基于系统动力学的网络业务研究
|
摘要
网络流量特征分析和建模是网络技术研究的一个分支. 由于网络拥赛控制
（包括丢包率、队列延时、网络吞吐率）和网络资源利用（如队列缓冲区容量、
带宽利用率及 QOS 保证）等关键技术都依赖于特定的流量特性，因而网络流量
的特性分析和建模对网络结构设计和性能优化具有重要的理论和实际意义.
在计算机网络模型的设计评价和优化中，网络业务模型起着非常重要的作用.
其中，时间序列模型作为研究网络业务的工具，有着很好的应用前景. 然而，传
统时间序列模型只能处理短相关，如泊松过程，Markov 过程，AR, MA，ARMA
和 ARIMA 过程等. 随着网络测量技术的发展，网络研究人员发现高速网络的业
务具有长相关性(long-range dependence), 亦称自相似性(self-similarity). 而这些
传统模型是不能处理的. 于是，一些长相关模型，如 FGN（分数高斯噪声，
Fractional Gaussian Noise）和 FARIMA(0,d,0)被用作网络业务模型. 新发展起来的
FARIMA(p,d,q)模型克服上述长相关模型的缺点，可同时处理长相关过程和短相
关过程. 但其预报是建立在概率基础上的，预报的步长也受到网络流量特性的制
约，从而限制了它们运用于实际控制. 目前，用混沌动力学处理时间序列问题正
在蓬勃发展，在许多领域得到或开始得到发展. 同时，网络流量的自相似性已
被证实，自相似性和混沌具有紧密联系，这为我们研究网络业务模型开辟了新的
途径. 我们注意到，用混沌方法研究网络流量的文献较少，仅有的研究仍停留在
网络流量的混沌特性上. 这启发我们用混沌理论对网络业务进行系统研究，探讨
网络流量混沌的成因. 神经网络具有并行处理及强大的非线性映射能力，对于未
知的动力系统，可以通过它来学习混沌时间序列，然后进行预测和控制.
本文应用混沌理论对网络流量的系统动力学特征进行了认真分析，并结合网
络流量的具体数据，计算了网络流量的 Hurst 参数，关联维数，Lyapunov 指数. 在
此基础上，运用小波理论对网络流量数据进行了去长相关处理，进一步对网络流
量混沌成因进行了探讨，指出网络流量的混沌与网络流量的长相关存在着联系.
在此基础上，运用 BP 神经网络理论，建立了相关模型，对实际网络流量进行了
预测. 研究表明，基于混沌理论建立的 BP 神经网络模型和 FARIMA(p,d,q)模型
都能较准确地对网络流量进行预测，而 BP 神经网络模型能够经过学习，获得较
长的预测步长.
The analysis and modeling of the network traffic is one of the branches of the
field of traffic technology. Because network congestion detection and control (such as
the efficiency of bandwidth, providing QoS) is connected with the character of
network traffic and because the utilization of network resource is dependent on it also,
it has important theoretical and practical meanings on the study of network traffic to
design and optimize the network framework.
In the design and optimization of network framework, the model of network
traffic is important. Especially, as a tool to analyze network traffic, time series has a
bright foreground of application. But traditional time series only deal with
short-dependence process, such as Poisson process, Markov process,
AR(Auto-Regressive), MA(Moving Average) ， ARMA(Autoregressive Moving
Average) and ARIMA(Autoregressive Integrated Moving Average). With the
development of network measuring, researchers have found that there is
long-dependence in the high-speed network, which is also called self-similarity. The
models above are not in point, so other long-dependence models such as FGN
(Fractional Gaussian Noise) and FARIMA (0,d, 0) are used in network traffic. The
recent model of FARIMA (p, d,q) gets over the scarcity of above models, which can
deal with long-dependence process and short-dependence process at the same time.
While its forecast is based on the probability and its forecast length is confined to the
character of network traffic, this restricts it to put into practice. At the present, the
method about the question of time series by system dynamics is developing, which is
used in many fields. On the other hand, the self-similarity of network traffic is really
certificated and self-similarity is connected with chaos closely, so we can use the
theory about chaos to study the model of network traffic. We find that there are few
articles using chaos theory to study network traffic, and these articles are attentive to
the character of network traffic. All of these suggest us to use chaos theory to study
network traffic and to argue about the cause about the chaos of network traffic.
