Synchronized Flow-Based Evacuation Route Planning

When a disaster occurs, we need a routing plan to evacuate all the people in the affected area as soon as possible. For this purpose, we can model the transportation network as a graph of nodes and edges with occupancy on nodes and capacity and travel time on edges, where nodes represent places such as cities and edges represent roads. Given a transportation network graph, we can compute routes to evacuate all the people in the dangerous area by selecting paths from the source nodes (the nodes of which residents need to be evacuated) to the destination nodes (the nodes where the evacuees can be transported to). With capacity and travel time constraints on the roads (or edges), calculation of the evacuation time on the graph requires the use of time-expanded graphs. The use of time-expanded graphs, which are merely duplications of the given graph flagged with discrete time stamps, explodes the time and space complexities of the calculation of evacuation times. This drawback results in low scalability, especially when the evacuation time or the number of evacuees is relatively big compared to the size of the graph, such as the number of nodes, edges, and paths. In this paper, we present a scalable algorithm, SYNChronized FLOw Evacuation(SyncFloE), to plan the evacuation routes based on synchronized flows. The novel concept of synchronized flows replaces the use of time-expanded graphs and provides higher scalability in terms of the evacuation time or the number of evacuees. SyncFloE has computation time that only depends on the number of source nodes and the size of the graph itself, such as the number of nodes, edges, and paths. The computational results that support our claim are presented and discussed.