Many network monitoring applications and performance analysis tools are based on the study of an aggregate measure of network traffic, for example, number of packets in transit (NPT). The simulation modeling and analysis of this type of performance indicator enables a theoretical investigation of the underlying complex system through different combination of network setups such as routing algorithms, network source loads or network topologies. To detect stationary increase of network source load, we propose a dynamic principal component analysis (PCA) method, first to extract data features and then to detect a stationary load increase. The proposed detection schemes are based on either the major or the minor principal components of network traffic data. To demonstrate the applications of the proposed method, we first applied them to some synthetic data and then to network traffic data simulated from the packet switching network (PSN) model. The proposed detection schemes, based on dynamic PCA, show enhanced performance in detecting an increase of network load for the simulated network traffic data. These results show usefulness of a new feature extraction method based on dynamic PCA that creates additional feature variables for event detection in a univariate time series. 1. Introduction The dynamics of many complex systems such as computer networks, financial systems, transportation systems, or power systems are mathematically intractable due to their complexity ([1–3]). Better understanding of states of the complex systems and how these states change is accomplished by analyzing the data coming from the underlying complex systems [4]. In network system performance analysis, the traffic data is measured over time and statistical quality control techniques such as process control are often applied to detect whether thresholds are exceeded based on the standard deviations of observed variables. Statistical process control is the application of statistical methods such as principal component analysis (PCA) to the monitoring and control of a process to ensure that it operates at its full potential to produce conforming product. Monitoring the changes of traffic load is a practical issue to ensure that network systems are not overridden by users [5], in particular, when the load increase is stationary. We define the stationary load increase as a state of network traffic that is before the phase transition. The phase transition is due to a large increase of network source load so that the amount of network traffic appears to be increasing upward. That is,
References
[1]
T. Sheldon, Encyclopedia of Networking & Telecommunications, Osborne/McGraw-Hill, Berkeley, Calif, USA, 2001.
[2]
A. Y. Tretyakov, H. Takayasu, and M. Takayasu, “Phase transition in a computer network model,” Physica A, vol. 253, no. 1–4, pp. 315–322, 1998.
[3]
L. Kocarev and G. Vattay, Eds., Complex Dynamics in Communication Networks, Springer, New York, NY, USA, 2005.
[4]
J. Wang, Z. Ma, and L. Li, “Detection, mining and forecasting of impact load in power load forecasting,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 29–39, 2005.
[5]
F. Mata, J. Aracil, and J. L. Garcia-Dorado, “Automated detection of load changes in large-scale networks,” in TMA 2009, M. Papadopouli, P. Owezarski, and A. Pras, Eds., vol. 5537 of Lecture Notes in Computer Science, p. 3441, Springer, Berlin, Germany.
[6]
B.-Y. Choi, J. Park, and Z.-L. Zhang, “Adaptive random sampling for load change detection,” Performance Evaluation Review, vol. 30, no. 1, pp. 272–273, 2002.
[7]
S. Storie and M. Sosonkina, “Packet probing as network load detection for scientific applications at run-time,” in Proceedings of the 18th International Parallel and Distributed Processing Symposium (IPDPS '04), pp. 871–880, April 2004.
[8]
G. E. P. Box, “Non-normality and tests on variances,” Biometrika, vol. 40, no. 3/4, Article ID 318335.
[9]
C. A. Markowski and E. P. Markowski, “Conditions for the effectiveness of a preliminary test of variance,” The American Statistician, vol. 44, no. 4, Article ID 322326, 1990.
[10]
R. Kwitt and U. Hofmann, “Unsupervised anomaly detection in network traffic by means of robust PCA,” in Proceedings of the International Multi-Conference on Computing in the Global Information Technology (ICCGI '07), 2007.
[11]
M. Shyu, S. Chen, K. Sarinnapakorn, and L. Chang, “A novel anomaly detection scheme based on principal component classifier,” in Proceedings of the 3rd IEEE International Conference on Data Mining (ICDM '03), pp. 172–179, Melbourne, Fla, USA, November 2003.
[12]
A. T. Lawniczak, A. Gerisch, and B. Di Stefano, “OSI network-layer abstraction: analysis of simulation dynamics and performance indicators, science of complex networks,” in Science of Complex Networks: From Biology to the Internet and WWW (CNET '04), J. F. Mendes, Ed., vol. 776 of AIP Conference Proceedings, pp. 166–200, 2005.
[13]
A. Gerisch, A. T. Lawniczak, and B. Di Stefano, “Building blocks of a simulation environment of the OSI network layer of packet switching networks,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering: Toward a Caring and Humane Technology (CCECE '03), pp. 1067–1070, Montreal, Canada, May 2003.
[14]
A. Gerisch, A. T. Lawniczak, and B. Di Stefano, “Building blocks of a simulation environment of the OSI network layer of packet-switching networks,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering: Toward a Caring and Humane Technology (CCECE '03), pp. 1067–1070, Montreal, Canada, May 2003.
[15]
A. T. Lawniczak and S. Xie, “Impact of source load and routing on QoS of packets delivery,” Journal of Computational Science, vol. 1, no. 2, pp. 121–129, 2010.
[16]
A. T. Lawniczak and S. Xie, “Number of packets in transit as a function of source load and routing,” in Proceedings of the 10th International Conference on Computational Science (ICCS '10), pp. 2363–2370, June 2010.
[17]
S. Xie and A. T. Lawniczak, “Detection of stationary network load increase using univariate network aggregate traffic data by dynamic PCA,” in IEEE Symposium Series on Computational Intelligence, Paris, France, April 2011.
[18]
W. Ku, R. H. Storer, and C. Georgakis, “Disturbance detection and isolation by dynamic principal component analysis,” Chemometrics and Intelligent Laboratory Systems, vol. 30, no. 1, pp. 179–196, 1995.
[19]
F. Tsung, “Statistical monitoring and diagnosis of automatic controlled processes using dynamic PCA,” International Journal of Production Research, vol. 38, no. 3, pp. 625–637, 2000.
[20]
I. T. Jolliffe, Principal Component Analysis, Springer Science, New York,, 2004.
[21]
R. H. Shumway and D. S. Stoer, Time Series Analysis and Its Applications With R Examples, Springer Science, New York, NY, USA, 2005.
