Closed form solutions for mapping general distributions to quasi-minimal PH distributions

Performance Evaluation

Volumn 63, Issue 6, 2006, Pages 524-552

  Osogami, Takayuki ^a   Harchol Balter, Mor ^a  

^a Carnegie Mellon University   (United States)

Author keywords

Closed form; Moment matching; Normalized moment; PH distribution

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; MARKOV PROCESSES; PARAMETER ESTIMATION; RANDOM PROCESSES;

CLOSED FORM; ERLANG-COXIAN DISTRIBUTIONS; MOMENT MATCHING; NORMALIZED MOMENT; PHASE-TYPE (PH) DISTRIBUTIONS;

MAPPING;

EID: 33645885335     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.peva.2005.06.002     Document Type: Article

References (29)

1. Aldous D., and Shepp L. The least variable phase type distribution is Erlang. Commu. Statist.-Stochast. Models 3 (1987) 467-473
2. Altiok T. On the phase-type approximations of general distributions. IIE Trans. 17 (1985) 110-116
3. Cumani A. On the canonical representation of homogeneous Markov processes modeling failure-time distributions. Microelectron. Reliab. 22 (1982) 583-602
4. Feldmann A., and Whitt W. Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. Perform. Eval. 32 (1998) 245-279
5. Franke H., Jann J., Moreira J., Pattnaik P., and Jette M. An evaluation of parallel job scheduling for ASCI blue-pacific. Proceedings of the Supercomputing'99 (November 1999) 679-691
6. A. Horváth, M. Telek, Approximating heavy tailed behavior with phase type distributions, in: Advances in Algorithmic Methods for Stochastic Models, Notable Publications, New Jersey, 2000, pp. 191-214.
7. Horváth A., and Telek M. Phfit: a general phase-type fitting tool. Proceedings of the TOOLS 2002 (April 2002) 82-91
8. Johnson M.A. Selecting parameters of phase distributions: combining nonlinear programming, heuristics, and Erlang distributions. ORSA J. Comput. 5 (1993) 69-83
9. Johnson M.A., and Taaffe M.F. An investigation of phase-distribution moment-matching algorithms for use in queueing models. Queueing Syst. 8 (1991) 129-147
10. Johnson M.A., and Taaffe M.R. Matching moments to phase distributions: mixtures of Erlang distributions of common order. Commun. Statist.-Stochast. Models 5 (1989) 711-743
11. Johnson M.A., and Taaffe M.R. Matching moments to phase distributions: density function shapes. Commun. Statist.-Stochast. Models 6 (1990) 283-306
12. Johnson M.A., and Taaffe M.R. Matching moments to phase distributions: nonlinear programming approaches. Commun. Statist.-Stochast. Models 6 (1990) 259-281
13. Karlin S., and Studden W. Tchebycheff Systems: With Applications in Analysis and Statistics (1966), Wiley, New Yrok
14. Khayari R.E.A., Sadre R., and Haverkort B. Fitting world-wide web request traces with the EM-algorithm. Perform. Eval. 52 (2003) 175-191
15. k / 1 / n queues. Proceedings of the Performance 1980 (1980) 117-125
16. O'Cinneide C.A. Phase-type distributions and majorization. Ann. Appl. Probab. 1 3 (1991) 219-227
17. T. Osogami, Analysis of multi-server systems via dimensionality reduction of Markov chains, PhD Thesis, School of Computer Science, Carnegie Mellon University, 2005.
18. Osogami T., and Harchol-Balter M. A closed-form solution for mapping general distributions to minimal PH distributions. Proceedings of the TOOLS 2003 (September 2003) 200-217
19. Osogami T., and Harchol-Balter M. Necessary and sufficient conditions for representing general distributions by Coxians. Proceedings of the TOOLS 2003 (September 2003) 182-199
20. Riska A., Diev V., and Smirni E. An EM-based technique for approximating long-tailed data sets with PH distributions. Perform. Eval. 55 1/2 (2004) 147-164
21. Sauer C., and Chandy K. Approximate analysis of central server models. IBM J. Res. Dev. 19 (1975) 301-313
22. Schmickler L. MEDA: mixed Erlang distributions as phase-type representations of empirical distribution functions. Commun. Statist.-Stochast. Models 8 (1992) 131-156
23. M. Squillante, Matrix-analytic methods in stochastic parallel-server scheduling models, in: Advances in Matrix-Analytic Methods for Stochastic Models, Notable Publications, New Jersey, 1998.
24. Starobinski D., and Sidi M. Modeling and analysis of power-tail distributions via classical teletraffic methods. Queueing Syst. 36 (2000) 243-267
25. Telek M., and Heindl A. Matching moments for acyclic discrete and continuous phase-type distributions of second order. Int. J. Simulat. 3 (2003) 47-57
26. van Houtum G., and Zijm W. Computational procedures for stochastic multi-echelon production systems. Int. J. Prod. Econ. 23 (1991) 223-237
27. van Houtum G., and Zijm W. Incomplete convolutions in production and inventory models. OR Spektrum 10 (1997) 97-107
28. Whitt W. Approximating a point process by a renewal process: two basic methods. Operat. Res. 30 (1982) 125-147
29. Zhang Y., Franke H., Moreira J., and Sivasubramaniam A. An integrated approach to parallel scheduling using gang-scheduling, backfilling, and migration. IEEE Trans. Parallel Distrib. Syst. 14 (2003) 236-247