On the calibration of the gravity model

Knowledge of Origin-Destination (OD) trip matrices is needed in many stages of transport planning. As direct observations of OD-flows are usually not available, a commonly used approach is to estimate them from traffic counts and other aggregated flow constraints. The under-specification that characterizes this estimation process can be resolved by requiring that OD-values conform to a model of travel demand. In this paper we consider a class of methods based on the gravity model, with either an exponential or a piecewise constant deterrence function. We focus on numerical methods to calibrate these models from traffic counts and establish a unifying analysis of them. The paper starts with a description of the gravity model, and a summary of the assumed modelling and observation error structures. Subsequently a likelihood expression is established which we seek to maximise. The paper then concentrates on methods that can be used for this purpose. Existing methods are discussed, and it is shown that some of the difficulties that occur when applying them can be resolved by a change of variables to logarithms of the model parameters. A key result concerns the matrix of second derivatives of the likelihood function. This result is then applied and leads to a new optimisation method. In a series of experiments this method is shown to be robust and computationally efficient