Alok Gupta

Dept. of MSIS, University of Texas at Austin

Dale O. Stahl

Dept. of Economics, University of Texas at Austin

Andrew B. Whinston

Dept. of MSIS, University of Texas at Austin.

Comments, Suggestions, Critique --> alok@cism.bus.utexas.edu

The Internet is by far the fastest growing economy in the world in terms of the number of users and information providers. Currently there are over 30 million users with an estimated 100% annual growth. As an economic system we view the information providers, including entertainment, news, and educational services as producers and the users as consumers. The Internet is already experiencing traffic jams. Given the growth rate of The Internet and the need to provide real time services in future, this congestion will become a severe problem if proper coordinating mechanisms are not designed and implemented. We have developed a priority pricing mechanism based on General Equilibrium theory in economics, and we use a measure based on the collective benefits obtained by the users to evaluate the performance of the system. We have developed a simulation model to test the validity of our approach and to show the gain in efficiency induced by pricing. Based on simulation results with a non-priority pricing scheme we show substantial improvements versus a free access policy. Furthermore, we address the issues concerning the development of new accounting/billing methods, cross subsidization of services, infrastructure investment, development of smart agents for dynamic scheduling and users' job management, and the possible competitive market structures which will evolve over The Internet.

Introduction

The Internet has become the primary means of communication for most of its users. It is no wonder that individuals who have access to it get more information through Internet than any other source. The Internet currently provides individuals access to e-mail, news groups, free software, data transferring capability, real-time conferencing, and many other services. For virtually any problem one faces, a posting to relevant news group(s) can provide solutions (or at least good suggestions) quicker than ever possible. Researchers can use The Internet facilities such as telnet, ftp, gopher, and World Wide Web (WWW) to obtain research articles, software tools, or to conduct a survey. Cronin (1994) appropriately states that "the impact of high-speed global communication on research and education is already so profound that The Internet has been dubbed the second Gutenberg revolution."

However, the use of this massive global network is not limited to academic/research purposes. Businesses, whether large or small, are using The Internet's capabilities for exchanging ideas, customer support, and trouble shooting, among others. Many businesses have recognized that an Internet connection can open new avenues to international access for business partners, customers, and markets. Companies which did not have resources for personal computer networks earlier no longer need to rely on more expensive and inefficient methods of data transfer and acquisition, e.g. using diskettes. A personal computer can now be a node on The Internet and access its vast resources in terms of information and data transfer capabilities. Multinational companies and companies in the service sector benefit from Internet's ability to provide an efficient, reliable, and inexpensive form of communication. Globalization of markets are forcing almost every business to be more efficient and to search ways of reducing cost. Businesses must increase their global awareness, monitor the (international) markets, and exploit every possible opportunity.

Volume at The Internet is growing faster than 100% a year. At last count the number of Internet users was about 15 million, as a conservative estimate. This phenomenal growth is primarily due to the fact that The Internet access is relatively inexpensive, and no fee is charged for using most of the valuable services provided by the servers on The Internet. Until recently practically no commercial services were available on The Internet; however, this situation is changing rapidly. The Internet already has a variety of services or is being used to access several services. Moreover, the infrastructure of The Internet is itself changing; NSF is withdrawing its support for the NSFNET, the major infrastructure backbone supporting The Internet today in USA. Many private companies are now interested in providing infrastructure and acting as an access provider to the network (e.g., SPRINT, PSINET, AT&T, etc.). These companies see enormous potential for growth and development of the services provided on The Internet. In effect The Internet will become a world-wide or global economy in itself with consumers armed with sophisticated access tools and firms providing digital services. In the near future, movies, television, other digital entertainment, news, books, lectures, and video-conferencing, all are candidates for a service on The Internet. In addition, economic transactions such as purchasing products and arranging contracts will also be supported.

