Congestion { Dependent Pricing of Network

We consider a service provider (SP) who provides access to a communication network or some other form of on-line services. Users access the network and initiate calls that belong to a set of diverse service classes, diiering in resource requirements, demand pattern, and call duration. The SP charges a fee per call, which can depend on the current congestion level, and which aaects users' demand for calls. We provide a dynamic programming formulation of the problems of revenue and welfare maximization, and derive some qualitative properties of the optimal solution. We also provide a number of approximate approaches, together with an analysis that indicates that near-optimality is obtained for the case of many, relatively small, users. In particular, we show analytically as well as computationally, that the performance of an optimal pricing strategy is closely matched by a suitably chosen static price, which does not depend on instantaneous congestion. This indicates that the easily implementable time-of-day pricing will often suuce. Throughout, we compare the alternative formulations involving revenue or welfare maximization, respectively, and draw some qualititative conclusions. For example, for a limiting case of practical interest, welfare maximization results in a single class-independent price per unit of traac volume, whereas a revenue maximizer may discriminate between diierent customer classes on the basis of their demand elasticities.