Modelling and analysis of LRD in packet networks: Tsallis entropy framework

Studies in Fuzziness and Soft Computing

Volumn 206, Issue , 2006, Pages 162-179

  Karmeshu, ^a   Sharma, Shachi ^b  

^a JAWAHARLAL NEHRU UNIVERSITY   (India)

^b CENTRE FOR DEVELOPMENT OF TELEMATICS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749257007     PISSN: 14349922     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-31757-0_5     Document Type: Article

References (53)

1. V. Lathora, A. Rapisarda and S. Ruffo, Lyapunov instablity and finite size effects in a system with long range forces, Physical review letters 80 (1998), 692-695.
2. C.K.Peng, S.V.Buldyrev, A.L. Goldberger, S. Havlin, F. Sciotino, M. Simons and H.E. Stanley, Long range correlations in nucleotide sequences, Nature 356 (1992), 168-170.
3. G. Malescio, N.V. Dokholyan, S.V. Buldyrev and H.E. Stanley, e-print cond-mat/0005178.
4. C. Beck, G.S.Lewis and H.L. Swinney, Measuring nonextensitivity parameters in a turbulent Couette-Taylor flows, Phys. Rev. E 63, 035303 (2001).
5. Karmeshu and A. Krishnamchari, Sequence variability and long range dependence in DNA: An information theoretic perspective in neural information processing, Lecture Notes in Computer Science 3316 (2004), 1354-1361.
6. A.H.Makse, S. Havlin and H.E. Stanley, Nature (London), 377 (608) (1995).
7. G.K. Zipf, Selective studies and the principle of relative frequency in language, Harvard University Press, Cambridge MA, 1937.
8. A. Robledo, Renormalization group, entropy optimization, and nonextensivity at criticality, Phys Rev. Lett. 83, 2289 (1999).
9. D.B. Walton and J. Rafelski, Equilibrium distribution of heavy quarks in Fokker-Planck dynamics, Phys Rev. Lett. 84 (2000), 31-34.
10. C. Tsallis, J.C. Anjos and E.P. Borges, e-print astro-ph/0203258.
11. H.S. Wio and S. Bouzat, Brazil journal of Physics, 29, 136 (1999).
12. E. Jaynes, Prior probabilities, IEEE Transactions on System Science Cybernetics SSC-4 (1968), 227-241.
13. C.E. Shannon, A mathematical theory of communication, Bell system technical journal 27 (1948), 379-423.
14. M. Gell-Mann and C. Tsallis, Nonextensive Entropy Interdisciplinary Applications-Preface, Oxford university press, 2004.
15. C. Tsallis, Possible generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics, 52 (12) (1988), 479-487.
16. E.W. Montroll and M.F. Shlesinger, On the wonderful world of random walks, Nonequilibrium phenomena II from stochastics to hydrodynamics, ed. J.L. Lebowitz and E.W. Montroll, North-Holland physics publishing, 1984.
17. V. Latora, M. Baranger, A. Rapisarda and C. Tsallis, The rate of entropy increase at the edge of chaos. Phys. Letters A 273 (90), (2000).
18. S. Abe and A.K. Rajagopal, Rates of convergence of non-extensive statistical distributions to Levy distributions in full and half-spaces. Journal of physics A 33 (48) (2000), 8723-8732.
19. S. Abe and N. Suzuki, J. Geophys Res. 108(B2) (2003) 2113.
20. S. Abe and N. Suzuki, Itineration of the internet over non equilibrium stationary states in Tsallis Statistics. Physical review E 67 (016106), (2003).
21. A. Erramilli, O. Narayan, W. Willinger, Experimental queueing analysis with LRD packet traffic, IEEE/ACM Transactions on Networking 4 (2) (1996), 209-223.
22. W. Leland, M.S. Taqqu, W. Willinger and D.V. Wilson, On the self-similar nature of Ethernet traffic, IEEE/ACM Transactions on Networking 2 (1) (1994), 1-15.
23. Mark E. Crovella and Azer Bestavros, Self-similarity in world wide web traffic: Evidence and possible causes, IEEE/ACM Transactions on Networking 5 (6) (1997), 835-846.
24. D. Duffy, A. McIntosh, M. Rosenstein, W. Willinger, Statistical analysis of CCSN/SS7 traffic data from working CCS subnetworks, IEEE journal on selected areas in communication 12 (3) (1994), 544-551.
