Distributed cost management in a selfish multi-operators ... - CiteSeerX

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Distributed cost management in a selfish multi-operators BGP network Dominique Barth(1), L´elia Blin(2), Loubna Echabbi(1), Sandrine Vial(2) (1)PR SM - CNRS, UMR 8636, Universit´e de Versailles, 45 Bld des Etats Unis, F-78035 VERSAILLES (2) LaMI UMR 8042 CNRS - Universit´e d’Evry Val d’Essonne, Genopole Tour Evry 2, 523 place des terrasses de l’Agora, F-91000 EVRY

Abstract— In this paper we deal with Inter-domain routing management from an economical point of view. We present a game theory based costing model that maps BGP peers (Autonomous Systems belonging to different operators) into a strategic (selfish) agents competing for transit traffic as a service provided and charged to their peers. Indeed, in our model each operator fixes a price to each neighbor for each transit traffic unit. Then, BGP routes choice is made based on a minimum cost criterion where the goal of each operator is to minimize its costs. We investigate some particular strategies of updating prices that operators can use locally in order to minimize their costs. We focus on BGP stabilization properties related to such strategies from a simulation point of view.

I. I NTRODUCTION During the last decade, the Internet has evolved from a cooperative into a highly competitive interconnected network. However, the protocol available today to route the traffic between these different domains namely the Border Gateway Protocol (BGP) does not take into account the complexity induced by this competitive context. Indeed, regardless from particular routing policies and transit restrictions, the BGP protocol routes the traffic on the shortest paths in term of hops and thus costs are not incurred. Individual peering agreements are typically negotiated between pairs based on the exchanged traffic (incurred by the routing) and are often confidential. Hence there is no mutual interaction between routing costs and payments or at least this interaction is not clear. This is quite incoherent with the current open competition context [1]. Furthermore, the current routing mechanism relay in obedience of agents (Autonomous Systems (AS), operators), i.e., agents follow the rules. However, in a competitive context, situations can arise where the overall welfare (connectivity) is not compatible with individual objectives (attract customers, coalition against This work was supported by ALCATEL CIT, by the French ARC INRIA PrixNet and by the NoE Euro-NGI.

other operators). Since agents are strategic, they are expected to behave according to their own interests. However the current routing mechanism could not deal with these situations since no incentives to follow the rules are involved. We suggest in this paper a model for inter-domain routing where cost management is involved in order to capture the economical issues related to this competitive context. We consider here a peer-to-peer BGP network connecting administrative domains, (AS), each one administrated by an operator [5]. Each AS has to manage two types of traffic. The first one concerns his own customers. That is local traffic which include incoming traffic (arriving to its own customers) and outgoing traffic (emitted from its own costumers). The second is transit traffic, i.e., packet crossing this AS by following a BGP route including this AS. Transit traffic has an additional cost for each crossed AS and this is why we mainly focus here on the transit traffic management by using costing approaches. The transit traffic management made by an AS can be seen as a service provided to the neighbors in the network, without willing of making benefit on this service (operators make profit with their own costumers, not with their peer-to-peer neighbors). Thus, to (fairly) manage these service exchanges, we propose a costing model where each AS sending transit traffic to one of its neighbor AS has to pay for this traffic according to a price fixed by this neighbor. This costing model has to be distributed on the network since each operator has its own price policy and knows only the traffic crossing it own ASs and prices proposed by its neighbors. A similar approach has been made in [3] where the problem of inter domain routing has been first considered from the algorithmic mechanism design perspective with a realistic economical and technical model. We join authors of [3] in considering ASs (nodes) rather than links as the strategic agents since a node in the inter-domain context is behaving as an individual entity with its own interests. We also consider that BGP routes choice is

