An improved Dial's algorithm for logit-based traffic assignment within a directed acyclic network

<title>Abstract</title> Dial's algorithm is one of the most effective and popular procedures for a logit-type stochastic traffic assignment, as it does not require path enumeration over a network. However, a fundamental problem associated with the algorithm is its simple definition of ‘efficient paths’, which sometimes produces unrealistic flow patterns. In this paper, an improved algorithm based on the route extension coefficient is proposed in order to circumvent this problem, in which ‘efficient paths’ <italic>simultaneously</italic> consider link travel cost and minimum travel cost. Path enumeration is still not required and a similar computing efficiency with the original algorithm is guaranteed. A limitation of the algorithm is that it can only be applied to a directed acyclic network because a topological sorting algorithm is used to decide the order of the sequential calculation. A numerical example based on the Beijing subway network illustrates the effectiveness of the proposed algorithm. It is found that it is able to exclude most unrealistic paths, but include all reasonable paths when compared with path enumeration and the original Dial's algorithm.