Geodesic
The parallel semi-Markov processes in objects group control tasks
Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 248-258.

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Functioning of complex objects, controlled with computer, is investigates. It id shown, that the abstract analogue of every control loop is the ordinary semi-Markov process. Such abstraction is insufficient for analytical modeling the object as a whole, this is why for the description of synchronizing processes it is necessary to have more complex model, which may be obtained by means integration of ordinary processes into complex semi-Markov processes. For determining of the abstraction the term “functional state”, as all possible combination of structural states is introduced. The method of calculation of complex process semi-Markov matrix elements is proposed. It is shown, how may be evaluated time intervals of wandering through complex semi-Markov process.
Keywords: group control, ergodic semi-Markov process, ctate combination, Cartesian product of semi-Markov matrices, wandering. 
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A. N. Privalov; E. V. Larkin. The parallel semi-Markov processes in objects group control tasks. Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 248-258. http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a18/

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