The paper analyses the kinetic characteristics of Internet traffic by using some
complexity theories, such as fractal and chaos theories. We obtain the fractal
characteristics, the extent of complexity, and the style of movement of the system.
Based on the above, we discussed relation between the chaos of Internet traffic and
long-range dependence by filtering the long-range dependence using wavelet analysis.
The conclusion as follow: there is fractal structure in the Internet traffic and the chaos
of Internet traffic is connected with long-range dependence. With phase space
reconstruction, the paper demonstrates the Internet traffic chaos phenomena lies in
Internet traffic, and computes some parameters such as correlative dimension,
Lyapunov exponent. Based on this, the paper constructs the BP neutral network model
to forecast the Internet traffic. Comparing with FARIMA (p, d, q) model, the BP
neutral network model has the same ability of forecast and has longer space of
forecast.
（包括丢包率、队列延时、网络吞吐率）和网络资源利用（如队列缓冲区容量、
带宽利用率及 QOS 保证）等关键技术都依赖于特定的流量特性，因而网络流量
的特性分析和建模对网络结构设计和性能优化具有重要的理论和实际意义.
在计算机网络模型的设计评价和优化中，网络业务模型起着非常重要的作用.
其中，时间序列模型作为研究网络业务的工具，有着很好的应用前景. 然而，传
统时间序列模型只能处理短相关，如泊松过程，Markov 过程，AR, MA，ARMA
和 ARIMA 过程等. 随着网络测量技术的发展，网络研究人员发现高速网络的业
务具有长相关性(long-range dependence), 亦称自相似性(self-similarity). 而这些
传统模型是不能处理的. 于是，一些长相关模型，如 FGN（分数高斯噪声，
Fractional Gaussian Noise）和 FARIMA(0,d,0)被用作网络业务模型. 新发展起来的
FARIMA(p,d,q)模型克服上述长相关模型的缺点，可同时处理长相关过程和短相
关过程. 但其预报是建立在概率基础上的，预报的步长也受到网络流量特性的制
约，从而限制了它们运用于实际控制. 目前，用混沌动力学处理时间序列问题正
在蓬勃发展，在许多领域得到或开始得到发展. 同时，网络流量的自相似性已
被证实，自相似性和混沌具有紧密联系，这为我们研究网络业务模型开辟了新的
途径. 我们注意到，用混沌方法研究网络流量的文献较少，仅有的研究仍停留在
网络流量的混沌特性上. 这启发我们用混沌理论对网络业务进行系统研究，探讨
网络流量混沌的成因. 神经网络具有并行处理及强大的非线性映射能力，对于未
知的动力系统，可以通过它来学习混沌时间序列，然后进行预测和控制.
本文应用混沌理论对网络流量的系统动力学特征进行了认真分析，并结合网
络流量的具体数据，计算了网络流量的 Hurst 参数，关联维数，Lyapunov 指数. 在
此基础上，运用小波理论对网络流量数据进行了去长相关处理，进一步对网络流
量混沌成因进行了探讨，指出网络流量的混沌与网络流量的长相关存在着联系.
在此基础上，运用 BP 神经网络理论，建立了相关模型，对实际网络流量进行了
预测. 研究表明，基于混沌理论建立的 BP 神经网络模型和 FARIMA(p,d,q)模型
都能较准确地对网络流量进行预测，而 BP 神经网络模型能够经过学习，获得较
长的预测步长.
The analysis and modeling of the network traffic is one of the branches of the
field of traffic technology. Because network congestion detection and control (such as
the efficiency of bandwidth, providing QoS) is connected with the character of
network traffic and because the utilization of network resource is dependent on it also,
it has important theoretical and practical meanings on the study of network traffic to
design and optimize the network framework.
In the design and optimization of network framework, the model of network
traffic is important. Especially, as a tool to analyze network traffic, time series has a
bright foreground of application. But traditional time series only deal with
short-dependence process, such as Poisson process, Markov process,
AR(Auto-Regressive), MA(Moving Average) ， ARMA(Autoregressive Moving
Average) and ARIMA(Autoregressive Integrated Moving Average). With the
development of network measuring, researchers have found that there is
long-dependence in the high-speed network, which is also called self-similarity. The
models above are not in point, so other long-dependence models such as FGN
(Fractional Gaussian Noise) and FARIMA (0,d, 0) are used in network traffic. The
recent model of FARIMA (p, d,q) gets over the scarcity of above models, which can
deal with long-dependence process and short-dependence process at the same time.