"Traffic Jams Already on the Information Highway" was the headline of a front page article that appeared in the November 3, 1993, New York Times. Armed with the ability to join The Internet through personal computers, thousands of new people join The Internet community every day. In the near future, both voice and video services could be provided on The Internet. Obviously, this will induce an enormous load on The Internet infrastructure, and the data has to be transferred at terabytes rates through many nodes. The fiber optics technology coupled with modern laser guided router technology are capable of handling such a load, but as the volume increases the chances for long delays, loss of messages, and blockage can increase faster than they can be handled. Clearly, a mechanism is required which both gives access to users who value it the most and minimizes the waste incurred due to loss and delays.

There are several other issues such as copyright protection, security, and data integrity (to name a few), which will be as complex as The Internet structure and culture itself. The technical issues involved in encryption and authentication of users and providers are also quite complex and have to be addressed. However, we concentrate here on the primary force needed to create and sustain a market - the pricing of services. We feel that pricing is one of the most important issues facing the development of commercial Internet services. We argue that appropriate pricing mechanisms will efficiently distribute the load on The Internet and minimize the losses and delays in services. We view The Internet as an economic system which can be analyzed by looking at the appropriate equilibrium conditions, which in turn can be often imposed by choosing appropriate prices. Specifically, we divide the services in two categories: (i) user services, i.e., services users want such as news or movies, and (ii) network services, i.e., the infrastructure services or the vehicle which delivers the user services. In this paper we concentrate on the pricing of network services which are enforced by infrastructure providers. We also discuss the form of the markets which could develop over The Internet and other issues related to user services pricing.

Future of The Internet Services and Pricing Issues

Currently Internet infrastructure is a highway of information paths with no usage based fee. Typically a connection fee is charged based on the size of the data "pipeline" connecting a server to The Internet. Whether or not to charge for network services is a complex question. A flat charge for services will result in large inefficiencies in usage because the services providing low value might require as much bandwidth as the ones providing relatively higher value. In addition, the delays and losses might reduce the values of the services considerably. Although a model incorporating fixed seasonal changes in prices (time of the day in case of The Internet) has a potential to improve the usage, it is far from the best practical solution.

In near future, The Internet is going to carry voice and video services all over the globe. These developments will provide opportunities for new types of services which potentially need real-time transmission and reception of data. As mentioned earlier the transmission layer of The Internet, i.e., the backbone(s) will probably be able to carry this data. However, depending upon the number of users or the total load at a server, it might not be able to handle the flow of data at such high rates. Clearly a simple solution to this problem is to have redundant capacity. However, it will be difficult to assess the potential demand, and in most cases redundant capacity will not be cost effective. Furthermore, servers providing the real time services, such as interactive video conferencing, will have to ensure that these services are uninterrupted. In a network environment with non-dedicated links[Footnote 1], providing uninterrupted services will be impossible without priority mechanism.[Footnote 2] A priority mechanism ensures that the jobs in a higher priority are completed before starting the processing of a lower priority job, regardless of the time of arrival. Thus, if uninterrupted services have to be provided, such as video conferencing, then a priority mechanism has to be developed so that these real time services are not interrupted by other jobs which might not require immediate handling.

A well designed priority pricing mechanism has the potential to handle these problems. The basic idea is to levy tolls on the users of the system's capacity. The priority mechanism ensures that users with higher value, and presumably a greater willingness to pay for services, can be distinguished from the users with lower value. This distinction in turn allows service providers to decide whose needs should be fulfilled first and whose services can be preempted if desired. Ideally, we want to charge higher prices for the services which require higher capacity and impose greater delays on other users. Furthermore, if many users require a service during a certain time interval, general economic principles dictate that prices for those services should be higher during that time interval. However, one potential problem exists with direct applicability of these ideas: the services on The Internet are essentially "public goods,"[Footnote 3] i.e., the usage by one user does not preclude its usage by the other - even though the quality (in terms of service time) may suffer, e.g., simultaneous access to a database by several users. We propose a priority pricing mechanism which considers the congestion costs suffered by the users due to other users and prices the access to services accordingly.

The Internet has one important distinction from other service networks: it is a network of computers. Thus the potential computing power could (or perhaps should) be used for development and implementation of a more real-time pricing system. In the next section, we provide the theoretical foundation of our proposed approach. Then we outline the simulation experiments we have developed to evaluate this mechanism. Finally, we present some simulation results and interpret them to assess the performance of a hypothetical network.

