网络业务自相似特性及其对排队性能影响的研究
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摘要
近年来对网络业务流量的测量和分析表明,网络业务是自相似(分形)的。网络业务的自相似特性对网络的分析、设计、控制和性能评价等均具有重大的影响。本文介绍了自相似的常见定义,描述了该随机过程在数学和物理上的若干特征,并讨论了多重分形的分析方法。实际业务流量在小时间尺度上符合多重分形特征。
本文研究了7种常见的估计Hurst系数的方法与实现。重点讨论了影响Hurst系数估计算法的因素:方差、周期信号和相关结构。本文通过调整FGN(Fractional Ganssian Noise)序列,产生具有部分尺度范围相关结构的序列,通过不断改变尺度范围并估计序列的Hurst系数,发现各个估计算法的估计结果依赖于特定尺度范围的相关结构,而尺度范围以外的相关结构的改变对估计结果无影响。对于实际业务流量,相关结构的变化导致各个估计算法估计结果的不同。通过对实际业务的分析验证了该观点。
ON/OFF、FGN、RMD(Random Midpoint Displacement)、FARIMA是四种常见自相似业务模型。本文介绍了这四种模型的实现过程,并分析了它们产生自相似业务的准确性。研究结果表明ON/OFF模型生成的序列接近期望值,但是序列的Hurst系数是不稳定的,随序列长度改变而改变。相比其它模型,Durbin FGN模型产生的业务比较稳定和准确。
在网络性能分析中排队性能是一个重要的指标。作者采用业务源产生的不同数据来驱动G/M/1模型进行仿真,从而讨论影响排队时延与队长的因素。经研究发现发包间隔时间的分布特征决定了排队性能;自相似序列比短相关序列有更大的排队时延,而且变化也更剧烈;方差对排队性能指标有重要影响;ON/OFF模型的排队性能与ON、OFF的Pareto分布有直接关系。
Large of monitoring result have shown the self-similar nature of network traffic. The characteristic of traffic has great effects on the analysis, design, control, and performance evaluation of computer networks. In this thesis, several mathematical definitions of self-similarity are given, some of their features are described and the methods of multi-fractal analysis are discussed. Research in recent years has presented that multi-fractal model is more precise than fractal model to discribe the characteristic of small time scale of real networks.In this thesis, the principle and implementation of seven estimate algorithms about Hurst coefficient are described. Three factors i.e. variance, periodic signal, and fractal structure, which affect the performance of the estimate algorithms, are discussed. By rearranging the FGN (Fractional Ganssian Noise ), the author constructs a new serial of correlation structure in a specific scale range serial. By changing the scale range continuously and estimating the new serial, the author concludes the estimation of each algorithm depends on the fractal structure in a specific scale range, but the structures out of the scale range have no effects on the estimation. The measurement of real network traffic shows that the differences of fractal structures result in the differences of the algorithms estimations.ON/OFF FGN RMD( Random Midpoint Displacement ), FARIMA are four usual self-similar traffic models. The thesis introduces the implementation of the models and analyses the precision of self-similarity traffic generated by the four models. Although the Hurst coefficient of sequence generated by ON/OFF model is close to the range of expected value, the Hurst value does not remain stable and changes according to the length of the sequence. Compared to other models, Durbin FGN model is more precise and stable.In network performance's analysis, queuing performance is a key point. The authors feeds different network traffic to the G/M/1 model to modulate and discuss
the factors affecting delay and length of the G/M/1 queue. The research shows that the queuing performance is determined by packet interval time;self-similar sequence generates much worse queuing performance than short dependence;sequence even then the variation is more violent.Variance has an important affect on the queuing performance.Finally,the research shows that sequence generated by ON/OFF model is related to the corresponding Pareto distribution in ON and OFF period.
