Phase space analaysis of frames traffic intensity in an Ethernet network

Arkadiusz Biernacki

Abstract


In this paper, a phase space of time series, which was constructed from measurement of frames traffic intensity in a ten-gigabyte Ethernet network, was reconstructed. For this purpose elements of dynamic systems theory were used. An embedding delay and embedding dimension for time series were estimated. In the reconstructed phase space attractors were found. Using Principle Component Analysis, dimension of the attractors was reduced and the attractors were drawn in a two-dimensional coordinate system.

Keywords


network traffic intensity modelling; dynamic system; attractor

Full Text:

PDF (Polski)

References


Abry P., Baraniuk R., Flandrin P., Riedi R., Veitch D.: Multiscale Nature of Network Traffic, Signal Processing Magazine, 2002.

Cao L.: Practical method for determining the minimum embedding dimension of a scalar time series, Physica D, 1997, pp. 43–50.

Casdagli M., Eubank S., Farmer J. D., Gibson J.: State space reconstruction in the pres-ence of noise, Physica D, No 51, 1991, pp. 52-98.

Dua A.: Modeling of Network Traffic. Technical Report. http://www.stanford.edu/~ dua/files/network_model.html

Endance Measurement Systems. http://www.endace.com.

Erramilli A., Broughan, M. Veitch D., Willinger W.: Selfsimilar traffic and network dy-namics, Proceedings of the IEEE, 2002.

Fekete A., Marodi M., Vattay G.: On the Prospects of Chaos Aware Traffic Modeling, ArXiv Condensed Matter e-prints, 2002.

Hegger R., Kantz H.: Practical implementation of nonlinear time series methods. The TISEAN software package, http://www.mpiipks-dresden.mpg.de/~tisean. Online docu-mentation, 1998.

Karagiannis T., Molle M., Faloutsos M, Broido A.: A Nonstationary Poisson View of Internet Traffic. IEEE INFOCOM, 2004.

Kennel M. B., Brown R., Abarbanel H.: Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A 45, 3403, 1992.

Leland W. E., Taqqu M. S., Willinger W., Wilson D. V.: On the Self- Similar Nature of Ethernet Traffic. ACM SIGComm, San Francisco, CA, USA, 1993.

National Laboratory For Applied Networking Research. Nlanr network analysis infrastructure. http://moat.nlanr.net. NLANR PMA and AMP datasets are provided by the National Laboratory for Applied Networking Research under NSF Cooperative Agreement ANI-9807579.

Pruthi P.: An Application of Chaotic Maps to Packet Traffic Modeling. Ph.D. Disserta-tion, Royal Institute of Technology, Stockholm 1995.

Rosenstein M. T., Collins J. J., DeLuca C. J.: Reconstruction expansion as a geometry-based framework for choosing proper delay times, Physica D, No 73, pp. 82-98.

Takens F.: Detecting Strange Attractors in Turbulence. Lecture Notes in Math., Vol. 898, Springer, 1981.

The Internet traffic archive, http://www.acm.org/sigcomm/ITA/, sponsored by ACM SIGCOMM.

The nonlinear time series analysis tool package TSTOOL and its documents, http://www.physik3.gwdg.de/tstool/index.html, 2001.

Veres A., Boda M.: The chaotic nature of TCP congestion control, Proc. IEEE INFOCOM 2000, pp. 1715–1723.

Zhang W. a.o: Chaotic Network Attractor in Packet Traffic Series. Comput. Phys. Com-mun, Vol. 161, No 3, 2004, pp.129-142




DOI: http://dx.doi.org/10.21936/si2005_v26.n3.584