An analysis of the reliability of an origin-destination trip matrix estimated from traffic counts

In recent years a large number of models have been developed to estimate an origin-destination (OD) trip matrix from link traffic count data. A key objective of the models is to guarantee the quality of the estimated OD matrix. Because traffic counts alone are generally not enough to identify the true OD matrix, it is important to evaluate the estimation accuracy of the model. This paper presents a theoretical investigation into the reliability of an estimated OD trip matrix employing the concept of ‘Maximum Possible Relative Error’ (MPRE). It is shown that the MPRE can be formulated as a simple quadratic programming problem. The proposed MPRE shows the upper bound of the real relative error for a particular fitted OD matrix and plays a useful role in the analysis of the reliability of the estimated OD trip matrix.