Refrences:
1.Neuts, M.F. Computational uses of the method of phases in the theory of queues", Computers & Mathematics with Applications, 1(2), pp. 151-166 (1975).
2. Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Johns Hopkins University, Baltimore (1981).
3. Fackrell, M. Modelling healthcare systems with phase-type distributions", Health Care Management Science, 12, pp. 11-26 (2009). 4. Thummler, A., Buchholz, P., and Telek, M. A novel approach for phase-type _tting with the EM algorithm", IEEE Transactions on Dependable and Secure Computing, 3(3), pp. 245-258 (2006). 5. Hu, L., Jiang, Y., Zhu, J., and Chen, Y. Hybrid of the scatter search, improved adaptive genetic, and expectation maximization algorithms for phase-type distribution _tting", Applied Mathematics and Computation, 219(10), pp. 5495-5515 (2013). 6. Anbazhagan, N., Stochastic Processes and Models in Operations Research, Hershey, Pennsylvania 701 E. Chocolate Avenue, Hershey, PA 17033, USA: IGI Global (2016). 7. Horv_ath, A. and Telek, M. Ph_t: A general phasetype _tting tool", Computer Performance Evaluation: Modelling Techniques and Tools, pp. 82-91 (2002). 8. Bobbio, A., Horv_ath, A., Scarpa, M., and Telek, M. Acyclic discrete phase type distributions: properties and a parameter estimation algorithm", Performance Evaluation, 54(1), pp. 1-32 (2003). 9. Callut, J. and Dupont, P. Sequence discrimination using phase-type distributions", Machine Learning: ECML 2006, pp. 78-89 (2006). 10. Asmussen, S., Nerman, O., and Olsson, M. Fitting phase-type distributions via the EM algorithm", Scandinavian Journal of Statistics, 23(4), pp. 419-441 (1996). 11. Bladt, M., Esparza, L.J.R., Nielsen, B.F., et al. Fisher information and statistical inference for phase-type distributions", Journal of Applied Probability, 48, pp. 277-293 (2011). 12. Mesz_aros, A., Papp, J., and Telek, M. Fitting tra_c traces with discrete canonical phase type distributions and Markov arrival processes", International Journal of Applied Mathematics and Computer Science, 24(3), pp. 453-470 (2014). 13. Horv_ath, I., Papp, J., and Telek, M. On the canonical representation of order 3 discrete phase type distributions", Electronic Notes in Theoretical Computer Science, 318, pp. 143-158 (2015). 14. Springer, T. and Urban, K. Comparison of the EM algorithm and alternatives", Numerical Algorithms, 67(2), pp. 335-364 (2014). 15. Verbelen, R., Phase-Type Distributions & Mixtures of Erlangs, University of Leuven (2013). 16. O'Hagan, A., Murphy, T.B., and Gormley, I.C. Computational aspects of _tting mixture models via the expectation-maximization algorithm", Computational Statistics & Data Analysis, 56(12), pp. 3843-3864 (2012). 17. Xu, J. and Ma, J. Fitting _nite mixture models using iterative Monte Carlo classi_cation", Communications in Statistics-Theory and Methods, 46(13), pp. 6684- 6693 (2017). 18. Bilmes, J.A. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models", International Computer Science Institute, 4(510), p. 126 (1998). 19. McLachlan, G. and Krishnan, T., The EM Algorithm and Extensions, 382, John Wiley & Sons (2007). 20. Dougherty, J., Kohavi, R., and Sahami, M. Supervised and unsupervised discretization of continuous feature", In Proceedings of 12th International Conference of Machine Learning, pp. 194-202 (1995). 21. MATLAB Release 2014a, MathWorks, Inc. (2015). 22. Bowers, J. and Mould, G. Managing uncertainty in orthopaedic trauma theatres", European Journal of Operational Research, 154(3), pp. 599-608 (2004). 23. Perez, J. and Riano, G. Benchmarking of _tting algorithms for continuous phase-type distributions", Working Paper, COPA Universidad de los Andes, pp. 1-20 (2007). 24. Chiarandini, M., Basso, D., and Stutzle, T. Statistical methods for the comparison of stochastic optimizers", In MIC2005: The Sixth Metaheuristics International Conference, pp. 189-196 (2005). 25. SAS Release, 9.1, SAS Institute Inc. (2003). 26. Bobbio, A. and Telek, M. A benchmark for PH estimation algorithms: results for Acyclic-PH", Stochastic Models, 10(3), pp. 661-677 (1994). 586 M. Varmazyar et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 571{588 27. Latouche, G. and Ramaswami, V., Introduction to Matrix Analytic Methods in Stochastic Modeling, 5, Siam (1999). 28. Alfa, A., Applied Discrete-time Queues, Springer- Verlag New York (2016). 29. Varmazyar, M., Akhavan-Tabatabaei, R., Salmasi, N., and Modarres, M. Classi_cation and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions", Journal of Industrial Engineering International (Nov 2018).
)