Skip to main content

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 33))

Abstract

Over the last decade there has been significant interest and attention devoted towards understanding the complex structure of the Internet, particularly its topology and the large-scale properties that can be derived from it. While recent work by empiricists and theoreticians has emphasized certain statistical and mathematical properties of network structure, this article presents an optimization-based perspective that focuses on the objectives, constraints, and other drivers of engineering design. We argue that Internet topology at the router-level can be understood in terms of the tradeoffs between network performance and the technological and economic factors constraining design. Furthermore, we suggest that the formulation of corresponding optimization problems serves as a reasonable starting point for generating “realistic, yet fictitious” network topologies. Finally, we describe how this optimization-based perspective is being used in the development of a still-nascent theory for the Internet as a whole.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 149.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abilene Network. Detailed information about the objectives, organization, and development of the Abilene network are available from http://www.internet2.edu/abilene.

    Google Scholar 

  2. L.A. Adamic and B.A. Huberman. Power-Law Distribution of the World Wide Web. Science 2000; 287(5461):2115.

    Article  Google Scholar 

  3. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows: Theory, Algorithms, and Applications, Upper Saddle River, NJ: Prentice-Hall. 1993.

    Google Scholar 

  4. W. Aiello, F. Chung, and L. Lu. A Random Graph Model for Massive Graphs. Proceedings of the 32nd Annual Symposium in Theory of Computing, 2000.

    Google Scholar 

  5. R. Albert, H. Jeong, and A.-L. Barabási. Diameter of the World Wide Web. Nature 1999; 401:130–131.

    Article  CAS  ADS  Google Scholar 

  6. R. Albert, H. Jeong, and A.-L. Barabási. Attack and error tolerance of complex networks. Nature 2000; 406: 378–382.

    Article  PubMed  CAS  ADS  Google Scholar 

  7. R. Albert, and A.-L. Barabási. Statistical Mechanics of Complex Networks. Reviews of Modern Physics 2002; 74:47–97.

    Article  MathSciNet  ADS  Google Scholar 

  8. D. Alderson. Technological and Economic Drivers and Constraints in the Internet’s “Last Mile”. Technical Report CIT-CDS-04-004, Engineering Division, California Institute of Technology, 2004.

    Google Scholar 

  9. D. Alderson, J. Doyle, R. Govindan, and W. Willinger. Toward an Optimization-Driven Framework for Designing and Generating Realistic Internet Topologies. In ACM SIGCOMM Computer Communications Review 2003; 33(1): 41–46.

    Article  Google Scholar 

  10. M. Andrews and L. Zhang. The access network design problem. Proceedings of the 39th Foundations of Computer Science, 1998.

    Google Scholar 

  11. D. Applegate and E. Cohen. Making Intra-Domain Routing Robust to Changing and Uncertain Traffic Demands: Understanding Fundamental Tradeoffs. Proceedings of ACM SIGCOMM 2003.

    Google Scholar 

  12. A. Balakrishnan, T.L. Magnanti, A. Shulman, and R.T. Wong. Models for planning capacity expansion in local access telecommunication networks. Annals of Operations Research 1991; 33: 239–284.

    Article  Google Scholar 

  13. A.-L. Barabási and R. Albert. Emergence of scaling in random networks. Science 1999; 286:509–512.

    Article  PubMed  MathSciNet  Google Scholar 

  14. E. Bender and R. Canfield. The asymptotic number of labeled graphs with given degree sequences. J. Combinatorial Theory Ser A 1978; 24: 296–307.

    Article  MathSciNet  Google Scholar 

  15. N. Berger, B. Bollobás, C. Borgs, J. T. Chayes, and O. Riordan. Degree Distribution of the FKP Network Model. Proceedings of ICALP 2003; 725–738.

    Google Scholar 

  16. N. Berger, C. Borgs, J.T. Chayes, R.M. D’Souza, and R.D. Kleinberg. Competition-Induced Preferential Attachment. Proceedings of ICALP 2004.

