Journal of the ACM (JACM)
A new average case analysis for completion time scheduling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Selfish routing with incomplete information
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Coordination mechanisms for selfish scheduling
WINE'05 Proceedings of the First international conference on Internet and Network Economics
A cost mechanism for fair pricing of resource usage
WINE'05 Proceedings of the First international conference on Internet and Network Economics
The Influence of Link Restrictions on (Random) Selfish Routing
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Resource Management in Large Networks
Algorithmics of Large and Complex Networks
Atomic routing games on maximum congestion
Theoretical Computer Science
Tradeoffs and Average-Case Equilibria in Selfish Routing
ACM Transactions on Computation Theory (TOCT)
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We consider the price of selfish routing in terms of tradeoffs and from an average-case perspective. Each player in a network game seeks to send a message with a certain length by choosing one of several parallel links that have transmission speeds. A player desires to minimize his own transmission time (latency). We study the quality of Nash equilibria of the game, in which no player can decrease his latency by unilaterally changing his link. We treat two important aspects of network-traffic management: the influence of the total traffic upon network performance and fluctuations in the lengths of the messages. We introduce a probabilistic model where message lengths are random variables and evaluate the expected price of anarchy of the game for various social cost functions. For total latency social cost, which was only scarcely considered in previous work so far, we show that the price of anarchy is Θ(n/t), where n is the number of players and t the total message-length. The bound states that the relative quality of Nash equilibria in comparison with the social optimum increase with increasing traffic. This result also transfers to the situation when fluctuations are present, as the expected price of anarchy is O(n/)/(E[T]), where (E[T] is the expected traffic. For maximum latency the expected price of anarchy is even 1 + o(1) for sufficiently large traffic. Our results also have algorithmic implications: Our analyses of the expected prices can be seen average-case analyses of a local search algorithm that computes Nash equilibria in polynomial time.