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

根据不同的理论基础，现有的基于交通统计数据估算OD矩阵的模型有不同的表述方式。迄今为止提出的这些模型的基本思想是，最可能的OD矩阵可以通过在估计和观察到的环节流之间获得一致性或良好的拟合来产生。此外，在大多数模型中，估计的OD矩阵和过时的OD矩阵之间的接近度量被纳入到公式中。但是，目前还不知道哪种形式的模型公式最适合实际使用。在此背景下，我们对不同的模型公式进行了比较研究，并研究了各种噪声或先验信息或给定数据中的错误引起的预测误差的模型性质。本文所提出的模型是根据估算值与观测值或实际流量之间的误差平方和的最小化来建立的，这可以看作是对现有模型的近似，如熵最大化原理或最似然法。这种简单的模型公式的优点是，一个OD矩阵的元素的估计可以很容易地通过线性方程组的联立得到，而不需要像许多现有的模型那样进行迭代过程。此外，由于在模型公式中仅将节点的生成行程视为未知变量，因此可以显著节省必要的计算机内存。在通过数值分析对模型性质进行对比研究时，考虑了以下三种模型的表述。模型A是只求估计的与观测到的线路流的误差平方和最小，模型B是在线路流一致性约束下，求估计的与节点上过时的代行程的误差平方和最小，模型C是求节点上和线路流上的总代行程误差平方和最小。对于这三种类型的模型公式，我们考察和比较了有关OD模式波动、路线选择概率变化、观测链路流量数据噪声和观测链路数量差异的预测误差的性质。本研究的目的是通过这些数值分析找出最适合实际使用的模型公式，即使给定数据和观测数据存在一定程度的误差，也可以得到更准确和更稳定的外径行程估计。少

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 In most of the models, moreover, a closeness measure between the estimated and the outdated OD matrices is incorporated into the formulation.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