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

Abstract

AbstractWe 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