Auctions are a well-established mechanism for efficient allocation of scarce resources and as such have already become a standard approach for pricing QoS-enabled future Internet services. This paper investigates networks where auctions are performed periodically and customers request bandwidth for sessions with holding times longer than one auction period. A simple mathematical model assuming constant session holding times, identical bandwidth requests and i.i.d. uniformly distributed bids allows to derive explicitly the resulting equilibrium market price. In the rest of the paper, this basic result is generalized by relaxing the original assumptions one after the other. Keywords Internet Economics, Generalized Vickrey Auction, Second-chance Auction, Nash Equilibrium