    Google Scholar 

  17. G. Birkan, J. Kennington, E. Olinick, A. Ortynski, G. Spiride. Optimization-Based Design Strategies for DWDM Networks: Opaque versus All-Optical Networks. Tech Report 03-EMIS-Ol, SMU, Dallas, TX; 2001.

    Google Scholar 

  18. U. Black. MPLS and Label Switching Networks, 2nd Edition. Prentice Hall PTR, 2002.

    Google Scholar 

  19. A. Broido and K. Claffy. Internet Topology: Connectivity of IP Graphs. Proceedings of SPIE ITCom WWW Conference 2001.

    Google Scholar 

  20. T. Bu and D. Towsley. On distinguishing Between Internet Power Law Topology Generators. Proceedings of IEEE Infocom 2002.

    Google Scholar 

  21. K.L. Calvert, M. Doar, and E. Zegura. Modeling Internet topology. IEEE Communications Magazine, June 1997.

    Google Scholar 

  22. J. M. Carlson and J. C. Doyle. Highly Optimized Tolerance: a mechanism for power laws in designed systems. Physics Review E 1999; 60:1412–1428.

    Article  CAS  ADS  Google Scholar 

  23. J.M. Carlson and J. Doyle. Complexity and Robustness. Proceedings of the National Academy of Science 2002; 99(Suppl. 1): 2539–2545.

    Google Scholar 

  24. H. Chang, R. Govindan, S. Jamin, S. Shenker, and W. Willinger. Towards Capturing Representative AS-Level Internet Topologies. Proceedings of ACM SIGMETRICS 2002.

    Google Scholar 

  25. H. Chang, S. Jamin, and W. Willinger. Internet Connectivity at the AS-level: An Optimization-Driven Modeling Approach Proceedings of MoMeTools 2003 (Extended version, Tech Report UM-CSE-475-03).

    Google Scholar 

  26. Q. Chen, H. Chang, R. Govindan, S. Jamin, S. Shenker, and W. Willinger. The Origin of Power Laws in Internet Topologies Revisited. Proceedings of IEEE INFOCOM 2002.

    Google Scholar 

  27. B. Cheswick, H. Burch, and S. Branigan. Mapping and Visualizing the Internet. Proceedings of Usenix 2000.

    Google Scholar 

  28. Cisco Catalog. Master Contract for the State of Washington. http://techmall.dis.wa.gov/master_contracts/intranet/routers_switches.asp

    Google Scholar 

  29. D. D. Clark. The design philosophy of the DARPA Internet protocols. Proceedings of the ACM SIGCOMM’88, in: ACM Computer Communication Reviews 1988; 18(4): 106–114.

    Article  Google Scholar 

  30. M. B. Doar. A Better Model for Generating Test Networks. Proceedings of Glohecom’ 96, Nov. 1996.

    Google Scholar 

  31. J. Doucette and W.D. Grover. Comparison of mesh protection and restoration schemes and the dependency on graph connectivity. 3rd International Workshop on Design of Reliable Communication Networks (DRCN) 2001; 121–128.

    Google Scholar 

  32. J. C. Doyle and J. M. Carlson. Power laws. Highly Optimized Tolerance and generalized source coding. Physics Review Letters 2000; 84(24):5656–5659.

    Article  CAS  ADS  Google Scholar 

  33. J. Doyle, J. Carlson, S. Low, F. Paganini, G. Vinnicombe, W. Willinger, J. Hickey, P. Parilo, L. Vandenberghe. Robustness and the Internet: Theoretical Foundations, In Robust design: A repertoire from biology, ecology, and engineering, E. Jen, Editor, Oxford University Press (to appear).

    Google Scholar 

  34. J. Duffy. “Cisco’s loss is Juniper’s gain.” Network World Fusion February 18, 2003. http://www.nwfusion.com/edge/news/2003/0218mktshare.html.

