Extremal dependence analysis of network sessions

Extremes

Volumn 14, Issue 1, 2011, Pages 1-28

  López Oliveros, Luis ^a   Resnick, Sidney I ^b  

^a Cornell University ^*  (United States)

^b School of Operations Research and Industrial Engineering   (United States)

Author keywords

Heavy tails; Network modeling; Peak transmission rate; Regular variation; Spectral measure

Indexed keywords

EID: 79952073894     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-009-0096-4     Document Type: Article

References (56)

1. Arlitt, M., Williamson C.: Web server workload characterization: the search for invariants. Master's thesis, University of Saskatchewan (1996).
2. Athreya, K. B.: Bootstrap of the mean in the infinite variance case. Ann. Stat. 15(2), 724-731 (1987).
3. Balkema, A. A., de Haan, L.: Residual life time at great age. Ann. Probab. 2(5), 792-804 (1974).
4. Beirlant, J., Goegebeur Y., Teugels, J., Segers, J.: Statistics of extremes. In: Wiley Series in Probability and Statistics, Theory and Applications, With contributions from Daniel De Waal and Chris Ferro. Wiley, Chichester (2004).
5. Brockwell, P., Davis, R.: Time Series: Theory and Methods, 2nd edn. Springer, New York (1991).
6. Coles, S.: An introduction to statistical modeling of extreme values. In: Springer Series in Statistics, xiv, 210 p. Springer, London (2001).
7. Crovella, M., Bestavros, A.: Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Trans. Netw. 5(6), 835-846 (1997).
8. Csörgo{double acute}, S., Deheuvels, P., Mason, D.: Kernel estimates for the tail index of a distribution. Ann. Stat. 13(3), 1050-1077 (1985).
9. Das, B., Resnick, S.: Conditioning on an extreme component: model consistency and regular variation on cones. Tech. rep., Cornell University, School of ORIE. http://arxiv.org/abs/0805. 4373 (2009a).
10. Das, B., Resnick, S.: Detecting a conditional extrme value model. Tech. rep., Cornell University, School of ORIE. http://arxiv.org/abs/0902. 2996 (2009b).
11. D'Auria, B., Resnick, S.: Data network models of burstiness. Adv. Appl. Probab. 38(2), 373-404 (2006).
12. D'Auria, B., Resnick, S.: The influence of dependence on data network models. Adv. Appl. Probab. 40(1), 60-94 (2008).
13. Davis, R., Resnick, S.: Tail estimates motivated by extreme value theory. Ann. Stat. 12(4), 1467-1487 (1984).
14. Davison, A. C., Smith, R. L.: Models for exceedances over high thresholds (with discussion). J. R. Stat. Soc. B. 52(3), 393-442 (1990).
15. Deheuvels, P., Mason, D., Shorack, G.: Some results on the influence of extremes on the bootstrap. Ann. Inst. Henri Poincaré Probab. Stat. 29(1), 83-103 (1993).
16. Dekkers, A., de Haan, L.: On the estimation of the extreme-value index and large quantile estimation. Ann. Stat. 17(4), 1795-1832 (1989).
17. Dietrich, D., de Haan, L., Hüsler, J.: Testing extreme value conditions. Extremes 5(1), 71-85 (2002).
18. Drees, H., de Haan, L., Li, D.: Approximations to the tail empirical distribution function with application to testing extreme value conditions. J. Stat. Plan. Inference 136(10), 3498-3538 (2006).
19. Embrechts, P., Kluppelberg, C., Mikosch, T.: Modelling Extreme Events for Insurance and Finance. Springer, Berlin (1997).
20. Geluk, J., de Haan, L., Resnick, S., Stǎricǎ, C.: Second-order regular variation, convolution and the central limit theorem. Stoch. Process. Their Appl. 69(2), 139-159 (1997).
21. Giné, E., Zinn, J.: Necessary conditions for the bootstrap of the mean. Ann. Stat. 17(2), 684-691 (1989).
22. Guerin, C., Nyberg, H., Perrin, O., Resnick, S., Rootzén, H., Stǎricǎ, C.: Empirical testing of the infinite source poisson data traffic model. Stoch. Models 19(2), 151-200 (2003).
23. de Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction. Springer, New York (2006).
24. de Haan, L., Peng, L.: Comparison of tail index estimators. Stat. Neerl. 52(1), 60-70 (1998).
25. de Haan, L., Resnick, S.: Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 40(4), 317-337 (1977).
26. de Haan, L., Resnick, S.: Estimating the limit distribution of multivariate extremes. Stoch. Models 9(2), 275-309 (1993).
27. de Haan, L., Resnick, S.: On asymptotic normality of the Hill estimator. Stoch. Models 14(4), 849-867 (1998).
28. Hall, P.: On some simple estimates of an exponent of regular variation. J. R. Stat. Soc. B 44(1), 37-42 (1982).
29. Hall, P.: Asymptotic properties of the bootstrap for heavy-tailed distributions. Ann. Probab. 18(3), 1342-1360 (1990).
