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