While its forecast is based on the probability and its forecast length is confined to the
character of network traffic, this restricts it to put into practice. At the present, the
method about the question of time series by system dynamics is developing, which is
used in many fields. On the other hand, the self-similarity of network traffic is really
certificated and self-similarity is connected with chaos closely, so we can use the
theory about chaos to study the model of network traffic. We find that there are few
articles using chaos theory to study network traffic, and these articles are attentive to
the character of network traffic. All of these suggest us to use chaos theory to study
network traffic and to argue about the cause about the chaos of network traffic.
The paper analyses the kinetic characteristics of Internet traffic by using some
complexity theories, such as fractal and chaos theories. We obtain the fractal
characteristics, the extent of complexity, and the style of movement of the system.
Based on the above, we discussed relation between the chaos of Internet traffic and
long-range dependence by filtering the long-range dependence using wavelet analysis.
The conclusion as follow: there is fractal structure in the Internet traffic and the chaos
of Internet traffic is connected with long-range dependence. With phase space
reconstruction, the paper demonstrates the Internet traffic chaos phenomena lies in
Internet traffic, and computes some parameters such as correlative dimension,
Lyapunov exponent. Based on this, the paper constructs the BP neutral network model
to forecast the Internet traffic. Comparing with FARIMA (p, d, q) model, the BP
neutral network model has the same ability of forecast and has longer space of
forecast.
引文
[1] Cisco, Cisco System’s Tag Switching Architecture Overview, RFC 2105, 1997
[2] L. Zhang, et al., RSVP: a new Resource reservation Protocol, IEEE Network
Magazine, 1993,Vol. 1, No.5: 8-19
[3] L. Kleinrock, Queuing systems, John Wiley and Sons, 1976
[4] D. Anick, et al., Stochastic theory of a data-handling system with multiple sources,
Bell system Technical Journal, 1982, 61: 1871-1894
[5] R. Jain, et al., Packet Trains: Measurements and a New Model for Computer
Network Traffic, IEEE Journal on Selected Areas in Communications, 1986, 4:
986-995
[6] H. Heffes, et al., A Markov Modulated Characterization of Packetized Voice and
Data Traffic and Related Statistical Multiplexer Performance, IEEE JSAC, 1986,
4: 856-868
[7] D.M. Lucantoni, The BMAP/G/1 Queue, in L.Donatielo, et al., editors, Models
and Techniques for Performance Evaluation of Computer and Communication
System, Springer-Verlag, New York, 1993: 335-358
[8] C. Partridge, The end of simple traffic models, IEEE Network, September 1993.
Editor’s Note
[9] V. Ramaswami, Traffic Performance Modeling for Packet Communications:
Whence Where and Whether, Proc. Of 3 Australian Teletraffic Seminar, Australia,
1998
[10] W. Leland, et al., On the self-similar nature of Ethenet traffic (extended version),
IEEE/ACM Transactions on Networking, 1994, 2(1): 1-15
[11] J. Beran, et al., Long-range dependence in Variable Bit Rate Video Traffic, IEEE
Transactions on Communications 1995, 43(2/3/4): 1566-1579
[12] V. Paxson, et al., Wide-area traffic: The failure of Poisson modeling, Proceedings
of the ACM sigcomm’94, London, UK, 1994: 257-268
[13] S. Klivansky and A. Muktherjee, On Long-range Dependence in Nsfnet Traffic,
GIT, Tech. Rep. GIT-CC-94-61, 1994
51
天津大学硕士学位论文 参考文献
[14] D.E.Duffy, A.Mclntosh, M. Rosenstein and W. Willinger, Statistical analysis of
CCSN/SS7 traffic data from working CCs subnetworks, IEEE Journal on
Selected Areas in Communications, 1994, 12: 544-551
[15] C.R. Cunha and M. Crovella, Characteristics of WWW Client-based Traces,
University of Boston, Tech. Rep. BU-CS-95-010, 1995
[16] Crovella M. E., et al Self—similarity in World Wide Web traffic: evidence and
possible causes, IEEE/ACM Transaction s on Networking, 1997,5(6): 834-846.
