Cluster-based fitting of phase-type distributions to empirical data

Computers and Mathematics with Applications

Volumn 64, Issue 12, 2012, Pages 3840-3851

  Reinecke, Philipp ^a   Krauß, Tilman ^a   Wolter, Katinka ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Data modelling; PH fitting; Phase type distribution

Indexed keywords

CLUSTER-BASED; EFFICIENT SIMULATION; EMPIRICAL DATA; PHASE TYPE DISTRIBUTIONS; USER FRIENDLY INTERFACE;

ALGORITHMS; DATA STRUCTURES; MATHEMATICAL MODELS;

CLUSTERING ALGORITHMS;

EID: 84870255840     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2012.03.016     Document Type: Article

References (30)

1. M. Telek, and A. Heindl Matching moments for acyclic discrete and continous phase-type distributions of second order International Journal of Simulation: Systems, Science & Technology 3 3-4 2002 47 57
2. A. Horváth, and M. Telek PhFit: a general phase-type fitting tool TOOLS'02: Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools 2002 Springer-Verlag London, UK 82 91
3. A. Thümmler, P. Buchholz, and M. Telek A novel approach for phase-type fitting with the EM algorithm IEEE Transactions on Dependable Secure Computing 3 3 2006 245 258 10.1109/TDSC.2006.27 (Pubitemid 44304211)
4. J. Wang, J. Liu, and C. She Segment-based adaptive hyper-Erlang model for long-tailed network traffic approximation The Journal of Supercomputing 45 2008 296 312 10.1007/s11227-008-0173-5
5. P. Reinecke, K. Wolter, L. Bodrog, M. Telek, On the cost of generating PH-distributed random numbers, in: G. Horváth, K. Joshi, A. Heindl (Eds.), Proceedings of the Ninth International Workshop on Performability Modeling of Computer and Communication Systems, PMCCS-9, Eger, Hungary, 2009, pp. 16-20.
6. G. Horváth, M. Telek, Acceptance-rejection methods for generating random variates from matrix exponential distributions and rational arrival processes, in: Int. Conf. on Martix Analytic Methods, MAM, New York, USA, 2011.
7. M.F. Neuts Matrix-geometric Solutions in Stochastic Models. An Algorithmic Approach 1981 Dover Publications, Inc. New York
8. P. Reinecke, M. Telek, and K. Wolter Reducing the costs of generating APH-distributed random numbers B. Müller-Clostermann, K. Echtle, E. Rathgeb, MMB & DFT 2010 LNCS vol. 5987 2010 Springer-Verlag Berlin, Heidelberg 274 286
9. A. Cumani On the canonical representation of homogeneous Markov processes modelling failure-time distributions Microelectronics and Reliability 22 1982 583 602
10. S. Mocanu, and C. Commault Sparse representations of phase-type distributions Communications in Statistics Stochastic Models 15 4 1999 759 778
11. S.P. Lloyd Least squares quantization in PCM IEEE Transactions on Information Theory 28 2 1982 129 136
12. D. Aldous, and L. Shepp The least variable phase-type distribution is Erlang Stochastic Models 3 1987 467 473
13. A. Riska, V. Diev, and E. Smirni Efficient fitting of long-tailed data sets into phase-type distributions SIGMETRICS Performance Evaluation Review 30 2002 6 8 http://doi.acm.org/10.1145/605521.605525
14. R. Sadre, and B. Haverkort Fitting heavy-tailed http traces with the new stratified EM-algorithm 4th International Telecommunication Networking Workshop on QoS in Multiservice IP Networks IT-NEWS 2008 IEEE Computer Society Press Los Alamitos 254 261 URL: http://doc.utwente.nl/64721/
15. J. Wang, H. Zhou, F. Xu, and L. Li Hyper-Erlang based model for network traffic approximation Y. Pan, D. Chen, M. Guo, J. Cao, J. Dongarra, Parallel and Distributed Processing and Applications Lecture Notes in Computer Science vol. 3758 2005 Springer Berlin, Heidelberg 1012 1023 10.1007/11576235101 (Pubitemid 43734204)
16. A. Feldmann, and W. Whitt Fitting mixtures of exponentials to long-tail distributions to analyze network Performance Evaluation 31 3-4 1998 245 279 (Pubitemid 128384209)
17. H. Ge, U. Harder, P. Harrison, Parameter estimation for MMPPs using the EM algorithm, in: UKPEW 2003, 2003.
18. M. Frank, and P. Wolfe An algorithm for quadratic programming Naval Research Logistics Quarterly 3 1-2 1956 95 110 10.1002/nav.3800030109
19. J.F. Pérez, and G. Riaño jPhase: an object-oriented tool for modeling phase-type distributions Proceeding from the 2006 Workshop on Tools for Solving Structured Markov Chains, SMCtools'06 2006 ACM New York, NY, USA http://doi.acm.org/10.1145/1190366.1190370
20. F. Bause, P. Buchholz, and J. Kriege ProFiDo - the processes fitting toolkit dortmund Proc. of the 7th International Conference on Quantitative Evaluation of SysTems QEST 2010 2010 IEEE Computer Society 87 96 http://doi.ieeecomputersociety.org/10.1109/QEST.2010.20
21. G. Casale, E.Z. Zhang, and E. Smirni Kpc-toolbox: simple yet effective trace fitting using Markovian arrival processes Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems 2008 IEEE Computer Society Washington, DC, USA 83 92 10.1109/QEST.2008.33 URL: http://dl.acm.org/citation.cfm?id=1446304.1447432
22. A. Bobbio, A. Horváth, and M. Telek Matching three moments with minimal acyclic phase type distributions Stochastic Models 21 2 2005 303 326 (Pubitemid 41663194)
23. R Development Core Team R: A Language and Environment for Statistical Computing 2006 R Foundation for Statistical Computing Vienna, Austria 3-900051-07-0 URL: http://www.R-project.org
24. L. Bodrog, P. Buchholz, A. Heindl, A. Horváth, G. Horváth, I. Kolossváry, Z. Németh, P. Reinecke, M. Telek, M. Vécsei, Butools: program packages for computations with PH, ME distributions and MAP, RAP processes, October 2011. http://webspn.hit.bme.hu/~butools.
25. P. Reinecke, K. Wolter, A simulation study on the effectiveness of restart and rejuvenation to mitigate the effects of software ageing, in: WoSAR 2010, 2010.
26. B. Blywis, M. Günes, F. Juraschek, O. Hahm, N. Schmittberger, Properties and topology of the DES-testbed (2nd extended revision), Tech. Rep. TR-B-11-04, Freie Universität Berlin, July 2011.
27. A. Lang, and J. Arthur Parameter approximation for phase-type distributions Matrix-Analytic Methods in Stocastic Modells 183 1996 151 206
28. K. Wolter, P. Reinecke, and A. Mittermaier Model-based evaluation and improvement of PTP syntonisation accuracy in packet-switched Backhaul networks for mobile applications N. Thomas, Computer Performance Engineering. Proceedings of the 8th European Performance Engineering Workshop, EPEW 2011 LNCS vol. 6977 2011 Springer 219 234
29. R. El Abdouni Khayari, R. Sadre, and B.R. Haverkort Fitting world-wide web request traces with the EM-algorithm Performance Evaluation 52 2-3 2003 175 191 URL: http://doc.utwente.nl/61888/
30. The Internet Traffic Archive, NASA-HTTP - two months of HTTP logs from a busy WWW server. URL: http://ita.ee.lbl.gov/html/contrib/NASA-HTTP.html.