A critical look at power law modelling of the Internet

Computer Communications

Volumn 33, Issue 3, 2010, Pages 259-268

  Clegg, Richard G ^a   Di Cairano Gilfedder, Carla ^b   Zhou, Shi ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b MARTLESHAM HEATH   (United Kingdom)

Author keywords

Heavy tails; Internet; Long range dependence; Network modelling; Power laws; Scale free networks

Indexed keywords

HEAVY-TAILS; LONG RANGE DEPENDENCE; NETWORK MODELLING; POWER LAW; SCALE FREE NETWORKS;

NETWORK PERFORMANCE; QUEUEING NETWORKS;

INTERNET;

EID: 74149093306     PISSN: 01403664     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comcom.2009.09.009     Document Type: Review

References (131)

1. Mitzenmacher M. A brief history of generative models for power law and lognormal distributions. Internet Math. 1 2 (2004) 226-251
2. Newman M. Power laws, Pareto distributions and Zipf's law. Contemp. Phys. 46 (2005) 323-351
3. W.E. Leland, M.S. Taqqu, W. Willinger, D.V. Wilson, On the self-similar nature of Ethernet traffic, in: D.P. Sidhu (Ed.), Proc. ACM SIGCOMM, San Francisco, California, 1993, pp. 183-193.
4. Leland W.E., Taqqu M.S., Willinger W., and Wilson D.V. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Networking 2 1 (1994) 1-15
5. Faloutsos M., Faloutsos P., and Faloutsos C. On power-law relationships of the Internet topology. Comput. Commun. Rev. 29 (1999) 251-262
6. Strogatz S.H. Exploring complex networks. Nature (London) 410 (2001) 268
7. Krapivsky P.L., and Redner S. Organization of growing random networks. Phys. Rev. E 63 (2001) 066123
8. Albert R., and Barabási A.L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002) 47-97
9. Bornholdt S., and Schuster H.G. Handbook of Graphs and Networks - From the Genome to the Internet (2002), Wiley-VCH, Weinheim Germany
10. L. Subramanian, S. Agarwal, J. Rexford, R.H. Katz, Characterizing the Internet hierarchy from multiple vantage points, in: Proc. IEEE INFOCOM, 2002, pp. 618-627.
11. Q. Chen, H. Chang, R. Govindan, S. Jamin, S. Shenker, W. Willinger, The origin of power laws in Internet topologies revisited, in: Proc. IEEE INFOCOM, 2002, pp. 608-617.
12. Dorogovtsev S.N., and Mendes J.F.F. Evolution of Networks - From Biological Nets to the Internet and WWW (2003), Oxford University Press, Oxford
13. G. Caldarelli, P.D.L. Rios, L. Pietronero, Generalized network growth: from microscopic strategies to the real Internet properties, 2004. Available from: arXiv:cond-mat/0307610v1.
14. Pastor-Satorras R., and Vespignani A. Evolution and Structure of the Internet - A Statistical Physics Approach (2004), Cambridge University Press, Cambridge
15. H. Chang, S. Jamin, W. Willinger, To peer or not to peer: modeling the evolution of the Internet's AS-level topology, in: Proc. IEEE INFOCOM, 2006, pp. 1-12.
16. W.S. Cleveland, D. Lin, D.X. Sun, IP packet generation: statistical models for TCP start times based on connection-rate superposition, in: Proc. SIGMETRICS, 2000, pp. 166-177.
17. Cao J., Cleveland W.S., Lin D., and Sun D.X. On the nonstationarity of Internet traffic. SIGMETRICS Perform. Eval. Rev. 29 (2001) 102-112
18. Beran J. Statistics for Long-Memory Processes (1994), Chapman & Hall, NY
19. Ganesh A., O'Connell N., and Wischik D. Big Queues. Lecture Notes in Mathematics vol. 1838 (2004), Springer
20. R. Kriesten, U. Kaage, F. Jondral, A unifying view to fractional modeling, in: Proc. IEEE GLOBECOM, 1999, pp. 221-226.
21. Park K., and Willinger W. Self-Similar Network Traffic and Performance Evaluation (2000), Wiley, NY
22. Gubner J.A. Theorems and fallacies in the theory of long-range dependent processes. IEEE Trans. Inf. Theory 51 3 (2005) 1234-1239
23. Heath D., Resnick S., and Samorodnitsky G. Heavy tails and long-range dependence in on/off processes and associated fluid models. Math. Oper. Res. 23 1 (1998) 145-165
