A survey of dynamic network flows
Annals of Operations Research
The Quickest Transshipment Problem
Mathematics of Operations Research
Journal of the ACM (JACM)
Minimum cost flows over time without intermediate storage
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Selfish versus coordinated routing in network games
Selfish versus coordinated routing in network games
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Flows over Time with Load-Dependent Transit Times
SIAM Journal on Optimization
Equilibria in Dynamic Selfish Routing
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Network games with atomic players
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Equilibria in Dynamic Selfish Routing
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Nash Equilibria and the Price of Anarchy for Flows over Time
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
A Stackelberg strategy for routing flow over time
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Contention issues in congestion games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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In both transportation and communication networks we are faced with "selfish flows", where every agent sending flow over the network desires to get it to its destination as soon as possible. Such flows have been well studied in time-invariant networks in the last few years. A key observation that must be taken into account in defining and studying selfish flow, however, is that a flow can take a non-negligible amount of time to travel across the network from the source to destination, and that network states like traffic load and congestion can vary during this period. Such flows are called dynamic flows (a.k.a. flows over time). This variation in network state as the flow progresses through the network results in the fundamentally different and significantly more complex nature of dynamic flow equilibria, as compared to those defined in static network settings. In this paper, we study equilibria in dynamic flows, and prove various bounds about their quality, as well as give algorithms on how to compute them. In general, we show that unlike in static flows, Nash equilibria may not exist, and the price of anarchy can be extremely high. If the system obeys FIFO (first-in first-out), however, we show the existence and how to compute an equilibrium for all single-source single-sink networks. In addition, we prove a set of much stronger results about price of anarchy and stability in the case where the delay on an edge is flow-independent.