Costas Courcoubetis - Volume price revisited

We analyze the interplay between the demand for downloads, the choice of congestion control mechanism, and the tariff structure at a single link, when users have preferences in terms of average download delay and they are charged according to the number of congestion signals (ECN marked packets) they receive. Our model involves a timescale separation approach, where in the fast timescales active flows compete for instantaneous bandwidth share using congestion control parameters tuned in a non-cooperative fashion in a slower time scale. This is modeled by letting flows correspond to utility functions within the network utility maximization framework laid down by Kelly. On a slower timescale, users selfishly change the utility functions of their flows (the congestion control parameters) and also shape their otherwise unrestricted demand for downloads based on the average experienced download delay and the charges incurred. We study the equilibrium of this loop of interactions from the point of view of social welfare. For homogeneous users we find that optimal equilibria are induced when they choose among linear utility functions, while this is not the case for logarithmic, i.e., proportionally fair congestion controllers. We next consider two types of users, web-browsing (delay-sensitive) and bittorrent (arbitrarily small delay sensitivity), where the latter are much less sensitive to download delay than the former. If bittorrent users respond to congestion according to proportionally fair utility functions the charge induced by ECN marked packets does not provide the correct signal for service differentiation and the resulting equilibrium is suboptimal. On the other hand, if flows are charged for the volume of bits they transfer as well, then social welfare maximum is attained for some price per bit. This reveals a new role for bit volume pricing: to provide bittorrent users the correct incentives for choosing congestion controllers that effectively give priority to web-browsing users. This occurs because adequate volume pricing forces bittorent users to spend an arbitrarily small budget on congestion charges, which turns them into second priority (their aggressivity choice at the equilibrium).