EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 21 (2017) ESAIM: PS, 21 (2017) 369-393 References
Free Access
Issue
ESAIM: PS
Volume 21, 2017
Page(s) 369 - 393
DOI https://doi.org/10.1051/ps/2017018
Published online 12 December 2017
  1. P. Abry, R. Baraniuk, P. Flandrin, R. Riedi and D. Veitch, Multiscale nature of network traffic. IEEE Signal Proc. Magazine 3 (2002) 28–46. [CrossRef] [Google Scholar]
  2. P. Abry, P. Borgnat, F. Ricciato, A. Scherrer and D. Veitch, Revisiting an old friend: on the observability of the relation between long range dependence and heavy tail. Telecommun. Syst. 43 (2010) 147–165. [Google Scholar]
  3. N. Antunes and V. Pipiras, Estimation of Flow Distributions from Sampled Traffic. ACM Trans. Model. Perform. Eval. Comput. Syst. 1 (2016) 11:1–11:28. [CrossRef] [Google Scholar]
  4. M.S. Bartlett, The spectral analysis of point processes. J. Roy. Stat. Soc. Series B. Methodological 25 (1963) 264–296. [Google Scholar]
  5. P. Carruthers, E.M. Friedlander, C.C. Shih and R.M. Weiner, Multiplicity fluctuations in finite rapidity windows. Intermittency or quantum statistical correlation? Phys. Lett. B 222 (1989) 487–492. [Google Scholar]
  6. D.R. Cox and V. Isham, Point Processes. Monographs on Applied Probability and Statistics. Chapman and Hall, London-New York (1980) [Google Scholar]
  7. D.J. Daley and D. Vere–Jones, An Introduction to the Theory of Point Processes. Elementary Theory and Methods. Vol. I, Probability and its Applications (New York), 2nd edn. Springer-Verlag, New York (2003). [Google Scholar]
  8. E.A. De Wolf, I.M. Dremin and W. Kittel, Scaling laws for density correlations and fluctuations in multiparticle dynamics. Phys. Rep. 270 (1996) 1–141. [Google Scholar]
  9. C. Dombry and I. Kaj, Moment measures of heavy-tailed renewal point processes: asymptotics and applications. ESAIM. PS 17 (2013) 567–591. [CrossRef] [EDP Sciences] [Google Scholar]
  10. V. Fasen and G. Samorodnitsky, A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime. Adv. Appl. Prob. 41 (2009) 393–427. [CrossRef] [Google Scholar]
  11. G. Faÿ, B. González–Arévalo, T. Mikosch and G. Samorodnitsky, Modeling teletraffic arrivals by a Poisson cluster process. Queueing Syst. 54 (2006) 121–140. [Google Scholar]
  12. R. Gaigalas and I. Kaj, Convergence of scaled renewal processes and a packet arrival model. Bernoulli 9 (2003) 671–703. [CrossRef] [MathSciNet] [Google Scholar]
  13. B. González-Arévalo and J. Roy, Simulating a Poisson cluster process for Internet traffic packet arrivals. Comput. Commun. 33 (2010) 612–618. [Google Scholar]
  14. F. Grüneis, M. Nakao and M. Yamamoto, Counting statistics of 1/f fluctuations in neuronal spike trains. Biol. Cybernet. 62 (1990) 407–413. [CrossRef] [Google Scholar]
  15. F. Grüneis, M. Nakao, M. Yamamoto, T. Musha and H. Nakahama, An interpretation of 1/f fluctuations in neuronal spike trains during dream sleep. Biol. Cybernet. 60 (1989) 161–169. [Google Scholar]
  16. C.A. Guerin, H. Nyberg, O. Perrin, S. Resnick, H. Rootzén and C. Stărică, Empirical testing of the infinite source Poisson data traffic model. Stoch. Models 19 (2003) 56–199. [CrossRef] [Google Scholar]
  17. A. Gut, Stopped Random Walks, Springer Series in Operations Research and Financial Engineering, 2nd edn. Springer, New York. Limit theorems and applications (2009) [Google Scholar]