    Google Scholar 

  35. P. Erdos and A. Renyi. On random graphs I Publ Math. (Debrecen) 9(1959), 290–297.

    Google Scholar 

  36. P. Erdos and A. Renyi. On the evolution of random graphs. In Publications of the Mathematical Institute of the Hungarian Academy of Sciences 1960; 5:17–61.

    MathSciNet  Google Scholar 

  37. A. Fabrikant, E. Koutsoupias, and C. Papadimitriou. Heuristically Optimized Trade-offs: A new paradigm for Power-laws in the Internet, Proceedings of ICALP 2002; 110–122.

    Google Scholar 

  38. M. Faloutsos, P. Faloutsos, and C. Faloutsos. On Power-Law Relationships of the Internet Topology. Proceedings of ACM SIGCOMM 1999.

    Google Scholar 

  39. B. Fortz and M. Thorup. Internet Traffic Engineering by Optimizing OSPF Weights. Proceedings of IEEE INFOCOM 2000.

    Google Scholar 

  40. L. Gao. On inferring autonomous system relationships in the Internet, in Proceedings of IEEE Global Internet Symposium 2000.

    Google Scholar 

  41. B. Gavish. Topological design of telecommunication networks—local access design methods. Annals of Operations Research 1991; 33:17–71.

    Article  MATH  Google Scholar 

  42. B. Gendron, T.G. Crainic and A. Frangioni. Multicommodity Capacitated Network Design. In B. Sansó and P. Soriano (eds), Telecommunications Network Planning, pp. 1–29. Kluwer, Norwell, MA. 1998.

    Google Scholar 

  43. C. Gkantsidis, M. Mihail, A. Saberi. Conductance and congestion in power law graphs Proceedings of ACM Sigmetrics 2003.

    Google Scholar 

  44. R. Govindan and H. Tangmunarunkit. Heuristics for Internet Map Discovery, Proceedings of IEEE INFOCOM 2000.

    Google Scholar 

  45. T.G. Griffin, A.D. Jaggard, and V. Ramachandran. Design Principles of Policy Languages for Path Vector Protocols. Proceedings of ACM SIGCOMM 2003.

    Google Scholar 

  46. M. Grötschel, C. Monma, and M. Stoer. Design of Survivable Networks, in Handbook in Operations Research and Management Science, Volume on “Networks”, 1993.

    Google Scholar 

  47. H. Höller and S. Vo. A Mixed Integer Linear Programming Model for Multi-Layer SDH/WDM Networks. Presented at Seventh Annual INFORMS Conference on Telecommunications 2004. Boca Raton, Florida.

    Google Scholar 

  48. H. Höller and S. Vo. Software Tools for a Multilayer Network Design. Proceedings of the Fourth International Conference on Decision Support for Telecommunications and Information Society (DSITS), 2004. Warsaw, Poland.

    Google Scholar 

  49. G. Huston. ISP Survival Guide: Strategies for Running a Competitive ISP New York: John Wiley & Sons, 2000.

    Google Scholar 

  50. IEEE Communications Magazine, Survivability Issue, August 1999.

    Google Scholar 

  51. Internet2 Consortium. Internet2 NetFlow: Weekly Reports. http://netflow.internet2.edu/weekly/.

    Google Scholar 

  52. C. Jin, Q. Chen, and S. Jamin. Inet: Internet Topology Generator. Technical Report CSE-TR443-00, Department of EECS, University of Michigan, 2000.

    Google Scholar 

  53. C. Jin, D.X. Wei and S.H. Low. FAST TCP: motivation, architecture, algorithms, performance. Proceedings of IEEE Infocom 2004.

    Google Scholar 

  54. D. Katabi, M. Handley, and C. Rohrs. Congestion Control for High Bandwidth-Delay Product Networks. Proceedings of ACM Sigcomm 2002.

    Google Scholar 

  55. J. Kleinberg, S. R. Kumar, P. Raghavan, S. Rajagopalan and A. Tomkins. The web as a graph: Measurements, models and methods. Proceedings of the International Conference on Combinatorics and Computing July 1999.

