Analysis of peering strategy adoption by transit providers in the Internet

Transcription

1 Analysis of peering strategy adoption by transit providers in the Internet Aemen Lodhi School of Computer Science Georgia Institute of Technology Amogh Dhamdhere CAIDA University of California San Diego Constantine Dovrolis School of Computer Science Georgia Institute of Technology Abstract We explore peering strategy adoption by transit providers in the Internet. We employ an agent-based network formation model for the Internet at the Autonomous System (AS) level. In our model, transit providers act in a myopic and decentralized manner and choose their peering strategies from a set of realistic strategies. Our results show that Open peering acts as an attractor with 68% transit providers adopting it. This large-scale adoption of Open peering, however, is associated with a loss in fitness of almost 7% of providers. We analyze the causes of the gravitation towards Open peering and the resulting loss in fitness. We explore the characteristics of providers that gain and lose in an Open peering environment. Finally, we investigate simple mechanisms through which the losses associated with Open peering can be alleviated. Keywords: Internet, Autonomous System interconnections, settlement-free peering, peering strategies, economic fitness I. INTRODUCTION Tens of thousands of Autonomous Systems (ASes) which constitute the Internet interconnect with one another through customer-provider (transit) and settlement-free peering links. These ASes have different interconnection objectives and constraints based on their business type enterprise customers, content providers, access ISPs, transit providers. In order to achieve these objectives the ASes adopt a set of criteria which are used to assess potential and existing settlementfree peering relationships. These relationships are bilateral in nature, i.e., for two ASes x and y to establish a peering relationship, they must satisfy each other s peering criteria, agree on costs, benefits and even administrative responsibilities. The set of criteria used by an AS for assessing potential peering relationships is referred to as its peering strategy. While the details of these peering strategies may differ from one AS to another, we commonly observe three peering strategies publicized by ASes in peeringdb [] Restrictive, Selective and Open. The peering strategy adopted by an AS depends on its business function and objectives, e.g., a transit provider would like to increase its revenue by selling transit services. Under the Restrictive strategy, ASes try to avoid peering links as far as possible; with the Selective strategy, ASes look for a certain degree of similarity (for some measure of similarity) in their peers; under the Open strategy, ASes are generally willing to peer with any AS that requests a peering relationship. Figure shows the strategy adoption by ASes of different categories taken from a recent snapshot of peeringdb []. We Fig.. Peering strategy adoption among ASes in the Internet find that Open is the dominant peering strategy among all AS categories, with more than 6% of ASes in each category using Open peering. The fact that 64% of NSPs (transit providers) use open peering is especially surprising. Transit providers prefer other ASes as their customers rather than peers, and so the fact that many transit providers use open peering is rather surprising. Why do transit providers tend to peer openly? What is the impact of Open peering on their economic fitness? In this paper, we use agent-based computational modeling to study peering strategy adoption by transit providers. We find that Open peering indeed acts as an attractor among peering strategies for transit providers. We explore the causes underlying the widespread adoption of Open peering, and show using simple examples how peering strategy decisions by individual nodes cascade through the entire network. We study the impact of Open peering on the fitness of transit providers, and find that the attraction towards Open peering is accompanied by a loss in economic fitness for a majority of transit providers. We study the characteristics of transit providers, e.g., their traffic volume and their customer tree sizes and explore correlations between these characteristics, their peering strategies, and their eventual fitness. Finally, we look into simple coordination mechanisms that may improve the fitness of transit providers even as they adopt open peering. We note that our model captures peering strategy adoption as a function of econonmic fitness. There are, however, other factors which also affect these decision processes, e.g., performance, reducing the number of hops to destinations, etc. We do not, however, take into account these factors in our modeling.

