The Community for Technology Leaders
RSS Icon
Issue No.09 - September (2010 vol.21)
pp: 1368-1372
Ming Li , East China Normal University, Shanghai
Wei Zhao , University of Macau, Macau
This paper presents a theoretical representation of a stochastic traffic bound (\sigma^\prime ,\rho^\prime ) that consists of two items, the burstiness bound \sigma^\prime and the bound of long-term average rate \rho^\prime. The novelty of the suggested representation is that the burstiness bound and the bound of long-term average rate are separately connected to the fractal dimension D that is the measure of the local self-similarity together with the small-scale factor r and the Hurst parameter H that is the measure of the long-range dependence (LRD) together with the large-scale factor a of traffic. More precisely, we obtain \sigma^\prime = r^{2D - 5} \sigma and \rho^\prime = a^{ - H} \rho , where \sigma is the conventional bound of burstiness and \rho the conventional bound of long-term average rate, respectively. Thus, the present bound (\sigma^\prime ,\rho^\prime ) takes the conventional bound, say (\sigma ,\rho ), as a special case when r = 1 and a = 1. Hence, the proposed representation provides us with a flexible way to tighten a traffic bound. Since we study the stochastically bounded modeling of traffic by taking into account the parameters in stochastic modeling, namely, D, H, r, and a, as well as the parameters in the deterministic modeling of traffic, i.e., \sigma and \rho , a new outlook regarding the stochastically bounded modeling of traffic is revealed. In addition, we open a problem to estimate r and a with respect to the possible applications of the proposed bound to the practice.
Traffic modeling, traffic bound, burstiness, long-term average rate, local self-similarity, long-range dependence.
Ming Li, Wei Zhao, "Representation of a Stochastic Traffic Bound", IEEE Transactions on Parallel & Distributed Systems, vol.21, no. 9, pp. 1368-1372, September 2010, doi:10.1109/TPDS.2009.162
[1] H. Michiel and K. Laevens, "Teletraffic Engineering in a Broad-Band Era," Proc. IEEE, vol. 85, no. 12, pp. 800-819, Dec. 1997.
[2] P. Borgnat, G. Dewaele, K. Fukuda, P. Abry, and K. Cho, "Seven Years and One Day: Sketching the Evolution of Internet Traffic," Proc. IEEE INFOCOM, pp. 711-719, May 2009.
[3] M. Li and S.C. Lim, "Modeling Network Traffic Using Generalized Cauchy Process," Physica A, vol. 387, no. 11, pp. 2584-2594, 2008.
[4] J. Beran, R. Shernan, M.S. Taqqu, and W. Willinger, "Long-Range Dependence in Variable Bit-Rate Video Traffic," IEEE Trans. Comm., vol. 43, nos. 2-4, pp. 1566-1579, Feb.-Apr. 1995.
[5] S. Uhlig, "On the Complexity of Internet Traffic Dynamics on the Topology," Telecomm. Systems, vol. 43, nos. 3-4, pp. 167-180, 2010.
[6] S. Song, J.K. Ng, and B. Tang, "Some Results on the Self-Similarity Property in Communication Networks," IEEE Trans. Comm., vol. 52, no. 10, pp. 1636-1642, Oct. 2004.
[7] C. Li and E. Knightly, "Schedulability Criterion and Performance Analysis of Coordinated Multihop Schedulers," IEEE/ACM Trans. Networking, vol. 13, no. 2, pp. 276-287, Apr. 2005.
[8] C. Li, A. Burchard, and J. Liebeherr, "A Network Calculus with Effective Bandwidth," IEEE/ACM Trans. Networking, vol. 15, no. 6, pp. 1442-1452, Dec. 2007.
[9] S. Wang, D. Xuan, R. Bettati, and W. Zhao, "Providing Absolute Differentiated Services for Real-Time Applications in Static-Priority Scheduling Networks," IEEE/ACM Trans. Networking, vol. 12, no. 2, pp. 326-339, Apr. 2004.
[10] S. Wang, Z. Mai, D. Xuan, and W. Zhao, "Design and Implementation of QoS-Provisioning System for Voice over IP," IEEE Trans. Parallel and Distributed Systems, vol. 17, no. 3, pp. 276-288, Mar. 2006.