Theoretical Foundation

Gupta, Stahl, and Whinston (1994) [click here to see the HTML version of this paper] present a priority pricing mechanism for distributed computing. The model presented there is based on General Equilibrium theory in economics, but departs from the Arrow-Debreu framework in a manner that makes the results computationally practical. In a pure Arrow-Debreu model, a commodity would be defined for every contingency and every moment in time. Given stochastic demands for computational services, the full state-space model would be much too large for practical purposes. In lieu of state-contingent equilibrium prices, Stahl and Whinston introduce the concept of a "stochastic equilibrium" in which (i) average flow rates of service requests are optimal for each user given the prices and anticipated delay, and (ii) the anticipated delays are the correct ex-ante expected delays given the average flow rates. Further, an optimal stochastic equilibrium is one which maximizes the net social benefits. They derive formula that characterize rental prices that support an optimal stochastic equilibrium.

This equilibrium concept and associated results has significant informational and computational implications. First, it allows the decentralization of the resource allocation process to the user level and reduces the information required for the user's decision problem to current rental prices and current expected delays. The administrative and communication costs of distributing this information pales in comparison to the associated costs of zillions of Arrow-Debreu contingency markets (or even spot auction markets). Secondly (as presented in more detail later), rental prices can be adjusted in real-time in a manner that pushes them into (and keeps in) a neighborhood of the theoretically optimal prices, and this process can be decentralized as well. Again the computational and communication costs of this mechanism pales in comparison to that of fixed-point algorithms for Arrow-Debreu equilibrium prices.

Although it might be impossible to achieve exact optimal pricing in practice for a volatile environment such as The Internet, we contend that it is possible to compute near- optimal prices in real-time. As a result of this near-optimal pricing, users with different values for the same service will choose different ways or time to obtain the same service. This, in turn, can provide substantial reduction in peak loads and will achieve better distribution of the load over time.

These results are based on an objective function which maximizes collective benefits of the system and its users. The natural question to ask is: why should service providers be concerned about collective benefits of the system? The primary reason is that the market on The Internet can essentially be viewed as a service industry, and customer satisfaction is directly related to the market share in the service industry. However, other objectives might be considered by the service providers, especially under the competitive market environment. Under these different objectives, there might be different pricing strategies, e.g., marginal revenue pricing. We will explore these issues in future research.

From the theoretical standpoint these results have significant importance. The rental prices at the servers decentralize the management and accounting problems. It gives the users or their clients access to an evaluation mechanism to decide when and what kind of service they want and at what priority [Footnote 4] . At the server level it will allow the management to assess the queues and delays more accurately and design their systems accordingly. Finally, at the network level it will allow for a better load distribution because excessively loaded and thus highly priced servers would be avoided by the users.

The price at a particular server for a particular priority class can be represented by the following system of equations [see Gupta, Stahl, and Whinston (1994) for derivation] [click here to see the HTML version of this paper] :

The optimal prices can only be computed if the optimal arrival rates are known and true equilibrium waiting times are known. Thus, we still need to find an approach for estimating the rental prices. We propose an iterative approach where the current estimates of the prices are computed given the historical information on flow rates and waiting times. This iterative approach can be implemented and analyzed by using simulation techniques where we estimate the prices using the transient information to guide the system towards a stochastic equilibrium. In the next section we first introduce the conceptual model of The Internet which we are using to evaluate our pricing scheme, and then we present the simulation model which we are using to estimate the prices and calculate the benefits.