    Google Scholar 

  56. F.P. Kelly. Mathematical modelling of the Internet. In Mathematics Unlimited-2001 and Beyond, B. Engquist and W. Schmid (eds). Berlin: Springer-Verlag 2001; 685–702.

    Google Scholar 

  57. F.P. Kelly, A. Maulloo and D. Tan. Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society 1998; 49: 237–252.

    Article  Google Scholar 

  58. T. Kelly. Scalable TCP: Improving Performance in Highspeed Wide Area Networks. Computer Communication Review 2003; 32(2).

    Google Scholar 

  59. Kennington, J., E. Olinick, K. Lewis, A. Ortynski, G. Spiride. Robust solutions for the DWDM routing and provisioning problem: models and algorithms. Optical Networks Magazine 2003; 4:74–84.

    Google Scholar 

  60. Kennington, J., E. Olinick, A. Ortynski, G. Spiride. Wavelength routing and assignment in a survivable WDM mesh network. Operations Research 2003; 51: 67–79.

    Article  MathSciNet  Google Scholar 

  61. A. Lakhina, J.W. Byers, M. Crovella, and P. Xie. Sampling Biases in IP topology Measurements, Proceedings of IEEE INFOCOM 2003.

    Google Scholar 

  62. L. Li, D. Alderson, W. Willinger, and J. Doyle. A First Principles Approach to Understanding Router-Level Topology. Proceedings of ACM SIGCOMM 2004.

    Google Scholar 

  63. M. Liljenstam, J. Liu, and D.M. Nicol. Development of an Internet Backbone Topology for Large-Scale Network Simulations. Proceedings of the 2003 Winter Simulation Conference, S. Chick, P. J. Sánchez, D. Ferrin, and D. J. Morrice (eds).

    Google Scholar 

  64. S. H. Low and D. E. Lapsley. Optimization Flow Control, I: Basic Algorithm and Convergence. IEEE/ACM Transactions on Networking 1999; 7(6):861–75.

    Article  Google Scholar 

  65. S. H. Low. A duality model of TCP and queue management algorithms. IEEE/ACM Transactions on Networking 2003.

    Google Scholar 

  66. T. Luczak. Sparse random graphs with a given degree sequence. Random Graphs, vol 2 Poznan, 1989.

    Google Scholar 

  67. T.L. Magnanti and R.T. Wong. Network Design and Transportation Planning: Models and Algorithms. Transportation Science 1984; 18(1): 1–55.

    Article  Google Scholar 

  68. D. Maltz, G. Xie, J. Zhan, H. Zhang, G. Hjalmtysson, and A. Greenberg. Routing Design in Operational Networks: A Look from the Inside. Proceedings of ACM SIGCOMM 2004.

    Google Scholar 

  69. A. Medina, A. Lakhina, I. Matta, and J. Byers. BRITE: An Approach to Universal Topology Generation, in Proceedings of MASCOTS, August 2001.

    Google Scholar 

  70. A. Medina, I. Matta, and J. Byers. On the Origin of Power Laws in Internet Topologies. ACM SIGCOMM Computer Communications Review 2000; 30(2).

    Google Scholar 

  71. B. Melián, M. Laguna and J. A. Moreno-Pérez. Capacity Expansion of Fiber Optic Networks with WDM Systems: Problem Formulation and Comparative Analysis. Computers and Operations Research 2003; 31(3): 461–472.

    Google Scholar 

  72. B. Melián, M. Laguna and J. A. Moreno-Pérez. Minimizing the Cost of Placing and Sizing Wavelength Division Multiplexing and Optical Cross-Connect Equipment in a Telecommunications Network. July 2004. Submitted for publication. Available from http://leeds.Colorado.edu/faculty/laguna/publications.htm

    Google Scholar 

  73. M. Minoux. Network Synthesis and Optimum Network Design Problems: Models, Solution Methods and Applications. Networks 1989; 19: 313–360.