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made under a lowest cost criterion. We also propose a distributed mechanism for cost management since, regardless from scalability issuers, there is no entity that can be trust to centralize all decisions under such competitive context. The main difference between our models is that in [3] each AS has a pre-determined cost incurred by each transit traffic packet and the mechanism presented provide a distributed way to calculate route costs and choosing the lowest cost ones. The main issue that the model deal with is incentive compatibility, that is each AS has incentive to tell the truth about its costs. In our model, we add a notion of AS capacity that models that an AS cannot accept a great amount of transit traffic without influencing the service provided to its own customers. Thus, we consider that the cost incurred by transit traffic is not null but evolve with respect to capacity constraint. In that way, costs can be used by ASs to prevent from being flooded by transit traffic. Hence, prices are updated as a response to route costs calculation where each AS is interested by its own costs and we focus on stability issues related to price fluctuations. In our model, the problem of costing transit traffic can be viewed as a multi-stage graphical game [4], [8] where each AS is a player wanting to minimize its cost and where the strategies consist in the way of updating prices. To respect the distributed aspect of such a game, we consider that each AS knows only the traffic which it is the origin or the destination, its own prices and the prices its neighbors fix to it. Another main aspect on the model we focus on, is that BGP deals with minimum costs and not as usually with minimum distances. Nevertheless, the price strategy is not independent from the routing choice, which make the game be very unstable. The AS has not a complete view of the topology of the peer to peer network and could not predict what wold be routes after BGP stabilization. Since ASs payoff depend on the BGP routes computation, each AS can not predict what would be a dominant strategy (the best reply whatever other players strategy). We expect then that the system could not reach any equilibrium unless the game is repeated. We propose that at each stage each AS operator defines its new strategy and computes the induced routes and costs. We investigate strategies reaching, from any initial configuration, some equilibrium point where ASs are satisfied by the induced costs in the logic of the target strategy. For routing stability issues, it is very important to reach such a point as fast as possible [5]. Hence, even if each AS has his own interests (minimum costs) some kind of cooperation can be useful to reach a common objective (stability).

We present here a distributed mechanism that models this game and evaluates using simulation analysis some particular strategies with different traffic scenarios. II. M ODEL

AND GAME

A. The network model The BGP peer-to-peer network is modeled by a nodeweighted, strongly-connected and symmetric digraph where the vertex set models logical ASs, the symmetric arc set models connected sessions between ASs and the function indicates the bandwidth capacity of each AS. Considering logical AS means in particular that each AS acts as a single BGP router, i.e., it only knows one route for each destination. The function gives the maximal traffic an AS can accept, where the traffic is the sum of the incoming one, the outgoing one and the transit one. The network we consider here is a multi-operator BGP network. An operator can be the owner of many ASs. traffic matrix where We consider a is the amount of traffic AS has to send to AS . This traffic is emitted by AS . It is a transit traffic in each internal AS of the BGP route chosen by AS to reach AS . And it is received by AS . We assume that the traffic matrix between the different ASs, can be obtained by monitoring the traffic during a previous significant period. In the costing model we propose, we assume that the objective of each operator is not to make benefit on transit traffic but rather to minimize its costs by taking lowest cost routes and updating its prices so as to equilibrate its incomes and outcomes. Consider two connected ASs and . Then, AS has to pay AS for all the transit traffic in sent by (i.e., traffic not destined to it). Indeed, each AS has not to pay to AS for the traffic which is destinated to it since this traffic is in fact destinated to the customers of AS and thus has necessarily to income . Thus, we consider a price matrix of real numbers, with the set of operators, where is what each AS of operator has to pay to each AS of operator for each transit traffic unit in sent by . Note that for any , we have and that for any , we consider to avoid silly stable situation where all prices are null.


   









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a finite number of strategies for each player (here if we consider an upper bound on integer prices ), then there always exists a set of strategies given a Nash equilibrium. Unfortunately, determining such a set of strategies is a NP-hard problem and finding a distributed process for updating prices in order to reach such an equilibrium seems to be complicated. Indeed, since we consider here that BGP choices are based on minimum cost and not on minimum distances, any change in a vector of prices could change the set of routes BGP converges on. This set is not necessarily unique. In this context, deciding whether or not a price matrix gives a Nash equilibrium is not an easy question to answer. Thus in this paper, we focus first on processes (set of individual local strategies) that are finite then analyze the efficiency of the obtained situation. Given an instance , a strategic process is a deterministic computing a new matrix of polynomial algorithm prices . Such a strategic process is said to be stabilizing if, from any initial instance (with an empty set), there exists a finite integer (i.e., the number of executions of the process ) such that . That is reaches a fixed point. Such a strategic process can also be studied in the context of self-stabilization [2]. Our objective here is to study some strategic processes based on simple and natural possible local strategies that enable operators to minimize their costs. In particular, we focus on the stabilization properties of some of these processes from a simulation point of view.

