GENESIS: an Agent-Based Model of Interdomain Network Formation, Traffic flow and Economics
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GENESIS: An agent-based model of interdomain network formation, traffic flow and economics Aemen Lodhi Amogh Dhamdhere Constantine Dovrolis School of Computer Science CAIDA School of Computer Science Georgia Institute of Technology University of California San Diego Georgia Institute of Technology [email protected] [email protected] [email protected] Abstract—We propose an agent-based network formation however, can have a global impact on the economic viability model for the Internet at the Autonomous System (AS) level. of all ASes and the structure of the Internet. The proposed model, called GENESIS, is based on realistic The Internet remains in a persistent state of flux subject to provider and peering strategies, with ASes acting in a myopic and decentralized manner to optimize a cost-related fitness function. changes in various exogenous factors. How will the Internet GENESIS captures key factors that affect the network formation change due to consolidation of content [1], large penetra- dynamics: highly skewed traffic matrix, policy-based routing, ge- tion of video streaming, falling transit prices [2], expanding ographic co-location constraints, and the costs of transit/peering geographic footprint of content providers [3], cheap local agreements. As opposed to analytical game-theoretic models, availability of peering infrastructure at IXPs [4]? We propose which focus on proving the existence of equilibria, GENESIS is a computational model that simulates the network formation a computational agent-based network formation model, called process and allows us to actually compute distinct equilibria (i.e., “GENESIS”, as a tool to study such questions. GENESIS is networks) and to also examine the behavior of sample paths modular and easily extensible, allowing researchers to exper- that do not converge. We find that such oscillatory sample paths iment with different peering or provider selection strategies, occur in about 10% of the runs, and they always involve tier- traffic matrix characteristics, routing policies, cost parameters, 1 ASes, resembling the tier-1 peering disputes often seen in practice. GENESIS results in many distinct equilibria that are etc. highly sensitive to initial conditions and the order in which ASes In this paper, we first introduce the main features of GEN- (agents) act. This implies that we cannot predict the properties of ESIS and then use simple yet realistic provider selection and an individual AS in the Internet. However, certain properties of peering strategies, as proof-of-concept, to study the properties the global network or of certain classes of ASes are predictable. We also examine whether the underlying game is zero-sum, and of the resulting networks. Starting from a population of ASes identify three sufficient conditions for that property. Finally, and initial topology, the model executes an iterative process we apply GENESIS in a specific “what-if” question, asking in which each AS acts asynchronously to optimize its set of how the openness towards peering affects the resulting network provider and peering links. We focus on the dynamic behavior in terms of topology, traffic flow and economics. Interestingly, of the model, identify the cause of some oscillatory sample we find that the peering openness that maximizes the fitness of different network classes (tier-1, tier-2 and tier-3 providers) paths (about 10% of the runs), and analyze the variability of closely matches that seen in real-world peering policies. the resulting equilibria. We show that under certain conditions about transit and peering costs, the set of transit providers I. INTRODUCTION engage in an (approximately) zero-sum game. We finally apply GENESIS in a specific “what-if” question, examining Tens of thousands of Autonomous Systems (ASes) intercon- the impact of a parameter, related to the openness of transit nect in a complex and dynamic manner to form the Internet. providers towards peering, on the topology, traffic flow, and These ASes belong to different categories e.g. enterprise economics of the resulting network. networks, content sources, access providers, transit providers, or various combinations of the aforementioned categories. II. RELATED WORK Additionally, they differ in geographic size (“expanse”) and economic parameters (e.g., transit prices). ASes connect with Most of the previous related work has focused on charac- one another mostly through two types of relations: customer- terizing and modeling the AS-level Internet topology. Various provider (or “transit”) links and settlement-free peering links. graph theoretic models aim to reproduce observed Internet Most interactions between ASes are local (unilateral in the topological properties (e.g., power-law degree distribution case of provider selection and bilateral in the case of peering), [5]) [6], [7], [8]. Another class of models take a bottom- decentralized and dynamic. These local connectivity decisions, up approach [9], modeling the optimization objectives and constraints of individual ASes, to create graphs that have the This research was financially supported by Google and the National Science same topological properties [9], [10], [11], [12]. GENESIS is Foundation (grant CNS-1017139). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of Google or different than that line of research because it does not aim NSF. to be a topology generation model or tool; instead, it captures interdomain traffic flow, geographic constraints and economics do not capture the local traffic within a network. The transit to model the network formation process. traffic VT (x) of x is the traffic volume that is neither generated A large body of work on game-theoretic network forma- nor consumed by x – it only passes through x enroute to tion models exists in the computer science and economics its destination. The transit traffic of a node depends on the literature. We refer the interested reader to two recent books underlying network topology and the routing algorithm. Even [13], [14]. Those models capture the objectives and potential if the interdomain traffic matrix T is constant, the transit traffic strategies of each node, as players in a non-cooperative game, of a node may change as the underlying topology changes. The and they focus on proving the existence of (typically many) total traffic volume of a node V (x) is given by the following equilibria. The need for mathematical tractability, however, expression: requires significant simplifications (such as lack of geographic constraints, simple cost functions, or uniform traffic flow V (x) = VC (x) + VG(x) + VT (x) (1) between nodes. Consequently, the resulting networks are typ- Economic attributes: The economic attributes of a node ically simple graphs, such as rings, trees or other regular include its transit prices (one for each location it is present structures. We avoid such simplifications in GENESIS. Ad- at). ditionally, few approaches in that line of work have focused Transit cost: Let x be a transit customer of y, and let P (x) on the dynamics of the network formation process and on the y be the lowest transit price of y across all regions in which x selection between multiple possible equilibria. and y overlap. If V (x) is the traffic exchanged between x Our work is most related to agent-based computational P and y, then the transit payment from x to y is: models that simulate the dynamics of the network formation process, capturing the asynchronous and decentralized process τ TC(x) = Py(x) × VP (x) (2) through which nodes adjust their connectivity. The model by Holme et al. [15] is similar to GENESIS but it does not where τ is a transit traffic exponent that captures the economies include peering and realistic routing. The model of Chang of scale observed in practice. The transit revenue TR(y) of y et al. [16] uses hard-wired strategies for provider and peer is simply the sum of transit costs paid by all customers of y. selection, among other differences. The model of Dhamdhere Peering cost: Nodes engaging in settlement-free peering et al. [17] is more similar to GENESIS but it assigns a specific relations share the underlying peering costs. There are two function to each node (e.g., content provider) and it focuses primary mechanisms for peering — private and public — that on the differences between two Internet instances (hierarchical have different cost structures. If the traffic exchanged between versus “flat”). two peers is less than a threshold Ψ they peer publicly at an IXP, otherwise they peer privately. In public peering, nodes III. MODEL DESCRIPTION exchange traffic over a common switching fabric at an IXP, We consider a population of N nodes (representing Au- aggregating traffic from different peering sessions through the tonomous Systems) which interconnect through two types same port, whereas in private peering they set up a direct link of links: customer-provider and peering. Each node has the with each peer. following attributes: a set of locations in which it is present, Private peering cost: Let VPP (x; y) be the traffic exchanged an amount of traffic it sends to and receives from every other between node x and its peer y over a private peering link. The node, and certain economic parameters, such as the transit total cost of private peering for x is given by: price it would charge to its potential customers at a given X β location. We do not assign an a priori business function to PCprv(x) = α× VPP (x; y) (3) nodes; a node may end up acting as tier-1 transit provider y in one equilibrium and as a content provider in another. We where α is the peering cost per Mbps and β is the peering next describe each component of GENESIS in more detail. A traffic exponent that accounts for the corresponding economies complete description of the model, with a longer justification, of scale. is available at a technical report [18].