Dynamic Optimal Pricing

This economic theory was first applied to computing environments by Naor (1969), Mendelson (1985), and Pick and Whinston (1989). Stahl and Whinston (1991, 1992) and Gupta, Stahl, and Whinston [GSW] (1996) extended these single-server models to network computing environments and investigated its practicality by using simulation. Subsequently, GSW (1995a-c) applied their network models to the Internet.

At the center of the GSW approach is a general mathematical representation of a computing network, a model of price- and time-sensitive user demand for services, and a stochastic model of traffic flows and buffers. It shows that a socially optimal allocation of scarce network resources can be achieved by imposing optimal priority pricing at each site of potential congestion. The optimal prices depend on the traffic flow at the site, the size of the packets, the priority class, and the social cost of time. The latter can be econometrically estimated from the sensitivity of traffic to actual price and throughput time fluctuations at the site. Gupta et al. (1997), for example, present a new non-parametric technique for estimating users' value of time from usage data in real time, and show that these real-time estimates are sufficiently accurate to cause no significant loss in the social benefits of optimal pricing (using these estimates) as compared to the benchmark case with perfect information. In GSW,

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a practical decentralized method of determining optimal prices in real time is proposed. A simulation model is constructed that demonstrates the feasibility of this proposal.

In GSW (1995a-c), the simulation model is calibrated to represent the Internet and to compare the historical free-access policy with the theoretical optimal pricing (see fig. 3.5). This calibrated simulation suggests that without effective management of the Internet (as provided by efficient pricing), congestion and misallocation of resources could cost the economy tens of billions of dollars of lost benefits per year. This same simulation also demonstrates that the potential social gains of optimal pricing, if sought solely from capacity expansion, could have a capital investment cost exceeding the social gains. Thus, they argue that congestion is a very real concern and not just a theoretical fine point.

Figure 3.5 Benefits with different pricing strategies.

In the GSW vision, a typical user deciding whether and when to access an Internet service would be presented with a menu of options including the monetary cost and (when relevant) expected throughput time for each option. The options would specify a priority class, and could also include a security/anonymity level, minimum guaranteed qualities, and contingency options such as "submit the service request when the cost falls below $b." The user would then select the most preferred option. A personalized smart agent could

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automate the user's decision process based on previously specified user preferences. Frequently updated price and time information would come from the user's access provider. Smart agent software could serve this function also, gathering information from posted prices of transport providers and network congestion status reports.

The user would not receive a bill from each node and link of the network, but would rather receive one bill from his access provider for the posted price of that access provider for the service requested. * In turn, the access provider would receive a bill from the transport providers to which it is connected based on posted prices and actual usage. Each network transport provider needs to keep accounts only for the adjacent providers to which it is connected, not the individual users. In the vertical direction, each telecommunication carrier (such as AT&T, MCI, Sprint) need to keep accounts only for the networks (such as PSI, AlterNet, ANS, and so forth) to which it provides IP transport. This disaggregated pricing and billing approach mirrors the wholesale pricing practices in most industries. Ultimately it is the responsibility of the access providers to charge the user and to cover its costs vis-a-vis the transport providers.

Capital investment decisions can be greatly improved by the imposition of optimal priority pricing. First, as demonstrated in GSW (1995), imposition of priority pricing alone may generate more benefits at much less cost than the cost of capacity expansion. Second, without priority pricing—because the physical resource allocation is inefficient—the observed congestion can be a bad signal about which parts of the infrastructure should be expanded first. By imposing optimal pricing first, the distribution of network traffic can change significantly, revealing a different ranking of the bottlenecks. Thus with optimal pricing, capital investment can be focused on projects that will produce the greatest benefits.

Although the general model deals with potential congestion anywhere in a computing network, in practice the most likely sites of congestion are the 56-or-less kbps pipelines and modems to information content providers, their LANs, and servers. Thus in the near term, while there is still excess capacity on

* Recall that we are dealing with network transport services only. The user might well receive bills for the content of the data transported from many independent content providers.

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