Solving Evacuation Problems Efficiently--Earliest Arrival Flows with Multiple Sources

Abstract

Abstract

Earliest arrival flows in networks with multiple sinks

“…As we already mentioned, earliest arrival flows do always exist in networks where |S − | = 1, even in the much more general setting with arbitrary transit times [1,4,6]. In the special case of zero transit times, the following lemma implies that they also exist if |S + | = 1.…”

“…It turns out that the number of sinks (modelling exits/escapes) is crucial in this context: Minieka [6] shows that earliest arrival flows do always exist if there is only one sink. On the other hand, very simple examples of networks are known that do not allow for an earliest arrival flow [1,2]. Consequentially, a lot of research has been devoted to single-sink networks and algorithms to compute earliest arrival flows in this special situation, both for single-source-single-sink networks [5,6,9] and for multiple-sources-single-sink networks [1,2,3].…”

“…Although in this setting earliest arrival flows may not exist in general, it might very well be the case that they do exist in the special case at hand. The question which networks with multiple sinks still allow for earliest arrival flows was stated as an open problem in [1] and has, to our knowledge, not been studied before. In this paper, we analyze flows over time in networks where all edge transit times are zero.…”

Traffic Networks and Flows over Time

“…Baumann and Skutella [9] (see also [7]) present a polynomial time algorithm for computing earliest arrival transshipments in the general multiplesource single-sink setting. All previous algorithms rely on time expansion of the network into exponentially many time layers.…”

An Emergency Evacuation Planning Model Using the Universally Quickest Flow

“…Although Minieka [7] firstly proved that the universally quickest flow always exists, the running time of the algorithm for solving it remained to be pseudo-polynomial. Recently, a polynomial time algorithm for solving it was proposed by Baumnn and Skutella [1]. When we apply this model to the emergency evacuation problem, we have to consider capacity constraints of refuges.…”