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.

起点-终点（OD）对之间有效路径的数量提供了交通网络中可能使用的路径的路径多样性程度，并具有许多重要的应用。现有的计数方法是基于Logit模型的贝尔加载法来确定任意两个节点之间的有效路径数，无需路径枚举。然而，这种方法时间复杂度高，需要大量不必要的计算，极大地阻碍了其在大规模网络中的应用。受 Logit 模型的 Dial 加载方法的启发，本文开发了一种更具计算吸引力的方法，不仅可以计算有效路径的数量，还可以计算使用每个链接/节点的有效路径的数量，以及这些路径的总/平均成本每个 OD 对之间。除了规避路径枚举，所提出的方法具有低得多的时间复杂度。然后提供数值例子来证明所提出方法的有效性和效率。