Vulnerability analysis of cut-capacity structure and OD demand using Gomory-Hu tree method

Abstract

Vulnerability analysis of transportation networks has rapidly become important in recent decades given the increasing numbers of transportation disasters. In this paper, we describe a method for calculating the minimum cuts between all pairs of nodes in a transportation network and develop two indices for analyzing vulnerability; these are derived from topology-based vulnerability/demand-accountable analyses and enable evaluation of cuts without assuming route-choice behaviors. We show that such analyses can be performed using a Gomory–Hu tree to reduce the computational load. This method is efficient, requiring only N − 1 calculations of the maximum flow problem even though the number of node pairs is N2, where N is the number of nodes. In addition, we show that the total demand passing each minimum cut, which is necessary for demand-accountable analysis, can be obtained by network loading onto the tree using the Gomory–Hu tree features. We apply the proposed method to the central region of Japan to illustrate the applicability of the two indices for identifying vulnerable links in the road network.