Estimation of Prices

Figure 1 presents a conceptual model of The Internet. Essentially, we model The Internet infrastructure as a black-box, i.e., we assume that the infrastructure has enough capacity and does not contribute significantly to the delays suffered by the users[Footnote 5] . The users are connected to The Internet through some access providers (which we can consider as a service in itself). The access providers and the service providers, e.g., news, movies, video-conferencing, databases, etc., are "directly" connected to The Internet through a data-pipeline of a certain capacity. The capacity of the data-pipeline is essentially the bottleneck for the service providers. In the absence of any pricing mechanism as more users demand a service, the quality of the service (in terms of data transfer rates) suffers [Footnote 6] . Furthermore, as the congestion increases at the data-pipeline, the backbone experiences more load also due to the resending of lost packets. Consequently, for our purposes The Internet reduces to a network of servers with various services, where users have direct access to any service. The network service providers are able to monitor the loads at different servers, and they impose prices according to the load imposed by the servers on the backbone due to the congestion at their gateways.

We simulate this model of The Internet and implement our pricing mechanism. The prices are computed based on the system of equations presented in the previous section. However, since these prices are not estimated at the equilibrium conditions, they are approximate at any given time. We implement the following iterative equation to update the prices at any given time (t+1):

The idea behind updating the price this way is to provide a shield against local fluctuations in demand and in the stochastic nature of the process. A lower value of the parameter a means that the price adjustment will be gradual in time, whereas a higher a will result in potentially large changes in the prices from period to period. In our experience with the simulations we have found that smaller values of a, of the order of 0.1, result in reasonably quick convergence and higher stability in prices. However, a number of parameters have to be fine-tuned for a good system design: namely, the time interval for successive updates and the price adjustment parameter a.

Figure 2 provides a flow diagram of the simulation model we are using at present. The parameters in this model, i.e., update interval, a, simulation length, etc., are just example values and provide a good starting point for our exploration; we explore the simulation results for a wide range of these values. In this model the service requests are generated according to a Poisson arrival process with a fixed exogenous arrival rate. Upon the arrival of a service request the type of service required is identified; a service is characterized by the amount of computational cycles required at a server. Then, the current estimates of prices and predicted waiting times [Footnote 7] are obtained for all the servers offering the particular service. The user then evaluates the total expected cost of this service in terms of her delay cost and the service cost against her value of the service. If the total cost of the service is higher than her value for the service the user quits the system, otherwise, she submits the request for obtaining the service. [Footnote 8]

A user's request is sent to the server which was chosen as the least cost server. For example, if a service is available at 5 servers, then the user estimates the total cost of the service by adding his expected delay cost and network services cost at all the 5 servers and chooses the one where the total cost is expected to be the smallest. If the server queue is empty, the request is immediately processed; however, if some job requests exist in the server queue, then the requests are handled in a FIFO manner. This sequential processing model is the first of the several exploratory models we intend to develop. In future research we will also look at the time sharing environment where an additional job in a priority class will slow down the processing of all the current jobs in that class and the jobs in lower priority classes.

The estimates of waiting times and prices are updated every 'T' units of time. Although we can conceivably update the expectations whenever a request is made, we find three major arguments against frequent updates in stochastic systems: (i) estimating waiting times and prices over a longer time period provides more stable results; (ii) once we are in the vicinity of the stochastic equilibrium, the small fluctuations in prices will not warrant frequent updates; and (iii) the computational effort required in recomputing the prices and waiting times at each request might negate any benefits derived from pricing. However, as other parameters are changed, the update interval also must be changed for any cross-comparison of results.

At present we have experimented with a model which has 50 servers and 100 services. The capacity of the servers is randomly generated to be in the range of 1-5 units of work per second. The size of each service is also randomly generated to be in the range 1-20 units of work. The number of servers providing a service is also generated randomly to be in the range 1 - 30. A server can provide several of the 100 services.

We examine this system under a free access policy and under our pricing policy for a wide range of arrival rates for service requests. A higher arrival rate induces more load on the system and helps in understanding the behavior of a network with fixed capacity under increasing load. Specifically, we examine this model for an arrival rate of 1 to 1000; this captures the system behavior under virtually no queues (at the arrival rate of 1) and under extremely long queues (at the arrival rate of 1000). Under these sets of conditions we present results with the following two types of estimation schemes: (i) the perfect waiting time information scenario: incoming service requests are provided with the exact information on their waiting times; however, the prices are updated every 10 units of time for pricing case; and (ii) periodic update scenario: information on waiting time and prices are both updated every 10 time units of time. Note that the perfect waiting time information scenario case is the "best-case" scenario for our implementation of the free access policy because users first check where can they get the fastest service and the information they get is exact.

