A Fixed Point Approach to Origin-Destination Matrices Estimation Using Uncertain Data and Fuzzy Programming on Congested Networks

Origin–destination (O–D) matrix estimation methods based on traffic counts have been largely discussed and investigated. The most used methods are based on Generalised Least Square estimators (GLS) that use as input data a starting O–D matrix and a set of traffic counts. In addition to traffic counts, the analysts could know other general information about travel demand or link flows, based on their experience, or spot data, but few works deal with the matter of including effectively these sources of information. This paper proposes a Fuzzy-GLS estimation method that allows to improve the estimation performances of classic GLS estimator by including, in addition to traffic counts, uncertain information about starting O–D demand (i.e. outdated estimates, spot data, expert knowledge, etc.). The methods explicitly take into account the relevant level of uncertainty by taking as much advantage as possible from the few vague available data. The method is developed using fuzzy sets theory and fuzzy programming that seems to be a convenient theoretical framework to represent uncertainty in the available data. A solution algorithm for the proposed problem is also presented. The method has been tested by numerical applications and then compared to the classical GLS method under different sets of constraints to the problem.