[17] K. Park, et al., On the Relationship Between File Sizes, Transport Protocols, and
self-similar Network Traffic, Proc. Of ICNP’s96 1996: 171-180
[18] Statistical analysis and simulation study of video teleconference traffic in ATM
network, IEEE Transaction CASVT, 1992, 2: 49-59
[19] B. B. Mandelbort, The Fractal Geometry of Nature, New York: Freeman, 1983
[20] B. B. Mandelbort and J. W. Van, Nees, Fractional Brownian motions, factional
noises and applications, SIAM Review, 1968, 10: 422-437
[21] B. B. Mandelbort and J. R. Wallis, Some long-run properties of geophysical
recods, Water Resources, 1969, 5: 321-340
[22] 戚兴华等，利用小波变换对 1/f 信号进行参数估计，高等学校计算数学学报，
2000，3：199-207
[23] D. P. Heyman, What are the Implications of Long-range Dependence for
VBR-traffic Engineering?, IEEE/ACM Tran. On Networking, 4(3) ：
301-317,1996
[24] 文兰，动力系统简介， 数学进展，2002，31（4）：293－294
[25] 盛昭瀚，马军海，非线性动力系统分析引论，科学出版社，2001
[26] 舒炎泰，王雷，张连芳等，基于 FARIMA 模型的 Internet 网络业务预报，计
算机学报，2001，24（1）：46-54
[27] M. Garrett.， Analysis, modeling and generation of Self-Similar VAR Video
Traffic ， Proceedings of SIGCOMM’94, London, 1994, 269-280
[28] Grassberger P, Procaccia I, Measuring the strangeness of strange attractors [J],
Physica D, 1983(9):189-208
[29] Grassberger P, Procaccia I. Characterization of stranger attractors [J], Phy Rev
Lett, 1983,50: 346-349
[30] H. S. Kim, et al., Nolinear dynamics, delay times, and embedding windows,
Physica D, 1999,127: 48-60
[31] 林嘉宇，王跃科，黄芝平等, 语音信号重构中的时间延迟的选择——复相关
法, 信号处理，1999，15（3）：220-225
[32] 邹新月，吕先进，时间序列关联纬数计算方法及其实证分析，系统工程，
2002，20（4）：77-80
52
天津大学硕士学位论文 参考文献
[33] F.Takens, Determing strange attractors in turbulence, Lecture notes in Math,
1981(898): 361-381
[34] A. Wolf. J. B. Swift, H.L, Swinney and J.A. Vastano. Determining Lyapunov
exponents from a time series, Physica 16D, 1985: 285-317
[35] G. Barana and I. Tsuda, A new method for computing Lyapunov exponents, Phys.
Lett. A, 1993(175): 421-427
[36] K. Briggs, An improved method for estimating Lyapunov exponents of chaotic
time series, Phys. Lett. A, 1990(151): 27-32
[37] M.T. Rosenstein, J. J. Collins and C. J. De luca, A practical method for
calculating largest Lyapunov exponents form small data sets, Physica D,
1993(65): 117-134
[38] Barnsley M F., Fractals Everywhere, Academic Press, 1993
[39] 李水根，吴纪桃，分形与小波，科学出版社，2002
[40] 金志刚，自相似网络业务预报与控制研究：[博士学位论文]，天津，天津
大学，1999
[41] G. Wornell, et al., Estimation of fractal signal from noisy measurements using
wavelet, IEEE Trans. SP, 1992, 40(3): 611-623
[42] Wornell, G. W., Synthesis, Analysis, and Processing of Fractal Signals, RLE Tech.
Rep., 1991(566)
[43] Daubechies I., Orthonormal Based of Compactly Supported Wavelets, Commu.