30. Heffernan, J., Resnick, S.: Limit laws for random vectors with an extreme component. Ann. Appl. Probab. 17(2), 537-571 (2007). doi: 10. 1214/105051606000000835.
31. Heffernan, J., Tawn, J.: A conditional approach for multivariate extreme values (with discussion). J. R. Stat. Soc. B 66(3), 497-546 (2004).
32. Hill, B.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3(5), 1163-1174 (1975).
33. Hohn, N., Veitch, D., Abry, P.: Cluster processes: a natural language for network traffic. IEEE Trans. Signal Process. 51(8), 2229-2244 (2003).
34. Huang, X.: Statistics of bivariate extreme values. Ph. D. thesis, Tinbergen Institute Research Series 22, Erasmus University Rotterdam, Postbus 1735, 3000DR, Rotterdam, The Netherlands (1992).
35. Hüsler, J., Li, D.: On testing extreme value conditions. Extremes 9(1), 69-86 (2006).
36. Keshav, S.: An Engineering Approach to Computer Networking; ATM Networks, the Internet, and the Telephone Network. Addison-Wesley, Reading (1997).
37. Lehmann, E., Romano, J.: Testing statistical hypotheses, 3rd edn. In: Springer Texts in Statistics. Springer, New York (2005).
38. Leland, W., Taqqu, M., Willinger, W., Wilson, D.: On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Trans. Netw. 2(1), 1-15 (1994). doi: 10. 1109/90. 282603.
39. Mason, D., Turova, T.: Weak convergence of the Hill estimator process. In: Galambos, J., Lechner, J., Simiu, E. (eds.) Extreme Value Theory and Applications, pp. 419-432. Kluwer Academic, Dordrecht (1994).
40. Maulik, K., Resnick, S., Rootzén, H.: Asymptotic independence and a network traffic model. J. Appl. Probab. 39(4), 671-699 (2002).
41. McNeil, A., Frey, R., Embrechts, P.: Quantitative risk management. In: Princeton Series in Finance, Concepts, Techniques and Tools. Princeton University Press, Princeton (2005).
42. Park, C., Shen, H., Marron, J. S., Hernandez-Campos, F., Veitch, D.: Capturing the elusive poissonity in web traffic. In: MASCOTS '06: Proceedings of the 14th IEEE International Symposium on Modeling, Analysis, and Simulation, pp. 189-196. IEEE Computer Society, Washington, DC (2006). doi: 10. 1109/MASCOTS. 2006. 17.
43. Paxson, V., Floyd, S.: Wide-area traffic: the failure of poisson modeling. IEEE/ACM Trans. Netw. 3(3), 226-244 (1995).
44. Peng, L.: Second order condition and extreme value theory. Ph. D. thesis, Tinbergen Institute, Erasmus University, Rotterdam (1998).
45. Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119-131 (1975).
46. Reiss, R. D., Thomas, M.: Statistical Analysis of Extreme Values, 3rd edn. Birkhäuser Verlag, Basel (2007).
47. Resnick, S.: Tail equivalence and its applications. J. Appl. Probab. 8, 136-156 (1971).
48. Resnick, S.: Modeling data networks. In: Finkenstadt, B., Rootzén, H. (eds.) SemStat: Seminaire Europeen de Statistique, Extreme Values in Finance, Telecommunications, and the Environment, pp. 287-372. Chapman-Hall, London (2003).
49. Resnick, S.: Heavy tail phenomena: probabilistic and statistical modeling. In: Springer Series in Operations Research and Financial Engineering. Springer, New York. iSBN: 0-387-24272-4 (2007).
50. Resnick, S.: Extreme Values, Regular Variation and Point Processes. Reprint of the 1987 Original. Springer, New York (2008).
51. Sarvotham, S., Riedi, R., Baraniuk, R.: Network and user driven on-off source model for network traffic. Special issue on Long-range Dependent Traffic. Comput. Networks 48, 335-350 (2005).
52. Willinger, W., Paxson, V.: Where mathematics meets the Internet. Not. Am. Math. Soc. 45(8), 961-970 (1998).
53. Willinger, W., Taqqu, M., Leland, M., Wilson, D.: Self-similarity in high-speed packet traffic: analysis and modelling of ethernet traffic measurements. Stat. Sci. 10, 67-85 (1995).
54. Willinger, W., Paxson, V., Taqqu, M.: Self-similarity and heavy tails: structural modeling of network traffic. In: Adler, R., Feldman, R., Taqqu, M. (eds.) A Practical Guide to Heavy Tails. Statistical Techniques and Applications, pp. 27-53. Birkhäuser Boston, Boston (1998).
55. Willinger, W., Taqqu, M., Sherman, R., Wilson, D.: Self-similarity through high variability: statistical analysis of ethernet lan traffic at the source level. IEEM/ACM Trans. Netw. 5(1), 71-86 (1997).
56. Zhang, Y., Breslau, L., Paxson, V., Shenker, S.: On the characteristics and origins of internet flow rates. In: ACM Sigcom 2002 Conference, Pittsburgh, 19-23 August 2002.