Abstract
We consider the optimal estimation problem for the states of a MAP event flow with two states; it is one of the mathematical models for an incoming stream of claims (events) in digital integral servicing networks. The observation conditions for this flow are such that each event generates a period of dead time during which other events from the flow are inaccessible for observation and do not extend the dead time period (unextendable dead time). We find an explicit form for posterior probabilities of the flow states. The decision about the flow state is made with the maximal a posteriori criterion. We show numerical results obtained with our explicit formulas and imitational modeling.
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References
Kingman, J.F.C., On Doubly Stochastic Poisson Process, Proc. Cambridge Philos. Soc., 1964, vol. 60, no. 4, pp. 923–930.
Basharin, G.P., Kokotushkin, V.A., and Naumov, V.A., On the Equivalent Substitutions Method for Computing Fragments of Communication Networks, Izv. Akad. Nauk USSR, Tekhn. Kibern., 1979, no. 6, pp. 92–99.
Basharin, G.P., Kokotushkin, V.A., and Naumov, V.A., On the Equivalent Substitutions Method for Computing Fragments of Communication Networks, Izv. Akad. Nauk USSR, Tekhn. Kibern., 1980, no. 1, pp. 55–61.
Neuts, M.F., A Versatile Markov Point Process, J. Appl. Probab., 1979, vol. 16, pp. 764–779.
Lucantoni, D.M., New Results on the Single Server Queue with a Batch Markovian Arrival Process, Commun. Stat. Stoch. Models, 1991, vol. 7, pp. 1–46.
Dudin, A.N. and Klimenok, V.I., Sistemy massovogo obsluzhivaniya s korrelirovannymi potokami (Queueing Systems with Correlated Flows), Minsk: Belarus. Gos. Univ., 2000.
Apanasovich, V.V., Kolyada, A.A., and Chernyavskii, A.F., Statisticheskii analiz sluchainykh potokov v fizicheskom eksperimente (Statistical Analysis of Random Flows in a Physical Experiment), Minsk: Universitetskoe, 1988.
Khazen, E.M., Metody optimal’nykh statisticheskikh reshenii i zadachi optimal’nogo upravleniya (Methods of Optimal Statistical Decisions and Optimal Control), Moscow: Sovetskoe Radio, 1968.
Gortsev, A.M. and Shmyrin, I.S., Optimal Estimation of States of the Double Stochastic Flow of Events in the Presence of Measurement Errors of Time Instants, Automat. Remote Control, 1999, vol. 60, no. 1, part 1, pp. 41–51.
Gortsev, A.M. and Nezhel’skaya, L.A., Estimating Parameters in a Synchronous MC Event Flow, Communication and Computer Networks: Abstracts of the 8th Belarus Winter School-Seminar on Queueing Theory, Minsk: Belarus. Gos. Univ., 1992.
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Original Russian Text © A.M. Gortsev, L.A. Nezhel’skaya, A.A. Solov’ev, 2012, published in Avtomatika i Telemekhanika, 2012, No. 8, pp. 49–63.
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Gortsev, A.M., Nezhel’skaya, L.A. & Solov’ev, A.A. Optimal state estimation in MAP event flows with unextendable dead time. Autom Remote Control 73, 1316–1326 (2012). https://doi.org/10.1134/S000511791208005X
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DOI: https://doi.org/10.1134/S000511791208005X