On Pure and Applied Mathematics, 1998, 41(7)： 909-996
[44] 程正兴, 小波分析算法与应用, 西安交通大学出版社, 1998
[45] 秦前清, 杨宗凯, 实用小波分析, 西安电子科技大学出版社, 1992
[46] 杨福生, 小波变换的工程分析与应用, 科学出版社, 1999
[47] Pentland, A.P., Fractal-based Description of Natural Scenes, IEEE Trans. Pattern
Anal. Machine Intell., 1984, 6：661-674
[48] Tewfik, A.H. and Kim. M., Correlation Structure of the Discrete wavelet
Coefficients of Fractional Brownian Motion, IEEE Trans. Inform. Theory, 1992,
38(2): 904-909
[49] Van der Ziel. A., Unified Presentation of 1/f Noise in Electronic Devices:
Fundamental 1/f Noise Sources, Proc. IEEE, 1988, 3: 233-258
[50] Keshner, M.S., 1/f noise, Proc. IEEE, 1982, 70: 212-218
[51] Van der Ziel. A., On the Noise Spectra of Semi-Conductor Noise and
Flicker Effect, Physica, 1950,16(4): 359-372
[52] L.M. Kaplan, et al., An improved algorithm for fractal estimation from noisy
measurements, IEEE, 1993: 89~92
[53] L.M. Kaplan, et al., Fractal estimation from noisy data via discrete fractional
Gaussian noise (DFGN) and Haar basis, IEEE Trans. SP, 1993, 41(12):
53
天津大学硕士学位论文 参考文献
3554~3562
[54] L.M. Kaplan, et al., Extending Self-Similarity for Fractional Brownian Motion,
Proc. IEEE, 1994, 42(12): 3526~3530
[55] 张志涌等, 掌握和精通 MATLAB, 北京航空航天出版社, 1997
[56] 楼顺天等, 基于 MATLAB 的系统分析与设计——信号处理, 西安电子科技
大学出版社, 2000
[57] 胡昌华等, 基于 MATLAB 的系统分析与设计——小波分析，西安电子科技
大学出版社，2000
[58] 刘嘉焜等，基于 FARIMA 过程的网络业务预报与应用，电子与信息学报，
2001，23（4）：403-404
[59] G. Wornell, A Karhunen-Loeve-like for 1/f processes via wavelet, IEEE Trans. IT,
1992,38(2): 910-917
[60] Sheng Ma, et al., Modeling Video Traffic in The Wavelet Domain, IEEE, 1998:
201-208
[61] J. S. Walker, Fourier analysis and wavelet analysis, Notices of the American
Mathematical Society, 1987, 44(6): 658-670
[62] 焦李成，神经网络系统理论，西安：西安电子科技大学出版社，1991：16-280
[63] Rumelhart D E, McClelland J L., Parallel Distributed Processing, Vol. 1-2 MIT
Press, Cambridge, 1986
[64] Alexander G Parlos, An accelerated learning algorithm for multiplayer perception
networks, IEEE Trans on Networks, 1994, 5(3): 493-497
[65] Hagan M T, Menhaj MB., Training feed forward networks with Marquart
algorithm, IEEE Trans on Neutral Network, 1994, 5(6): 989-993
[66] Vogl T P, Mangis J, etc., Accelerated the convergence of the back propagation
method, Bio Cybern, 1988, 59(9): 256-264
[67] 王文剑，一种输入驱动的 BP 网络高效学习算法，系统工程理论与实践，
2000，1：99-101
[68] 郝海，顾培亮，卢奇，石油价格的系统动力学特征分析，系统工程，2002，
20（4）：37-43
[69] 徐凌，基于小波分析的网络业务的研究：[硕士学位论文],天津，天津大学，
2003
[2] L. Zhang, et al., RSVP: a new Resource reservation Protocol, IEEE Network
Magazine, 1993,Vol. 1, No.5: 8-19
[3] L. Kleinrock, Queuing systems, John Wiley and Sons, 1976
[4] D. Anick, et al., Stochastic theory of a data-handling system with multiple sources,
Bell system Technical Journal, 1982, 61: 1871-1894
[5] R. Jain, et al., Packet Trains: Measurements and a New Model for Computer
Network Traffic, IEEE Journal on Selected Areas in Communications, 1986, 4:
986-995
[6] H. Heffes, et al., A Markov Modulated Characterization of Packetized Voice and
Data Traffic and Related Statistical Multiplexer Performance, IEEE JSAC, 1986,
4: 856-868
[7] D.M. Lucantoni, The BMAP/G/1 Queue, in L.Donatielo, et al., editors, Models
and Techniques for Performance Evaluation of Computer and Communication
System, Springer-Verlag, New York, 1993: 335-358
[8] C. Partridge, The end of simple traffic models, IEEE Network, September 1993.
