Assessing network vulnerability using shortest path network problems

Abstract

This paper identifies and evaluates critical components of a flow-based network from the perspective of the shortest path problem. Two network optimization models are proposed: the first model, called the shortest path network model (SPN), is an extended version of a single shortest path problem to apply for all origin-destination pairs in a network while considering passenger flows; the assessing nodal disruption in shortest paths network model (AND-SPN), which is based on the SPN, assesses the influence of r nodes’ disruption of the network flow pattern. In this paper, network performance is assessed not only by the transport cost as an objective function but also through supplementary criticality indicators reflecting average arc use, average s-t pair cost, and average arc flow. In the case study of the Amtrak rail network, the criticality of stations is evaluated in terms of objective function and of criticality indicators—highlighting the effect of the disruption and allowing comprehensive exploration of it. Aided by the provided list of criticality rankings, decision makers can decide which stations are the most important to protect during special events or disasters or when seeking to enhance transportation network security.