Chaotic maps for traffic modelling and queueing performance analysis

Performance Evaluation

Volumn 43, Issue 4, 2001, Pages 223-240

  Mondragon R J ^a   Arrowsmith, D K ^a   Pitts, J M ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BENCHMARKING; CHAOS THEORY; CONGESTION CONTROL (COMMUNICATION); QUEUEING THEORY; TELECOMMUNICATION TRAFFIC;

CHAOTIC MAPS; SELF-SIMILAR TRAFFIC;

QUEUEING NETWORKS;

EID: 0034817734     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-5316(00)00047-X     Document Type: Article

References (29)

1. H.H. Fowler, W. Leland, Local area network traffic characteristics, with implications for broadband network congestion management, IEEE J. Sel. Areas Commun. 9 (1991) 1139-1149.
2. W.E. Leland, M.S. Taqqu, W. Willinger, D. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Trans. Networking 2 (1) (1994) 1-15.
3. I. Norros, Studies on a model for connectionless traffic, based on fractional Brownian motion, Proceedings of the Conference on Applied Probability in Engineering, Computer and Communication Sciences, Paris, June 1993, pp. 16-18.
4. A. Erramilli, O. Narayan, W. Willinger, Experimental queueing analysis with long-range dependent packet traffic, IEEE/ACM Trans. Networking 4 (2) (1996) 209-223.
5. B.E. Huberman, R.M. Lukose, Social dilemmas and Internet congestion, Science 277 (1997) 535.
6. M. Roughan, D. Veitch, A study of the daily variation in the similarity of real data traffic, Technical Report 0070, SERC, Software Engineering Research Centre, Level 3, 110 Victoria St., Carlton, Vic. 3053, Australia, 1997.
7. B. Mandelbrot, Self-similar error clusters in communication systems and the concept of conditional stationarity, Proceedings of the IEEE Transactions on Communication Technology, March 1965, pp. 71-90.
8. B. Mandelbrot, J.R. Wallis, Computer experiments with fractional Gaussian noise, Water Resour. Res. 5 (1) (1968) 228-267.
9. D. Veitch, Novel models of broadband traffic, Proceedings of the Seventh Australian Teletraffic Research Seminar, Murray River, Australia, 1992.
10. C. Huang, M. Devetsikiotis, I. Lambadaris, R. Kaye, Fast simulation for self-similar traffic in ATM networks, IEEE ICC'95, Seattle, WA, 1995, pp. 438-444.
11. B. Slimane, T. Le-Ngoc, A doubly stochastic Poisson model for self-similar traffic, IEEE ICC'95, Seattle, WA, 1995, pp. 456-460.
12. W. Lau, W.A. Erramilli, J.L. Wang, W. Willinger, Self-similar traffic generation: the random midpoint displacement algorithm and its properties, IEEE ICC'95, Seattle, WA, 1995, pp. 473-477.
13. W. Willinger, M.S. Taqqu, R. Sherman, D.V. Wilson, Self-similar through high-variability: statistical analysis of Ethernet LAN traffic at the source level, in: ACM/SIGCOMM'95, 1995.
14. A. Erramilli, R.P. Singh, P. Pruthi, Chaotic maps as models of packet traffic, in: Proc. ITC 14, The Fundamental Role of Teletraffic in the Evolution of Telecommunication Networks, 1994, pp. 329-338.
15. A. Erramilli, R.P. Singh, P. Pruthi, An application of deterministic chaotic maps to model packet traffic, Queueing Syst. 20 (1995) 171-206.
16. P. Pruthi, A. Erramilli, Heavy-tailed ON/OFF source behaviour and self-similar traffic, Proc. ICC'95, June 1995.
17. O. Narayan, Exact asymptotic queue length distribution for fractional Brownian traffic, Adv. Performance Anal. 1 (1) (1998) 39-63.
18. O.J. Boxma, J.W. Cohen, The M/G/1 queue with heavy-tailed service time distribution, IEEE J. Sel. Areas Commun. 16 (5) (1998) 749-763.
19. L.G. Samuel, J.M. Pitts, R.J. Mondragón, D.K. Arrowsmith, The maps control paradigm: using chaotic maps to control telecom networks, in: P. Kühn, R. Ulrich (Eds.), Broadband Communications, The Future of Telecommunications, Chapman & Hall, London, 1998, pp. 371-382.
20. R.J. Mondragón, A model of packet traffic using a random wall model, Int. J. Bifur. Chaos 9 (7) (1999) 1381-1392.
21. R. Jain, S.A. Routhier, Packet trains: measurements and a new model for computer network traffic, IEEE J. Sel. Areas Commun. 4 (1986) 986-995.
22. W.A. Lasota, A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Am. Math. Soc. 186 (1973) 481.
23. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, London, 1980.
24. W.H. Press, S.A. Teukolky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C, 2nd ed., Cambridge University Press, Cambridge, UK, 1992.
25. A. Erramilli, P. Pruthi, W. Willinger, Modelling packet traffic with chaotic maps, ISRN KTH/IT/R-94/18-SE, Stockholm-Kista, Sweden, 1994.
26. H.G. Schuster, Deterministic Chaos: An Introduction, 3rd ed., VCH, Weinheim, 1995.
27. R.J. Mondragón, Intermittency maps and queues: modelling self-similar traffic and its performance, Preprint, 1999.
28. F. Brichet, J. Roberts, A. Simonian, D. Veitch, Heavy traffic analysis of a storage model with long range dependent ON/OFF sources, Queueing Syst. 23 (1996) 197-215.
29. R.J. Mondragón, D.K. Arrowsmith, On control of coupled map lattices: using local dynamics to predict controllability, Int. J. Bifur. Chaos 7 (2) (1996) 383-399.