Auction Models for Multi-Provider Internet Connections

Transcription

1 Auction Models for Multi-Provider Internet Connections Peter Reichl, George Fankhauser, Burkhard Stiller Computer Engineering and Networks Laboratory TIK, ETH Zürich, Gloriastrasse 35, CH 8092 Zürich, Switzerland, [ reichl stiller ]@tik.ee.ethz.ch, gfa@acm.org Abstract Auctions are a widely used approach for determining the current market price for congested resources. However, using them for real systems, such as the Internet, the auction algorithms require modifications as soon as connections cover links from more than one Internet Service Provider. This paper presents work in progress on two new auction schemes that have been designed to overcome this problem. 1 Introduction As current developments are driving the Internet more and more towards commercial use, the question of charging users for using the Internet has become of rapidly increasing importance. The last years have seen a couple of proposals for pricing models for communication services (for a summarizing overview cf., e.g., [1]). Unfortunately, most of them remain on a rather theoretical level, without paying too much attention to practical problems, such as implementability with minimized overhead or scalability in tomorrow s Internet architecture, and as they are tackled, e.g., within a project aimed at building a charging and accounting platform for integrated services Internet traffic [2]. One of the overall problems to be solved in charging of communication services is determined on one hand by the goal to provide incentive-compatible charging approaches (including revenue perspectives for providers as well as transparent pricing structures for end customers) and on the other hand by the objective to minimize the technical efforts allowing for a clear and unique identification of these incentives. This paper deals with two extensions of the wellknown concept of Generalized Vickrey Auctions (GVA, also known as Second-Price Auctions) which are under discussion for use in such a platform and have been designed to allow for a dynamic pricing of flow-based Internet traffic crossing more than one Internet Service Provider (ISP). To this end, Section 2 introduces shortly the main ideas behind GVAs, whereas Section 3 discusses a first adaptation, i.e. the concept of Delta Auctions (DA), and surveys some recent implementation results. A new auction model called CHiPS (Connection-Holder-is-Preferred-Scheme) is proposed in Section 4, before a short summary concludes the paper. 2 Generalized Vickrey Auctions In a seminal paper, [3] introduced the idea of a Smart Market as an efficient mechanism for congestion control by usage-sensitive pricing schemes. Here, the price for sending a packet usually varies on a very short time scale (e.g. minute by minute). Each packet contains a bid field were the user states the price she is willing to pay for the packet to be transmitted by the network. The packet is transmitted if the corresponding bid exceeds the current marginal cost of transportation. An important feature is that the user usually does not pay her actual bid, but rather the lower market-clearing price, i.e. the maximum of bids by users that could not be admitted. This concept of GVA has the advantage that the optimal strategy for the user is to bid her true value of the respective resource - trying to fool the market can be shown to yield non-optimal results for the user (incentive compatibility). This concept has been extended from the original centralized packet-oriented case into various directions, especially towards floworiented reservation-based scenarios ([4], [5]). 3 Delta Auction Distributing Classical Auctions for Multiple Resources over Time As a basic model for flow-based dynamic pricing using auctions (as proposed by [4]) we assume a reservation protocol (signalling) that is able to transport pricing and bidding information. As shown in Figure 1, the bidding and reservation request start at the data flow s receiving side (this can be reversed or split, but for the sake of simplicity we assume a receiver based model here). Each provider performs independent local auc-

2 tions over all flows currently active on a particular outgoing link. S P P P P R DATA FLOW Figure 1. Basic resource reservation signalling is used to transport bids from receivers (R) to providers (P) and finally back to the sender (S) along a connection s path. Bid Applying such a Smart Market scheme towards a real Internet charging and pricing system poses a first major difficulty with respect to signalling: Auctions taking place at discrete moments in time may cause huge signalling bursts immediately after each auction. Moreover, bidding users always have to wait until the next auction has been finished for getting an answer to their requests (with multi-provider connections this holds in fact for each subsequent node). This adds up to an additional reservation setup delay of ( n 2) p i on average, where n is the number of providers and p is the reservation period at provider i (or the auction interval). Since so-called refresh-periods of Internet resource reservation protocols are in the order of tens of seconds, this approach is not practical. Therefore, in [6] we have proposed the concept of Delta Auctions (DA) in order to allow auctions to take place continuously. Arriving requests are processed immediately, and bids that are too low are refused right away (thus preventing users from unnecessary waiting at each provider). Sufficient bids are accepted provisionally, but there is the possibility that bids arriving later may exceed those and thus oust them from the auction. The main advantage of this scheme is that a user is informed very early about refused reservations, and moreover the signalling traffic is distributed over time in a quite uniform way. On the other hand, for users that have been provisionally accepted there remains some uncertainty about whether their provisional reservation will in fact be finally confirmed. We have implemented and evaluated DAs with two reservation protocols, namely SSP (State Setup Protocol) [9] and RSVP (Resource Reservation Protocol) [7] which both are receiver initiated. The observation made in this paper were obtained by running RSVP with DAs on the ns-2 simulation platform [8]. For