24. M. Crovella, A. Bestavros, Explaining world wide web traffic self-similarity, Tech. Rep., TR-95-015 Computer Science Department, Boston University, 1995.
25. Willinger W., Taqqu M., Sherman R., and Wilson D. Self-similarity through high variability: statistical analysis of Ethernet LAN traffic at the source level. IEEE/ACM Trans. Networking 5 1 (1997) 71-86
26. Liu Z. Long range dependence and heavy tail distributions. Perform. Eval. 61 2-3 (2005) 91-93
27. Neidhardt A.L., and Wang J.L. The concept of relevant time scales and its application to queuing analysis of self-similar traffic (or is Hurst naughty or nice?). SIGMETRICS Perform. Eval. Rev. 26 1 (1998) 222-232
28. Karagiannis T., Molle M., and Faloutsos M. Long-range dependence: ten years of Internet traffic modeling. IEEE Internet Comput. (2004) 57-64
29. Taqqu M.S., and Teverovsky V. Robustness of Whittle type estimators for time series with long-range dependence. Stoch. Models 13 (1997) 723-757
30. Bardet J.-M., Lang G., Oppenheim G., Phillipe A.S.S., and Taqqu M.S. Semi-parametric estimation of the long-range dependence parameter: a survey. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Theory and Applications of Long-Range Dependence (2003), Birkhäuser 557-577
31. Paxson V., and Floyd S. Wide-area traffic: the failure of Poisson modeling. IEEE/ACM Trans. Networking 3 (1995) 226-244
32. Crovella M., and Bestavros A. Self-similarity in WWW traffic: evidence and possible causes. IEEE/ACM Trans. Networking 5 (1997) 835-846
33. A. Feldmann, A.C. Gilbert, W. Willinger, Data networks as cascades: investigating the multi-fractal nature of Internet WAN traffic, in: Proc. ACM SIGCOMM, 1998, pp. 42-55.
34. K. Park, G. Kim, M. Crovella, On the relationship between file sizes, transport protocols, and self-similar network traffic, Tech. Rep. 1996-016, Boston University, 1996.
35. Hernández-Campos F., Marron J.S., Samorodnitsky G., and Smith F.D. Variable heavy tails in Internet traffic. Perform. Eval. 58 2-3 (2004) 261-284
36. Xia C.H., Liu Z., Squillante M.S., Zhang L., and Malouch N. Web traffic modeling at finer time scales and performance implications. Perform. Eval. 61 2-3 (2005) 181-201
37. Park C., Hernández-Campos F., Marron J.S., and Smith F.D. Long-range dependence in a changing Internet traffic mix. Comput. Netw. (2005) 401-422
38. Riedi R.H. Multifractal processes. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Theory and Applications of Long-Range Dependence (2003), Birkhäuser 625-716
39. R.H. Reidi, J.L. Véhel, Multifractal properties of TCP traffic: a numerical study, Tech. Rep. 3129, INRIA, 1997. Available from: .
40. Véhel J.L., and Riedi R. Fractional Brownian Motion and Data Traffic Modeling: The Other End of the Spectrum (1997), Springer
41. A. Erramilli, O. Narayan, A.L. Neidhardt, I. Saniee, Performance impacts of multi-scaling in wide-area TCP/IP traffic, in: Proc. IEEE INFOCOM, 2000, pp. 352-359.
42. Z. Zhang, V. Ribeiro, S. Moon, C. Diot, Small-time scaling behaviors of Internet backbone traffic: an empirical study, in: Proc. IEEE INFOCOM, 2003, pp. 1826-1836.
43. H. Jiang, C. Dovrolis, The origin of TCP traffic burstiness in some time scales, Tech. rep., Georgia Institute of Technology, GIT-CERCS-04-09, 2004.
44. Uhlig S. High-order scaling and non-stationarity in TCP flow arrivals: a methodological analysis. Comput. Commun. Rev. 34 2 (2004) 9-24
45. Hohn N., Veitch D., and Abry P. Multifractality in TCP/IP Traffic: the case against. Comput. Netw. J. 48 (2005) 293-313
46. A. Feldmann, A.C. Gilbert, P. Huang, W. Willinger, Dynamics of IP traffic: a study of the role of variability and the impact of control, in: Proc. ACM SIGCOMM, 1999, pp. 301-313.
47. A. Veres, M. Boda, The chaotic nature of TCP congestion control, in: Proc. IEEE INFOCOM, 2000, pp. 1715-1723.
48. Figueiredo D.R., Liu B., Feldmann A., Misra V., Towsley D., and Willinger W. On TCP and self-similar traffic. Perform. Eval. 61 2-3 (2005) 129-141
49. N. Hohn, D. Veitch, P. Abry, Does fractal scaling at the IP level depend on TCP flow arrival processes? in: Proc. The Second Internet Measurement Workshop, 2002, pp. 63-68.
50. Figueiredo D.R., Liu B., Misra V., and Towsley D. On the autocorrelation structure of TCP traffic. Comput. Netw. 40 3 (2002) 339-361
51. J.M. Peha, Retransmission mechanisms and self-similar traffic models, in: IEEE/ACM/SCS Communications Networks and Distributed Systems Modelling and Simulation Conference, 1997, pp. 47-52.
52. Veres A., Kenesi Z., Molnar S., and Vattay G. TCP's role in the propagation of self-similarity in the Internet. Comput. Commun. 26 8 (2003) 899-913
53. M. Borella, G. Brewster, Measurement and analysis of long-range dependent behavior of Internet packet delay, in: Proc. IEEE INFOCOM, 1998, pp. 497-504.
54. Solé R.V., and Valverde S. Information transfer and phase transitions in a model of Internet traffic. Physica A 289 (2001) 595-605
55. Woolf M., Arrowsmith D.K., Mondragon R.J., and Pitts J.M. Optimization and phase transitions in a chaotic model of data traffic. Phys. Rev. E 66 4 (2002) 046106
56. R. Macfadyen, Network traffic characterisation, Master's thesis, UCL, 1999.
57. M. Garrett, W. Willinger, Analysis, modelling, and generation of self-similar VBR video traffic, in: Proc. ACM SIGCOMM, 1994, pp. 269-280.
58. R. Addie, M. Zukerman, T. Neame, Fractal traffic: measurements, modelling, and performance evaluation, in: Proc. IEEE INFOCOM, 1995, pp. 977-984.
59. Norros I. A storage model with self-similar input. Queuing Syst. 16 (1994) 387-396
60. M. Parulekar, A. Makowski, Tail probabilities for a multiplexer with self-similar traffic, in: Proc. IEEE INFOCOM, 1996, pp. 1452-1459.
61. Tsybakov B., and Georganas N. Self-similar traffic and upper bounds to buffer overflow in an ATM queue. Perform. Eval. 36 (1999) 359-386
62. Kherania A.A., and Kumar A. Long range dependence in network traffic and the closed loop behaviour of buffers under adaptive window control. Perform. Eval. 61 2-3 (2005) 95-127
63. Y. Chen, Z. Deng, C.L. Williamson, A model for self-similar Ethernet LAN traffic: design, implementation,and performance implications, in: Summer Computer Simulation Conference, 1995, pp. 831-837.
64. M. Grossglauser, J. Bolot, On the relevance of long-range dependence in network traffic, in: Proc. ACM SIGCOMM, 1996, pp. 15-24.
65. Ryu B.K., and Elwalid A. The importance of long-range dependence of VBR video traffic in ATM traffic engineering: myths and realities. Comput. Commun. Rev. 26 (1996) 3-14
66. Paxson V. Fast, approximate synthesis of fractional gaussian noise for generating self-similar network traffic. Comput. Commun. Rev. 27 (1997) 5-18
67. J. Roberts, U. Mocci, J. Virtano (Eds.), Broadband network teletraffic, in: Performance Evaluation and Design of Broadband Multiservice Networks, Final Report of Action COST 242, Lecture Notes in Computer Science, vol. 1155, Springer, 1996.
68. A. Erramilli, R.P. Singh, P. Pruthi, Chaotic maps as models of packet traffic, in: Proc. 14th Int. Teletraffic Cong., vol. 1, 1994, pp. 329-338.
69. P. Pruthi, A. Erramilli, Heavy-tailed on/off source behaviour and self-similar traffic, in: ICC, 1995, pp. 445-450.
70. Burrus C., Gopinath R., and Guo H. Introduction to Wavelets and Wavelet Transforms: A Primer (1998), Prentice Hall
71. Riedi R.H., Crouse M.S., Ribeiro V.J., and Baraniuk R.G. A multifractal wavelet model with application to network traffic. IEEE Spec. Issue Inf. Theory 45 April (1999) 992-1018
72. F. Huebner, D. Liu, J.M. Fernandez, Queueing performance comparison of traffic models for Internet traffic, in: Proc. IEEE GLOBECOM, 1998, pp. 471-476.
73. R.G. Clegg, Simulating Internet traffic with Markov-modulated processes, in: Proc. UK Perf. Eng. Workshop, 2007, pp. 26-37.
74. Quoitin B., Pelsser C., and Swinnen L. Interdomain traffic engineering with BGP. IEEE Commun. Mag. 41 5 (2003) 122-128
