Dealing with fractional dynamics of ip network delays

International Journal of Bifurcation and Chaos

Volumn 22, Issue 4, 2012, Pages

  Tejado, Inés ^a   Hosseinnia, S Hassan ^a   Vinagre, Blas M ^a   Song, Xiaona ^b   Chen, Yangquan ^c  

^a UNIVERSITY OF EXTREMADURA   (Spain)

^b HENAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c UTAH STATE UNIVERSITY   (United States)

Author keywords

Delay dynamics; fractional calculus; model; networked control systems

Indexed keywords

CALCULATIONS; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEMS; DYNAMICS; MODELS; TRANSPORTATION;

DELAY DYNAMICS; FRACTIONAL CALCULUS; FRACTIONAL DYNAMICS; FRACTIONAL ORDER MODELS; IMPORTANT FEATURES; NETWORK TRAFFIC MODELS; ROBUST CONTROLLERS; TRAFFIC CHARACTERISTICS;

NETWORKED CONTROL SYSTEMS;

EID: 84861203933     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127412500897     Document Type: Article

References (51)

1. Abry, P. &Veitch, D. [1998] "Wavelet analysis of longrange- dependent traffic," IEEE Trans. Inf. Th. 44, 2-15
2. Aguirre, C., Campos, D., Pascual, P. &V́azques, L. [2006] "Computer simulations for a fractional calculus derived internet traffic model," Proc. 5th Int. Conf. Eng. Comput. Technol.
3. Bierḿe, H. &Scheffler, H. [2008] "Fourier series approximation of linear fractional stable motion," J. Fourier Anal. Appl. 14, 180-202
4. Bogdan, P. &Marculescu, R. [2009] "Statistical physics approaches for network-on-chip traffic characterization," Proc. 7th IEEE/ACM Int. Conf. Hardware/ Software Codesign and Syst. Synthesis, pp. 461-470
5. Chen, Y., Sun, R., Zhou, A. &Zaveri, N. [2008] "Fractional order signal processing of electrochemical noises," J. Vib. Contr. 14, 1443-1456
6. Chen, Y. Q. [2010] "Fractional calculus, delay dynamics and networked control systems," Proc. 3rd Int. Symp. Resilient Contr. Syst. (ISRCS'10), pp. 58-63
7. Cheng, Y., Zhuang, W. &Ling, X. [2007a] "FBM model based network-wide performance analysis with service differentiation," Proc. 4th Int. Conf. Heterogeneous Networking for Quality, Reliability, Security and Robustness and Workshops (QSHINE'07), pp. 1-7
8. Cheng, Y., Zhuang, W. &Ling, X. [2007b] "Towards an FBM model based network calculus framework with service differentiation," Mobile Netw. Appl. 12, 335-346
9. da Silva, J. L. &Erraoui, M. [2011] "The ?-dependence of stochastic differential equations driven by variants of ?-stable processes," Tech. Rep., University of Madeira, Portugal
10. Dobrushin, R. [1979] "Gaussian and their subordinated self-similar random generalized fields," Ann. Probab. 7, 1-28
11. Filatova, D. [2008] "Mixed fractional Brownian motion: Some related questions for computer network traffic modeling," Proc. 2008 Int. Conf. Signals and Electronic Syst. (ICSES'08), pp. 393-396
12. Gorenflo, R. &Mainardi, F. [1998] "Fractional calculus and stable probability distributions," Arch. Mech. 50, 377-388
13. Gubner, J. [2006] Probability and Random Processes for Electrical and Computer Engineers (Cambridge University Press)
14. Karasaridis, A. &Hatzinakos, D. [1997] "On the modeling of network traffic and fast simulation of rare events using alpha-stable self-similar processes," Proc. IEEE Signal Process. Workshop Higher-Order Statistics, pp. 268-272
15. Laskin, N., Lambadaris, I., Harmantzis, F. &Devetsikiotis, M. [2002] "Fractional Ĺevy motion and its application to network traffic modeling," Comput. Netw. 40, 363-375
16. Li, M. &Chi, C.-H. [2003] "A correlation-based computational model for synthesizing long-range dependent data," J. Franklin Instit. 340, 503-514
17. Li, M. [2008] "Detection of variations of local irregularity of traffic under DDOS flood attack," Math. Probl. Eng. 2008, 11
18. Li, M. [2010] "Fractal time series - A tutorial review," Math. Probl. Eng. 2010, 26.
19. Li, M., Zhao,W. &Chen, S. [2010] "FGN based telecommunication traffic models," WSEAS Trans. Comput. 9, 706-715
20. Li, Y., Sheng, H. &Chen, Y. Q. [2011] "On distributed order integrator/differentiator," Sign. Process. 91, 1079-1084
21. Lorenzo, C. F. &Hartley, T. T. [2002] "Variable order and distributed order fractional operators," Nonlin. Dyn. 29, 57-98
22. Mainardi, F., Parasidi, P. &Gorenflo, R. [1999] "Probability distributions generated by fractional diffusion equations," Tech. Rep., Universtiy of Bologna and Free University of Berlin
23. Mayor, G. &Silvester, J. [2002] "Performance modeling and network management for self-similar traffic," Performance Evaluation and Applications of ATM Networks (Springer, US), pp. 355-386
