Abstract
The Optimal estimation of the states of a MAP—a particular case of the BMAP—flow of events is studied. Expressions for the a posteriori probabilities of the states of the control process of the MAP flow are derived. An optimal estimation algorithm for determining the states from the maximal a posteriori state probabilities is designed and the numerical results it generated in imitation modelling of an event flow are presented.
Similar content being viewed by others
REFERENCES
Cox, D.R. and Miller, H.D., The Theory of Stochastic Processes, New York: Wiley, 1965.
Gortsev, A.M. and Nezhel'skaya, L.A., Estimation of Dead Periods and Parameters of a Semisynchronous Double Stochastic Flow of Events, Izmeritel'naya Tekhn., 2003, no. 6, pp. 7–13.
Gortsev, A.M. and Shmyrin, I.S., Optimal State Estimation for a Double Stochastic Flow of Events under Time Measurement Errors, Avtom. Telemekh., 1999, no. 1, pp. 52–66.
Dudin, A.N. and Klimenok, V.I., Sisitemy massovogo s korrelirovannymi potokami (Queue Systems with Correlated Flows), Minsk: Belarus. Gos. Univ., 2000.
Lucantoni, D.M., New Results on the Single-Server Queue with a Batch Markovian Arrival Process, Commun. Stat. Stochastic Models, 1991, vol. 7, pp. 1–46.
Bekkerman, E.N., Kataev, S.G., and Kataeva, S.S., A Recognition Algorithm for an MC Flow of Events, Vest. Tomsk. Gos. Univ., 2000, vol. 271, pp. 41–45.
Nezhel'skaya, L.A., A State Estimation Algorithm for a Synchronous MC Flow, in Trudy 11 Belorus. shk.-seminara po massovomu obsluzhivaniyu (Proc. 11 Belarus. Workshop on Queueing Systems), Minsk, 1995, pp. 93–94.
Hazen, E.M., Metody optimal'nykh statisticheskikh reshenii i zadacha optimal'nogo upravleniya (Optimal Statistical Decision Methods and Optimal Control Problems), Moscow: Sovetskoe Radio, 1968.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shmyrin, I.S. States of a Map Flow of Events: Optimal Estimation by the Maximal a Posteriori State Probability Criterion. Automation and Remote Control 65, 1444–1451 (2004). https://doi.org/10.1023/B:AURC.0000041422.00327.01
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000041422.00327.01