Alternatives to Dial's logit assignment algorithm

Abstract

Two logit assignment methods for transportation networks are proposed as alternatives to Dial's algorithm. While retaining the absence of a need for the enumeration of paths, they dispense with both forward and backward passes. They, therefore, do not require minimum node-to-node cost information beforehand. Both methods admit loops and paths that are otherwise inefficient in the Dial sense, which can arise in practice as a result of driver searching behaviour. The first method considers a finite number of paths and the second method an infinite number of paths in the presence of loops. The absence of any efficiency constraint on the set of feasible paths makes the algorithms attractive for use in stochastic user equilibrium methods or in the approximation of a user equilibrium assignment through stochastic user equilibrium methods. The similarity of the structure of one of the proposed algorithms with that of the Floyd-Warshall shortest path algorithm would allow the two to be combined.