[11] Y.-M. Jiang, "Per-Domain Packet Scale Rate Guarantee for Expedited Forwarding," IEEE/ACM Trans. Networking, vol. 14, no. 3, pp. 630-643, June 2006.
[12] Y.-M. Jiang and Y. Liu, Stochastic Network Calculus. Springer, 2008.
[13] X. Jia, "A Distributed Algorithm of Delay Bounded Multicast Routing for Multimedia Applications in Wide Area Networks," IEEE/ACM Trans. Networking, vol. 6, no. 6, pp. 828-837, Dec. 1998.
[14] M. Li, "Change Trend of Averaged Hurst Parameter of Traffic Under DDOS Flood Attacks," Computers and Security, vol. 25, no. 3, pp. 213-220, 2006.
[15] R. Bettati, W. Zhao, and D. Teodor, "Real-Time Intrusion Detection and Suppression in ATM Networks," Proc. First USENIX Workshop Intrusion Detection and Network Monitoring, vol. 1, pp. 1-12, Apr. 1999.
[16] A. Raha, S. Kamat, and W. Zhao, "Guaranteeing End-to-End Deadlines in ATM Networks," Proc. IEEE Int'l. Conf. Distributed Computing Systems (ICDCS '95), pp. 60-68, May 1995.
[17] R.L. Cruz, "A Calculus for Network Delay, Part I: Network Elements in Isolation, Part II: Network Analysis," IEEE Trans. Information Theory, vol. 37, no. 1, pp. 114-141, Jan. 1991.
[18] O. Yaron and M. Sidi, "Performance and Stability of Communication Networks via Robust Exponential Bounds," IEEE/ACM Trans. Networking, vol. 1, no. 3, pp. 372-385, June 1993.
[19] A.K. Parekh and R.G. Gallager, "A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single-Node Case," IEEE/ACM Trans. Networking, vol. 1, no. 3, pp. 344-357, June 1993.
[20] D. Starobinski and M. Sidi, "Stochastically Bounded Burstiness for Communication Networks," IEEE Trans. Information Theory, vol. 46, no. 1, pp. 206-212, Jan. 2000.
[21] S.C. Lim and M. Li, "Generalized Cauchy Process and Its Application to Relaxation Phenomena," J. Physics A: Math. and General, vol. 39, no. 12, pp. 2935-2951, 2006.
[22] B.B. Mandelbrot, The Fractal Geometry of Nature. W.H. Freeman, 1982.
[23] J.T. Kent and A.T. Wood, "Estimating the Fractal Dimension of a Locally Self-Similar Gaussian Process by Using Increments," J. Royal Statistical Soc. B, vol. 59, no. 3, pp. 679-699, 1997.
[24] M.S. Taqqu, V. Teverovsky, and W. Willinger, "Estimators for Long-Range Dependence: An Empirical Study," Fractals, vol. 3, no. 4, pp. 785-798, 1995.
[25] J.W. Kantelhardt, E. Koscielny-Bunde, and H.H.A. Rego, "Detecting Long-Range Correlations with Detrended Fluctuation Analysis," Physica A, vol. 295, nos. 3/4, pp. 441-454, 2001.
[26] J. Beran, Statistics for Long-Memory Processes. Chapman & Hall, 1994.
[27] G. Chan, P. Hall, and D.S. Poskitt, "Periodogram-Based Estimators of Fractal Properties," The Annals of Statistics, vol. 23, no. 5, pp. 1684-1711, 1995.
[28] P. Hall and A. Wood, "On the Performance of Box-Counting Estimators of Fractal Dimension," Biometrika, vol. 80, no. 1, pp. 246-252, 1993.
[29] Y.Q. Chen, R. Sun, and A. Zhou, "An Improved Hurst Parameter Estimator Based on Fractional Fourier Transform," Telecomm. Systems, vol. 43, nos. 3-4, pp. 197-206, 2009.
[30] A.J. Adler, The Geometry of Random Fields. Wiley, 1981.
[31] V. Paxson and S. Floyd, "Wide Area Traffic: The Failure of Poison Modeling," IEEE/ACM Trans. Networking, vol. 3, no. 3, pp. 226-244, June 1995.
13 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool