Price Discovery at Network Edges Gurjeet S. Arora , Murat Yuksel , Shivkumar Kalyanaraman , Thiagarajan Ravichandran , Aparna Gupta CS Department, ECSE Department, School of Management, DSES Department Rensselaer Polytechnic Institute 110 8th Street, Troy, NY, 12180, USA garora@emc.com, yuksem@cs., shivkuma@ecse., ravit@, guptaa@ rpi.edu Keywords—Network Pricing, Congestion Pricing, QoS, Optimization Abstract—Congestion-sensitive pricing for providing better than best effort ser- vice has received significant attention in the last decade. In this paper we identify a robust parameter for capturing congestion conditions in an edge-to-edge framework and propose a family of adaptive pricing schemes for premium network services. The parameter is the ratio of two values: Edge queue and estimated edge-to-edge capacity. By coordination between edge routers, both of the values are available at the ingress point in an edge-to-edge framework. Thus, the pricing schemes deployable. Based on the identified parameter, we propose a new adaptive pricing framework, Price Discov- ery. Based on the Price Discovery framework and the identified pricing parameter, we develop and analyze four pricing schemes. We compare the pricing schemes, and se- lect the best one in performance. We identify stability conditions for the best scheme. This is followed by evaluation of the best pricing scheme with extensive simulations of various scenarios. I. I NTRODUCTION The players that engage in transactions involving bandwidth can be grouped in the following three categories: Capacity providers, re-sellers (Internet service providers and other bandwidth service providers) and end-consumers. The transactions between the capacity providers and re-sellers are best handled in an exchange kind of envi- ronment This is because the environment offers the capacity providers and re-sellers a variety of options by providing access to a large number of capacity providers and re-sellers. Another advantage of exchanges is transparent pricing, which encourages healthy competition. This kind of pricing where typical transactions (between capacity providers and re-sellers) are for a large amount of bandwidth is, what we call, band- width pricing. Re-sellers create value by catering to the variety of needs of end- users (their diverse applications which vary in terms of their delay and jitter sensitivities). Bandwidth, among its other uses, is used for Inter- net services as well. The domain of pricing bandwidth for providing Internet services to end users (transaction between re-sellers and end- users)is known as Internet pricing. Several proposals have been made for Internet pricing. We can classify those proposals into two major groups: congestion-sensitive pricing proposals (e.g. [1], [2], [3], [4], [5], [6], [7], [8]), static pricing proposals (e.g. [9], [10], [11]). In congestion-sensitive pricing, as the name suggests, price per unit traffic volume varies by time depending upon the actual network congestion. In static pricing, price per unit service (as traffic volume or service du- ration) is fixed. Congestion-sensitive pricing is becoming popular as a method for network resource allocation and congestion control. The main moti- vation behind this is that network performance cannot be solely de- rived from congestion control protocols [12]. During periods of re- source contention or congestion epochs, there is a need to distinguish one packet from the other based on their importance as indicated by a utility function (utility functions are typically a combination of user preferences and application requirements). Thus during congestion, in- creasing prices of network services makes an allocation closer to Pareto This work is sponsored by NSF under contract number ANI9819112. G. S. Arora is now with EMC Corporation. efficient [13] (i.e. allocates resources to users such that the overall user surplus is close to the highest possible) and gives users right incentives to adjust their demands to alleviate congestion [2]. We can also classify the pricing proposals based upon their granular- ity. Some of the congestion-sensitive pricing proposals have used per- packet charging, while others have used per-contract charging which provides price information to the user prior to charging. MacKie Ma- son and Varian’s Smart Market [3] proposesto use per-packet charges based upon the total marginal congestion cost the packet imposes on other users. For price determination, Gibbens and Kelly’s Packet Mark- ing scheme (also known as Proportional Fair Pricing) [2] also uses per- packet charging by using the number of packets marked at a congested network router. Wang Schulzrinne’s Resource Negotiation and Pricing (RNAP) [7] is an example of congestion-sensitive pricing scheme with per-contract charging. RNAP combines admission control with congestion pricing by using the service level agreement flexibility of diff-serv [14] archi- tecture. RNAP leave the job of price determination to local network routers and uses probing techniques to determine edge-to-edge prices. Also, Dynamic Capacity Contracting (DCC) framework [8] uses per- contract charges by making price determination on an edge-to-edge ba- sis at the edge routers rather than leaving it to local network routers (a major difference from RNAP). In this paper, we propose a new pricing framework, Price Discov- ery, to solve the problem of allocating premium (better than best effort) Internet services without making any assumptions about user behav- ior. Price discovery is deployable in a general contracting framework in which end users and ISPs enter into service level agreements at the beginning of a contracting period for service. The ISPs vary price from one period to another in order to meet the service level agreements. Price for premium services does not change during a period in con- tracting framework. Price Discovery attempts to employ congestion-sensitive pricing at network edges and uses an adaptive event-based algorithm to increase or decrease price. It operates in cycles of queue drain and queue build while discovering the price in an adaptive manner. In order to deter- mine the price in period , it uses two parameters: queue length at the edge (edge queue) and estimated capacity . With a simple co- ordination between ingress and egress edge routers, both and are available in an edge-to-edge framework. By using edge-to-edge congestion detection techniques (e.g. [15]), can be varied to alle- viate congestion, it typically decreases during congestion epochs (so that a part of available capacity can be used for draining the queues that build up during congestion) and increases (to increase utilization of the edge-to-edge capacity) when there is no congestion. So, Price Discovery takes advantage of the available information in an edge-to- edge framework and employs congestion-sensitive pricing to control the queue lengths at the network edges. Price Discovery is a general framework that can be applied to any scenario where and or their logical equivalents are available for price determination. DCC, for instance, provides both the parameters.