An Emergency Evacuation Planning Model Using the Universally Quickest Flow

In recent years, catastrophic disasters by massive earthquakes have been increasing in the world, and disaster management is required more than ever. In the case of disasters such as tsunamis, a slight delay in evacuation may deprive evacuees of life. In this article, we formalize the emergency evacuation planning model for evacuation from tsunamis and other disasters based on the idea of the universally quickest flow. We show that there does not always exist a universally quickest flow when the capacity constraint of refuges is taken into account. Therefore, we propose an alternative criterion that approximates a universally quickest flow, and presents an algorithm for finding an optimal flow for this criterion. Numerical experiments are carried out for the evacuation of a local city in Japan where tsunami damages are assumed to occur when a large earthquake occurs in the ocean nearby.