75. RIPE, Routing Information Service, RIPE Network Coordination Center. Available from: .
76. The National Laboratory for Applied Network Research (NLANR). Available from: .
77. The Route Views Project, University of Oregon, Eugene. Available from: .
78. The Topology Project, University of Michigan, Ann Arbor. Available from: .
79. Chang H., Govindan R., Jamin S., Shenker S., and Willinger W. Towards capturing representative AS-level Internet topologies. Comput. Netw. J. 44 6 (2004) 737-755
80. Y. He, G. Siganos, M. Faloutsos, S. Krishnamurthy, A systematic framework for unearthing the missing links: measurements and impact, in: Proc. Fourth USENIX Symposium on Networked Systems Design & Implementation, 2007, pp. 187-200.
81. The Cooperative Association for Internet Data Analysis (CAIDA). Available from: .
82. M. Murray, K.C. Claffy, Measuring the immeasurable: global Internet measurement infrastructure, in: Proc. PAM, 2001, pp. 159-167.
83. The DIMES Project. Available from: .
84. Y. Hyun, A. Broido, K. Claffy, Traceroute and BGP AS Path Incongruities. Available from: .
85. R.V. Oliveira, B. Zhang, L. Zhang, Observing the evolution of Internet AS topology, in: Proc. ACM SIGCOMM, 2007, pp. 313-324.
86. Mahadevan P., Krioukov D., Fomenkov M., Huffaker B., Dimitropoulos X., Claffy K., and Vahdat A. The Internet AS-level topology: three data sources and one definitive metric. Comput. Commun. Rev. 36 1 (2006) 17-26
87. R. Cohen, D. Raz, The Internet dark matter - on the missing links in the AS connectivity map, in: Proc. IEEE INFOCOM, 2006, pp. 1-12.
88. A. Lakhina, J.W. Byers, M.M. Crovella, P. Xie, Sampling biases in IP topology measurements, in: Proc. IEEE INFOCOM, vol. 1, 2003, pp. 332-341.
89. Clauset A., and Moore C. Accuracy and scaling phenomena in Internet mapping. Phys. Rev. Lett. 94 (2005) 018701
90. Dall-Asta L., Alvarez-Hamelin I., Barrat A., Vazquez A., and Vespignani A. Exploring networks with traceroute-like probes: theory and simulations. Theor. Comput. Sci. 355 (2006) 6-24
91. H. Tangmunarunkit, R. Govindan, S. Jamin, S. Shenker, W. Willinger, Network topology generators: degree-based vs. structural, in: Proc. ACM SIGCOMM, 2002, pp. 147-159.
92. L. Li, D. Alderson, W. Willinger, J. Doyle, A first-principles approach to understanding the Internet's router-level topology, in: Proc. ACM SIGCOMM, 2004, pp. 3-14.
93. Alderson D., Li L., Willinger W., and Doyle J.C. Understanding Internet topology: principles, models, and validation. IEEE/ACM Trans. Networking 13 6 (2005) 1205-1218
94. Zhou S., and Mondragón R. Structural constraints in complex networks. New J. Phys. 9 173 (2007) 1-11
95. Pastor-Satorras R., Vázquez A., and Vespignani A. Dynamical and correlation properties of the Internet. Phys. Rev. Lett. 87 (2001) 258701
96. Newman M.E.J. Assortative mixing in networks. Phys. Rev. Lett. 89 (2002) 208701
97. Newman M.E.J. Mixing patterns in networks. Phys. Rev. E 67 (2003) 026126
98. Maslov S., Sneppenb K., and Zaliznyaka A. Detection of topological patterns in complex networks: correlation profile of the Internet. Physica A 333 (2004) 529-540
99. Zhou S., and Mondragón R.J. The rich-club phenomenon in the Internet topology. IEEE Commun. Lett. 8 3 (2004) 180-182
100. Watts D.J., and Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 393 (1998) 440
101. Carmi S., Havlin S., Kirkpatrick S., Shavitt Y., and Shir E. A model of Internet topology using k-shell decomposition. PNAS 104 27 (2007) 11150-11154
102. S.L. Tauro, C. Palmer, G. Siganos, M. Faloutsos, A simple conceptual model for the Internet topology, in: Prof. Global Internet, 2001, pp. 1667-1671.
103. P. Mahadevan, D. Krioukov, K. Fall, A. Vahdat, Systematic topology analysis and generation using degree correlations, in: Proc. ACM SIGCOMM, 2006, pp. 135-146.
