Lexicographically optimal earliest arrival flows

Evacuation by Earliest Arrival Flows

Earliest Arrival Flows with Multiple Sources

Earliest arrival flows capture the essence of evacuation planning. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink “as quickly as possible”. The latter requirement is made more precise by the earliest arrival property which requires that the total amount of ...

Earliest arrival flows on series-parallel graphs

We present an exact algorithm for computing an earliest arrival flow in a discrete time setting on series-parallel graphs. In contrast to previous results for the earliest arrival flow problem this algorithm runs in polynomial time.

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...

Earliest Arrival Flows in Networks with Multiple Sinks

Earliest arrival flows model a central aspect of evacuation planning: In a dangerous situation, as many individuals as possible should be rescued at any point in time. Unfortunately, given a network with multiple sinks, flows over time satisfying this condition do not always exist. We analyze the special case of flows over time with zero transit times and characterize which networks always allo...