In our initial model we have single priority queues only. The results presented here are suggestive of the benefit of applying a single-priority pricing scheme to The Internet services. Essentially, without a pricing mechanism users with zero or low delay cost have nothing to discourage them from over utilizing the services; however, with a pricing mechanism they are forced to obtain only the services for which their value is higher than the cost.

Simulation Results

In this section, we provide some preliminary simulation results from our non-priority pricing scheme as compared to a free access policy. The simulations are run on a HP workstation, using the CSIM [Footnote 9] simulation environment. We present the global or network-wide results in this paper which address the overall performance of the system. However, we also provide some waiting time results at a randomly chosen server.

As discussed earlier, we present results under two conditions where: i) the information on the waiting time is exact - referred to as the perfect information scenario [Footnote 10]; and ii) a new prediction about future average waiting times is made every 10 units of time. The former case is a best case scenario for free access policy, however, in practice it will be hard to implement because of several reasons: i) the information requirements are intense - a sampling of waiting times has to be done at the arrival of every request; and ii) in a real system several requests may be arriving at the same time and the exact information may never be acquired. We present this scenario solely as a bench-mark to compare the benefits due to pricing versus free access. The second case is a more realistic setting; here the predictions about average waiting times are made every 10 time units. We use a single-lag autoregressive model to make these predictions; this model was chosen after an empirical analysis of the collected waiting-time data.

Figure 3 presents the comparison of benefits [Footnote 11] accumulated under the free access and pricing policies using the perfect information scenario. The figure shows net-benefits accumulated per unit of time as the exogenous arrival rate is increased. In addition, it also shows the rental-benefits and user-benefits separately with the pricing policy. The figure clearly indicates that the net benefits are substantially higher under a pricing policy at higher arrival rates (i.e., with higher loads) and are never worse than those under the free access. For example, the net-benefits are approximately 10, 000 units/time-unit with pricing policy and less than 2, 500 units/time-unit with free access when the exogenous arrival rate is 40 requests/time-unit; however, at an exogenous arrival rate of 1, 000 requests/time-unit, the net-benefits with pricing are more than 30, 000 units/time-unit whereas they remain almost the same with free access. The reason for this phenomenon is that under free access policy a lot of users who have negligible delay costs and low value for services continue to enter the system even when the waiting times are quite high; however, users with higher delay costs (even if they have relatively higher service values) do not enter the system, and eventually the system may be congested with users having low values for the services. However, when the pricing is introduced, the users who have low value for the service do not enter the system, and thus the net benefits are higher. Note that when the arrival rates are very small, the prices are negligible and thus the system behaves essentially as it would under free access.

Furthermore, the net benefits under free access are equal to the gross user benefits (since rental revenues, being a cost to users and a benefit to the system, cancel each other in the calculation of net social benefits). However, it is also interesting to compare the net benefits to users (gross benefits less rental revenue). Such a comparison with free access policy show that the average net benefits to the users are also higher over the whole range of exogenous arrival rates under the pricing policy even though significant rental revenue is generated at the servers as indicated by the rental-benefits in the figure 3.

Figure 4 provides the same comparison when the waiting time information is predicted every 10 units of time. The benefits under free access are much smaller and become negative when arrival rates are high. The benefits become negative because the predictions about the waiting times are not accurate, and the decisions to submit the jobs are based on this incorrect information. However, under the pricing policy we still see considerable positive net benefits.

Figure 5 provides a comparison of the net benefits with pricing under perfect information versus periodic update. As expected the net benefits with periodic update are smaller; however, we still obtain a similar trend of increasing benefits with increasing exogenous arrival rate. This result indicates that pricing obtains much better allocation even when relatively inferior information is available.

