van Zijpp, NJ;
Improved algorithms for calibrating gravity models.
In: Bell, MGH, (ed.)
(99 - 113).
ELSEVIER SCIENCE BV
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 OD-matrices from traffic counts. The under-specification that characterizes this estimation problem can be resolved by requiring that OD-matrices 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 discretized deterrence function. We focus on solution methods and establish a unifying analysis of them. A key result presented in the paper is an expression for the matrix of second derivatives of the likelihood objective function. Based on this result, a minimization method is developed with a greatly improved speed and convergence. Numerical experiments based on a set of empirical data obtained from a French tollroad have shown that speed has improved by a factor that typically is in the range 6 - 15 and can in some cases be as large as 400 relative to existing methods. The new method has good robustness in that it converges successfully under a wide variety of circumstances including those under which other methods fail. Moreover, this result provides an effective convergence criterion that can also be applied in combination with other solution methods, such as Gauss-Seidel and gradient search methods.
|Title:||Improved algorithms for calibrating gravity models|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science
UCL > School of BEAMS > Faculty of Engineering Science > Civil, Environmental and Geomatic Engineering
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