A model of packet traffic using a random wall model

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 9, Issue 7, 1999, Pages 1381-1392

  Mondragón, Raúl J C ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033164272     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/s021812749900095x     Document Type: Article

References (34)

1. Chen, H. M., Mellor, J. & Mars, P. [1996] "Comparisons of simulation algorithms for self-similar traffic models," Proc. 13th IEE UK Teletraffic Symp., Glasgow.
2. Erramilli, A., Pruthi, P. & Willinger, W. [1994a] "Modelling packet traffic with chaotic maps," ISRN KTH/IT/R-94/18-SE, Stockholm-Kista, Sweden.
3. Erramilli, A., Singh, R. P. & Pruthi, P. [1994b] "Chaotic maps as models of packet traffic," ITC 14, 329-338.
4. Erramilli, A., Singh, R. P. & Pruthi, P. [1995] "An application of deterministic chaotic maps to model packet traffic," Queueing Syst. 20, 171-206.
5. Fowler, H. J. & Leland, W. [1991] "Local area network traffic characteristics, with implications for broadband network congestion management," IEEE J. Sel. Areas Commun. 9, 1139-1149.
6. Geisel, T., Nierwetberg, J. & Zacherl, A. [1985] "Accelerated diffusion in Josephson Junctions and relted chaotic systems," Phys. Rev. Lett. 54, 616-619.
7. Gradshteyn, I. S. & Ryzhik, I. M. [1980] Table of Integrals, Series and Products (Academic Press).
8. Hayot, F. [1991], "Lévy walks in lattice-gas hydrodynamics," Phys. Rev. A43, 806-810.
9. Huang, C., Devetsikiotis, M., Lambadaris, I. & Kaye, R. [1995] "Fast simulation for self-similar traffic in ATM networks," IEEE ICC95, Seattle, Washington, pp. 438-444.
10. Huberman, B. M. & Lukose, R. M. [1997] "Social dilemmas and Internet congestion," Science 277, 535-538.
11. Hurst, H. E. [1951] "Long-term storage capacity of reservoirs," Trans. Am. Soc. Civil Engin. 116, 770-799.
12. Hurst, H. E. [1955] "Methods of using long-term storage in reservoirs," Proc. Inst. Civil Engin., Part 1, pp. 519-577.
13. Lau, W., Erramilli, W. A., Wang, J. L. & Willinger, W. [1995] "Self-similar traffic generation: The random midpoint displacement algorithm and its properties," IEEE ICC95, Seattle, Washington, pp. 473-477.
14. Lasota, A. & Yorke, W. A. [1973] "On the existence of invariant measures for piecewise monotonic transformations," Trans. Am. Math. Soc. 186, 481-488.
15. Mandelbrot, B. [1965] "Self-similar error clusters in communication systems and the concept of conditional stationarity," IEEE Trans. Commun. Technol. COM13, 71-90.
16. Mandelbrot, B. & van Ness, J. W. [1968] "Fractional Brownian motions, fractional noises and applications," SIAM Rev. 10(4), 422-437.
17. Mandelbrot, B. & Wallis, J. R., "Computer experiments with fractional Gaussian noise," Water Resources Res. 5(1), 228-267.
18. Manneville, P. [1980] "Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems," J. Physique 41, 1235-1243.
19. McCauley, J. L. [1995] Chaos, Dynamics and Fractals and Algorithmic Approach to Deterministic Chaos (Cambridge University Press).
20. Mondragón, R. J., Samuel, L. G., Arrowsmith, D. K. & Pitts, J. M. [1998] in preparation.
21. Norros, I. [1993] "Studies on a model for connectionless traffic, based on fractional Brownian motion," Conf. Applied Probability in Engineering, Computer and Communication Sciences, Paris, pp. 16-18.
22. Paxson, V. & Floyd, S. [1995] "Wide area traffic: The failure of Poisson modelling," IEEE/ACM Trans. Networking 3(3), 226-244.
23. Pruthi, P. & Erramilli, A. [June 1995] "Heavy-tailed ON/OFF source behaviour and self-similar traffic," Proc. ICC 95, pp. 1-6.
24. Riedi, R. H. & Lévy Véhel, J. [1997] "Multifractal properties of TCP traffic: A numerical study," IEEE Trans. Networking, to appear; http:// www.ece.rice.edu/vried:/publications.html
25. Roughan, M. & Veitch, D. [1997] "A study of the daily variation in the self-similarity of real data traffic," Technical Report 0070, SERC, Software Engineering Research Centre, Level 3, 110 Victoria St, Carlton Vic, 3053, Australia.
26. Samuel, L. G., Pitts, J. M. & Mondragón, R. J. [1997] "Towards the control of communication networks by chaotic maps: Source aggegation," Proc. ITC15, Teletraffic Contributions for the Information Age (Elsevier), pp. 1369-1378.
27. Samuel, L. G., Pitts, J. M., Mondragón, R. J. & Arrowsmith, D. K. [1998] "The maps control paradigm: Using chaotic maps to control telecoms networks," in Broadband Communications, the Future of Telecommunications, eds. Kühn, P. & Ulrich, R. (Chapman Hall), pp. 371-382.
28. Shlesinger, M. F., West, B. J. & Klafter, J. [1987] "Lévy dynamics of enhanced diffusion: Application to turbulence," Phys. Rev. Lett. 58, 1100-1103.
29. Slimane, B. & Le-Ngoc, T. [1995] "A doubly stochastic Poisson model for self-similar traffic," IEEE ICC95, Seattle, Washington, pp. 456-460.
30. Schuster, G. H. [1995] Deterministic Chaos an Introduction, 3rd edition (VCH Verlagsgesellschaft, Weinheim Germany).
31. Solomon, T. H., Weeks, E. R. & Swinney, H. L. [1993] "Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating fluid," Phys. Rev. Lett. 71, 3975-3978.
32. Taqqu, M. S., Willinger, W. & Sherman, R. [1997] "Proof of a fundamental result in self-similar traffic modelling," Comp. Commun. Rev. 27(2), 5-23.
33. Veitch, D. [1992] "Novel models of broadband traffic," 7th Australian Teletraffic Research Seminar, Murray River, Australia.
34. Willinger, W., Taqqu, M. S., Sherman, R. & Wilson, D. V. [1995] "Self similar through high-variability: Statistical analysis of Ethernet LAN traffic at the source level," in ACM/Sigcomm'95. pp. 100-113.