2 II. MODEL DESCRIPTION In this section, we briefly describe our agent-based model of network formation which is a variant of GENESIS [2]. We consider a population of N nodes (representing Autonomous Systems). The nodes do not have any a priori business function or topological role assigned to them. As a result of the model s network formation process the nodes can broadly be divided into two classes transit providers and stubs. Transit providers have at least one transit customer whereas stubs have none. Nodes interconnect with one another through two types of links customer-provider and settlement-free-peering. Stubs have a passive role in the network formation process, limited only to choosing the cheapest transit provider. Transit providers, in addition to themselves choosing transit providers (if required), choose the peering strategy that maximizes their economic fitness. We next describe each component of the model in brief. A complete description of GENESIS, with analysis of its default parameters and convergence properties can be found in [2], [3]. Our model in this paper differs from GENESIS only in peering strategy selection. Geographical presence: The model has a total of G M locations and a node x is present in G(x) locations. Each location corresponds to an IXP. Two nodes are co-located if they are present in at least one common location. Co-location is necessary to establish any type of link between two nodes. Traffic matrix and traffic components: An N N matrix T represents the traffic exchanged between nodes in the network with T xy representing traffic sent from node x to y. The total traffic generated and consumed by x is given by V G (x) and V C (x) respectively. The transit traffic V T (x) of a transit provider x is the traffic that is neither generated nor consumed by x but transits x en route to its destination. The total traffic V (x) of a node x is the sum of V G (x), V C (x) and V T (x), and is used in the model as a measure of the size of the node. We parameterize the traffic matrix so that a few nodes generate and consume a majority of the total traffic, as observed by Labovitz et al. [4]. Economic attributes: Each node maintains a distinct transit price P g (x) in each location g in which it is present. Each node x that requires a transit provider to reach other nodes in the network makes a transit payment T C(x) to its transit provider y which is given by: T C(x) = P y (x) V P (x) τ () where P y (x) is the transit price per Mbps that y charges from x and τ is the transit traffic exponent that captures the economies of scale observed in transit pricing. The sum of all transit payments from the customers of y constitute its transit revenue T R(y). GENESIS captures both public and private peering. Both public and private peering incur a cost on their participants, with private peering being more costly than its public counterpart. The total peering cost incurred by a node, P C(x), is the sum of public and private peering costs. The We assume that T represents the 95th percentile, or billable traffic volume. economic fitness of a node x represents its net profit and is given by: F (x) = T R(x) T C(x) P C(x) (2) The objective of each node is to maximize its fitness by choosing the best provider and peering strategy. Provider Selection: Node x chooses a transit provider if it cannot reach all other nodes in the network using customer and settlement free peering links. In this case, x chooses y as its transit provider if (a) y is co-located with x (b) y has at least as many points-of-presence as x i.e. G(y) G(x) (c) y carries more transit traffic than x i.e. V T (y) > V T (x) (d) y offers the cheapest price amongst all transit providers satisfying the first three conditions. If there is no node that satisfies the first three conditions for x then it becomes a Tier- node and establishes peering links with all existing Tier- nodes. Settlement-free peering: Nodes enter into setttlement-free peering relationships with one another based on their peering strategies. In this paper we consider the following three peering strategies, based on the dominant strategies published and widely discussed at peeringdb [] and NANOG [5]: ) Restrictive: A node that uses this strategy does not peer with any other node unless it is necessary to prevent network partitioning. 2) Selective: A node x that uses this strategy agrees to peer with nodes of similar size. As previously mentioned, GENESIS uses V (x) as a measure of a node s size. Thus, node x agrees to peer with y if Vx V y σ (σ > ). σ is a universal threshold that quantifies the similarity among nodes for the purpose of peering. 3) Open: A node that uses this strategy agrees to peer with any other co-located node except direct customers. All stubs follow Open strategy only. Computing strategy equilibrium: An execution of GEN- ESIS proceeds in discrete steps called iterations. During an iteration, each provider performs a what-if analysis by hypothetically adopting each of the above peering strategies. The provider uses traffic flows and network topology at the time of evaluation to compute the effect of each peering strategy on its fitness. After each evaluation, the provider chooses the peering strategy that maximizes its fitness. It is important to note that providers carry out this evaluation myopically and without any coordination with other nodes. Providers are unable to predict the long term effects of their strategy choice, as they have no knowledge of the possible responses from other nodes. Thus, providers selfishly try to optimize their fitness with limited foresight. If during an iteration there are no changes in the network topology and strategies of all nodes, then it can be shown that the network has reached a stable state or an equilibrium [2], and no node will change its connectivity and strategy thereafter. III. SELECTIVE VS. OPEN PEERING STRATEGY We begin by comparing two scenarios: Conservative vs. Non-Conservative. Under the Conservative scenario, transit

