The Estimation of an Origin-Destination Matrix from Traffic Counts

In this paper, a model is described that will under certain circumstances yield the most likely origin-destination matrix which is consistent with measurements of link traffic volumes. Given knowledge of the proportionate usage of each link by the traffic between each zone pair, the model parameters scale each element of a prior estimate of the origin-destination matrix up or down so that the measurements of link traffic volumes are reproduced. The fitted values are shown by example to be invariant to the application of uniform scaling to the prior estimates. A Newton model fitting procedure is outlined. In reality, measurements of link traffic volumes are random variables and the proportionate usage of links by the traffic for each zone pair is not known with certainty. An expression is derived for the variances and covariances of the logarithms of the fitted values in terms of the variances and covariances of the measured link volumes, taking the proportionate usage of links as given. The expression permits the calculation of asymmetric confidence intervals for the elements of the fitted origin-destination matrix.