Abstract
Recently, an efficient and stable method to compute moments of first passage times from a subset of states classified as safe to the other states in ergodic discrete-time Markov chains (DTMCs) has been proposed. This paper shows that the same method can be used to compute moments of discrete phase-type (DPH) distributions, analyzes its complexity on various acyclic DPH (ADPH) distributions, and presents results on a set of DPH distributions arising in a test suite of DTMCs.
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References
Bobbio, A., Horváth, A., Scarpa, M., Telek, M.: Acyclic discrete phase type distributions: properties and a parameter estimation algorithm. Performance Evaluation 54(1), 1–32 (2003)
Bobbio, A., Horváth, A., Telek, M.: The scale factor: a new degree of freedom in phase-type approximation. Performance Evaluation 56(1–4), 121–144 (2004)
Dayar, T.: Software for computing moments of phase type distributions (2005), Available from, http://www.cs.bilkent.edu.tr/~tugrul/software.html
Dayar, T., Akar, N.: Computing moments of firt passage times to a subset of states in Markov chains. SIAM Journal on Matrix Analysis and Applications, to appear. Also as Technical Report BU-CE-0414, Department of Computer Engineering, Bilkent University, Ankara, Turkey (December 2004), Available from http://www.cs.bilkent.edu.tr/tech-reports/2004/BU-CE-0414.pdf
Dayar, T., Stewart, W.J.: Comparison of partitioning techniques for two-level iterative methods on large, sparse Markov chains. Technical Report BU-CEIS-9805, Department of Computer Engineering and Information Science, Bilkent University, Ankara, Turkey (April 1998), Available from, http://www.cs.bilkent.edu.tr/tech-reports/1998/BU-CEIS-9805.ps.gz
Dayar, T., Stewart, W.J.: A test suite of Markov chains (2005), Available from, http://www.cs.bilkent.edu.tr/~tugrul/matrices.html
Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley Publishing Company, Reading (1989)
Grassmann, W.K., Taksar, M.I., Heyman, D.P.: Regenerative analysis and steady state distributions for Markov chains. Operations Research 33(5), 1107–1116 (1985)
Haverkort, B.R.: Performance of Computer Communication Systems: A Model-based Approach. John Wiley & Sons, Chichester (1998)
Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM Press, Philadelphia (1999)
Nakazawa, S., Kawahara, K., Yamaguchi, S., Oie, Y.: Performance comparison with layer 3 switches in case of flow- and topology-driven connection setup. In: IEEE Global Telecommunications Conference, GLOBECOM 1999, Rio de Janeiro, Brazil, December 1999, vol. 1a, pp. 79–86. IEEE Press, New York (1999)
Neuts, M.F.: Probability distributions of phase type. In: Liber amicorum Prof. Emeritus H. Florin. Department of Mathematics, pp. 173–206. University of Louvain, Belgium (1975)
Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore (1981)
Robert, S., Le Boudec, J.-Y.: New models for pseudo self-similar traffic. Performance Evaluation 30(1–2), 57–68 (1997)
Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)
Telek, M., Heindl, A.: Matching moments for acyclic discrete and continuous phase-type distributions of second order. International Journal of Simulation: Systems, Science & Technology 3(3–4), 47–57 (2002)
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Dayar, T. (2005). On Moments of Discrete Phase-Type Distributions. In: Bravetti, M., Kloul, L., Zavattaro, G. (eds) Formal Techniques for Computer Systems and Business Processes. EPEW WS-FM 2005 2005. Lecture Notes in Computer Science, vol 3670. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549970_5
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DOI: https://doi.org/10.1007/11549970_5
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