Pricing Internet Services With Multiple Providers∗Linhai He and Jean WalrandDept. of Electrical Engineering and Computer ScienceUniversity of California at BerkeleyBerkeley, CA 94709linhai, [email protected] of the challenges facing the networking industry today is to increase theprofitability of service providers. This calls for economic mechanisms that can en-able providers to charge more for better services and collect a fair share of theresulting increased revenue. In this paper we present a generic model for pricingInternet services in a multi-provider network. We show that non-cooperative pric-ing is unfair and may discourage future upgrades of the network. As an alternative,we propose a simple revenue-sharing policy and show that it is more efficient andencourages providers to collaborate without cheating. We also suggest a scalablealgorithm for providers to implement this policy in a distributed way and study itsconvergence properties.1 IntroductionFor historical reasons, the current architecture of the Internet lacks the support forimplementing efficient market mechanisms. Consequently, service providers have limitedeconomic incentives to invest in technology for new services. This situation limits thefuture evolution of the Internet. To correct this state of affairs, it is essential to implementeconomic mechanisms that would enable service providers to charge more for betterservices and collect a fair share of the resulting increased revenue. In this paper weinvestigate how to design pricing schemes that could meet these criteria.The idea of using economic mechanisms in network design is not new. For example,[1] [2] [3] propose pricing mechanisms that can be used for congestion control in theInternet. However, in these schemes the network acts as a social-welfare maximizer withno self-interest. This assumption does not reflect the situation in today’s Internet, asmost network service providers are in the business for making profit and are primarilyinterested in maximizing their own benefits [4]. Our pricing schemes try to include thesefacts into the models. We believe that a good pricing scheme should provide the rightincentives for providers to follow the protocol and not to cheat. In addition, it should befair for all providers involved and encourage upgrades to the network. In other words, aprovider should be able to collect more revenue by increasing the capacity of its network.Finally, a pricing scheme should be scalable, i.e., feasible for large-scale deployment.∗This research is supported in part by DARPA Grant No. BAA00-18.Our paper is organized as follows. In Section 2, we describe the basic models forthe providers and the services that they offer. In the following two sections, we firststudy the case in which providers adopt non-cooperative pricing strategies. Throughsimple examples, we show that such strategies would result in undesirable equilibria. Wethen suggest a revenue sharing policy as an alternative and show that it would lead toa better equilibrium. In addition, it could be reached through a distributed algorithm.We conclude the paper with discussions on future work.2 Basic ModelWe consider a group of providers offering services with a certain level of QoS guarantee.For simplicity, we assume that those QoS requirements could be translated into localcapacity constraints. For instance, the maximum utilization on a link may be limited tobe less than, say, 25% to ensure all packets experience only small delay going throughthat link.We assume that there exists a set of routes across the network. On any of theseroutes each provider charges a price for its share of the service. The providers mayadjust their prices dynamically and signal them to end users to control the demandfor the services. There are many possible approaches for implementing such a pricingscheme, for applications with either fixed or elastic bandwidth requirements. However,for the purpose of modelling, we do not specify details of implementation in this paper.We simply model that when a price p is posted for a route r, the resulting traffic loadon that route is given by a function dr(p), which is strictly decreasing and differentiable.Moreover, mechanisms exist for providers to collect revenues based on the amount oftraffic that they have forwarded and the prices that they set.We assume that when a provider sets its price, its objective is to maximize its ownrevenues, while maintaining the QoS for the service that it offers by respecting its localcapacity constraint. Therefore, in the case of only one provider offering the service,the optimal price can be determined by solving the following constrained optimizationprogrammaxp≥0J = p · d(p)s.t. d(p) ≤ C(1)where C is the capacity constraint. The first-order condition for the solution is p∗=µ − d(p∗)/d0(p∗) where µ ≥ 0 is some constant that satisfies µ(d(p∗) − C) = 0. It iseasy to show that a unique solution exists if d(p)/d0(p) is an increasing function of p. Inthat case, the solution is also a maximizer. So in the rest of the paper, we consider onlydemand functions that satisfy this property. For later use, we define g(p) , −d(p)/d0(p).Notice that g(p) indicates the elasticity of the demand function.To simplify analysis, we assume that all providers have sufficient capacity on theirinternal links. Capacity may be limited only on the links between providers. Local QoSrequirements by each provider are fixed and not affected by prices. All routes betweensources and destinations are also fixed. We choose this assumption because in today’sInternet routing between providers is often performed based on a set of provisionedpolicies instead of short-term costs or performance measures.3 Non-Cooperative Pricing StrategiesIn this section we try to understand how providers would set their prices when they haveto work together to offer a service. We assume that each provider acts in its own interest.In addition, each provider keeps its own capacity constraint as private information, butit may be possible for each provider to observe prices marked by others (depending onthe implementation).All these assumptions suggest a game-theoretic formulation of the problem in whicheach provider is a strategic player. Under different assumptions on what strategic in-formation is available to the providers, different types of formulation, such as Nash,Stackelberg, etc., are possible. However, we argue that only a Nash
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