24. Mukhopadhyay, S., Han, Y. &Chen, Y. [2009] "Fractional order networked control systems and random delay dynamics: A hardware-in-the-loop simulation study," Proc. 2009 American Control Conf. (ACC'09), pp. 1418-1423
25. Munoz-Rodŕ?guez, D., Villarreal Reyes, S., Vargas Rosales, C., Angulo Bernal, M., Torres-Roḿan, D. &Rizo Doḿ?nguez, L. [2006] "Heavy tailed network delay: An alpha-stable," Computacíon y Sistemas 10, 16-27
26. Nolan, J. [2005] "Stable.exe program," http://academic2. american.edu/jpnolan/stable/stable.html.
27. Nolan, J. [2011] Stable Distributions - Models for Heavy Tailed Data (Birkḧauser, Boston), in progress, Chapter 1, http://academic2.american. edu/jpnolan/ stable/chap1.pdf
28. Oliveira, M. J., Silva, J. L. &Streit, L. [2011] "Intersection local times of independent fractional Brownian motions as generalized white noise functionals," Acta Appl. Math. 113, 17-39
29. Ortigueira, M. [2008] "An introduction to the fractional continuous-time linear systems: The 21st century systems," IEEE Circuits Syst. Mag. 8, 19-26
30. Pipiras, V. &Taquu, M. [2003] "Fractional calculus and its connections to fractional Brownian motion," Theory and Applications of Long-range Dependence (Birkḧauser), pp. 165-201
31. Qin, W., Wang, Q. &Sivasubramiam, A. [2009] "An ?- stable model-based linear-parameter-varying control for managing server performance under self-similar workloads," IEEE Trans. Contr. Syst. Technol. 17, 123-134
32. Ribeiro, V., Riedi, M., Crouse, R. H. &Baraniuk, R. [1999] "Multiscale modeling and queuing analysis of long-range-dependent network traffic," Tech. Rep., Rice University, USA.
33. Rizk, A. &Fidler, M. [2010a] "Sample path bounds for long memory FBM traffic," Proc. IEEE Int. Conf. Comput. Commun. (INFOCOM'10), pp. 1-5
34. Rizk, A. &Fidler, M. [2010b] "Statistical end-to-end performance bounds for networks under long memory FBM cross traffic," Proc. 18th Int. Workshop Quality of Service (IWQoS'10), pp. 1-9
35. Samorodnitsky, G. &Taqqu, M. [1994] Stable Non- Gaussian Random Processes (Chapman and Hall)
36. Samorodnitsky, G. [2007] Long Range Dependence (Now Publishers Inc.)
37. Scherrer, A., Larrieu, N., Owezarski, P., Borgnat, P. &Abry, P. [2007] "Non-gaussian and long memory statistical characterizations for Internet traffic with anomalies," IEEE Trans. Depend. Secur. Comput. 4, 56-70
38. Sheludin, O., Smolskiy, S. &Osin, A. [2007] Self-Similar Processes in Telecommunications (John Wile &Sons, Ltd.)
39. Sheng, H., Sun, H., Chen, Y. &Qiu, T. [2011] "Synthesis of multifractional Gaussian noises based on variableorder fractional operators," Sign. Process. 91, 1645-1650
40. Song, X., Tejado, I. &Chen, Y. [2010] "Remote stabilization for fractional-order systems via communication networks," Proc. 2010 Amer. Contr. Conf. (ACC'10), pp. 6698-6703
41. Stoev, S. &Taqqu, M. [2004] "Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform," Fractals 12, 95-121
42. Tafti, P., Van De Ville, D. &Unser, M. [2009] "Invariances, laplacian-like wavelet bases, and the whitening of fractal processes," IEEE Trans. Imag. Process. 18, 689-702
43. Tian, Y.-C. &Levy, D. [2008] "Dealing with network complexity in real-time networked control," Int. J. Comput. Math. 85, 1235-1253
44. Voit, J. [2003] The Statistical Mechanics of Financial Markets, Texts and Monographs in Physics (Springer- Verlag)
45. Wu, W. B., Michailidis, G. &Zhang, D. [2004] "Simulating sample paths of linear fractional stable motion," IEEE Trans. Inf. Th. 50, 1086-1096
46. Xiaohu, G., Guangxi, Z. &Yaoting, Z. [2003] "A new model for network traffic based on alpha-stable selfsimilar processes," Proc. 11th IEEE Int. Conf. Netw. (ICON'03), pp. 1-5
47. Xiaohu, G., Guangxi, Z. &Yaoting, Z. [2004] "On the testing for alpha-stable distributions of network traffic," Comput. Commun. 27, 447-457
48. Yin, J. &Petropulu, A. [1998] "On the relationship between 1/f and alpha-stable processes," Proc. IEEE Int. Symp. Inf. Theory, pp. 302-305
49. Zaborovsky, V. &Meylanov, R. [2001] "Informational network traffic model based on fractional calculus," Proc. 2001 Int. Conf. Info-Tech and Info-Net (ICII'01), pp. 58-63
50. Zaborovsky, V. [2003] "Multiscale network processes: Fractal and p-adic analysis," Proc. 10th Int. Conf. Telecommun. (ICT'03), pp. 1065-1070
51. Zhang, B. &Sun, Y. [2006] "Fractional alpha stable network traffic model and its application in QoS routing," J. Netw. Comput. Appl. 29, 1-10.