    Article  MATH  MathSciNet  Google Scholar 

  74. M. Mitzenmacher. A Brief History of Generative Models for Power Law and Lognormal Distributions. Internet Mathematics 2004; 1(2).

    Google Scholar 

  75. J. Mo and J. Walrand. Fair end-to-end window-based congestion control. IEEE/ACM Transactions on Networking 2000.

    Google Scholar 

  76. G. Mohan and C.S.R. Murthy. Light-path restoration in WDM optical networks. IEEE Network, pp.24–32, November/December 2000.

    Google Scholar 

  77. M. Molloy and B. Reed. A Critical Point For Random Graphs With A Given Degree Sequence, Random Structures and Algorithms 1995; 6:161–180.

    Article  MathSciNet  Google Scholar 

  78. Computer Science and Telecommunications Board (CSTB), National Research Council. The Internet’s Coming of Age. National Academy Press, Washington, D.C., 2001.

    Google Scholar 

  79. M.E.J. Newman. Assortative Mixing in Networks. Phys. Rev Lett. 2002; 89(208701).

    Google Scholar 

  80. D. Moore, C. Shannon, G. Voelker, and S. Savage. Internet Quarantine: Requirements for Containing Self-Propagating Code. Proceedings of IEEE Infocom 2003.

    Google Scholar 

  81. A.M. Odlyzko. Internet traffic growth: Sources and implications, in Optical Transmission Systems and Equipment for WDM Networking II, B. B. Dingel, W. Weiershausen, A. K. Dutta, and K.-I. Sato, eds., Proc. SPIE, 5247:1–15, 2003.

    Google Scholar 

  82. F. Paganini, Z. Wang, S. H. Low and J. C. Doyle. A new TCP/AQM for stable operation in fast networks. Proceedings of IEEE Infocom 2003.

    Google Scholar 

  83. C. R. Palmer and J. G. Steffan. Generating network topologies that obey power laws. Proceedings of GLOBECOM 2000.

    Google Scholar 

  84. President’s Commission on Critical Infrastructure Protection. Critical Foundations. Technical report. The White House, 1997.

    Google Scholar 

  85. S. Ramamurthy and B. Mukherjee. Survivable WDM mesh networks. Part I-Protection. Proceedings of IEEE Infocom 1999; 744–751.

    Google Scholar 

  86. S. Ramamurthy and B. Mukherjee. Survivable WDM mesh networks. Part II-Restoration. Proceedings of IEEE International Conference on Communications (ICC) 1999; 2023–2030.

    Google Scholar 

  87. Route Views. University of Oregon Route Views Project, Available at http://www.antc.uoregon.edu/route-views/.

    Google Scholar 

  88. G. Siganos, M. Faloutsos, P. Faloutsos, C. Faloutsos. Power laws and the AS-level internet topology. IEEE/ACM Transactions on Networking 2003; 11(4): 514–524.

    Article  Google Scholar 

  89. Cooperative Association for Internet Data Analysis (CAIDA). Skitter. Available at http://www.caida.org/tools/measurement/skitter/.

    Google Scholar 

  90. N. Spring, R. Mahajan, and D. Wetherall. Measuring ISP Topologies with Rocketfuel. Proceedings of ACM SIGCOMM 2002.

    Google Scholar 

  91. N. Spring, D. Wetherall, and T. Anderson. Reverse-Engineering the Internet. Proceedings of ACM Workshop on Hot Topics in Networking (HotNets-II). November 2003.

    Google Scholar 

  92. L. Subramanian, S. Agarwal, J. Rexford, and R. Katz. Characterizing the Internet Hierarchy from Multiple Vantage Points. Proceedings of IEEE INFOCOM 2002.

    Google Scholar 

  93. SURFnet Press Release. “SURFnet Builds Advanced Research Network Based on Solutions, Services from Nortel Networks, Avici Systems, Telindus”. Utrecht, 24 March 2004. Available at http://www.gigaport.nl/publicaties/pers/en_pers240304.html.

