基于α-稳定自相似过程的网络业务建模与性能分析
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摘要
在21世纪的信息时代,随着网络应用的普及和网络用户数量的日益增长,网络已经成为人类活动不可或缺的一部分。所以,对网络特性的研究与分析变得更为紧迫。长期以来,网络流量建模和分析以泊松分布和马尔可夫过程理论为基础,而近年来大量网络业务测量分析结果表明网络业务具有普遍自相似和长相关特性,这种特征不能由传统模型描述。因而人们提出了一些自相似流量模型来刻画网络特征,最常用的是分形布朗运动(FBM)模型。而最近的研究进一步指出网络不仅仅具有自相似和长相关特性,同时也存在强突发和重尾特性,现有的流量模型不能同时刻画流量的自相似与突发特性,迫切需要研究新的模型来刻画网络流量的强突发和重尾特性。
论文首先对网络流量特性的自相似特点进行研究,描述了自相似对网络性能的影响和常用自相似参数的估算方法,分析了现有网络流量建模的常用方法。
论文接着在深入研究FBM建模方法的基础上,指出FBM模型存在的问题,验证了网络流量的非高斯性,引出了用α-稳定分布来刻画网络流量分布特性,通过与高斯刻画进行分析对比,验证了用α-稳定分布刻画流量分布的可行性和有效性,在此基础上进一步引入了基于线性分形稳定噪音的流量模型,这种模型可以同时刻画网络的突发性与长相关特性。论文详细描述了基于分形稳定噪音的流量模型4个参数的估算方法和产生该模型流量的算法,并分别使用FBM模型与基于分形稳定噪音的流量模型对贝尔实验室的经典网络流量进行数据拟合,发现基于分形稳定噪音的流量模型更能反映数据流的突发特性。在前人得出的基于分形稳定噪音流量模型的丢包率公式的基础上,论文推导出了时延、抖动等性能指标计算公式。
论文最后使用理论与仿真相结合的手段,研究了影响网络性能的关键因素,得到了一系列有意义的成果,如我们总能发现流量突发程度越强,节点利用率越高,会导致网络的丢包率、时延、时延抖动的情况变的糟糕。而自相似对网络的影响相对要复杂得多,它在不同的缓冲区大小和不同的相对网络速率情况下对网络的影响都不一样,论文对各种情况都做了详细研究。论文还研究了规模效应对网络性能的影响,通过设置简单的场景模型,分析了规模效应使网络性能得到改善的原因。
In the information age of 21 century, with the popularization of network application and growth of the network user, the network has become an indispensable part of human activity. So, the research and analysis of the characteristic of the network become more urgent. For a long time, traffic modeling and analysis is based on Poisson distribution and Markov's theory. But recently measures of network traffic have shown that packet/cell traffic through telecommunication networks exhibits long-range dependence and self-similarity, and this kind of characteristic can't be described by traditional model. Therefore, people have proposed some self-similar traffic models to portray the characteristic of the network, the most frequently used one is Fractional Brownian Motion (FBM) process model. Further studies have also indicated that besides self-similarity and long-range dependence, network traffic exhibits more complicated characteristic, such as strong burstiness. For FBM model can't capture this characteristic, we need to study the new model that can capture long-range dependence and strong burstiness as well.
Firstly, this thesis carries on research on the self-similarity characteristic of network traffic, the impact on performance of the network of the self-similarity, the estimation method of the self-similarity coefficient, and the analysis of the existing modeling method of traffic.
Secondly, this thesis points out the problem of FBM model on the basis of further investigating the model. We verify the non-Gaussianity of network traffic and propose the use of alpha stable distribution in traffic modeling. Based on the research on alpha stable distribution, this paper introduces linear fractional stable noise (LFSN) process model which can capture long-range dependence and strong burstiness. This paper provides the estimation methods of the 4 parameters of this model and the algorithm producing the flow. Moreover, the advantage of the model is verified by modeling real traffic data. By using FBM and LFSN traffic model to fit the classical Bellcore network traffic, we find that the LFSN model can reflect the burstiness more effectively. Based on the available buffer overflow probability of LFSN model, the formulas for computing the average queue length, the variance of queue length, average delay and the variance of the delay are derived.
Finally, the variance of the system performance indices is studied through theoretical analysis and simulation. The results show that stronger burstiness or higher the link utilization will cause the worse of packet loss probability, average delay and jitter. The influence of Hurst index is much more complicated, the impact on performance of network is different in different buffer or speed. We give detailed research on various kinds of situations and studied the impact on performance of the network of the scale effect. Through setting up the simple scene model, the improved reason for the performance of the network caused by the scale effect is analyzed.
