Traffic Demand Modeling and Origin-Destination Matrix Estimation

For most kind of analyses in the field of traffic modeling, there is a need for origin-destination (OD) matrices, which specify the travel demands between the origin and destination nodes in the network. The process of obtaining OD-matrices is long, complicated and expensive. The counting of traffic, which provides link flow observations, therefore is an opportune possibility for easily up-dating the information on the travel demand. This thesis concerns the estimation of OD-matrices from traffic counts. We will consider the problem to estimate OD-matrices for both time-indepenent and time-dependent models. Many models have been suggested for the time-independent case, where the quantities represent and average situation. If a user equilibrium is assumed for the link flows in the network, a bilevel problem structure is recognized, where the link flows are implicitly expressed as a traffic assignment of the present OD-matrix. A descent heuristic, which is an adaptation of the well-known projected gradient method, is proposed. Special attention is given to the problem of approximating the Jacobian matrix, which expresses the change of a certain link flow with respect to a unit change of the travel demand in a certain pair of origin and destination.When a time dimension is introduced, the estimation problem becomes more complex. Besides the problem of distributing the travel demand onto different routes, the flow propagation with respect to time must be handled. A general time-dependent extension of the estimation problem is given and the complications with dynamic traffic assignment are discussed. In a case study, the conventional solution technique is improved by introducing pre-adjustment schemes, which the structure of the information provided by the OD-matrix and the link flow observations.