本文研究了7种常见的估计Hurst系数的方法与实现。重点讨论了影响Hurst系数估计算法的因素:方差、周期信号和相关结构。本文通过调整FGN(Fractional Ganssian Noise)序列,产生具有部分尺度范围相关结构的序列,通过不断改变尺度范围并估计序列的Hurst系数,发现各个估计算法的估计结果依赖于特定尺度范围的相关结构,而尺度范围以外的相关结构的改变对估计结果无影响。对于实际业务流量,相关结构的变化导致各个估计算法估计结果的不同。通过对实际业务的分析验证了该观点。
ON/OFF、FGN、RMD(Random Midpoint Displacement)、FARIMA是四种常见自相似业务模型。本文介绍了这四种模型的实现过程,并分析了它们产生自相似业务的准确性。研究结果表明ON/OFF模型生成的序列接近期望值,但是序列的Hurst系数是不稳定的,随序列长度改变而改变。相比其它模型,Durbin FGN模型产生的业务比较稳定和准确。
在网络性能分析中排队性能是一个重要的指标。作者采用业务源产生的不同数据来驱动G/M/1模型进行仿真,从而讨论影响排队时延与队长的因素。经研究发现发包间隔时间的分布特征决定了排队性能;自相似序列比短相关序列有更大的排队时延,而且变化也更剧烈;方差对排队性能指标有重要影响;ON/OFF模型的排队性能与ON、OFF的Pareto分布有直接关系。
Large of monitoring result have shown the self-similar nature of network traffic. The characteristic of traffic has great effects on the analysis, design, control, and performance evaluation of computer networks. In this thesis, several mathematical definitions of self-similarity are given, some of their features are described and the methods of multi-fractal analysis are discussed. Research in recent years has presented that multi-fractal model is more precise than fractal model to discribe the characteristic of small time scale of real networks.In this thesis, the principle and implementation of seven estimate algorithms about Hurst coefficient are described. Three factors i.e. variance, periodic signal, and fractal structure, which affect the performance of the estimate algorithms, are discussed. By rearranging the FGN (Fractional Ganssian Noise ), the author constructs a new serial of correlation structure in a specific scale range serial. By changing the scale range continuously and estimating the new serial, the author concludes the estimation of each algorithm depends on the fractal structure in a specific scale range, but the structures out of the scale range have no effects on the estimation. The measurement of real network traffic shows that the differences of fractal structures result in the differences of the algorithms estimations.ON/OFF FGN RMD( Random Midpoint Displacement ), FARIMA are four usual self-similar traffic models. The thesis introduces the implementation of the models and analyses the precision of self-similarity traffic generated by the four models. Although the Hurst coefficient of sequence generated by ON/OFF model is close to the range of expected value, the Hurst value does not remain stable and changes according to the length of the sequence. Compared to other models, Durbin FGN model is more precise and stable.In network performance's analysis, queuing performance is a key point. The authors feeds different network traffic to the G/M/1 model to modulate and discuss
the factors affecting delay and length of the G/M/1 queue. The research shows that the queuing performance is determined by packet interval time;self-similar sequence generates much worse queuing performance than short dependence;sequence even then the variation is more violent.Variance has an important affect on the queuing performance.Finally,the research shows that sequence generated by ON/OFF model is related to the corresponding Pareto distribution in ON and OFF period.
引文
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[2] D. Duffy, A. Mclntosh, M. Rosenstein and D. Wilson. Statistical Analysis of CCSN/SS7 Traffic Data from Working CCS Subnetworks. IEEE JSAC, vol. 12, no. 3, 1994, 544-551
[3] W. E. Leland, M. S. Taqqu, W. Willinger and D. V. Wilson. On the Self-Similar Nature of Ethernet Traffic(Extended Version). IEEE/ACM Trans. On Networking, Feb, 1994, 2(1), 1-15
[4] W. Willinger, M. Taqqu, R. Sherman and D. Wilson. Self-similarity Through High Variability: Statistical Analysis of Ethemet LAN Traffic at the Source Level. SIGCOMM'95, Cambridge, MA, August 1995, 100-113.
[5] W. Willinger, M. Taqqu, R. Sherman and D. Wilson. Self-similarity Through High Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level, IEEE/ACM Trans. On Networking 5(1), 1997, 71-86.
[6] V. Paxon and S. Floyd. Wide-area traffic: the failure of Possion Modeling. In Proc. ACM SIGCOMM'94, pp. 257-268, 1994.
[7] DUFFY D, MCINTOSH A, ROSENSTE1N M. Statistical analysis of CCSN/SS7 traffic data from working CCS subnetworkings[J]. IEEE Journal on Selected Areas in Communications, 1994, 12(3): 544-551.
[8] D. P. Hayman, A. Tabatabai and T. V. Lakshman. Statistical Analysis and Simulation Study of Video Teleconference Traffic in ATM Networks. IEEE Trans. On Circuits and System for Video Technology, Vol. 2, No. 1, 1992, 49-59.
[9] M. Crovella and A. Bestavros. Self-similarity in World Wide Web traffic: evidence and possible cause. In Proceedings of the 1996 ACM SIGMETRUCS International Conference on Measurement and Modeling of Computer Systems, May 1996.
[10] BERAN J, SHERMAN M, TAQQU S. Long-range dependence in variable-bit-rate video traffic[J]. IEEE/ACM Transactions on Communications, 1995, 43(2, 3, 4): 1566-1579.
[11] 张连芳.自相似网络业务的建模分析与性能评价研究[D].博士学位论文,天津大学,1998.
[12] Feldmann, A., Gilbert, A. C., Willinger, W. Data networks as cascades: investigating the multifractal nature of lnternet WAN traffic. In: Steenstrup, M., ed. Proceedings of the ACM/SIGCOMM'98. New York: ACM Press, 1998. 42-55.