Editor’s Note
[9] V. Ramaswami, Traffic Performance Modeling for Packet Communications:
Whence Where and Whether, Proc. Of 3 Australian Teletraffic Seminar, Australia,
1998
[10] W. Leland, et al., On the self-similar nature of Ethenet traffic (extended version),
IEEE/ACM Transactions on Networking, 1994, 2(1): 1-15
[11] J. Beran, et al., Long-range dependence in Variable Bit Rate Video Traffic, IEEE
Transactions on Communications 1995, 43(2/3/4): 1566-1579
[12] V. Paxson, et al., Wide-area traffic: The failure of Poisson modeling, Proceedings
of the ACM sigcomm’94, London, UK, 1994: 257-268
[13] S. Klivansky and A. Muktherjee, On Long-range Dependence in Nsfnet Traffic,
GIT, Tech. Rep. GIT-CC-94-61, 1994
51
天津大学硕士学位论文 参考文献
[14] D.E.Duffy, A.Mclntosh, M. Rosenstein and W. Willinger, Statistical analysis of
CCSN/SS7 traffic data from working CCs subnetworks, IEEE Journal on
Selected Areas in Communications, 1994, 12: 544-551
[15] C.R. Cunha and M. Crovella, Characteristics of WWW Client-based Traces,
University of Boston, Tech. Rep. BU-CS-95-010, 1995
[16] Crovella M. E., et al Self—similarity in World Wide Web traffic: evidence and
possible causes, IEEE/ACM Transaction s on Networking, 1997,5(6): 834-846.
[17] K. Park, et al., On the Relationship Between File Sizes, Transport Protocols, and
self-similar Network Traffic, Proc. Of ICNP’s96 1996: 171-180
[18] Statistical analysis and simulation study of video teleconference traffic in ATM
network, IEEE Transaction CASVT, 1992, 2: 49-59
[19] B. B. Mandelbort, The Fractal Geometry of Nature, New York: Freeman, 1983
[20] B. B. Mandelbort and J. W. Van, Nees, Fractional Brownian motions, factional
noises and applications, SIAM Review, 1968, 10: 422-437
[21] B. B. Mandelbort and J. R. Wallis, Some long-run properties of geophysical
recods, Water Resources, 1969, 5: 321-340
[22] 戚兴华等，利用小波变换对 1/f 信号进行参数估计，高等学校计算数学学报，
2000，3：199-207
[23] D. P. Heyman, What are the Implications of Long-range Dependence for
VBR-traffic Engineering?, IEEE/ACM Tran. On Networking, 4(3) ：
301-317,1996
[24] 文兰，动力系统简介， 数学进展，2002，31（4）：293－294
[25] 盛昭瀚，马军海，非线性动力系统分析引论，科学出版社，2001
[26] 舒炎泰，王雷，张连芳等，基于 FARIMA 模型的 Internet 网络业务预报，计
算机学报，2001，24（1）：46-54
[27] M. Garrett.， Analysis, modeling and generation of Self-Similar VAR Video
Traffic ， Proceedings of SIGCOMM’94, London, 1994, 269-280
[28] Grassberger P, Procaccia I, Measuring the strangeness of strange attractors [J],
Physica D, 1983(9):189-208
[29] Grassberger P, Procaccia I. Characterization of stranger attractors [J], Phy Rev
Lett, 1983,50: 346-349
[30] H. S. Kim, et al., Nolinear dynamics, delay times, and embedding windows,
Physica D, 1999,127: 48-60
[31] 林嘉宇，王跃科，黄芝平等, 语音信号重构中的时间延迟的选择——复相关
法, 信号处理，1999，15（3）：220-225
[32] 邹新月，吕先进，时间序列关联纬数计算方法及其实证分析，系统工程，
2002，20（4）：77-80
52
天津大学硕士学位论文 参考文献
[33] F.Takens, Determing strange attractors in turbulence, Lecture notes in Math,
1981(898): 361-381
[34] A. Wolf. J. B. Swift, H.L, Swinney and J.A. Vastano. Determining Lyapunov
exponents from a time series, Physica 16D, 1985: 285-317
[35] G. Barana and I. Tsuda, A new method for computing Lyapunov exponents, Phys.
