An annotated overview of dynamic network flows

The need for more realistic network models led to the development of the dynamic network flow theory. In dynamic flow models it takes time for the flow to pass an arc, the flow can be delayed at nodes, and the network parameters, e.g., the arc capacities, can change in time. Surprisingly perhaps, despite being closer to reality, dynamic flow models have been overshadowed by the classical, static model. This is largely due to the fact that while very efficient solution methods exist for static flow problems, dynamic flow problems have proved to be more difficult to solve. Our purpose with this overview is to compensate for this eclipse and introduce dynamic flows to the interested reader. To this end, we present the main flow problems that can appear in a dynamic network, and review the literature for existing results about them. Our approach is solution oriented, as opposed to dealing with modelling issues. We intend to provide a survey that can be a first step for readers wondering whether a given dynamic network flow problem has been solved or not. Besides restating the problems, we also describe the main proposed solution methods. An additional feature of this paper is an annotated list of the most important references about the subject. Key-words: Flows, dynamic networks, time-dependent flows, algorithms, complexity This work was partially supported by the European FET project CRESSCO and the French CNRS AS Dynamo. I3S & INRIA Sophia Antipolis. The author received a scholarship from the European RTN project ARACNE. Un état de l’art commenté sur les réseaux de flots dynamiques Résumé : Un réseau de flots est dit dynamique si la traversée des arcs prend du temps, si le flot peut être retenu dans les nœuds, ou encore si les paramètres du réseau, par example, la capacité des arcs, peut évoluer au cours du temps. Dans ce rapport nous proposons un état de l’art des principaux problèmes liés aux réseaux de flots dynamiques, qui se veut une introduction au domaine. Nous y présentons les problèmes, les principales méthodes proposées pour les résoudre et nous fournissons une liste annotée des principales références bibliographiques sur le sujet. Mots-clés : Flots, résaux dynamiques, flots dynamiques, algorithmes, complexité An annotated overview of dynamic network flows 3