3 providers only peer with nodes with similar traffic volumes and can only adopt two peering strategies: Restrictive and Selective. The Non-Conservative scenario adds Open peering to the pool of available strategies, thus allowing transit providers to peer freely with co-located nodes. We computed the results for sample paths of the model, with each sample path having a unique population of nodes. The parametrization of the model for these results is given in the appendix. Our results show that under the Conservative scenario, 9% of providers use Selective peering, and the remaining % use Restrictive. In this scenario, peering among transit providers is restricted by their traffic volume, with most providers peering with other nodes with similar traffic volume and hierarchical status. Their peers also include stubs which are large content providers and consumers which satisfy their Selective peering criteria by virtue of their large traffic volumes. However, the network undergoes a radical change under the Non-Conservative scenario, where Open peering becomes a possible choice along with Selective and Restrictive. We find that under this scenario, 7% of transit providers adopt Open peering, 28% adopt Selective peering, while only 2% adopt Restrictive. Open peering thus acts as an attractor in the pool of peering strategies. In order to identify the characteristics of transit providers that adopt certain strategies, we classify them into 4 classes, based on the traffic volume and the number of nodes in their customer cones. We use these criteria as they give us a measure of both the market share of a provider in the transit market, as well as its size based on local traffic volume. Based on this classification we have the following 4 classes: ) Small traffic volume and small number of customers 2) Small traffic volume and large number of customers 3) Large traffic volume and small number of customers 4) Large traffic volume and large number of customers For both traffic volume and number of customers we identify the top and bottom 3% nodes. Thus nodes in class 4 are providers which constitute the top 3% providers by traffic volume and top 3% providers by the number of customers. We identify providers in the other three classes similarly. Figure 2 shows the percentage of providers in each class following a particular strategy. We find that providers with smaller traffic volume and customer trees are more attracted towards Open peering strategy than the ones with larger traffic volume and customer cones. The affinity for Open peering decreases as the traffic volume and customer cones become larger. While the majority of providers in classes 3 and 4 adopt Open peering, a significant percentage uses Selective peering. Only a small percentage of nodes in classes 3 and 4 adopt Restrictive peering. IV. IMPACT OF OPEN PEERING ON FITNESS How does the gravitation towards Open peering affect the fitness of transit providers? We measure the sum of fitness of all providers in an equilibrium network, i.e., the ensemble fitness of the transit provider population. Figure 3 shows the sum of fitness of all providers at equilibria for both Fig. 2. Sum of fitness with Open strategy Fraction of number of providers Fig. 3. Fig. 4. Transit Revenue Ratio Peering Cost Ratio 2.3e+7 2.2e+7 2.e+7 2e+7.9e+7.8e+7.7e+7.6e+7 Peering strategy adoption by transit providers Sum of fitness under Conservative vs. Non-conservative scenario.5e+7.6e+7.7e+7.8e+7.9e+7 2e+7 2.e+7 2.2e+7 2.3e+7 Sum of fitness with Selective strategy Distribution of fitness difference Open - Selective Normalized fitness difference Peering strategy adoption by transit providers Transit Revenue Ratio vs. Transit Cost Ratio Transit Cost Ratio Peering Cost Ratio vs. Transit Cost Ratio Transit Cost Ratio Variation in fitness components with Open peering Conservative and Non-conservative sample paths. The ensemble fitness across Non-conservative scenarios is lower than that across Conservative scenarios in 98% of sample paths. Certain invidual providers, however, do show an improvement in fitness by adopting Open peering. Figure 3 shows the CDF of the difference in fitness (Fx Selective Fx Open ) of individual providers that switch to Open peering under the Non-conservative scenario. Although the overall fitness of provider population declines after the introduction of Open peering, 3% of providers show an improvement in fitness by adopting Open peering. While the gain in fitness for most providers switching to Open peering appears relatively small, a small fraction of providers undergoes a significant improvement in fitness.