Lett. A, 1993(175): 421-427
[36] K. Briggs, An improved method for estimating Lyapunov exponents of chaotic
time series, Phys. Lett. A, 1990(151): 27-32
[37] M.T. Rosenstein, J. J. Collins and C. J. De luca, A practical method for
calculating largest Lyapunov exponents form small data sets, Physica D,
1993(65): 117-134
[38] Barnsley M F., Fractals Everywhere, Academic Press, 1993
[39] 李水根，吴纪桃，分形与小波，科学出版社，2002
[40] 金志刚，自相似网络业务预报与控制研究：[博士学位论文]，天津，天津
大学，1999
[41] G. Wornell, et al., Estimation of fractal signal from noisy measurements using
wavelet, IEEE Trans. SP, 1992, 40(3): 611-623
[42] Wornell, G. W., Synthesis, Analysis, and Processing of Fractal Signals, RLE Tech.
Rep., 1991(566)
[43] Daubechies I., Orthonormal Based of Compactly Supported Wavelets, Commu.
On Pure and Applied Mathematics, 1998, 41(7)： 909-996
[44] 程正兴, 小波分析算法与应用, 西安交通大学出版社, 1998
[45] 秦前清, 杨宗凯, 实用小波分析, 西安电子科技大学出版社, 1992
[46] 杨福生, 小波变换的工程分析与应用, 科学出版社, 1999
[47] Pentland, A.P., Fractal-based Description of Natural Scenes, IEEE Trans. Pattern
Anal. Machine Intell., 1984, 6：661-674
[48] Tewfik, A.H. and Kim. M., Correlation Structure of the Discrete wavelet
Coefficients of Fractional Brownian Motion, IEEE Trans. Inform. Theory, 1992,
38(2): 904-909
[49] Van der Ziel. A., Unified Presentation of 1/f Noise in Electronic Devices:
Fundamental 1/f Noise Sources, Proc. IEEE, 1988, 3: 233-258
[50] Keshner, M.S., 1/f noise, Proc. IEEE, 1982, 70: 212-218
[51] Van der Ziel. A., On the Noise Spectra of Semi-Conductor Noise and
Flicker Effect, Physica, 1950,16(4): 359-372
[52] L.M. Kaplan, et al., An improved algorithm for fractal estimation from noisy
measurements, IEEE, 1993: 89~92
[53] L.M. Kaplan, et al., Fractal estimation from noisy data via discrete fractional
Gaussian noise (DFGN) and Haar basis, IEEE Trans. SP, 1993, 41(12):
53
天津大学硕士学位论文 参考文献
3554~3562
[54] L.M. Kaplan, et al., Extending Self-Similarity for Fractional Brownian Motion,
Proc. IEEE, 1994, 42(12): 3526~3530
[55] 张志涌等, 掌握和精通 MATLAB, 北京航空航天出版社, 1997
[56] 楼顺天等, 基于 MATLAB 的系统分析与设计——信号处理, 西安电子科技
大学出版社, 2000
[57] 胡昌华等, 基于 MATLAB 的系统分析与设计——小波分析，西安电子科技
大学出版社，2000
[58] 刘嘉焜等，基于 FARIMA 过程的网络业务预报与应用，电子与信息学报，
2001，23（4）：403-404
[59] G. Wornell, A Karhunen-Loeve-like for 1/f processes via wavelet, IEEE Trans. IT,
1992,38(2): 910-917
[60] Sheng Ma, et al., Modeling Video Traffic in The Wavelet Domain, IEEE, 1998:
201-208
[61] J. S. Walker, Fourier analysis and wavelet analysis, Notices of the American
Mathematical Society, 1987, 44(6): 658-670
[62] 焦李成，神经网络系统理论，西安：西安电子科技大学出版社，1991：16-280
[63] Rumelhart D E, McClelland J L., Parallel Distributed Processing, Vol. 1-2 MIT
Press, Cambridge, 1986
[64] Alexander G Parlos, An accelerated learning algorithm for multiplayer perception
networks, IEEE Trans on Networks, 1994, 5(3): 493-497
[65] Hagan M T, Menhaj MB., Training feed forward networks with Marquart
algorithm, IEEE Trans on Neutral Network, 1994, 5(6): 989-993
[66] Vogl T P, Mangis J, etc., Accelerated the convergence of the back propagation
method, Bio Cybern, 1988, 59(9): 256-264
[67] 王文剑，一种输入驱动的 BP 网络高效学习算法，系统工程理论与实践，
2000，1：99-101
[68] 郝海，顾培亮，卢奇，石油价格的系统动力学特征分析，系统工程，2002，
20（4）：37-43
[69] 徐凌，基于小波分析的网络业务的研究：[硕士学位论文],天津，天津大学，
2003