104. P. Mahadevan, C. Hubble, D. Krioukov, B. Huffaker, A. Vahdat, ORBIS: rescaling degree correlations to generate annotated Internet topologies, in: Proc. ACM SIGCOMM, 2007, pp. 325-336.
105. S.N. Dorogovtsev, Networks with Given Correlations. Available from: .
106. Mitzenmacher M. The future of power law research. Internet Math. 2 4 (2005) 525-534
107. Leskovec J., Kleinberg J., and Faloutsos C. Graph evolution: densification and shrinking diameters. ACM Trans. Knowl. Discov. Data 1 1 (2007) 1-40
108. A. Medina, I. Matta, Brite: a flexible generator of Internet topologies, Tech. Rep. BU-CS-TR-2000-005, Boston University, 2000.
109. J. Winick, S. Jamin, Inet-3.0 Internet topology generator, Tech. Rep. UM-CSE-TR-456-02, University of Michigan, 2002.
110. Barabási A., and Albert R. Emergence of scaling in random networks. Science 286 (1999) 509
111. Dorogovtsev S.N., and Mendes J.F.F. Scaling behaviour of developing and decaying networks. EuroPhys. Lett. 52 33 (2000) 33
112. T. Bu, D. Towsley, On distinguishing between Internet power law topology generators, in: Proc. IEEE INFOCOM, 2002, p. 638.
113. G. Bianconi, G. Caldarelli, A. Capocci, Number of h-cycles in the Internet at the autonomous system level, 2003. Available from ArXiv:cond-mat/0310339.
114. Krapivsky P.L., Redner S., and Leyvraz F. Connectivity of growing random networks. Phys. Rev. Lett. 85 4629 (2000) 4629
115. Status report of IRTF routing research group's (RRG) future domain routing (FDR) scalability research subgroup (RR-FS), 2005. Available from: .
116. Zhou S., and Mondragón R.J. Accurately modelling the Internet topology. Phys. Rev. E 70 (2004) 066108
117. Krapivsky P., and Krioukov D. Scale-free networks as pre-asymptotic regimes of super-linear preferential attachment. Phys. Rev. E 72 (2008) 026114
118. H. Haddadi, D. Fay, A. Jamakovic, O. Maennel, A.W. Moore, R. Mortier, M. Rio, S. Uhlig, Beyond node degree: evaluating AS topology models, Tech. Rep. UCAM-CL-TR-725, University of Cambridge, 2008.
119. Zhou S., Zhang G.-Q., and Zhang G.-Q. i Chinese Internet AS-level topology. IET Commun. 1 2 (2007) 209-214
120. Vázquez A., Pastor-Satorras R., and Vespignani A. Large-scale topological and dynamical properties of Internet. Phys. Rev. E 65 (2002) 066130
121. S.T. Park, D. Pennock, C.L. Giles, Comparing static and dynamic measurements and models of the Internet's AS topology, in: Proc. IEEE INFOCOM, 2004, pp. 1616-1627.
122. Handley M. Why the Internet only just works. BT Technol. J. 24 3 (2006) 119-129
123. C. Labovitz, A. Ahuja, R. Wattenhofer, S.Venkatachary, The impact of Internet policy and topology on delayed routing convergence, in: Proc. IEEE INFOCOM, 2001, pp. 537-546.
124. S.T. Park, A. Khrabrov, D.M. Pennock, S. Lawrence, C.L. Giles, L.H. Ungar, Static and dynamic analysis of the Internet's susceptibility to faults and attacks, in: Proc. IEEE INFOCOM, 2003, pp. 2144-2154.
125. Park K., and Lee H. On the effectiveness of route-based packet filtering for distributed DoS attack prevention in power-law Internets. Comput. Commun. Rev. 31 4 (2001) 15-26
126. D. Krioukov, K. Fall, X. Yang, Compact routing on Internet-like graphs, in: Proc. ACM SIGCOMM, vol.1, 2004, p. 219.
127. Y. Wang, D. Chakrabarti, C. Wang, C. Faloutsos, Epidemic spreading in real networks: an eigenvalue viewpoint, in: Proc. 22nd International Symposium on Reliable Distributed Systems (SRDS), 2003, pp. 25-34.
128. Albert R., Jeong H., and Barabasi A. Error and attack tolerance of complex networks. Nature 406 (2000) 378
129. Krioukov D., Chung F., Claffy K.C., Fomenkov M., Vespignani A., and Willinger W. The workshop on Internet topology (WIT) report. Comput. Commun. Rev. 37 1 (2007) 69-73
130. D. Arrowsmith, M. Woolf, Modelling of TCP packet traffic in a large interactive growth network, in: Proc. IEEE Systems and Circuits, Vancouver, 2004, pp. 477-480.
131. Floyd S., and Kohler E. Internet research needs better models. Comput. Commun. Rev. 33 1 (2003) 29-34