Estimation of origin–destination matrices from link flows on uncongested networks

Given link flow data from an uncongested network over a number of time periods, the problem of estimating the origin–destination (O–D) traffic intensities is considered. A statistical model of the transport system with Poisson distributed O–D flows is developed, in which the variation of route choice proportions is represented. The distribution theory of the model is discussed, parameter identifiability investigated, and the full likelihood function derived. This function proves somewhat too cumbersome for practical use but two feasible estimation procedures are established, both based upon maximization of multivariate normal approximations to the likelihood. Although these methods can operate using link flow data alone, incorporation of prior information into the inferential process is also detailed. The basic statistical model is then extended to encompass measurement error in the link flow data and modified methods of parameter estimation are investigated. The paper finishes with a numerical study of the proposed estimation procedures and discussion of some suggested avenues for future research.