论文首先对网络流量特性的自相似特点进行研究,描述了自相似对网络性能的影响和常用自相似参数的估算方法,分析了现有网络流量建模的常用方法。
论文接着在深入研究FBM建模方法的基础上,指出FBM模型存在的问题,验证了网络流量的非高斯性,引出了用α-稳定分布来刻画网络流量分布特性,通过与高斯刻画进行分析对比,验证了用α-稳定分布刻画流量分布的可行性和有效性,在此基础上进一步引入了基于线性分形稳定噪音的流量模型,这种模型可以同时刻画网络的突发性与长相关特性。论文详细描述了基于分形稳定噪音的流量模型4个参数的估算方法和产生该模型流量的算法,并分别使用FBM模型与基于分形稳定噪音的流量模型对贝尔实验室的经典网络流量进行数据拟合,发现基于分形稳定噪音的流量模型更能反映数据流的突发特性。在前人得出的基于分形稳定噪音流量模型的丢包率公式的基础上,论文推导出了时延、抖动等性能指标计算公式。
论文最后使用理论与仿真相结合的手段,研究了影响网络性能的关键因素,得到了一系列有意义的成果,如我们总能发现流量突发程度越强,节点利用率越高,会导致网络的丢包率、时延、时延抖动的情况变的糟糕。而自相似对网络的影响相对要复杂得多,它在不同的缓冲区大小和不同的相对网络速率情况下对网络的影响都不一样,论文对各种情况都做了详细研究。论文还研究了规模效应对网络性能的影响,通过设置简单的场景模型,分析了规模效应使网络性能得到改善的原因。
In the information age of 21 century, with the popularization of network application and growth of the network user, the network has become an indispensable part of human activity. So, the research and analysis of the characteristic of the network become more urgent. For a long time, traffic modeling and analysis is based on Poisson distribution and Markov's theory. But recently measures of network traffic have shown that packet/cell traffic through telecommunication networks exhibits long-range dependence and self-similarity, and this kind of characteristic can't be described by traditional model. Therefore, people have proposed some self-similar traffic models to portray the characteristic of the network, the most frequently used one is Fractional Brownian Motion (FBM) process model. Further studies have also indicated that besides self-similarity and long-range dependence, network traffic exhibits more complicated characteristic, such as strong burstiness. For FBM model can't capture this characteristic, we need to study the new model that can capture long-range dependence and strong burstiness as well.
Firstly, this thesis carries on research on the self-similarity characteristic of network traffic, the impact on performance of the network of the self-similarity, the estimation method of the self-similarity coefficient, and the analysis of the existing modeling method of traffic.
Secondly, this thesis points out the problem of FBM model on the basis of further investigating the model. We verify the non-Gaussianity of network traffic and propose the use of alpha stable distribution in traffic modeling. Based on the research on alpha stable distribution, this paper introduces linear fractional stable noise (LFSN) process model which can capture long-range dependence and strong burstiness. This paper provides the estimation methods of the 4 parameters of this model and the algorithm producing the flow. Moreover, the advantage of the model is verified by modeling real traffic data. By using FBM and LFSN traffic model to fit the classical Bellcore network traffic, we find that the LFSN model can reflect the burstiness more effectively. Based on the available buffer overflow probability of LFSN model, the formulas for computing the average queue length, the variance of queue length, average delay and the variance of the delay are derived.
Finally, the variance of the system performance indices is studied through theoretical analysis and simulation. The results show that stronger burstiness or higher the link utilization will cause the worse of packet loss probability, average delay and jitter. The influence of Hurst index is much more complicated, the impact on performance of network is different in different buffer or speed. We give detailed research on various kinds of situations and studied the impact on performance of the network of the scale effect. Through setting up the simple scene model, the improved reason for the performance of the network caused by the scale effect is analyzed.
引文
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[2] D. Heath, S. Resnick, and G. Samorodnitsky. Heavy tails and long range dependence in on/off processes and associated fluid models[J]. Math. Oper. Res., 23(1), 1998:145-165
[3] I. Norros. On the use of fractional Brownian motion in the theory of connectionless networks[J]. IEEE Journal on Selected Areas in Communication, 1995, 13(6): 953-962
[4] N. Sadek, A. Khotanzad and T. Chen, ATM Dynamic Bandwidth Allocation Using FARIMA Prediction Model[C]. in Proceedings of International Conference on Computer Communications and Networks, 20-22, October 2003, 359-363
[5] M.S Taqqu. and J.B Levy.Using renewal processes to generate long range of Ethernet LAN Traffic at the Source level[J]. IEEE/ACM Trans. On Networking, 1997, 5(1): 71-86
[6] DUFFY D, MCINTOSH A, ROSENSTEIN 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.