4 Fig. 5. Illustration of impact on fitness components Fitness of nodes is a function of transit costs, peering costs, and transit revenue. How does introduction of Open peering affect each of these individual fitness components? Figure 4 shows the fitness components of transit providers with Open peering vs. Selective peering. We use fitness component ratios to compare the fitness components of a node under different scenarios, e.g., transit cost ratio = transit cost Open transit cost Selective. We find that 99.7% of non-t providers see lower transit costs under Open peering. Simultaneously, 96% of providers also see lower transit revenues. Peering costs undergo the most significant change, with 9% of providers showing an increase. We illustrate these changes by means of the example in figure 5. Transit providers B and C reduce their upstream transit costs by peering Openly with other nodes. At the same time, they lose transit revenue, as their customers D and E also peer openly. The interplay of fitness components thus leads to a situation where only 3% providers have their fitness increased through Open peering while the rest lose. A. Weakening the competitive ability and flattening the hierarchy When the customers of a transit provider x engage in Open peering, they reduce the transit traffic of x. This reduces their transit costs, and also reduces x s transit revenue. Transit traffic volume is a key criterion in the provider selection process, as described in section II. The larger the transit volume of a provider x, the greater its ability to attract transit customers. The loss of transit traffic volume for a transit provider thus adversely affects its competitive ability in the transit market. Extensive peering in the network results in some nodes no longer choosing x as a transit provider. Further, as x loses traffic, it may no longer be able to refuse peering with nodes it previously refused to peer with using the Selective strategy. The weakening of transit providers, and increasing opportunities to peer with nodes which previously refused peering allows many lower hierarchy providers to elevate their positions in the network. We categorize the hierarchy of nodes as follows: tier-(t) providers (they do not have a provider), tier-2(t2) providers (their provider is a T node), and tier-3(t3) providers (all other providers). We find that 3.5% transit providers that adopt Open peering change their hierarchical status as compared to their status in the Conservative scheme. We find that.5% of such providers elevate from T3 to T, 6% from T2 to T, 22.5% from T3 to T2 while only % have their status lowered from T2 to T3. Overall we also observe a flattening of the network hierarchy, as more horizontal relationships are formed. For example, we observe that the average percentage of T2 nodes in the networks increases from 2.4% to 37.42% from Conservative to Non-conservative scenarios. The average percentage of T3 nodes decreases from 75.89% to 56.77%. This, however, brings up the following important question: If there are many more nodes in the lower hierarchies of the network and a significant number of them also elevate themselves in the hierarchy with the introduction of Open peering, then we should observe a siginificantly larger percentage of nodes with improvement in fitness. Why is it that only 3% of the nodes improve their fitness? We explore this question in the following sections. V. CAUSES FOR GRAVITATION TOWARDS OPEN PEERING The previous section showed that gravitation towards Open peering results in reduced fitness for almost 7% providers. In this section we analyze this worsening of fitness. Why do transit providers lose fitness given the maximum degree of freedom for peering with the Open strategy? Why do transit providers not switch to a different strategy after discovering that their decision to adopt Open peering results in a loss? Analysis reveals that this situation is the result of collective behavior of providers where they adopt peering strategies myopically, selfishly and without coordination. Open peering leads to providers peering with customers of their peers, resulting in a situation we refer to as inadvertent traffic stealing. Such behavior results in reciprocal responses from peers, and also a loss of aggregation of peering traffic. This phenomenon can be explained by means of the example in figure 6. The figure shows two transit providers x and y peering with each other. Since y uses Open peering, it also peers with z, a customer of x. If y was not peering with z, it could have aggregated the peering traffic on a single link x-y. Because of the peering link y-z, traffic z y and z w bypasses x, thereby reducing its fitness. If, however, x also adopts open peering and peers with w, it can partially restore its transit traffic, since traffic w z will pass through x. This action alleviates x s loss in fitness but reduces y s fitness at the same time. x is thus pushed to adopt Open peering. Note, however, that both x and y are now in worse shape than they would have been had they only peered among themselves. Additionally, since x and y neither coordinate nor can predict each other s actions and strategy selections, they will not unilaterally refrain from peering with each other s customers. Thus, myopic and decentralized adoption of Open peering creates a feedback effect where more providers are forced to adopt Open peering over time. Contention Metric: The above example shows that reduction in fitness of nodes is also associated with traffic-stealing from a peer. To what extent is this behavior observed in the

