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This paper examines the behavior of the price of anarchy as a function of thetraffic inflow in nonatomic congestion games with multiple origin-destination(O/D) pairs. Empirical studies in real-world networks show that the price ofanarchy is close to 1 in both light and heavy traffic, thus raising thequestion: can these observations be justified theoretically? We first show thatthis is not always the case: the price of anarchy may remain a positivedistance away from 1 for all values of the traffic inflow, even in simplethree-link networks with a single O/D pair and smooth, convex costs. On theother hand, for a large class of cost functions (including all polynomials),the price of anarchy does converge to 1 in both heavy and light traffic,irrespective of the network topology and the number of O/D pairs in thenetwork. We also examine the rate of convergence of the price of anarchy, andwe show that it follows a power law whose degree can be computed explicitlywhen the network's cost functions are polynomials.

When is selfish routing bad? The price of anarchy in light and heavy traffic