A Fast EM Algorithm for Fitting Marked Markovian Arrival Processes with a New Special Structure

1. Anderson, T.W., Goodman, L.A.: Statistical inference about Markov chains. The Annals of Mathematical Statistics, 89–110 (1957)

   Google Scholar 

2. Asmussen, S., Nerman, O., Olsson, M.: Fitting phase-type distributions via the EM algorithm. Scandinavian Journal of Statistics, 419–441 (1996)

   Google Scholar 

3. Bause, F., Horváth, G.: Fitting Markovian Arrival Processes by Incorporating Correlation into Phase Type Renewal Processes. In: 2010 Seventh International Conference on the Quantitative Evaluation of Systems (QEST), pp. 97–106. IEEE (2010)

   Google Scholar 

4. Breuer, L.: An EM algorithm for batch Markovian arrival processes and its comparison to a simpler estimation procedure. Annals of Operations Research 112(1-4), 123–138 (2002)

   Article  MathSciNet  MATH  Google Scholar 

5. Buchholz, P.: An EM-algorithm for MAP fitting from real traffic data. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol. 2794, pp. 218–236. Springer, Heidelberg (2003)

   Chapter  Google Scholar 

6. Buchholz, P., Kemper, P., Kriege, J.: Multi-class Markovian arrival processes and their parameter fitting. Performance Evaluation 67(11), 1092–1106 (2010)

   Article  Google Scholar 

7. Buchholz, P., Kriege, J.: A heuristic approach for fitting MAPs to moments and joint moments. In: Sixth International Conference on the Quantitative Evaluation of Systems, QEST 2009, pp. 53–62. IEEE (2009)

   Google Scholar 

8. Casale, G., Zhang, E.Z., Smirni, E.: KPC-toolbox: Simple yet effective trace fitting using Markovian arrival processes. In: Fifth International Conference on Quantitative Evaluation of Systems, QEST 2008, pp. 83–92. IEEE (2008)

   Google Scholar 

9. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 1–38 (1977)

   Google Scholar 

10. El Abdouni Khayari, R., Sadre, R., Haverkort, B.R.: Fitting world-wide web request traces with the EM-algorithm. Performance Evaluation 52(2), 175–191 (2003)

    Article  Google Scholar 

11. He, Q., Neuts, M.F.: Markov chains with marked transitions. Stochastic Processes and their Applications 74, 37–52 (1998)

    Article  MathSciNet  MATH  Google Scholar 

12. Horváth, A., Horváth, G., Telek, M.: A traffic based decomposition of two-class queueing networks with priority service. Computer Networks 53(8), 1235–1248 (2009)

    Article  MATH  Google Scholar 

13. Horváth, G., Buchholz, P., Telek, M.: A MAP fitting approach with independent approximation of the inter-arrival time distribution and the lag correlation. In: Second International Conference on the Quantitative Evaluation of Systems, pp. 124–133. IEEE (2005)

    Google Scholar 

14. Klemm, A., Lindemann, C., Lohmann, M.: Modeling IP traffic using the batch Markovian arrival process. Performance Evaluation 54(2), 149–173 (2003)

    Article  Google Scholar 

15. Latouche, G., Ramaswami, V.: Introduction to matrix analytic methods in stochastic modeling. Society for Industrial and Applied Mathematics, vol. 5 (1987)

    Google Scholar 

16. Okamura, H., Dohi, T.: Faster maximum likelihood estimation algorithms for Markovian arrival processes. In: Sixth International Conference on the Quantitative Evaluation of Systems, QEST 2009, pp. 73–82. IEEE (2009)

    Google Scholar 

17. Okamura, H., Dohi, T., Trivedi, K.S.: A refined EM algorithm for PH distributions. Performance Evaluation 68(10), 938–954 (2011)

    Article  Google Scholar 

18. Rydén, T.: An EM algorithm for estimation in Markov-modulated Poisson processes. Computational Statistics & Data Analysis 21(4), 431–447 (1996)

    Article  MathSciNet  MATH  Google Scholar 

19. Telek, M., Horváth, G.: A minimal representation of Markov arrival processes and a moments matching method. Performance Evaluation 64(9), 1153–1168 (2007)

    Article  Google Scholar 

20. Thummler, A., Buchholz, P., Telek, M.: A novel approach for phase-type fitting with the EM algorithm. IEEE Transactions on Dependable and Secure Computing 3(3), 245–258 (2006)

    Article  Google Scholar 

Download references