Alternative method of counting the number of efficient paths in a transportation network

The number of efficient paths between an origin-destination (O-D) pair provides the route diversity degree of possibly used paths in a transportation network and has many important applications. The existing counting method was based on the Bell loading method for Logit model to determine the number of efficient paths between any two nodes without path enumeration. However, this method has a high time-complexity and requires many unnecessary computations, which significantly hinder its use in large-scale networks. Inspired by the Dial loading method for Logit model, this paper develops a more computationally attractive method to count not only the number of efficient paths, but also the number of efficient paths using each link/node, and the total/average cost of these paths between each O-D pair. Besides circumventing path enumeration, the proposed method has a much lower time-complexity. Numerical examples are then provided to demonstrate the validity and efficiency of the proposed method.