Table 1 and Table 2 provide the waiting time data for a randomly chosen server under the two scenarios; the behavior of waiting times is similar at other servers. The tables clearly indicate that under free access too many requests may be submitted, resulting in highly inferior performance. As the exogenous arrival rate increases, the waiting times at the servers become several magnitudes larger under the free access policy as compared to our pricing policy, and only users with negligible cost of delay will tend to use the system for most of the time. For example, under the perfect information scenario (Table 1), the average waiting time for a service is 4345.79 time-units with free access as compared to 31.28 time-units with pricing when the exogenous arrival rate is 100 requests/time-unit. This difference is further magnified as the exogenous arrival rate increases. Similar trends can be observed with periodic update scenario (Table 2).

These preliminary results clearly indicate that even a non-priority based pricing will result in a better system performance at higher congestion levels. Furthermore, the simulation results indicate that an iterative pricing mechanism can be implemented using the approximate prices at any point in time to achieve significant benefits.

We believe that a priority mechanism can further refine our pricing scheme, and higher net benefits could be realized since users with high value and high delay cost may potentially choose a higher priority class. A further refinement of the pricing mechanism will include the idea of local equilibrium, where users can recompute their expected costs in the queues and switch the server if new estimates make another server seem more attractive at that point in time. The idea of having smart (software) agents, described later, will be used there. In the next section, we outline some important implementation issues which should be addressed before a successful market can emerge over The Internet.

Implementation Issues

Several related issues should be explored and developed before a pricing scheme can be successfully implemented on The Internet. Some of these issues are related to the peripheral support for a pricing mechanism, such as client processes which evaluate users' requests, query agents and mechanisms, accounting and billing, etc. Others relate to the market structures which could evolve over The Internet. Furthermore, the important issue of supporting the infrastructure costs and investment must be addressed. We plan to explore these issues in detail in future research. However, in the following discussion we pose some relevant questions and provide outline for the directions of future research in these areas.

(i) Accounting/Billing System

Clearly, a cost-effective accounting/billing scheme is needed to implement a service pricing scheme for The Internet. We will study several schemes. First, each server could meter charges at its location and periodically send an electronic bill to the client-machine, which in turn will process these charges and present the user with a monthly bill. Alternatively, a service request could incorporate a "bill" portion, and each server would record its charges so when the request returns to the client-machine, it contains a complete bill. The client-machine would process these bills and generate periodic reports (and perhaps execute the appropriate funds transfers to settle the accounts).

It may not be cost-effective to bill for usage below some minimum level. In such cases, "non-billables" would become part of the fixed costs. To economize on billing costs, as well as on search costs (see (v) and (iv) later), "brokerage" services are likely to arise. The brokers would have the volume to justify many accounts with many servers even though individual users may have only a few active accounts.

(ii) Cross Subsidization

Since all The Internet services may not be "profitable," but may be socially important, we need to incorporate strategies which will allow cross-subsidization of these services through profitable services. To develop a robust approach, both theoretical and empirical ways must be determined to incorporate such services in the present model.

(iii) Investment in the Infrastructure

The profitability of each server (based on prices) can be used as a guide for investment and design decisions. The ratio of expected profits to the capital cost of the server can be used as an indicator of rate of return on the investment. This information can be used to decide whether to invest in another server (or increase the capacity of existing server) or to remove the server from the network. However, since the addition/removal of a server may affect the performance of other servers, other considerations must be kept in mind, and proper analysis (possibly using simulation) should be done before making any decisions.

(iv) Search Costs and Number of Services

Besides the actual cost of usage (e.g., article retrieval), we must consider the cost associated with the search of the server which can provide the service. Also, the cost of computing the least-cost alternative must be considered when more than one server provides the same service. As mentioned earlier, most of the cost is incurred in searching the relevant information, and often this cost is difficult to predict. For efficient utilization of The Internet more effective methodology must be developed for searching as well as for predicting the search pattern. We plan to use the idea of smart agents (possibly using artificial intelligence techniques) to handle the search activities. Etzioni, et al (1993), Moore, et al (1991), and Moore, et al (1992) for building blocks for designing smart agents.

