A study on logit assignment which excludes all cyclic flows

This paper first studies the Van Vliet formula in calculating the link choice probabilities for the logit assignment without cyclic flows. We show that this formula may still contain the cyclic flow contribution although the node-to-node weights matrix used in it does not. The correct formula is provided but with the need for path enumeration. The paper then presents an efficient approach to generate all non-looping paths and applies it to solve stochastic user equilibrium problem in conjunction with the method of successive averages. A numerical example is used to validate our study.