saving further signalling traffic it has been decided to express the bid for a packet in terms of percent of the current market price. The evaluation has shown, however, that this may yield to preferring bids that arrive later within an auction period. As a solution of this problem it has been investigated whether it makes sense to use the marketclearing price of the previous auction as a fixed price and calculate the bids relatively to that. Figure 2 shows an example of eight bidders that use the same link and take part in the same auction therefore. Bidder 1 is always the first while bidder 8 is always the last one to enter the auction process. The solid line was obtained by calculating the bid relative to the current market price. Out of the 300 auctions performed, the late comers show a clear advantage since they base their bids on pricing information of the soonto-be-closed market. The dashed line shows a rather fair distribution of winners since the market price used is that of the previous period i-1 and is therefore constant over the auction period i. The obvious drawback of this scheme is a slight error to the pure form of a 2nd price auction. However, it is only as worse as the degree of market fluctuations. # of auctions won Bid relative to market Bid relative to previous price time of reservation Figure 2. Bidding relative to ongoing Delta Auctions gives an advantage to late comers. Another aspect that has been evaluated is whether it is possible for a user to analyze signalling messages in a clever way and thus finding out the exact auction moments which could give her a certain competition advantage, but it has turned out that this yields no major fairness problem for sufficiently high numbers of providers and bidders. In practice, intercepting signalling between two hosts where an attacker does not have access is not impossible but quite difficult. Doing so for several links and possible thousands of flows to gain a market advantage is even harder. 4 CHiPS A Multi-Provider Auction Model As shown in Section 3, the concept of Delta Auctions provides a solution for the delay problem caused by multiple auctions being necessary for setting up a connection crossing a couple of Internet Service Providers. The current section deals with another aspect of multi-provider Internet connections. Assume that an end-to-end connection has already been established and

3 is refreshed from time to time by performing auctions respectively. Imagine that due to unlucky circumstances the market situation on a small part of the connection changes suddenly and the respective next auction is lost therefore. Then this local loss causes eventually the whole connection to be torn down, because resources have to be guaranteed end-to-end. Therefore, it is necessary to develop a scheme that first tries to solve such local problems locally, i.e. at the ISP itself. We propose a scheme that is based on a different interpretation of the auction outcome: the auction mechanism still is used to determine a ranking among the bidders as well as the market-clearing price. But for a newly arriving bidder being highly ranked is no longer equivalent with being allocated the desired resource. Instead, the holders of already running connections are preferred in the sense that even if their bids should have been too low w.r.t. the current market situation, they still get a second chance to improve their bids while their connections are not torn down for the immediate future (i.e. for the next auction cycle). The resulting scheme is called CHiPS (Connection- Holder-is-Preferred-Scheme). Summarized shortly, it has been developed based on the concepts introduced in the previous sections, with respect to the following important aspects: Dynamic pricing of multi-provider connections in the context of a real RSVP-based Internet charging and accounting system. Preventing multi-provider connections from being torn down because one auction has been lost locally, i.e. at only one of a couple of providers. Reinterpretation of the concept of user budgets: Classical auction schemes require each bidder to consider her budget (or spending cap), i.e. a user cannot bid more than her budget allows. But this concept does not bear in mind that with GVAs, the user actually pays less than her bid, hence usually won t spend the full amount of her budget. One of the major advantages of CHiPS is that the user s spending cap limits her real expenses instead of her bids. As with DAs, CHiPS requires that for each resource auctions take place regularly after each expiration of a given time period, and that reservations are possible and valid only for whole time periods. Moreover, each customer is allowed to send only one bid per time slot. Note that it may clearly happen that more than one auction is lost at the same moment (in fact, if the spending cap is very low, it is possible that more or less all auctions may fail), but for the sake of simplicity we deal first with the case of only one lost auction, as this is a very typical situation due to certain bottlenecks within a network. CHiPS may well deal with the case of more than one lost auction, too. Moreover, if there is a large number of auctions lost in one instant, this is a clear indication that the bids are generally too low and that hence the spending cap in connection with the relative bid strategy may not be sufficient for the requested connection at the current market situation. 