  18. N. Hohn, D. Veitch and P. Abry, Cluster processes: a natural language for network traffic. IEEE Trans. Signal Process. 51 (2003) 2229–2244. [Google Scholar]
  19. I. Kaj, Stochastic Modeling in Broadband Communications Systems, SIAM Monographs on Mathematical Modeling and Comput.. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. (2002) [Google Scholar]
  20. A.F. Karr, Point Processes and their Statistical Inference. Vol. 7 of Probability: Pure and Applied, 2nd edn. Marcel Dekker, Inc., New York (1991). [Google Scholar]
  21. P.M. Krishna, V. Gadre and U.B. Desai, Multifractal Based Network Traffic Modeling. Springer Science and Business Media (2012). [Google Scholar]
  22. W.E. Leland, M.S. Taqqu, W. Willinger and D.V. Wilson, On the self-similar nature of Ethernet traffic (Extended version). IEEE/ACM Trans. Netw. 2 (1994) 1–15. [CrossRef] [Google Scholar]
  23. A.W.P. Lewis, A branching Poisson process model for the analysis of computer failure patterns (with discussion). J. Roy. Stat. Soc. Series B. Methodological 26 (1964) 398–456. [Google Scholar]
  24. S.B. Lowen and M.C. Teich, Fractal-Based Point Processes. Wiley Series in Probability and Statistics. Wiley-Interscience [John Wiley and Sons], Hoboken, NJ (2005) [Google Scholar]
  25. B. Mandelbrot, A case against the lognormal distribution. Fractals and Scaling in Finance’, Springer New York (1997) 252–269. [Google Scholar]
  26. T. Mikosch, S. Resnick, H. Rootzén and A. Stegeman, Is network traffic approximated by stable Lévy motion or fractional Brownian motion?. Ann. Appl. Prob. 12 (2002) 23–68. [CrossRef] [MathSciNet] [Google Scholar]
  27. T. Mikosch and G. Samorodnitsky, Scaling limits for cumulative input processes. Math. Oper. Res. 32 (2007) 890–918. [CrossRef] [Google Scholar]
  28. C. Onof, R.E. Chandler, A. Kakou, P. Northrop, H.S. Wheater and V. Isham, Rainfall modelling using Poisson-cluster processes: a review of developments. Stoch. Environ. Res. Risk Assess. 14 (2000) 384–411. [Google Scholar]
  29. G. Peccati and M.S. Taqqu, Wiener Chaos: Moments, Cumulants and Diagrams of Bocconi. Vol. 1 Springer Series, Springer (2011) [Google Scholar]
  30. V.J. Ribeiro, Z.-L. Zhang, S. Moon and C. Diot, Small-time scaling behavior of Internet backbone traffic. Comput. Netw. 48 (2005) 315–334. [CrossRef] [Google Scholar]
  31. E.A.B. Saleh, and M.C. Teich, Multiplied-Poisson noise in pulse, particle, and photon detection. Proc. IEEE 70 (1982) 229–245. [CrossRef] [Google Scholar]
  32. D. Veitch, N. Hohn and P. Abry, Multifractality in TCP/IP traffic: the case against. Comput. Netw. 48 (2005) 293–313. [CrossRef] [Google Scholar]
  33. H. Wendt, P. Abry and S. Jaffard, Bootstrap for empirical multifractal analysis. IEEE Signal Process. Magazine 24 (2007) 38–48. [CrossRef] [Google Scholar]
  34. M. Westcott, Results in the asymptotic and equilibrium theory of Poisson cluster processes. J. Appl. Probl. 10 (1973) 807–823. [CrossRef] [Google Scholar]
  35. R. Willink, Relationships between central moments and cumulants, with formulae for the central moments of gamma distributions. Commun. Statist. Theory Methods 32 (2003) 701–704. [CrossRef] [Google Scholar]
  36. P. Zeephongsekul, G. Xia and S. Kumar, Software reliability growth models based on cluster point processes. Int. J. Sys. Sci. 25 (1994) 737–751. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.