5 Fig. 6. Avg. Contention metric Dynamics of fitness reduction with Open peering Fig Percentage of providers using Open peering Contention metric Sum of fitness Contention behavior under Open peering network? We define the Contention metric to quantify this behavior: Let x and y be two nodes peering with each other. Let O y (x) be the set of customers of y which overlap with x. Let P P y (x) be the customers of y which peer with x. (Note P P y (x) O y (x)). Similar definitions hold for y. Then contention between x and y is given by: Contention = P P x(y) + P P y (x) O x (y) + O y (x) If x and y are peering with all overlapping customers of each other then they have the highest level of Contention between them, i.e.,. For each sample path in Nonconservative scenario, we computed the Contention metric for each pair of providers peering with each other, and computed the average of all pairwise contention values. Figure 7 shows the average Contention and the sum of fitness of providers vs. the percentage of providers using Open peering. The Pearson correlation coefficient between the percentage of providers using Open peering and the average contention is.9. The correlation coefficient between the percentage of providers using Open peering and the sum of fitness of providers is Thus, the traffic-stealing behavior becomes more prevalent as more providers adopt open peering, and is also accompanied by a greater overall loss in fitness. VI. ANALYSIS OF PROVIDERS ADOPTING OPEN PEERING STRATEGY In this section, we identify the characteristics of providers which gain (or lose) fitness by adopting Open peering. We use the same classification as in section III, i.e. classification along two axes traffic volume and the size of customer cone Normalized Sum of fitness of providers Figure 8 shows the fitness comparison of nodes belonging to classes and 4 when they switch from Selective strategy in the Conservative scenario to Open strategy in the Nonconservative scenario. Providers in class, small traffic volume and small customer cones, benefit most by switching to Open peering. However providers in class 4, large traffic volume and customer cones, mostly stand to lose by adopting Open peering with 84% nodes in the class showing a loss in fitness by the switch. For reasons explained later in this section, it is difficult to predict the impact of Open peering on the fitness of nodes in classes 2 and 3. Class : These providers, with small traffic volumes and customer cones, represent the only class which clearly benefits from adopting Open peering. 9% of providers from class show an increase in their fitness. Owing to their small traffic volumes, these providers are denied peering by large transit providers under Selective peering. Open peering enables them to peer with large providers higher in the network hierarchy, significantly reducing their transit costs. Their small customer cones also make them less vulnerable to traffic being stolen from them while at the same time they can steal traffic from larger providers. Classes 2 and 3: Providers in classes 2 and 3 have less predictable behavior due to their apparently contradictory characteristics. As Open peering becomes prevalent, 75% of the providers in class 2 (with small traffic volume but large customer cones) see a decrease in customer transit traffic owing to traffic being stolen from them. 53% providers in class 3 show a decrease in fitness. For providers in class 3 (with small customer cones), traffic stolen is not the main issue. The large traffic volumes of these nodes allow them to aggregate traffic over fewer peering links with Selective peering. These nodes lose this traffic aggregation under Open peering, resulting in a loss of fitness. Class 4: The loss in fitness of class 4 providers is related to both large traffic volume and large customer cone. Given the large traffic volume, such providers are able to peer with large co-located providers using Selective peering. Such nodes benefit in the selective peering environment, as they will be able to aggregate traffic over fewer peering links. By adopting Open peering, they lose this traffic aggregation over peering links and therefore experience a loss in fitness. Their large customer cones also make them most vulnerable to traffic stealing by other providers. As a result less customer traffic transits through them. Thus, small providers benefit from switching to Open peering. Large providers lose the most in an environment where Open peering is aggressively pursued by stubs and smaller providers. VII. OPEN PEERING VARIANTS In this section, we investigate whether simple co-ordination mechanisms can alleviate providers loss in fitness. We introduce coordination in the form of simple rules-of-thumb that providers follow. We impose a universal constraint that