4.1 Auctions under CHiPS Even if we consider a multi-provider scenario, the single auctions are still performed locally, e.g. at each separate provider. Therefore, we first deal with the way a separate auction looks like under CHiPS. Consider a single resource (capacity C) with auctions taking place at times t 1, t 2 etc., where t 2 t 1 = t 3 t 2 =... = const. Let us assume that at time t 1 it is known that at time t 2 a certain number of reservations will terminate or will be forced to terminate, and that therefore an amount C of link capacity will be free. Furthermore, between t 1 and t 2 a couple of reservation requests with unit price bids for the period starting with time t 2 arrive. Then there are two questions: Which of the reserved requests should be allocated? And which price has to be paid for using allocated resources? Classical Generalized Vickrey auctions couple these two questions in the sense that the highest bidders are allocated their desired resources and pay the market clearing price for them. On the contrary, CHiPS decouples these two issues as follows Allocation of Reservation Requests The obvious answer to the first question still is: the requests with highest bids are allocated, but this is only the case for the free capacity C instead as for the total capacity C, moreover the auction takes place only between newly arriving requests. In other words: an normal auction over capacity C takes place between the requests arriving newly between t 1 and t 2, with the highest bidding requests winning the allocation of the partial capacity C free at time t 2. Note that this allows sending negative acknowledges already during the period as soon as it is clear that a certain request won t belong to the winning ones Pricing Allocated Reservations To calculate the correct market price at time t 2, a fictitious auction has to take place between all relevant users, i.e. the ones already holding capacity and all the new bidders. Among these users, a second-price auction reveals the correct market price. Now, it is possible that some of the connection-holders have bids below that market price. These users receive a message telling them to increase their bids for that period ex post such that it excesses the calculated market price, otherwise they are forced to terminate the reservation at time t 3. This mechanism guarantees that no user is forced to pay more than she previously has agreed to.

4 4.2 Consequences As all incoming bids are considered in the fictitious auction, the price paid by allocated reservations equals essentially the correct market price of a second-price auction (except for holding users with bids below the market price which are not willing to rise their bids. Note that the ISP has to bear that risk and may want to distribute this slight overhead o the service in general, either in form of a flat fee or factor to the market price). This gives rise to the hope that incentive compatibility, the essential advantage of GVAs, might be preserved by that scheme. Currently, an extensive simulative investigation is performed to answer this question. No user will ever pay more than she previously has agreed to. In case the price for the connection is about to increase, the user is given the chance to withdraw without additional payment. Traditional auctions concentrate the signalling load heavily around the auction moment. The new scheme aims at distributing the signalling continuously over time. E.g., the first part of the interauction period can be used for the rebidding procedures of holding users bidding below the market price, the second part can be used for messages to new arriving requests which have no chance to be allocated. Current simulation are optimizing this point as well. One of the most important advantages of the new scheme is the fact that it does not interrupt running connections abruptly. There is always one slot time for rebidding. Note that the proposed scheme is equivalent to a second-price auction where the set of the auction winners is not identical to the set of allocated reservation requests. But the market price itself is calculated correctly as the fictitious auction considers all bidding users and takes place in the usual smart market way. Another advantage lies in holding users bidding quietly with their bid used so far. This might save additional signalling messages. Summarized shortly, using traditional auctions to determine the total price for connections which consist of a sequence of resources (esp. from different Internet Service Providers) immediately encounters a couple of difficulties like: The auctions for the single resources are not synchronized at all. Therefore, it is difficult for the user to maintain consistent information about the number, location, current market situation etc. of the different resources she has to gather for her actual connection. Moreover, she is not supposed to bid separately for each single resource, but to set the price she is willing to pay for reserving the connection as a whole (i.e. without dividing her bid explicitly among the independent auctions for each necessary resource). For establishing a connection, valid reservations on each link belonging to the respective route are necessary. With common models, as soon as the auction for one link is lost, the whole connection is breaking down instantaneously. The new model deals with these issues in an elegant way. Provided a connection is already established, the user may well loose an auction for a single link without the connection being automatically interrupted. Instead, the user receives a message telling her that on a certain link the market price has risen and asking whether she is willing to pay the new market price. In this case, the user has enough time to check her overall budget and accepting the new price for the relevant single link. In this way, the auctions necessary for the whole connection are decoupled. 4.3 Implementation Issues There remain two issues to be solved: Is there a clever way to establish a multi-provider connection, and how does increasing the bid ex post after a lost auction can work in practice. Whereas the first question is subject of future investigations, we present some alternatives to deal with the second one. Using RSVP, it is possible to address messages directly to a single ISP. We have already seen in Section 3 (cf. Figure 1) that it is possible to use RSVP messages for exchanging bids. To be more detailed, an RSVP message is composed of an RSVP header and an RSVP body, which itself contains RSVP objects. In addition, a couple of specific pricing objects have been designed [7] which are contained in the RSVP body as well. Amongst others, these pricing objects include a BID-object that is used to deliver the bid relative to the current or previous market price (as with DA, Section 3) and a PROVIDER-object containing a provider key that allows identifying the ISP where the local auction has been lost. Hence, as soon as an auction has been lost, it is possible to send an RSVP error message to the user which contains a specific provider key. The user is then able to increase explicitly the bid for this very auction.

