Congestion-dependent pricing of online Internet services

We consider a service provider (SP) who provides access to a communication network or some other form of online services. Users initiate calls that belong to a set of diverse service classes. The SP charges a fee per call, which can depend on the current congestion level, and which affects users' demand for calls. We provide a dynamic programming formulation of the problems of revenue and welfare maximization, and derive qualitative properties of the optimal solution. We show that the performance of an optimal pricing strategy is closely matched by a suitably chosen static price, which does not depend on instantaneous congestion. We establish that static pricing is asymptotically optimal in a number of limiting regimes, including one of many, relatively small users. In nonstationary demand conditions this leads to the easily implementable time-of-day pricing. Throughout, we compare the alternative formulations involving revenue or welfare maximization, respectively, and draw some qualitative conclusions.