6 - Small Customer Cone Small Traffic Volume Sum of fitness distribution of Open strategy variants Normalized fitness under Open scheme Normalized fitness under Open scheme Fitness improvement Fitness reduction Fitness improvement Fitness reduction Normalized fitness under Selective scheme Large Customer Cone Large Traffic Volume Fraction of sample paths Selective Open Open NPIC Open NPCT Normalized fitness under Selective scheme 5e+6 e+7.5e+7 2e+7 2.5e+7 Sum of fitness Fig. 8. Fitness variation of four classes of providers Fig. 9. Sum of fitness distribution with Open variants transit providers do not peer with customers of their peers. We evaluate two variants of this constraint: ) No Peer Immediate Customer (NPIC): Providers do not peer with direct customers of their peers. 2) No Peer Customer Tree (NPCT): Providers do not peer with any node in the customer tree of their peers. We evaluate both constraints in the same way we evaluated the regular Open peering strategy. Figure 9 shows the sum of fitness distribution of nodes which switch to Open peering (and its variants) across sample paths. The figure shows that under both variants, the ensemble fitness of providers is greater than with regular Open peering. However, among the two variants only NPIC approaches the values observed under Selective peering. Unlike regular Open peering, which showed that only 3% providers improve their fitness over Selective peering, we observe that 5% and 54% nodes improve their fitness under NPCT and NPIC, respectively. NPIC shows an improvement in fitness as transit providers no longer steal traffic from their peers, and can also reduce peering costs by aggregating peering traffic over fewer peering links. NPCT shows smaller overall fitness as compared to NPIC, because the model allows providers to peer with indirect customers. Let c p denote a customer-provider relationship. Let z y x be the customer chain of x. Additionally, let x z and x w denote two existing peering relationships in the network. Under NPCT, w will not peer with z, since it is in the customer tree of its peer x. However, since z is also a peer of x, w cannot use the x w peering link to reach z (valley-free routing policy). w is thus forced to use its transit provider to reach z. Thus, we find that simple rules-of-thumb that enforce that nodes not peer with their peers customers improves upon the fitness of nodes as compared to regular Open peering. However, the customers of providers are free to peer with other non-peer nodes and therefore some loss of fitness is inevitable. VIII. RELATED WORK Our work is most closely related to agent-based computational models of network formation in the context of the Internet. Such models capture the decentralized and asynchronous processes through which ASes in the Internet make peering decisions. The model of Chang et al. [6] employs a one-to-one cost-benefit centric approach to peering decisions as opposed to adopting peering strategies publicized by the ASes which is also the approach we follow in our paper. Holme et al. [7] propose a model similar to ours but do not capture peering and realistic routing. In the model of Dhamdhere et al. [8], node types and peering strategies are pre-assigned, and the goal is to see how these factors affect the resulting network properties, whereas in our work they are an outcome of the model. Another line of work [9], [], [], [2] models the optimization objectives and constraints of ASes to produce certain topologies. Our work does not focus on topology generation. It explains the interdependencies in peering strategy adoption as a result of interactions of ASes. Game theoretic analysis of AS transit and peering relations has been carried out in [3], [4], [5], [6]. However, for reasons of mathematical tractability these works simplify many realistic constraints of AS interconnections in the Internet e.g. geographic co-location, non-uniform traffic matrices, multiple prices per AS etc. which have been incorporated in our work. IX. CONCLUSIONS In this paper, we used an agent-based computational model to explore the apparently counterintuitive adoption of Open peering by transit providers. Our analysis shows that myopic, decentralized adoption of peering strategies creates network effects resulting in a large percentage of transit providers adopting Open peering. We show that although the economic impact of this strategy on a significant percentage of transit providers is negative, transit providers are stuck in a suboptimal equilibrium from which they cannot unilaterally withdraw. Our results reveal that transit providers with relatively smaller number of customers and traffic volume benefit the most by adopting Open peering. Whereas, extensive Open peering in the network most negatively affects transit providers with large customer trees and traffic volume. Finally, we show that using simple universal coordination mechanisms, most transit providers can alleviate their fitness loss.

