Computing earliest arrival flows with multiple sources

Earliest arrival flows are motivated by applications related to evacuation. 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 flow that has arrived at the sink is maximal for all points in time simultaneously. It is a classical result from the 1970s that, for the special case of a single source node, earliest arrival flows do exist and can be computed by essentially applying the Successive Shortest Path Algorithm for min-cost flow computations. While it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open. We present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem

Dynamic matchings and quasi-dynamic fractional matchings, part I

Bibliography: p. 23-24.James B. Orlin

Maximum Contraflow Evacuation Planning Problems On Multi-network

Contraflow approach for the evacuation planning problem increases outbound capacity of the evacuation routes by the reversal of anti-parallel arcs, if such arcs exist. The existing literature focuses on network contraflow problems that allow only anti-parallel arcs with equal transit time. However, the problems modeled on multi-network, allowing parallel as well as anti-parallel arcs with not necessarily equal transit time, seem more realistic. In this paper, we study the maximum dynamic contraflow problem for multi-network and propose efficient solution techniques to them with discrete as well as continuous time settings. We also extend the results to solve earliest version of the problem for two terminal series parallel (TTSP) multi-network

Atomic Splittable Flow Over Time Games

In an atomic splittable flow over time game, finitely many players route flow dynamically through a network, in which edges are equipped with transit times, specifying the traversing time, and with capacities, restricting flow rates. Infinitesimally small flow particles controlled by the same player arrive at a constant rate at the player's origin and the player's goal is to maximize the flow volume that arrives at the player's destination within a given time horizon. Here, the flow dynamics are described by the deterministic queuing model, i.e., flow of different players merges perfectly, but excessive flow has to wait in a queue in front of the bottle-neck. In order to determine Nash equilibria in such games, the main challenge is to consider suitable definitions for the players' strategies, which depend on the level of information the players receive throughout the game. For the most restricted version, in which the players receive no information on the network state at all, we can show that there is no Nash equilibrium in general, not even for networks with only two edges. However, if the current edge congestions are provided over time, the players can adapt their route choices dynamically. We show that a profile of those strategies always lead to a unique feasible flow over time. Hence, those atomic splittable flow over time games are well-defined. For parallel-edge networks Nash equilibria exists and the total flow arriving in time equals the value of a maximum flow over time leading to a price of anarchy of 1.ISSN:1868-896

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