Even if this search is provided free, as with Gopher menus, the user incurs a cost in terms of the time spent in the search. As the number of services of the same type increase, the time spent in searching for the best alternative will also increase. From a network management and investment point-of-view, management can consider the rate of return on investment (through rental prices) to make a decision on providing more services or eliminating some. Users, on the other hand, can use their experience or expertise to narrow their search to a limited number of servers.

(v) Smart Agents

Smart agents are the software tools which make appropriate decisions without excessive user input. For example, a user may specify vague guidelines of obtaining some information at lowest cost in the next 24 hours. A smart agent will automatically get this information for the user at an appropriate time (by possibly monitoring the prices and analyzing them through appropriate model) within next 24 hours. Moore, Richmond, and Whinston (1991 and 1992) offer decision theoretic approaches for database search, in which the search strategy optimizes the user's search by incorporating the tradeoff between the cost of search and expected increase in the value of information. This tradeoff is achieved by estimating a user's individual preference function, using the economic and marketing models [for example see Bettman (1979) and Lancaster (1966)]. Specifically, a functional representation of a user's preferences can be obtained by using self explicated weights or various forms of conjoint analysis as in Hagerty (1986).

We envision that users will either develop or obtain these smart agents by using the techniques similar to those mentioned above. These agents will act on the behalf of the users and will replicate the users' behavior in terms of their delay sensitivity and information needs and will obtain and compute the necessary information to fulfill the users' requests. These tools will be essential for users to assimilate and process the information required to make the appropriate decisions. Furthermore, we envision these smart agents computing real time decisions and dynamically assessing new emerging opportunities for cheaper or better services over time. As mentioned earlier, we plan to explore the possibility of a pricing refinement in which a smart agent can change the chosen server in the future, for example, if another server becomes more attractive at that time.

(vi) Competition Among Services

Until now we have discussed the issue of socially optimal prices. However, since potentially thousands of providers of the services will be "on-line" soon, we will also explore competitive strategies for price setters. The existence of many competitive entities may provide impetus for innovative pricing strategies, narrowly defined services, niche marketing strategies, etc., to obtain a better portion of the respective information markets. If, however, a few major entities control the market, queue management for a few highly desired services may be required while other services have to be subsidized. Loch (1991) looks at perfect and imperfect competition in oligopoly. We will draw results from Loch's study, extend these models of competitive markets, analyze the entry/exit incentives for service providers, and explore the competitive equilibrium issues for The Internet in the future research.

Furthermore, if the marginal cost of providing a service is negligible then the service providers might implement marginal revenue pricing for their services. This scheme will completely alter the pricing of congestion since for larger services the revenues will be larger providing incentive to subsidize the congestion costs of large users. The result will be a complete opposite of the proposed approach. We will also explore this issue in the future research.

Conclusions

In this paper we modeled The Internet as an economy where the users of the network services are consumers of the economy and the service providers are the producers. We modeled the user service requests as a stochastic arrival process and proposed that a transaction based priority price be associated with each server of the network. These prices are a "congestion toll" in which each service request entering the system pays the incremental delay cost imposed by it on all other users. With these prices, the system reaches a state of "stochastic equilibrium" in which user expectations are fulfilled on average, and demand is equal to the net benefit maximizing level.

We presented the results from a simulation model where we compare a non-priority pricing scheme to a free access scheme. The results conclusively demonstrate that pricing provides much higher net benefits than free access as the exogenous arrival rate of service requests increases. The net benefits decline under free access due to (i) negative externalities and (ii) forecasting errors in the predicted waiting times. Optimal pricing reduces the negative externality and is relatively robust against the forecasting errors in the predicted waiting times. It is conceivable that performance under free access can be improved by developing more sophisticated forecasting models (than the one lag autoregressive model which we use in this study) and incorporating them in the decision making process. However, we contend that under those conditions the performance under our pricing mechanism will also improve. Most significantly, we demonstrated that an iterative pricing mechanism can be employed which provides significant improvement in the system performance. The iterative mechanism makes the pricing approach practically attractive when the exogenous arrival rates are changing over time and where exact economic prices can not be calculated in advance.