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STRATEGIC CHOICES

The global strategy we focus on is based on a simple concept [9]. If the global cost of an operator is positive, then it tries to equilibrate its incomes and outcomes with any operator it exchanges traffic with. Consider an AS in . Consider the instance obtained after executions of , for each neighbor . Each new price is computed as follows: Let us consider the total incoming transit traffic in as with

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¼»½¿¾*¾WÀmÀmÁPÂoÁ  à Š(à …—{~…—Ä Ä ½-Å jPU?n œ  U ¢ º P j W U V  X n  W  ¹ · ¸ˆ ˜^D ©oÆ-j–XNV U?n ¯ WU V X  ³ ±²   E  " 8 5 if ‚ ]w Z Y ²´¶µ if ]kw  Z  Y ¿S5 This global strategy is based on two parameters: a É 2 Ë [ s Ê ¬ 5  Ì . We talk about a real and an integer  32O -strategy.µÈÇ The first strategyDWwe focus on is the  D H5* -strategy in which prices do not consider penalties Ç only be increased. The process ends with and can Çof operators that make benefit and another oner witha setno traffic in entrance. Note that, considering a covering tree of the target graph on which all the traffic is routed, we such that can easily construct an instance . We then deal with some -strategies, with in which a node with no input transit traffic from one of its neighbor decreases its price to it. At end, we focus on the -strategy in which prices take the penalty into account.

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IV. S IMULATION

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ANALYSIS

1) (1,0)-Strategy: We consider a simple scenario with a graph of 40 ASs each one belonging to an operator. We assume here that all operators choose to play according to (1,0)-strategy that is an operator try to equilibrate its incomes and outcomes until its costs are negative( it makes benefit) or when we has no traffic in entrance so it just pay for its outgoing traffic. At a first time we consider that prices are bounded in order to enforce the convergence. Then we consider that prices can be unbounded. We can see from figure1 and figure2 that in both cases a stable situation is reached. For simplicity we draw the global costs related to only three operators but ,in fact, all the system reach stability in both cases. Indeed, figure3 gives the number of operators that reach a stable situation during the evolution of the process, and we can see that all operators reach a stable situation, more quickly with bounded prices than with unbounded ones. This is quite predictable since while bounding prices we limit the space of price variation. We obtain similar results with different scenarios (topologies, traffic matrix, initial costs). Hence if all operators play this simple strategy then the system seems to reach stability in a finite number of steps. 2) ( ,0)-strategy: Now, we consider that players choose the ( ,0)-strategy that is similar to the previous strategy except that when an operator has no traffic in entrance and that his costs are positive it decreases it prices by a a ratio hoping that it will enable it to

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give the evolution of some operator costs with in figure4, in figure5, and in figure6. We can observe from figure4 that cost functions oscillate around some equilibrium values but never reach stability. The oscillation phenomena is intensified with lower values of . The same phenomena has been observed with different scenarios and it seems to be more interesting to reach stability with the previous strategy since the obtained improvements in costs functions with ,0)-strategy doesn’t worth in our opinion the stability of the system. But this assumes that all operators follow the rule, so we can ask what would happen if hybrid strategies are involved or if all players agree to play according to the same scheme ((1,0)-strategy) in order to reach stability and that one of the players violate this agreement.

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Fig. 1.

(1,0)-strategy with bounded prices

Fig. 2.

(1,0)-strategy with unbounded prices

Fig. 3.

Fig. 4.

(1,0.8)strategy

Fig. 5.

(1,0.5)strategy

Convergence with bounded and unbounded prices

attract more transit traffic and improve his situation. We simulate the process where all players choose this strategy with the same parameter . For instance, we

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3) Hybrid strategies and malicious behaviors: In this scenario, we assume that either ASs choose between

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Fig. 6.

(1,0.3)-strategy

both previous (intuitive) strategies or that all ASs agree to play according to (1-0)-strategy and that one of the players (for instance here AS10) violates the agreement. Figure7 gives operator costs when all players play (10)-strategy, then in figure8, 9,10 AS 10 plays (the one with cost function oscillating around 1000) the ( ,0)strategy with mu=0.9,0.6 and 0.3 . We notice that its choice affect not only its cost function but also those of other operators since they also loss their stability. This phenomena is intensified with low values of . One point of interest is that from cost function curves only, detecting which player is violating the rule (in case we assume there is some agreement to play under (1-0) strategy scheme) is not obvious. This kind of behaviors, where a player is playing a strategy even if it is not benifical (instability) to it in order to harm other players exist in Byzantine behaviors. Since we consider that players are strategic and that stability worth little improvement of costs functions we claim that players will be more interested in following the rule. 4) (1,1)-strategy: In the following, we consider that operators take into account penalty while updating prices. The intuition behind this strategy is that prices announced to other operators will be updated differently. That is, when capacity constraint is violated the variation in prices will be correlated with corresponding incoming traffic. This strategy seems to be more fair and provides incentives to avoid situations where ASs are flooded by some malicious competitors. In the following, we simulate that an operator can have more than one AS. We consider graphs of 50 ASs. . Figure11 illustrates We take for instance here, some operator (from 27 ones for this simulation) cost functions. We plot only three of this functions for simplicity but all the system reach a stable situation (as

Fig. 7.

