A novel approach for phase-type fitting with the EM algorithm

IEEE Transactions on Dependable and Secure Computing

Volumn 3, Issue 3, 2006, Pages 245-258

  Thümmler, Axel ^b   Buchholz, Peter ^a,b   Telek, Miklós ^c  

^a IEEE

^b TU DORTMUND UNIVERSITY   (Germany)

^c BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Communication networks; Hyper Erlang distributions; Markov processes; Performance analysis and design aids; Traffic modeling

Indexed keywords

ALGORITHMS; BENCHMARKING; CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; NUMERICAL METHODS; TELECOMMUNICATION NETWORKS;

HYPER-ERLANG DISTRIBUTIONS; PARAMETER FITTING; PERFORMANCE ANALYSIS; TRAFFIC MODELING;

SECURITY OF DATA;

EID: 33748117946     PISSN: 15455971     EISSN: None     Source Type: Journal    
DOI: 10.1109/TDSC.2006.27     Document Type: Conference Paper

References (25)

1. S. Asmussen, O. Nerman, and M. Olsson, "Fitting Phase-Type Distributions via the EM Algorithm," Scandinavian J. Statistics, vol. 23, pp. 419-441, 1996.
2. A. Bobbio, A. Horváth, M. Scarpa, and M. Telek, "Acyclic Discrete Phase Type Distributions: Properties and a Parameter Estimation Algorithm," Performance Evaluation, vol. 54, pp. 1-32, 2003.
3. A. Bobbio and M. Telek, "A Benchmark for Estimation Algorithms: Results for Acyclic-PH," Stochastic Models, vol. 10, pp. 661-677, 1994.
4. P. Buchholz, "An EM-Algorithm for MAP Fitting from Real Traffic Data," Proc. Int'l Conf. Computer Performance Evaluation-Modelling Techniques and Tools (TOOLS '03), pp. 218-236, 2003.
5. A. Cumani, "On the Canonical Representation of Homogeneous Markov Processes Modeling Failure-Time Distributions," J. Microekctronics and Reliability, vol. 22, pp. 583-602, 1982.
6. A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum Likelihood from Incomplete Data via the EM Algorithm," J. Royal Statistical Soc., vol. 39, pp. 1-38, 1977.
7. A. Edelman and H. Murakami, "Polynomial Roots from Companion Matrix Eigenvalues," Math, of Computation, vol. 64, pp. 763-776, 1995.
8. R. El Abdouni Khayari, R. Sadre, and B.R. Haverkort, "Fitting World-Wide Web Request Traces with the EM-Algorithm," Performance Evaluation, vol. 52, pp. 175-191, 2003.
9. Y. Fang, "Hyper-Erlang Distribution Model and Its Application in Wireless Mobile Networks," Wireless Networks, vol. 7, pp. 211-219, 2001.
10. A. Feldmann and W. Whitt, "Fitting Mixtures of Exponentials to Long-Tail Distributes to Analyze Network Performance Models," Performance Evaluation, vol. 31, pp. 245-258, 1998.
11. B.R. Haverkort, "Markovian Models for Performance and Dependability Modeling," Proc. Conf. Formal Methods and Performance Analysis (FMPA '00), pp. 38-83, 2001.
12. G-FIT Software, Is4-www.cs.uni-dortmund.de/home/thummler, 2005.
13. A. Horváth and M. Telek, "Markovian Modeling of Real Data Traffic: Heuristic Phase Type and MAP Fitting of Heavy Tailed and Fractal Like Samples," Proc. Conf. Evaluation of Complex Systems: Techniques and Tools (Performance '02), pp. 405-434, 2002.
14. A. Horváth and M. Telek, "Phfit: A General Phase-Type Fitting Tool," Proc. Int'l Conf. Computer Performance Evaluation-Modelling Techniques and Tools (TOOLS '02), T. Fields, P.G. Harrison, J. Bradley, and U. Harder, eds., pp. 82-91, 2002.
15. M.A. Johnson, "Selecting Parameters of Phase Distributions: Combining Nonlinear Programming, Heuristics, and Erlang Distributions," ORSA J. Computing, vol. 5, pp. 69-83, 1993.
16. M.A. Johnson and M.R. Taaffe, "The Denseness of Phase Distributions," Purdue School of Industrial Eng. Research Memoranda, no. 88-20, 1988.
17. M.A. Johnson and M.R. Taaffe, "Matching Moments to Phase Distributions: Mixtures of Erlang Distributions of Common Order," Stochastic Models, vol. 5, pp. 711-743, 1989.
18. M.A. Johnson and M.R. Taaffe, "Matching Moments to Phase Distributions: Nonlinear Programming Approaches," Stochastic Models, vol. 6, pp. 259-281, 1990.
19. T. Krishnan and G.J. McLachlan, The EM Algorithm and Extensions. John Wiley and Sons, 1997.
20. A. Lang and J.L. Arthur, "Parameter Approximation for Phase-Type Distributions. Matrix Analytical Methods in Stochastic Models," Lecture Notes in Pure and Applied Math., vol. 183, pp. 151-206, 1997.
21. A. Mandelbaum, A. Sakov, and S. Zeltyn, "Empirical Analysis of a Call Center," technical report, Technion, Israel Inst. of Technology, 2000.
22. S. Resnick, "Modeling Data Networks," Technical Report TR-1345, School of Operations Research and Industrial Eng., Cornell Univ., 2002.
23. A. Riska, V. Diev, and E. Smirni, "An EM-Based Technique for Approximating Long-Tailed Data Sets with PH Distributions," Performance Evaluation, vol. 55, pp. 147-164, 2004.
24. L. Schmickler, "MEDA: Mixed Erlang Distributions as Phase-Type Representations of Empirical Distribution Functions," Stochastic Models, vol. 8, pp. 131-156, 1992.
25. K.S. Trivedi, Probability and Statistics with Reliability, Queuing and Computer Science Applications, second ed. John Wiley and Sons, 2002.