Computing earliest arrival flows with multiple sources

Earliest arrival flows are motivated by applications related to evacuation. In typical evacuation situations, the most important task is to get people out of an endangered building or area as fast as possible. Since it is usually not known how long a building can withstand a fire before it collapses or how long a dam can resist a flood before it breaks, it is advisable to organize an evacuation such that as much as possible is saved no matter when the inferno will actually happen. In the more abstract setting of network flows over time, the latter requirement is captured by so-called earliest arrival flows. Before we discuss this in more detail, we first give a short and descriptive introduction into flows over time.