[7] W. E. Leland, M. S. Taqqu and W. Willinger, et al. On the self-similar nature of Ethernet traffic (extended version)[J]. IEEE/ACM Trans. on Networking, 1994, 2(1): 1-15
[8] W.Willinger, M.Taqqu, R.Sherman and D.Wilson. Self-similarity Through High Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level. SIGCOMM' 95, Cambridge, MA,August 1995, 100-113.
[9] S. Y. Yin and X. K. Lin, Traffic Self-Similarity in Mobile Ad Hoc Networks[C].in Proceedings of Second IFIP International Conference on Wireless and Optical Communications Networks, 2005, 285-289
[10] A. Athanasopoulos, E. Topalis, C. D. Antonopoulos et ed., Evaluation Analysis of the Performance of IEEE 802.11b and IEEE 802.11g Standards[C]. in Proceedings of International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies, available at: http:// doi.ieeecomputersociety.org/10.1109/ICNICONSMCL.2006.92
[11] M. Jiang, M. Nikolic, S. Hardy et al. Impact of self-similarity on wireless data network performance[C]. ICC 2001. IEEE International Conference on Communications,2001,Vol. 2(11-14): 477-481
[12] Zh. Junshan, H. Ming, N. B. Shroff. Bursty data over CDMA: MAI self-similarity, rate control and admission control[C]. In proceedings of IEEE INFOCOM 2002, 2002, Vol. 1(23-27): 391-399
[13] Kalden R., Ibrahim S.: Searching for Self-Similarity in GPRS[C], The 5th Annual Passive & Active Measurement Workshop, PAM 2004, France, April 2004.
[14] Bisio, I.; Marchese, M.; Bandwidth Allocation in Geostationary Satellite Faded Channels for Internet Traffic[C]. 2nd International Symposium on Wireless Communication Systems, 2005. 5-7 Sept. 2005, 878 - 882
[15] K.Park, et al.. On the relationship between file sizes, transport protocols, and self-similar network traffic[C]. In Proc. of ICNP'96, Columbus, Ohio, 1996.10.29-11.1:171-180
[16] S.Resnick, et al.. Heavy Tail Modeling and Teletraffic Data[R]. Preprint, Cornell University, 1995.
[17] B.B.Mandelbort. Long-run linearity, locally Gaussian process, H-spectra and infinite variance[J]. International Economic Review, 10,1994:54-60.
[18] R. M. Rodriguez-Dagnino and H. Takagi.Wireless cellular networks with Pareto distributed call holding times[C]. in Proc. SPIE, ITCom 2001 Conference on Internet Performance and Control of Network Systems II, vol. 4523, 202-210.
[19] T. Mikosch, S. Resnick, H. Rootz'en, and A. Stegeman. Is network traffic approximated by stable L'evy motion or fractional Brownian motion[J]. Annals of Applied Probability, vol. 12, 2002: 23-68
[20] J. P. Nolan. Fitting data and assessing goodness-of-fit with stable distributions[DB/OL].http: //academic2.american.edu/-jpnolan/stable/stable.html, 2002
[21] Harmantzis, Fotios C.,Data network traffic modeling and engineering using stable and fractal processes[D].Ph.D. thesis,University of Toronto (Canada). 2002
[22] Taqqu M.S., Willinger W., Sherman R.: Proof of a Fundamental Result in Self-Similar Traffic Modeling[J], Computer Communication Review, 27, 1997, 5-23.
[23] Addie R. G., Zukerman M., Neame T. D.: Broadband Traffic Modeling:Simple Solutions to Hard Problems[J], IEEE Communications Magazine, 36(8), August 1998, 88-95.
[24] Duffield N., O'Connell N. Large Deviations and Overflow Probabilities for the General Single-Server Queue[C], with Applications, Mathematical Proceedings of the Cambridge Philosophical Society, 118, 1995: 363-374.
[25] Narayan O.: Exact Asymptotic Queue Length Distribution for Fractional Brownian Traffic[J], Advances in Performance Analysis, 1(1), 1998: 39-63.
[26] Massoulie L., Simonian A.: Large Buffer Asymptotics for the Queue with FBM Input[J], Journal of Applied Probability, 36(3), 1999: 894-906.
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