Congestion{dependent Pricing of On-line Internet Services 1

We consider a service provider (SP) who provides access to a communication network or some other form of on-line 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 aaects 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. In this paper, we consider a service provider (SP) who provides access to a communication network, such as the Internet, 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 are interested in the problem of determining an optimal pricing strategy, that maximizes an appropriate performance measure such as social welfare or the provider's revenue. For the case of a revenue maximizing provider, we have essentially a problem of yield management, similar to the problems that arise in the airline and other service industries 2]. The common element in such problems is that the marginal cost of serving an additional customer , e.g., an airline passenger or a new call, is negligible once a ight has been scheduled or a communications infrastructure is in place. The pricing problem in communication networks, such 1 A full version of the paper is in 1]. as the Internet, is complex and multifaceted, because one needs to take into account engineering issues (compatibility with existing or planned protocols), nancial issues (cost recovery), a diverse set of desired services (e.g., elastic versus real-time traac with or without quality of service requirements), and other considerations (such as simplicity, social welfare, etc.). The current Internet relies on technical means to …