5 Another proposal tries to avoid sending a message from the user to an ISP lying somewhere on the route by introducing a new bid structure: Assume, each bid b i has the form b i = a i + m i f (1) where m i is the current market price at ISP i, f is a factor transported by the BID-object to deliver a bid in terms of percent of the current market price, and a i is a constant held locally at the auctioneer which is initialized as 0. As soon as an auction is lost, an RSVP error message is sent from the respective ISP to both endpoints of the connection. This message contains the difference d between the current market price (i.e. the auction outcome) and the absolute value of the last bid. On its way to both sender and receiver, this message passes every other ISP involved in the connection and asks him to decrease the respective constant a i by the value of d. Now the bidder is able to decide whether her spending cap allows her to increase the expenses for the lost part of the connection by d ; if she eventually agrees with increasing her bid for the specific lost auction, she performs a rebidding procedure by using a normal RSVP end-to-end-message that asks each ISP to increase the constant a i by d. In this way, the bids finally have not changed except for the lost auction where the bid has been increased exactly by the necessary amount. Moreover, with this linear bid structure of (1) it is possible to bid for risky auctions (i.e. auctions where the market price tends to vary heavily) in a specific way, i.e. by adding for security reasons a constant amount towards each bid, independently of the relative bidding factor f. Both these approaches as well as problems connected with a possible partial loss of the RSVP error message are currently subject of further investigations. 5 Summary and Conclusions This paper has presented two auction concepts that are currently investigated for use within a real charging and accounting platform for an Integrated Services Internet. This is still work in progress. Dynamic pricing as a method to achieve economically efficient prices may be deployed in the Internet, since the technical efforts required do not pose a major additional overhead. Furthermore, price transparency and long-term stability may be offered as an additional service level through brokers that are willing to take over the risk at a premium. Current research deals especially with a clever method for establishing new end-to-end connections in a CHiPS-governed multi-provider network. Of course, besides these auction models, also volume-based pricing is under discussion as an alternative charging support. It is currently adapted to the special needs of an Internet charging and accounting platform. As long as dynamic pricing schemes are (a) efficiently implementable, (b) volume-based pricing schemes are requested for, and (c) flat-fee pricing schemes exist, a combination of these schemes in real networks will co-exist, mainly depending on the service class requested or the quality demanded for. Important to note, besides the selection of a pricing model for an ISP, the question of setting the base price for a service class in terms of monetary units remains open and depends also on the underlying business model. Acknowledgements Thanks to Marc Greis for providing a preview release of RSVP on ns-2 and to Beat Spielmann for many helpful discussions. References [1] P. Reichl, S. Leinen, B. Stiller: A Practical Review of Pricing and Cost Recovery for Internet Services. Internet Economic Workshop Berlin, Germany, May 28 29, [2] B. Stiller, T. Braun, M. Günter, B. Plattner: The CATI Project Charging and Accounting Technology for the Internet; 4th European Conference on Multimedia Applications, Services, and Techniques (ECMAST 99), Madrid, Spain, LNCS Vol. 1629, Springer, Berlin, Germany, May 26 28, 1999, pp [3] J. K. MacKie-Mason, H. Varian: Pricing the Internet. In: Kahin and Keller (eds.): Public Access to the Internet. Prentice Hall [4] J. MacKie-Mason: A Smart Market for Resource Reservation in a Multiple Quality of Service Information Network. Technical Report, University of Michigan, U.S.A., September [5] A. Lazar, N. Semret: Auctions for Network Resource Sharing. CTR Technical Report. Columbia University New York, U.S.A., February [6] G. Fankhauser, B. Stiller, C. Vögtli, B.Plattner: Reservation-based Charging in an Integrated Services Network. 4th INFORMS Telecommunications Conference, Bocca Raton, Florida, U.S.A., March [7] M. Foser: Pricing und Routen-Selektion für RSVP Flows in einer Simulationsumgebung. Student s thesis, TIK, ETH Zürich, Switzerland, February [8] UCB/LBNL/VINT Network Simulator - ns (version 2), [9] H. Adiseshu, G. Parulkar, R. Yavatkar: A State Management Protocol for IntServ, DiffServ and Label Switching. ICNP 98, 6th IEEE International Conference on Network Protocols, October 1998.