The Adjustment/estimation of O-D Matrices: Some Caveats

The Adjustment/estimation of O-D Matrices: Some Caveats


M Florian, S Velan, Y Noriega, University of Montreal, CA


The adjustment/estimation of out-of-date origin destination matrices by using traffic counts is an often used method. The sensitivity of the method is demonstrated with new model formulations which are solved by using a gradient method.


The purpose of this paper is to point out some relevant facts related to the use of current observed flows to update (or adjust, estimate) origin-destination (O-D) demand matrices which are ?out-of-date?. The updating of such matrices by using counts is a common practice for achieving short term forecasts without the use of a full scale update of a demand forecasting model in the absence of new survey data. The practice is quite common and several O-D adjustment methods are available in some commercial packages used in practice. A short survey of the methods that have been developed for matrix adjustment follows.

Due to its practical importance, the adjustment of an origin-destination (O-D) matrix by using observed flows (counts) on the links and turns of a transportation planning network has attracted the attention of many researchers. The methods proposed may be subdivided into two categories, depending whether the network considered is assigned constant travel times (uncongested) or flow-dependent (congested) travel times.

Some of the contributions made for O-D matrix adjustment on uncongested networks include those of Van Zuylen and Willumsen (1980), Maher (1983), Cascetta (1984), Bell (1984), Spiess (1987), Tamin and Willumsen (1989), Willumsen (1984), Bell (1991) and Bierlaire and Toint (1994).

When the network considered for the O-D matrix adjustment is subject to congestion the underlying route choice method is an equilibrium assignment. Some of the numerous contributions made for this version of the problem are those of LeBlanc and Farhangian (1982), Nguyen (1984), Fisk (1988, 1989), Spiess (1990), Kawakami et al (1992), Florian and Chen (1995), Yang et al (1992) and Yang et al (1994). In this case the O-D matrix adjustment method may be formulated as a bi-level optimization problem or, as others denote such problems, a mathematical programming problem with equilibrium constraints (MPEC).

Several of these methods have been implemented in practice (see for instance Van Vliet, 1982, and Spiess, 1990, INRO, 2007), and are used on a regular basis for the adjustment of an out-of-date O-D matrix for the evaluation of contemplated network changes for a short term planning horizon.

In the following a multi-class O-D adjustment model is formulated, a solution algorithm is developed and numerical results are reported. The inclusion of the demand term into the simultaneous class formulation and the resulting gradient based algorithm are new developments.


Association for European Transport