Use of alpha-stable self-similar stochastic processes for modeling traffic in broadband networks

Abstract In this article, we propose a new model for aggregate network traffic. This model, besides reflecting self-similarity and long-range dependence, is able to capture the appropriate level of burstiness of different types of traffic by selecting the proper parameters. Different types of self-similar traffic traces (LAN/WAN, WWW, VBR video) are analysed by estimating their self-similarity coefficient H, as well as the parameters of their marginal distributions. When comparing the real traces with our artificial traces, the agreement, which was evaluated both qualitatively (visually) and quantitatively (by means of the marginal CDF and the periodogram), is better than that achieved with previously proposed models. By analysing different types of traffic traces, the model is shown to be flexible enough to be applied to a variety of communications scenarios. A queue with our proposed traffic as input is analysed. A proof of convergence of aggregate traffic to α-stable processes is also included, as well as the conditions under which the Gaussian assumption is appropriate.

[1]  S. McLaughlin,et al.  Testing the Gaussian assumption for self-similar teletraffic models , 1997, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics.

[2]  P. Glynn,et al.  Logarithmic asymptotics for steady-state tail probabilities in a single-server queue , 1994, Journal of Applied Probability.

[3]  Walter Willinger,et al.  Long-range dependence in variable-bit-rate video traffic , 1995, IEEE Trans. Commun..

[4]  Takis Konstantopoulos,et al.  Macroscopic models for long-range dependent network traffic , 1998, Queueing Syst. Theory Appl..

[5]  Patrice Abry,et al.  Wavelet Analysis of Long-Range-Dependent Traffic , 1998, IEEE Trans. Inf. Theory.

[6]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[7]  D. Hatzinakos,et al.  A non-Gaussian self-similar process for broadband heavy traffic modeling , 1998, IEEE GLOBECOM 1998 (Cat. NO. 98CH36250).

[8]  Walter Willinger,et al.  Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level , 1997, TNET.

[9]  Nick Duffield,et al.  Large deviations and overflow probabilities for the general single-server queue, with applications , 1995 .

[10]  Stephen M. Kogon,et al.  Signal modeling with self-similar α-stable processes: the fractional Levy stable motion model , 1996, IEEE Trans. Signal Process..

[11]  Boaz Porat,et al.  A course in digital signal processing , 1996 .

[12]  Oliver Rose,et al.  Statistical properties of MPEG video traffic and their impact on traffic modeling in ATM systems , 1995, Proceedings of 20th Conference on Local Computer Networks.

[13]  Nicolas D. Georganas,et al.  On self-similar traffic in ATM queues: definitions, overflow probability bound, and cell delay distribution , 1997, TNET.

[14]  E. Fama,et al.  Parameter Estimates for Symmetric Stable Distributions , 1971 .

[15]  D.B. Williams,et al.  On the characterization of impulsive noise with /spl alpha/-stable distributions using Fourier techniques , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[16]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[17]  Arif Ghafoor,et al.  Dynamic Resource Allocation for Multimedia Services in Mobile Communication Environments , 1995, IEEE J. Sel. Areas Commun..

[18]  Richard G. Baraniuk,et al.  A Multifractal Wavelet Model with Application to Network Traffic , 1999, IEEE Trans. Inf. Theory.

[19]  Steve McLaughlin,et al.  The effective bandwidth of stable distributions , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[20]  Ioannis A. Koutrouvelis,et al.  Regression-Type Estimation of the Parameters of Stable Laws , 1980 .

[21]  Frank Kelly,et al.  Notes on effective bandwidths , 1994 .

[22]  Cheng-Shang Chang,et al.  Stability, queue length, and delay of deterministic and stochastic queueing networks , 1994, IEEE Trans. Autom. Control..

[23]  Benoit B. Mandelbrot,et al.  Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity , 1965 .

[24]  Henry J. Fowler,et al.  Local Area Network Traffic Characteristics, with Implications for Broadband Network Congestion Management , 1991, IEEE J. Sel. Areas Commun..

[25]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[26]  Daniel P. Heyman,et al.  Performance implications of very large service-time variances , 1998, Other Conferences.

[27]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[28]  I. A. Koutrouvelis.  An iterative procedure for the estimation of the parameters of stable laws , 1981 .

[29]  Gunnar Karlsson,et al.  Performance models of statistical multiplexing in packet video communications , 1988, IEEE Trans. Commun..

[30]  Chen-Shang Chang,et al.  Effective Bandwith in High-Speed Digital Networks , 1995, IEEE J. Sel. Areas Commun..

[31]  Ilkka Norros,et al.  On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995, IEEE J. Sel. Areas Commun..

[32]  Sally Floyd,et al.  Wide area traffic: the failure of Poisson modeling , 1995, TNET.

[33]  A. S. Paulson,et al.  Some properties of modified integrated squared error estimators for the stable laws , 1984 .

[34]  Patrice Abry,et al.  Wavelet based estimator for the self-similarity parameter of /spl alpha/-stable processes , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[35]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.

[36]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1997, TNET.

[37]  Patrice Abry,et al.  Wavelet based estimator for the self-similarity parameter of α-stable processes. , 1999 .

[38]  S. McLaughlin,et al.  The estimation of stable distribution parameters , 1997, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics.

[39]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.