Reserve price in progressive second price auctions

Pricing has become mandatory to overcome congestion and to offer service differentiation in communication networks. Whereas many pricing schemes have been designed in the literature, we focus here on the so-called progressive second price auction that allocates bandwidth on an auction-basis: users sequentially declare the amount of bandwidth they expect and how much they value it. At each time, the network allocates bandwidth to users with the highest willingness-to-pay and charge them with the bid of those excluded from the game by their presence. Convergence, efficiency and incentive compatibility have been verified in the literature for this scheme. Nevertheless one degree of freedom still remains in the model, namely the reserve price that is the minimal unit price at which the network accepts to sell the bandwidth. We propose here to determine the reserve price maximizing the network revenue. This analysis is based on the assumption that the demand functions and distribution of the (a priori random) number of users in the network are known.