Terminal Reliability of Road Networks with Multiple Destination Options

In crisis situations such as natural disasters, it is essential that people can be reached by fire and rescue services as well as police forces. Moreover, access to food and water supply should be ensured for everyone, for instance. In all cases, people depend on the (potentially damaged) road infrastructure – modelled as a graph network – that for all nodes in the network should provide connections to at least one supply node of each type (i.e., fire department, hospital etc.) even if some links in the network are currently unavailable. Assuming that there are multiple supply nodes per type among the whole network, the present contribution discusses the risk that a given node of the network becomes isolated from all of these supply nodes depending on the topological structure of the network. For this purpose, the well-known concept of terminal reliability is adapted to the situation with multiple possible destinations which is realized by appropriately modifying the original graph. An algorithm is presented that allows finding all relevant cut sets in the modified graph which can be used for computing the probability Rsys that a given node remains connected to at least one of the supply nodes considered depending on the link failure probabilities pi. A simple clustering approach together with Boolean algebra finally yields explicit numbers for Rsys  depending on pi. The whole concept is demonstrated based on an illustrative example showing the different endangerment among the nodes of the network including a discussion about the specific criticality of each network link with regard to ensuring the connectivity between supply nodes and other nodes. Thus, by identifying critical links and quantifying the risk of isolation for all nodes in the network, the present contribution provides useful tools for prevention in crisis management.