Proportional Pricing for Efficient Traffic Equilibrium at Internet Exchange Points

We analyze traffic exchange between Internet Service Providers (ISPs) at an Internet Exchange Point (IXP) as a non-cooperative game with ISPs as self-interested agents. Each ISP has the choice of exchanging traffic either using the shared IXP facilities, or outside the IXP – through their transit providers or private peering. We analyze the efficiency (social cost optimality) of the traffic exchange equilibrium at the IXP taking into consideration the congestion cost experienced by the ISPs at the IXP, under a proportional pricing model where the per-unit price charged to ISPs is proportional to the aggregate level of congestion at the IXP. We obtain worst case bounds on the efficiency at traffic exchange equilibrium under two different models of the congestion cost (delay) functions. Simulations conducted using data for actual IXPs obtained from PeeringDB demonstrate that the theoretical bounds derived for social cost optimality at equilibrium (measured as the Price of Anarchy) are fairly tight, and correctly capture the performance trends against the variation of key model parameters. Further, the results show that for a certain range of the proportionality constant, proportional pricing not only results in significantly better efficiency compared to zero pricing, but also attains nearoptimal social cost and near-optimal IXP revenue simultaneously.