An application of the correlation structure of a Markov chain for the estimation of shift parameters in queueing systems
Authors:
O. A. Voĭna and E. Czapla
Translated by:
V. V. Semenov
Journal:
Theor. Probability and Math. Statist. 71 (2005), 53-61
MSC (2000):
Primary 62M05, 60J27; Secondary 60J99, 93E11
DOI:
https://doi.org/10.1090/S0094-9000-05-00647-2
Published electronically:
December 28, 2005
MathSciNet review:
2144320
Full-text PDF Free Access
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Additional Information
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
- O. A. Voĭna and O. O. Zhigaĭlo, On parametric estimates for Markov systems by partially deformed observations, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 2 (2001), 70–74 (Ukrainian, with English summary). MR 1837074
- O. A. Voĭna and E. Chaplya, Estimation of the shift parameters for a queueing system from observations of mixed input and output flows, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 8 (2001), 54–57 (Ukrainian, with English summary). MR 1887243
- A. A. Voĭna, Statistical estimation in a scheme of random variables on a Markov chain in the presence of incomplete observations, Teor. Veroyatnost. i Mat. Statist. 37 (1987), 16–26, 134 (Russian). MR 913905
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR 0058896
- Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
References
- O. A. Voĭna and O. O. Zhigaĭlo, 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)
- O. A. Voĭna 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
- A. A. Voĭna, 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)
- J. Doob, Stochastic Processes, John Wiley–Chapman and Hall, New York, 1953. MR 0058896 (15:445b)
- 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. Voĭna
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
Received by editor(s):
August 30, 2003
Published electronically:
December 28, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
