Importance Analysis for Capacitated Network Systems

A network, where links have different capacities, is considered to be in functioning state if a specified amount of flow can be transmitted through the network. In this paper, we consider the measures of importance of a link in such networks. We define the structural importance and reliability importance of a link when the required amount of flow is given. We also present the performability importance, which can be used to determine which links should be improved first in order to make the greatest improvement in the expected maximum flow of network. Numerical examples are presented as well for illustrative purpose.