25. William Stallings, High speed networks and internets: Performance and quality of service, Second Edition, Pearson, 2002.
26. Paxon and Floyd, Wide area traffic: The failure of Poisson modelling, IEEE/ACM Transactions on Networking 3 (3) (1995), 226-244.
27. S. Abe, Tsallis entropy: How unique?, preprint (2001).
28. C. Beck and F. Schlogl, Thermodynamics of chotic systems - an introduction, Cambridge University Press, 1993.
29. S. Abe, A note on the q-deformation theoretic aspect of the genealized entropies in non-extensive physics, Phys Letters A 224 (1997) 326.
30. F. Jackson, Mess. Math., 38 (1909) 57.
31. F. Jackson, Quart. J. Pure Appl. Math, 41 (1910) 1993.
32. J.N.Kapur and H.K.Kesavan, Entropy optimization principles with application, Academic Press Inc, London, 1992.
33. Shachi Sharma, Krishanmachari and Karmeshu, Validity of Jaynes' entropy concentration theorem: Tsallis and other generalized entropy measures, preprint (2005 a).
34. S. Martin, G. Morison, W. Nailon and T. Durrani, Fast and accurate image registration using Tsallis entropy and simultaneous perturbation stochastic approximation, Electonics Letters, 40 (10) (2004).
35. J. Havrda and F. Charvat, Quantification method of classification processes: Concept of structural α-entropy, Kybernetika 3 (1967), 30-35.
36. C. Tsallis, Non-extensive statistical mechanics: Construction and physical interpretation, in Nonextensive Entropy Interdisciplinary Applications ed. M. Gellmann and C. Tsallis, Oxford university press, 2004, 1-52.
37. A. Renyi, On measures of entropy and information, Proceedings Fourth Berkeley Symp. Math. Statist and Prob., University of California Press 1 (1961), 547-561.
38. A.M. Mathai and P.N. Rathie, Basic concepts in information theory and statistics, Johan Wiley and sons, 1975.
39. S. Abe, Stability of Tsallis entropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions, physical review E 66 (046134) (2002).
40. A.I. Khinchin, Mathematical foundations of information theory, Dover publications, 1957.
41. D.K. Fadeev, On the concept of entropy of a finite probabilistic scheme (Russian), Uspeki Mat. Nauk 11 (1956), 227-231.
42. Hiroki Suyari, Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy, IEEE transactions on information theory, 50 (8) (2004), 1783-1787.
43. Karmeshu and N.R. Pal, Uncertainty, entropy and maximum entropy principle - an overview, in Entropy measures, maximum entropy principle and emerging applications, ed. Karmeshu, Springer-Verlag, 2003.
44. B. Forte and C.T. Ng, On a characterization of the entropies of degree β, Utilitas Mathematica 4 (1973), 193-205.
45. Karmeshu and Shachi Sharma, Queue length distribution of network packet traffic: Tsallis entropy maximization with fractional moments, IEEE communication letters, 10 (2006), 34-36.
46. Karmeshu and Shachi Sharma, Long tail behavior of queue lengths in broadband networks: Tsallis entropy framework, preprint (2005 b).
47. T.M. Apostol, Introduction to analytic number theory, Springer-verlag, Newyork, 1976.
48. B. Mandelbrot, The fractal geometry of nature, Freeman, San Francisco, 1983.
49. S. Abe and A.K. Rajgopal, Micro canonical foundation for systems with power-law distributions. Journal of physics A 33 (48), 8733-8738 (2000).
50. S. Abe and G.B. Bagci, Necessity of q-expectation value in nonextensive statistical mechanics. Physical review E 71 (016139), (2005).
51. Shachi Sharma and Karmeshu, Asymptotic power law characteristics in queueing systems-using maximum Tsallis entropy principle, preprint (2005 c).
52. J.Y. Hui and E. Karasan, A thermodynamic theory of broadband networks with application to dynamic routing, IEEE journal of selected areas in communications 13 (6) (1995), 991-1003.
53. V.E.Benes, Mathematical theory of connecting networks and telephone traffic, NewYork, Academic, 1965.