Pricing of Dialup Services: an Example of Congestion-Dependent Pricing in the Internet

Recent research on pricing multiclass loss networks [19] has shown that the performance of optimal static pricing approaches that of optimal dynamic (congestion-dependent) pricing in the many small sources limit. In our own work with similar models, we have found it difficult to obtain large gains over static pricing in realistic settings, even when the many small sources assumption is violated. In this paper we give an example which is a stochastic control model for congestion-dependent pricing of Internet services. The model describes a local Internet service provider (ISP) with a single link to a peer network and two types of customers: (1) large institutions who are refunded for loss-rate violations and (2) small dialup users who “pay per click” on the world wide web according to prices set by the ISP. To understand the limits of performance, we assume that price information can be communicated instantaneously to the users. Our formulation captures the basic tradeoff in allocating bandwidth to the two classes of users in maximizing average net revenue. Optimal pricing requires that the ISP anticipate and respond to changes in bandwidth consumption. Our goal is to quantify the gain that can be achieved through dynamic pricing over open loop pricing strategies which may or may not account for time-of-day effects. We frame the problem as a continuous-time Markov decision process for which we numerically compute optimal solutions. We interpret the results for a wide range of parameter settings to isolate scenaria where real-time price feedback can substantially improve upon time of day pricing.