Abstract
The problem of Markov-modulated Poisson process intensities estimating is studied. A new approach based on sequential change point detection method is proposed to determine switching points of the flow parameter. Both the intensities of the controlling Markovian chain and the intensities of the flow of events are estimated. The results of simulation are presented.
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References
Neuts, M.F.: A versatile Markovian point process. J. Appl. Probab. 16, 764–774 (1979)
Lucantoni, D.M., Meier-Hellstern, K.S., Neuts, M.F.: A single server queue with server vacations and a class of non-renewal arrival processes. Adv. Appl. Probab. 22, 676–705 (1990)
Dudina, O., Dudin, S.: Queueing system MAP/M/N/N + K operating in random environment as a model of call center. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 83–92. Springer, Heidelberg (2013)
Dudin, S.: The servicing system MAP(PH) plus MAP/PH/N/R as a model of optimizing an HTTP server with blockings. Autom. Remote Control 1, 28–38 (2010)
Fackrell, M.: Health Care Manage. Sci. Modelling healthcare systems with phase-type distributions 12, 11–26 (2008). Springer Science + Business Media, LLC
Asmussen, S.: Phase-type distributions and related point processes: fitting and recent advances. In: Chakravarthy, S.R., Alfa, A.S. (eds.) Matrix-analytic Methods in Stochastic Models. Lecture Notes in Pure and Applied Mathematics, pp. 137–149. Marcel Dekker, New York (1997)
Breuer, L., Kume, A.: An EM algorithm for Markovian arrival processesobserved at discrete times. In: Müller-Clostermann, B., Echtle, K., Rathgeb, E.R. (eds.) MMB&DFT 2010. LNCS, vol. 5987, pp. 242–258. Springer, Berlin (2010)
Okamura, H., Dohi, T., Trivedi, K.S.: Markovian arrival process parameter estimation with group data. IEEE/ACM Trans. Netw. 17(4), 1326–1340 (2009)
Gerhardt, I., Nelson, B.L.: On capturing dependence in point processes: matching moments and other techniques. Technical report, Northwestern university (2009)
Duffie, D., Glynn, P.: Estimation of continuous-time markov processes sampled at random time intervals. Econometrica 72, 1773–1808 (2004)
Gortsev, A.M., Zuevich, V.L.: Optimal estimation of parameters of an asynchronous doubly stochastic flow of events with arbitrary number of the states. Tomsk State Univ. J. Control Comput. Sci. 4(17), 25–40 (2011)
Page, E.S.: Continuous inspection schemes. Biometrica 42(1), 100–115 (1956)
Gortsev, A.M., Kalyagin, A.A., Nezhelskaya, L.A.: Optimum estimation of states in generalized semi-synchronous flow of events. Tomsk State Univ. J. Control Comput. Sci. 2(11), 66–81 (2010)
Lorden, G.: Procedures for reacting to a change in distribution. Ann. Math. Stat. 42, 1897–1908 (1971)
Acknowledgements
This paper is supported by The National Research Tomsk State University Academic D.I. Mendeleev Fund Program (NU 8.1.55.2015 L) in 2014–2015.
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Burkatovskaya, Y., Kabanova, T., Vorobeychikov, S. (2015). CUSUM Algorithms for Parameter Estimation in Queueing Systems with Jump Intensity of the Arrival Process. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_24
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DOI: https://doi.org/10.1007/978-3-319-25861-4_24
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