Only (1,0)-strategy is used

Fig. 8.

AS 10 uses (1,0.9)-strategy

Fig. 9.

AS 10 uses (1,0.6)-strategy

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with (1,0)strategy) in a few steps. We obtain the same behavior with 47 operators(figure12). The number of operators does not seem to influence

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the number of routing updates with different number of operators (2, 12, 22, 32, 42 and 47) over 50 ASs and we can see the more the network is diversified (the more there is competition) the more we need of steps to reach stability but this number is still realistic.

Fig. 10.

AS 10 uses (1,0.3)-strategy

Fig. 13.

routing update for different number of operators

5) Routing: The last figure14 illustrates the distribution of the obtained BGP routes after stabilization. We can see that the routes are still concentrated on some edges of the network which confirms that the obtained routing is still coherent.

Fig. 11.

Costs with 27 operators

Fig. 14.

Fig. 12.

Costs with 47 operators

the stabilizing behavior of the model but it has an influence on the number of required steps to reach stability as we can see in figure13. Indeed, this figure gives

Distribution of routes over edges

V. C ONCLUSION

AND

F UTURE

WORK

We present in this paper a costing model for interdomain-routing based on the BGP protocol. This is in our knowledge the first attempt to deal with Inter-domain routing in the context of competitive economy where each operator only cares about its own interests and

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where prices are used to prevent ASs from being flooded by transit traffic. We discuss the difficulty added by the distributed nature of inter-domain routing management which makes it difficult to an operator to figure out what would be an optimal strategy to adopt. We focus on strategies where the system is insured to reach stable situation since it is an important issue on this context. We give some simulation results related to the adoption of some particular strategies. Some of these strategies (if adopted by all players) seem to drive the system into a stable state while other ones clearly make the system unstable. We highlight some situations where it is difficult to detect which operator is the origin of the instability of the system. We are still working on the analysis of observed behavior of the model and we are trying to prove the stability of strategies (1,0) and (1,1). Some selfstabilization techniques may be useful in that sense. We are also interested in the impact of malicious behavior and situations where operator objective is not only to minimize its costs but also increase its benefits. That is an operator can continue to increase its prices even if it makes already benefits. Such behavior can be adopted by some well positioned operators and can seriously harm the stability of the system.

We also investigate what would be the impact on stability of BGP and other technical considerations when using costs in spite of distances as a routing criterion. R EFERENCES [1] C. Courcoubetis, R. Weber. Pricing Communication Networks: Economics, Technology and Modelling. Wiley Pub., March 2003. [2] S. Dolev, Self-stabilization, MIT Press, Cambridge, MA, 2000. [3] J. Feigenbaum, C. Papadimitriou, R. Sami and S. Shenker. A BGP-based mechanism for lowest-cost routing. Proceedings of the 2002 ACM Symposium on Principles of Distributed Computing. [4] P. Fuzesi and A. Vidacs. Game Theoretic Analysis of Network Dimensioning Strategies in Differentiated Services Networks. Proc. of IEEE International Conference on Communications (ICC2002), New York, USA, 2002. [5] T.G. Griffin and G. Wilfong. An analysis of BGP convergence properties. In Proc. of SIGCOMM’99, ACM Press, PP. 277-288, 1999. [6] M. Kearns, M. LLittman, S . Singh. Graphical model for game theory. In proc. of Conf. on Uncertainly in Artificial Intelligence, pp. 253-260, 2001. [7] M. Mavronicolas. Game Theory in Network Routing: A Primer. Tutorial of Europar 2002 in LNCS 2400, 2002. [8] M.J.Osborne, A. Rubinstein. A course in game theory.The MIT Press, 1994. [9] N. Dos Santos, Pricing models for an internet BGP network. Master thesis, Universit´e de Versailles, 2004.

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