7 REFERENCES [] PeeringDB, October 2. [2] A. Lodhi, A. Dhamdhere, and C. Dovrolis, Genesis: An agent-based model of interdomain network formation, traffic flow and economics, in INFOCOM, 22. [3] GENESIS, lodhi/genesis.pdf. [4] C. Labovitz, S. Iekel-Johnson, D. McPherson, J. Oberheide, and F. Jahanian, Internet Inter-domain Traffic, in Proceedings of ACM SIG- COMM, 2. [5] North American Network Operators Group, 2. [6] H. Chang, S. Jamin, and W. Willinger, To Peer or Not to Peer: Modeling the Evolution of the Internets AS-level Topology, in Proceedings of IEEE INFOCOM, 26. [7] P. Holme, J. Karlin, and S. Forrest, An Integrated Model of Traffic, Geography and Economy in the Internet, ACM SIGCOMM Computer Communications Review (CCR), 28. [8] A. Dhamdhere and C. Dovrolis, The Internet is Flat: Modeling the Transition from a Transit Hierarchy to a Peering Mesh, in Proceedings of ACM CoNEXT, 2. [9] L. Li, D. Alderson, J. C. Doyle, and W. Willinger, Towards a Theory of Scale-free Graphs: Definition, Properties, and Implications, Internet Mathematics, 25. [] A. Fabrikant, E. Koutsoupias, and C. H. Papadimitriou, Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet, in Proceedings of ICALP, 22. [] H. Chang, S. Jamin, and W. Willinger, Internet Connectivity at the AS-level: An Optimization-driven Modeling Approach, in Proceedings of the ACM SIGCOMM workshop on Models, methods and tools for reproducible network research (MoMeTools), 23. [2] J. Corbo, S. Jain, M. Mitzenmacher, and D. C. Parkes, An Economically-Principled Generative Model of AS Graph Connectivity, in Proceedings of the IEEE INFOCOM Mini-Conference, 29. [3] N. Badasyan and S. Chakrabarti, A simple game theoretic analysis of peering and transit contracting among internet access providers, in In Telecommunications Policy Research Conference, 25. [4] S. Lippert and G. Spagnolo, Internet peering as a network of relations, Telecommun. Policy, 28. [5] P. Baake and T. Wichmann, On the economics of internet peering, Netnomics, vol., pp. 89 5, 999. [6] E. Anshelevich, B. Shepherd, and G. Wilfong, Strategic Network Formation through Peering and Service Agreements, in In FOCS, 26. [7] Peering Strategy Survey, Policies/A-Study-of-28-Peering-Policies.html. [8] VoxNet IP Services, [9] Internet Transit Prices: Historical and Projected, white-papers/internet-transit-pricing-historical-and-projected.php. [2] H. Chang, S. Jamin, Z. Mao, and W. Willinger, An Empirical Approach to Modeling Inter-AS Traffic Matrices, in Proceedings of the ACM SIGCOMM Internet Measurement Conference (IMC), 25. [2] A. Feldmann, N. Kammenhuber, O. Maennel, B. Maggs, R. De Prisco, and R. Sundaram, A Methodology for Estimating Interdomain Web Traffic Demand, in Proceedings of the ACM SIGCOMM Internet Measurement Conference (IMC), 24.

8 APPENDIX TABLE I INPUT PARAMETERS FOR THE MODEL Parameter, Symbol, Description Value Explanation Number of ASes N 5 Simulation time constraints Number of geographic locations G Max 5 Based on approximate ratio of IXPs to peering networks in the Internet. PeeringDB ratio.27. GENESIS ratio. [] Geographic expanse distribution Zipf(.6) Based on data about number of participants at each IXP collected from PeeringDB []. G(x) assigned randomly to each node Maximum expanse for an AS 5 Generated traffic distribution Zipf(.2) Produces a heavy-tailed distribution of outgoing traffic. With this distribution,.% of the ASes generate nearly 28% of the total traffic. This is consistent with the behavior reported in [2], [2] & [4], which show that the traffic produced by high-ranking ISPs and content providers follows a Zipf distribution. V G (x) assigned randomly to each node Consumed traffic distribution Zipf(.8) Produces heavy-tailed distribution of incoming traffic, similar to measured traffic distribution at Georgia Tech. Mean consumed traffic 5 Mbps V C (x) G(x), rationale being that a node with large expanse will also have a large number of access customers Private peering threshold Ω 5 Mbps Survey of peering strategies [7] Transit cost multiplier range P (x) $[35,45]/Mbps per iteration Parameterized based on IP transit prices advertised by VoxNet [8]. P (x) assigned randomly Transit cost exponent τ.75 Parameterized based on data from [6] and [7] Peering cost multiplier α $2/Mbps per iteration Peering cost exponent β.4 Selective peering ratio σ 2.