Path Flow and Trip Matrix Estimation Using Link Flow Density

A macroscopic model is presented that simultaneously estimates route flows and trip matrices for congested road networks using data on link densities instead of link flows. The advantage of this approach is that it avoids errors that may occur in the individual links’ flow-cost relationships when congestion is heavy. Under the proposed methodology, both the flows and the matrices are estimated by the model using an image of the network such as an aerial photograph in which the number of vehicles on each link can be identified. The model itself is formulated as a maximum entropy optimization problem subject to linear constraints given by vehicle densities on the links, and is validated using analytic examples and traffic microsimulations. The results demonstrate the superiority of the link-density approach over the traditional flow-based method.