    Google Scholar 

  94. H. Tangmunarunkit, R. Govindan, S. Jamin, S. Shenker, and W. Willinger. Network Topology Generators: Degree-Based vs. Structural. Proceedings of ACM SIGCOMM 2002.

    Google Scholar 

  95. R. Teixeira, A. Shaikh, T. Griffin, and G.M. Voelker. Network Sensitivity to Hot-Potato Disruptions. Proceedings of ACM SIGCOMM 2004.

    Google Scholar 

  96. J. Wang and L. Li and S. H. Low and J. C. Doyle. Can TCP and shortest-path routing maximize utility? Proceedings of IEEE Infocom 2003.

    Google Scholar 

  97. B.M. Waxman. Routing of multipoint connections. IEEE Journal of Selected Areas in Communication, 1988; 6(9).

    Google Scholar 

  98. The White House. The National Strategy to Secure Cyberspace. February 2003.

    Google Scholar 

  99. W. Willinger and J. C. Doyle. Robustness and the Internet: Design and Evolution. In Robust design: A Repertoire of Biological, Ecological, and Engineering Case Studies, E. Jen, Editor, Oxford University Press (to appear).

    Google Scholar 

  100. W. Willinger, R. Govindan, S. Jamin, V. Paxson and S. Shenker. Scaling Phenomena in the Internet: Critically examining Criticality Proceedings of the National Academy of Science 2002; 99(1):2573–2580.

    Article  Google Scholar 

  101. K. Wu and A. Liu. The Rearrangement Inequality, http://matholymp.com/TUTORIALS/Rear.pdf

    Google Scholar 

  102. S.-H. Yook, H. Jeong, and A.-L. Barabási. Modeling the Internet’s large-scale topology, PNAS Proceedings of the National Academy of Science 2002; 99:13382–13386.

    Article  CAS  ADS  Google Scholar 

  103. H. Zang. WDM Mesh Networks: Management and Survivability. Kluwer Publishing, December 2002.

    Google Scholar 

  104. H. Zang, J. Jue, and B. Mukherjee. A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks. Optical Networks Magazine 2000; 1:47–60.

    Google Scholar 

  105. H. Zang, J.P. Jue, L. Sahasrabuddhe, R. Ramamurthy, and B. Mukherjee. Dynamic light-path establishment in wavelength routed networks. IEEE Communications Magazine 2001; 39(9): 100–108.

    Article  Google Scholar 

  106. E. W. Zegura, K. L. Calvert, and S. Bhattacharjee. How to model an internetwork. Proceedings of INFOCOM 1996.

    Google Scholar 

  107. E. Zegura, K.L. Calvert, and M.J. Donahoo, A quantitative comparison of graph-based models for Internet topology. IEEE/ACM Transactions on Networking 1997; 5(6).

    Google Scholar 

  108. Y. Zhang, M. Roughan, C. Lund and D. Donoho. An information-theoretic approach to traffic matrix estimation, Proc. of ACM Sigcomm, Karlsruhe, Germany, 2003. In Computer Communication Review 2003; 33(4).

    Google Scholar 

  109. D. Zhou and S. Subramaniam. Survivability in Optical Networks. IEEE Network, pp.16–23, November/December 2000.

    Google Scholar 

  110. X. Zhu, J. Yu and J.C. Doyle. Heavy Tails, Generalized Coding, and Optimal Web Layout. Proceedings of IEEE Infocom 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, Inc.

About this paper

Cite this paper

Alderson, D., Willinger, W., Li, L., Doyle, J. (2006). An Optimization-Based Approach to Modeling Internet Topology. In: Raghavan, S., Anandalingam, G. (eds) Telecommunications Planning: Innovations in Pricing, Network Design and Management. Operations Research/Computer Science Interfaces Series, vol 33. Springer, Boston, MA. https://doi.org/10.1007/0-387-29234-9_6

Download citation

Publish with us

Policies and ethics