Asymmetry in Some Common Assignment Algorithms: The Dispersion Factor Solution

Many common assignment algorithms are based on Dial's original design to determine the paths that trip makers will follow from a given origin to destination centroids. The purpose of this paper is to show that the rules that have to be applied result in two unwanted properties. The first is that trips assigned from an origin centroid i to a destination j can be dramatically different to those resulting from centroid j to centroid i, even if the number of trips is the same and the network is perfectly symmetric. The second is that the number of paths that are ‘accepted’ by the algorithm can be surprisingly small. Asymmetry can cause numerous problems in transport model applications. It will not only produce unrealistic results, but also, as is demonstrated here, makes convergence toward supply — demand equilibrium impossible. The paper describes the principles on which Dial-type algorithms are based, the way in which they affect the transport model structure, and how the unwanted characteristics arise. An alternative algorithm, based on a dispersion factor and multipath search is presented, pointing out the advantages, both theoretical and operational, and some difficulties. A simple network is used as an example throughout the paper, and references to real applications are made.