[13] Feldmann, A., Gilbert, A. C., Willinger, W., et al. The changing nature of network traffic: scaling phenomena. Computer Communication Review, 1998, 28(2): 5～29.
[14] Gilbert, A. C., Willinger, W., Feldmann, A. Scaling analysis of random cascades, with applications to network traffic. IEEE Transactions on Information Theory, 1999, 45(3): 971～991.
[15] Goncaves, P., Riedi, R., Baraniuk, R. Simple statistical analysis of wavelet-based multifractal spectrum estimation. In: Abry, P., Veitch, D., eds. Proceedings of the 32nd Conference on Signals, Systems and Computers. Pacific Grove: CA, 1998. 109～121.
[16] Riedi, R., Crouse, M., Ribeiro, V., et al. A multifractal wavelet model with applications to network traffic. IEEE Transactions on Information Theory, 1999, 45(3): 991～1018.
[17] Taqqu, M. S., Teverovsky, V., W. illlinger, W. Is network traffic self-similar or multifractal? Fractals, 1997, 5(1): 63～73.
[18] M. Csenger, Early ATM Users Lose Data, Communications Week, May 16, 1994.
[19] Ashok Erramilli, Onuttom Narayan, Walter Willinger, Experimental queueing analysis with long-range dependent packet traffic, IEEE/ACM Transactions on Networking (TON), v. 4 n. 2, p. 209-223, April 1996
[20] Stallings W. Viewpoint: self-similarity upsets data traffic auumptions. IEEE Spectrum, 1997, 1
[21] K. Claffy, Monk T. What't next for internet data analysis. Status and challenges facing the community[J]. Proceedings of the IEEE, 1997, 85(10): 1563-1571.
[22] 褚立文,廖建新,陈俊亮.自相似业务合成流的建模及排队性能分析.通信学报.1999,20(8):7-12.
[23] Likhanov N. Analysis of an ATM buffer with self-similar(fractal) input traffic. INFOCOM'95, 1995.
[24] T. Tuan, K. Park, Multiple time scale congestion control for self-similar network traffic, Performance Evaluation, 1999, 359-386
[25] T. Tuan, K. Park, Multiple time scale redundancy control for QoS-sensitive transport of real-time traffic, In: IEEE INFOCOM '00, 2000.
[26] T. Tuan, K. Park, "Performance evaluation of multiple time scale TCP under self-similar traffic conditions, Technical report, Dept. of Computer Sciences, Purdue University, 1999, CSD-TR-99-040.
[27] 吴援明,宁正容,梁恩志.网络自相似业务模型进展[J].通信学报,2004,25(3):97-104
[28] LIKHANOV N, TSYBAKOV B, GEORGANAS N. Analysis of an ATM buffer with self-similar ("fractal") input traffic[A]. INFOCOM'95[C]. Boston, MA, USA, 1995. 985-992.
[29] TSYBOKO B, GEORGANAS N. On self-similar traffic in ATM queues: definitions, overflow probability bound, and cell delay distribution[J]. IEEE/ACM Transactions on Networking, 1997, 5(3): 397-409.
[30] COX D R. Statistics: An Appraisal[M]. Iowa: Iowa State University Press, 1984. 55-74.
[31] ALEXANDER R, BROWNLEE N, ZIEDINS I. Modeling self-similar network traffic[R]. University of Auckland, 1995.
[32] Tsybakov B, Georganas N D. On self-similar traffic in ATM queues: definitions, overflow probability bound, and cell delay distribution. [J] IEEE/ACM Trans On Networking, 1997, 5(3), 397 409
[33] 宁正容.网络自相似业务产生的研究[D].硕士学位,电子科技大学,2003.
[34] COX D R. Long-range dependence: A review. IA: Iowa State Univ. Press, 1984, 55-74.
[35] 李成忠,张新有等.计算机网络原理与设计[M].西南交通大学,2004
[36] WILLINGER W, PAXSON V, TAQQU M S. Self-Similarity and Heavy Tails: Structural Modeling of Network Traffic, a Practical Guide to Heavy Tails: Statistical Techniques and Applications[M]. Boston, 1998. 27-53.
[37] TAQQU M, LEVY J. Using renewal processes to generate LRD and high variability[J]. Progress in Probability and Statistics, 1986, 11: 73-89.
[38] Grassberger P. Generalized dimensions of strange attractors [J]. ]Physics Letters A, 1983, 97: 227～230
[39] 胡可乐,李平.Logistic映射中奇怪吸引子的盒维数计算[J].江苏理工大学学报.1998,Vol.19.No.5:62～65
[40] Brown G, Michon G, Peyriere J. On the multifractal analysis of measures [J]. Journal of Stat Phys., 1992, 66: 775～790
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