This study is a starting point for our exploration of the complex issues involving the pricing of the services at The Internet. The next step in this direction would be the introduction of priority classes with the current objective of maximizing collective benefits of the users. Simultaneously, we will explore the market structure which could evolve over The Internet. For example, the marginal cost pricing of the product is conveniently assumed for the competitive market assumption. However, the marginal cost of providing services might be negligible over The Internet, especially if fixed access charges for the network backbone are used. How then should the products be priced? One answer could be marginal revenue pricing. However, under this scheme the competition can erode the congestion pricing, i.e., service providers will have incentives to subsidize users' network service charges. A subsidy in network charges could, in turn, essentially recreate the current situation with inflated service request rates and could severely affect the load management capabilities since prices no longer support the optimal flow rates. We plan to study theoretical issues and provide some potential solutions.

Furthermore, we have considered The Internet backbone as a black-box, ignoring the questions regarding investment in it and its sustainability. In the future the NSF subsidy for the current Internet backbone, the NSFnet, will be removed, and the commercial providers will provide the infrastructure. While the revenues from pricing might achieve better load management, they need not necessarily cover the cost of investment; thus, efficient cost recovering pricing for network infrastructure must be developed. The lack of dedicated links over The Internet makes the telephone billing mechanism invalid for use. The cable pricing model (the current model of charging based on capacity of the pipeline) can easily be implemented, and under sufficient capacity might be the best one to use. However, further research needs to be done to understand and address this issue completely.

In the next phase of our study, we will incorporate priority pricing in our simulation model. We expect to achieve even better system performance with priority pricing. We will also develop alternative strategies for choosing servers using dynamic forecasting, e.g., software smart agents to help users monitor the system status continuously and reroute when beneficial.

We believe that our simulation model is an important tool which can be used to address several policy issues and explore important questions. For example, simulation can be used to evaluate the emerging market structures, the effect of monopolistic inefficiencies, and marginal cost v/s marginal revenue pricing for services. Furthermore, simulation can be used to test the various approaches which can be used to pay for the infrastructure, i.e., how should infrastructure providers recover their fixed costs.

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Footnotes

footnote 1: TCP/IP, the communication protocol used at the Internet allows a link to be used by several users by probabilistic multiplexing of the packets from different users.

footnote 2: We concentrate here on queuing mechanisms; however, much of this argument can be developed for time sharing mechanisms.

footnote 3: This applies to both user and network services.

footnote 4: By a priority class we mean that jobs in the highest priority class are processed before all the other jobs. At any time if a higher priority job (than the rest in the queue) arrives it is put first in the queue. Thus, jobs in the highest priority class impose delays on the jobs in all other priority classes, whereas the jobs in lowest priority classes do not impose any delay on the jobs in other priority classes.

footnote 5: This assumption is based on empirical observations made by several researchers and on personal conversations with Smoot Carl-MItchell, an expert on the Internet at Texas Internet Consulting here in Austin, Texas.

footnote 6: Note that some users might decide not to get the service because of the excessive delays, however, users with negligible delay costs will try to obtain the service regardless of the delays. Thus, with no pricing mechanism the services can potentially be accessed by only the users who value it the least.

footnote 7: We use a one lag autoregressive process to predict the future waiting times.

footnote 8: Realistically, this work would be done by a smart agent executing on a client on the users machine. We discuss this and more implementation issues later in the paper.

footnote 9: CSIM is a process based simulation programming environment developed by H. Schwetman, an expert in computer performance evaluation at Mesquite Software, Inc. at Austin, Texas. It provides functions in C/C++ which can be used to control the simulation flow and gather queue statistics at each server. CSIM also has the capability of simulating parallel processing.

footnote 10: As mentioned earlier, the price updates are still made after 10 units of time, i.e., only the waiting time information is exact. Thus, only for free access policy is this a true perfect information scenario.

footnote 11: Net Benefits = Total of user values - Total delay costs suffered by the users.
Rental Benefits = Rental charges collected at servers.
User Benefits = Net Benefits - Rental Benefits.