k-Fault tolerance of the Internet AS graph

Abstract Internet disruptions such as the Northeast Blackout (2003) and the Taiwan earthquake (2006) highlight the fragility of today’s Internet. Our goal in this paper is to investigate the robustness of inter-domain communication at the level of autonomous systems (ASes), taking into account both topological connectivity and compliance to routing policies. To this end, we introduce the concept of k-fault tolerance for Type-of-Relationship (ToR) graphs, which requires that any two nodes (ASes) remain reachable from each other even after removing arbitrary k nodes from the AS graph. Our main contribution is theoretical and concerns the complexity of the k-fault tolerance decision problem. Drawing on strong evidence about the hierarchical structure of the Internet AS graph, we derive sufficient and necessary conditions for determining whether the graph is k-fault tolerant or not in polynomial time. We then apply this theoretical result to study the network-wide resilience properties of AS-level topology instances, as inferred from large-scale experimental data sets. We find that even single-node failures can disconnect up to hundred of ASes and that approximately 1500 ASes do not avail any real redundancy for their global reachability despite having two or more upstream links. Augmenting AS-level graphs for 1-fault tolerance improves overall resilience to failures, but requires a considerable number of AS-level edges (>7000) to be added. Interestingly, such additional upstream links are mainly needed at stub networks rather than at transit ASes, pointing out the need for multi-homing at stub networks.

[1]  G. Di Battista,et al.  Computing the types of the relationships between autonomous systems , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[2]  Samir Khuller,et al.  Flow in planar graphs with vertex capacities , 1990, Algorithmica.

[3]  Walter Willinger,et al.  A first-principles approach to understanding the internet's router-level topology , 2004, SIGCOMM 2004.

[4]  Dmitri V. Krioukov,et al.  AS relationships: inference and validation , 2006, CCRV.

[5]  Anja Feldmann,et al.  Building an AS-topology model that captures route diversity , 2006, SIGCOMM 2006.

[6]  Randy H. Katz,et al.  Characterizing the Internet hierarchy from multiple vantage points , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[7]  Michalis Faloutsos,et al.  Power laws and the AS-level internet topology , 2003, TNET.

[8]  Lixin Gao,et al.  On inferring and characterizing Internet routing policies , 2003, Journal of Communications and Networks.

[9]  Danny Dolev,et al.  Internet resiliency to attacks and failures under BGP policy routing , 2006, Comput. Networks.

[10]  Gordon T. Wilfong,et al.  The stable paths problem and interdomain routing , 2002, TNET.

[11]  Lixin Gao,et al.  On inferring autonomous system relationships in the Internet , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[12]  Youngseok Lee,et al.  Experience with Restoration of Asia Pacific Network Failures from Taiwan Earthquake , 2007, IEICE Trans. Commun..

[13]  Lixin Gao,et al.  Hierarchical structure of the logical Internet graph , 2001, SPIE ITCom.

[14]  Ratul Mahajan,et al.  Measuring ISP topologies with rocketfuel , 2002, TNET.

[15]  Daniel Massey,et al.  Towards a New Internet Routing Architecture: Arguments for Separating Edges from Transit Core , 2008, HotNets.

[16]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[17]  Yakov Rekhter,et al.  A Border Gateway Protocol 4 (BGP-4) , 1994, RFC.

[18]  Olaf Maennel,et al.  Internet optometry: assessing the broken glasses in internet reachability , 2009, IMC '09.

[19]  Dogu Arifler,et al.  A factor analytic approach to inferring congestion sharing based on flow level measurements , 2007, TNET.

[20]  Olivier Bonaventure,et al.  Quantifying ases multiconnectivity using multicast information , 2009, IMC '09.

[21]  Egon Wanke,et al.  Oriented Paths in Mixed Graphs , 2004, ISAAC.

[22]  Jennifer Rexford,et al.  Stable internet routing without global coordination , 2001, TNET.

[23]  Jp McGeehan,et al.  SPIE ITCOM 2001 , 2001 .

[24]  Thomas Erlebach,et al.  Cuts and Disjoint Paths in the Valley-Free Path Model , 2004, Internet Math..

[25]  Jia Wang,et al.  Towards an accurate AS-level traceroute tool , 2003, SIGCOMM '03.

[26]  Frits C. R. Spieksma,et al.  Connectivity Measures for Internet Topologies on the Level of Autonomous Systems , 2009, Oper. Res..

[27]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[28]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[29]  Kang G. Shin,et al.  Internet routing resilience to failures: analysis and implications , 2007, CoNEXT '07.

[30]  Rob Sherwood,et al.  Discarte: a disjunctive internet cartographer , 2008, SIGCOMM '08.

[31]  Éva Tardos,et al.  Algorithm design , 2005 .

[32]  Jennifer Rexford,et al.  BGP routing policies in ISP networks , 2005, IEEE Network.