Partial Node Failure in Shortest Path Network Problems

Abstract

This paper investigates the impact of partial node failure from the perspective of shortest path network problems. We propose a network model that we call shortest path network problems for partial node failure, designed to examine the influence of partial node failures in a flow-based network using a set of indicators. The concept of partial node failure was applied to a special type of hub station, a mandatory transfer in subway or railway systems where multiple lines are arranged for the transfer of passengers. Numerical experiments were carried out on the Washington Metropolitan Area Transit Authority network (WMATA). The results or analysis detail how changes in flow distribution in the network were measured when a station partially failed, as well as ways of identifying heavily impacted stations with respect to different indicators. Various partial node failure scenarios were simulated for origin–destination (OD) flows by days, providing comprehensive information with which to evaluate plans for partial node failures, such as those related to scheduling maintenance, along with insights with which to make contingent plans for potential closure of stations. A major finding emphasizes that the rankings of station criticality are highly sensitive to the different OD flows by days when partial node failures are assumed in network modeling.