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An application of the correlation structure of a Markov chain for the estimation of shift parameters in queueing systems

Author(s): O. A. Voina; E. Czapla
Translated by: V. V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 71 (2004).
Journal: Theor. Probability and Math. Statist. No. 71 (2005), 53-61.
MSC (2000): Primary 62M05, 60J27; Secondary 60J99, 93E11
Posted: December 28, 2005
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Abstract: The problem on the estimation of shift parameters of a queueing system $ M/M/1/0$ from distorted data observed during a time interval between two sequential states of the system is considered in this paper. The information about the states of the system is not available. Asymptotic properties of the estimators are studied.

References:

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O. A. Vo{\u{\i\/}}\kern.15emna and O. O. Zhiga{\u{\i\/}}\kern.15emlo, The estimation of parameters for Markov systems with partially deformed observations, Dopovidi Akad. Nauk Ukrainy Ser. A (2001), no. 2, 70-74. (Ukrainian) MR 1837074 (2002c:62128)

2.
O. A. Vo{\u{\i\/}}\kern.15emna and E. Czapla, The estimation of shift parameters for queueing systems from observations of mixed input and output flows, Dopovidi Akad. Nauk Ukrainy Ser. A (2001), no. 8, 54-57. (Ukrainian) MR 1887243

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A. A. Vo{\u{\i\/}}\kern.15emna, Statistical estimation in a scheme of random variables on Markov chains, with incomplete observations, Teor. Veroyatnost. Matem. Statist. 37 (1987), 16-26; English transl. in Theory Probab. Math. Statist. 37 (1988), 19-28. MR 0913905 (88k:62164)

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J. Doob, Stochastic Processes, John Wiley-Chapman and Hall, New York, 1953. MR 0058896 (15:445b)

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P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, New York-London-Sydney-Toronto, 1968. MR 0233396 (38:1718)

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Additional Information:

O. A. Voina
Affiliation: Department of Economics and Management, Chair for Quantitative Methods, Technical University of Koszalin, Koszalin, Poland
Email: avoina@hotmail.com

E. Czapla
Affiliation: Department of Economics and Management, Chair for Quantitative Methods, Technical University of Koszalin, Koszalin, Poland

DOI: 10.1090/S0094-9000-05-00647-2
PII: S 0094-9000(05)00647-2
Received by editor(s): 30/AUG/2003
Posted: December 28, 2005
Copyright of article: Copyright 2005, American Mathematical Society

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