Abstract
The problem of developing an control algorithm for a queuing system is considered. This system has a finite number of states the dynamics of which is described by a conditional Markov chain; the system is observed using indicators whose readings are error prone. Optimal and approximately optimal solutions based on the theory of systems with random jump structure are found. By way of example, the problem of synthesis of an approximately optimal algorithm for the recognition of state and for control of aviation raids on a military facility that is alternatively damaged and restored in the course of air combat operations.
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References
V. A. Bukhalev, A. A. Skrynnikov, and A. Yu. Fedotov, “Analyzing queuing systems by methods of theory of systems with random jump structure,” J. Comput. Syst. Sci. Int. 52, 599–607 (2013).
V. A. Boldinov, V. A. Bukhalev, and A. A. Skrynnikov, “Recognition Algorithm for the State of the Queuing System Based on Theory of Systems with Random Jump Structure,” J. Comput. Syst. Sci. Int. 53, 327–337 (2014).
V. A. Bukhalev, “Analysis of accuracy of dynamic systems with random structure described by a conditional Markov chain,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 3, 179–185 (1976).
V. M. Artem’ev, Theory of Systems with Random Changes of Structure (Vysheish. shk, Minsk, 1979) [in Russian].
V. A. Bukhalev, E. V. Efimov, and I. E. Kazakov, “Combined processing of measuring instrument data and indicators in dynamic systems with conditionally Markov structure,” Avtom. Telemekh., No. 1, 61–71 (1988).
A. Nemura and E. Klekis, Estimation of State and Parameters of Systems: Systems with Jump-like Varying Properties (Mokslas, Vilnus, 1988) [in Russian].
I. E. Kazakov, “Stochastic systems with randomly changing structure (survey),” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 1, 58–78 (1989).
V. A. Bukhalev, “Optimal control in systems with random jump structure,” Avtom. Telemekh., No. 4, 88–97 (1992).
I. E. Kazakov, V. M. Artem’ev, and V. A. Bukhalev, Analysis of Random Structure Systems (Nauka, Moscow, 1993) [in Russian].
V. A. Bukhalev, Recognition, Estimation, and Control in Systems with Random Jump Structure (Nauka, Moscow, 1996) [in Russian].
A. I. Buravlev and I. E. Kazakov, “A model of the reliability of a self-regenerating system with a random structure,” J. Comput. Syst. Sci. Int. 40, 40–42 (2001).
V. A. Bukhalev, Foundations of Automation and Control Theory (VVIA im. prof. N. E. Zhukovskogo, Moscow, 2006) [in Russian].
E. S. Wentzel, Probability Theory (Nauka, Moscow, 1969) [in Russian].
A. T. Bharucha-Reid, Elements of the Theory of Markov Processes and Their Applications (McGraw-Hill, New York, 1960; Nauka, Moscow, 1969).
T. L. Saaty, Elements of Queueing Theory, with Applications (McGraw-Hill, 1961; Sovetskoe radio, Moscow, 1971).
L. Kleinrock, Queueing Systems: Theory (Wiley, New York, 1975–1976; Mashinostroenie, Moscow, 1979).
G. I. Ivchenko, V. A. Kashtanov, and I. N. Kovalenko, Queuing Theory (Vysshaya shkola, Moscow, 1982) [in Russian].
R. Bellman, Dynamic Programming (Princeton Univ. Press, Princeton, 1957; Inostrannaya Literatura, Moscow, 1960).
M. Aoki, Optimization of Stochastic Systems (Academic, New York, 1967; Nauka, Moscow, 1971).
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Original Russian Text © V.A. Boldinov, V.A. Bukhalev, S.P. Pryadkin, A.A. Skrynnikov, 2015, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2015, No. 2, pp. 56–67.
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Boldinov, V.A., Bukhalev, V.A., Pryadkin, S.P. et al. Control algorithm for a queuing system based on the theory of systems with random jump structure. J. Comput. Syst. Sci. Int. 54, 218–229 (2015). https://doi.org/10.1134/S1064230715010025
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DOI: https://doi.org/10.1134/S1064230715010025