Bottleneck links, variable demand, and the tragedy of the commons

  • Authors:
  • Richard Cole;Yevgeniy Dodis;Tim Roughgarden

  • Affiliations:
  • Department of Computer Science, New York University, 251 Mercer Street, New York 10012, New York;Department of Computer Science, New York University, 251 Mercer Street, New York 10012, New York;Department of Computer Science, Stanford University, 462 Gates Building, Stanford 94305 California

  • Venue:
  • Networks
  • Year:
  • 2012

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Abstract

We study the price of anarchy of selfish routing with variable traffic rates and when the path cost is a nonadditive function of the edge costs. Nonadditive path costs are important, for example, in networking applications, where a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. We prove the following results. In multicommodity networks, the worst-case price of anarchy under the ℓp path cost with 1 p ≤∞ can be dramatically larger than under the standard ℓ1 path cost. In single-commodity networks, the worst-case price of anarchy under the ℓp path cost with 1 p ∞ is no more than with the standard ℓ1 path norm. (A matching lower bound follows trivially from known results.) This upper bound also applies to the ℓ∞ path cost if and only if attention is restricted to the natural subclass of equilibria generated by distributed shortest path routing protocols. For a natural cost-minimization objective function, the price of anarchy with endogenous traffic rates (and under any ℓp path cost) is no larger than that in fixed-demand networks. Intuitively, the worst-case inefficiency arising from the “tragedy of the commons” is no more severe than that from routing inefficiencies. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012 (An extended abstract of this article appeared in the Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, January 2006.)