

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The existing models for estimating OD matrix from traffic count data on links have been formulated in different ways depending on the theoretical grounds. The basic idea common to these kinds of models proposed so far is that the most likely OD matrix can be produced by obtaining a consistency or a goodness of fit between the esimated and the observed link flows. In most of the models, moreover, a closeness measure between the estimated and the outdated OD matrices is incorporated into the formulation. It has not known, however, what form of the model formulation is the most appropriate for practical use. On this context, we make comparative study on the different model formulations and examine the model properties concerning the prediction errors caused by various kinds of noises or errors in the prior informations or the given data. The models presented in this paper are formulated in terms of minimization of the sum of square errors between the estimated and the observed or the outd … More ated flows, which can be considered as an approximation of the model formulations for the exixsting models derived from such as the entropy maximizatiom principle or the most likelyhood method. The merit of this simple model formulation is that the estimates of the elements of an OD matrix can be easily obtained by simultaneous linear equations, which is unnecessary to perform iterative procedure as seen in the many existing models. In addition, since the generation trips from nodes only are regarded as unknown variables in the model formulation, we can achieve outstanding savings of necessary computer memories.In this comparative study on the model properties through the numerical analyses, the follwing three types of model formulations are considered. Model A is formulated by minimization of the sum of square errors between the estimated and the observed link flows only, Model B by that of the sum of square errors between the estimated and the outdated generation trips at nodes under the constraints of consistency of link flows, Model C by that of the total sum of square errors in the generation trips at nodes and in the link flows. For these three types of model formulations, we examine and compare the properties concernig the prediction errors by fluctuations in OD pattern, variations in route choice probabilities, noises in observed link flow data and differences in the number of observed links by using hypothetical data made artificialy. The aim of this research is to find out the most appropriate model formulation for practial use through these numerial analyses, which can yield the more accurate and the more stable estimates of OD trips even if there exist some degree of errors in the given and the observed data. Less