Adjustment of Trips-matrices in Large-scale Networks

Adjustment of Trips-matrices in Large-scale Networks


S Hansen, O Anker Nielsen, Technical University of Denmark, Department of Transport, DK; R Dyhr Frederiksen, Rapidis, DK


This paper evaluates how the MPME-method for adjusting trip-matrices based on counts performs in large-scale networks. Knowledge from various projects and further test concerning input-data are used to discuss method strengths and weaknesses.


Trip-matrices have traditionally been estimated based on comprehensive and often costly traffic surveys. However, in the recent years the amount of collected data on actual counted flows has increased significantly and the quality of counts have become more reliable due to improved automatic counting methods. Methods for estimating matrices from traffic counts are therefore interesting and relevant alternatives to more expensive survey methods.

One such method called Multi Path Matrix Estimation (MPME) was formulated by Otto Anker Nielsen in 1994 (Nielsen, 1998). MPME is a heuristic method where an existing trip-matrix is adjusted based on traffic counts. This is done in that way, that each cell in the matrix is adjusted according to all counts found on the routes between the zones in network. The method is integrated with the assignment model which makes it possible to use more complex route choice models like the stochastic user equilibrium, where counts are weighted according to the probabilities of the routes. Overall the weighted square deviation between assigned matrices and counts are minimized by changing a base-matrix as little as possible (again by minimizing the weighted square deviation). Another advantage is that the method can be applied on large-scale networks and that it can handle non-consistent counts.

The main objective of this paper is to evaluate the MPME-method and how it performs in large-scale networks. Secondly data requirements for the method will be investigated and especially the number and geographical spreading of counts are analyzed with respect to the quality of the matrix estimation. Finally the paper will introduce improvements to the method.

The MPME-method has recently been used for updating matrices for the regional model in Copenhagen (the OTM-model, Nielsen 2008). Likewise the method has been used to adjust matrices to the new freight model covering the east Denmark and southern parts of Sweden (the Øresund freight model), matrices for the urban train system in Copenhagen, and European transport matrices in the EU Trans-tools model (as being re-estimated in the TEN-CONNECT project). Based on knowledge gained in the projects some key measurements to evaluate the adjustments are defined. The results of the adjusted matrices are discussed and the methods strengths and weaknesses are reveled.

To a get detailed insight in the methods validity, further tests are carried out based on selected cases. This is done by first modeling traffic flows into a network to obtain synthetically counts on all links. Then the MPME-methods ability to reproduce the original matrix when fed with a different matrix is tested. By removing counts by random as well as in geographically patterns the necessity of counts is evaluated. Finally it is also analyzed how big impact the correctness of the input-matrix has on the methods ability to reproduce the original matrix.

The results show that MPME adjustments did improve the trip-matrices for the large-scale-models. In assignments carried out with the adjusted matrices the flows are more consistent with the counts. However, the results also reveal that the method has a tendency to reduce the average trip lengths - especially in cases with fewer counts in the network. The tests carried out furthermore shows that the result of the adjustment is highly depending on the input-matrix. This is especially true in case with few and/or geographically poorly distributed counts.

To improve the method a couple of suggestions are presented. These are designed to solve the method tendency to reduce the average trip lengths.


Nielsen, Otto Anker (1998). Two new methods for estimating Trip Matrices from Traffic Counts. Chapter in Travel Behaviour Research: Updating the state of play. Edited by Ortúzar, H. D., Hensher, D & Jara-Díaz, D. Elsevier Science Ltd. Oxford, UK. 1998. pp. 221-250.

Nielsen, Otto Anker; Hansen, Christian Overgaard & Vuk, Goran (1998). Traffic Model for Copenhagen ? Updating of trip matrices. Transportation Research Board Annual Meeting Session 337. Washington. January 13-17.


Association for European Transport