FINITE MARKOV CHAINS IN THE MODEL REPRESENTATION OF THE HUMAN OPERATOR ACTIVITY IN QUASI-FUNCTIONAL ENVIRONMENT
Read the full article ';
For citation: Serzhantova M.V., Ushakov A.V. Finite Markov chains in the model representation of the human operator activity in quasi-functional environment. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 3, pp. 524–532. doi: 10.17586/2226-1494-2016-16-3-524-532
Subject of Research. We analyze the problems of finite Markov chains apparatus application for simulating a human operator activity in the quasi-static functional environment. It is shown that the functional environment stochastic nature is generated by a factor of interval character of human operator properties. Method. The problem is solved in the class of regular (recurrent) finite Markov chains with three states of the human operator: with a favorable, median and unfavorable combination of the values of mathematical model parameters of the human operator in a quasi-static functional environment. The finite Markov chain is designed taking into account the factors of human operator tiredness and interval character of parameters of the model representation of his properties. The device is based on the usage of mathematical approximation of the standard curve of the human operator activity performance during work shift. The standard curve of the human operator activity performance is based on the extensive research experience of functional activity of the human operator with the help of photos of the day, his action timing and ergonomic generalizations. Main Results. The apparatus of regular finite Markov chains gave the possibility to evaluate correctly the human operator activity performance in a quasi-static functional environment with the use of the main information component of these chains as a vector of final probabilities. In addition, we managed to build an algorithmic basis for estimating the stationary time (time study for transit of human operator from arbitrary initial functional state into a state corresponding to a vector of final probabilities) for a used chain after it reaches the final state based on the analysis of the eigenvalues spectrum of the matrix of transition probabilities for a regular (recurrent) finite Markov chain. Practical Relevance. Obtained theoretical results are confirmed by illustrative examples, which demonstrate their suitability for possible use in the organization of the quasi-static and functional environment to solve the problems of its perfection. The results can be used for the rational organization of functional environment in which the human operators could optimally realize their potential.
Acknowledgements. This work was supported by the Government of the Russian Federation (Grant 074-U01) and the Ministry of Education and Science of the Russian Federation (Project 14. Z50.31.0031)
1. Dudarenko N.A., Polyakova M.V., Ushakov A.V. Formation of the interval vector-matrix modeling representations of anthropocomponents-operators as a part of complex dynamic systems. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2010, no. 6 (70), pp. 32–36. (In Russian)
2. Dudarenko N.A., Polinova N.A., Serzhantova M.V., Ushakov A.V. Multiple binomial structures in the problem of approximation of dynamic circuit with a pure delay unit. Journal of Instrument Engineering, 2014, vol. 57, no. 7, pp. 12–17.
3. Serzhantova M.V., Ushakov A.V. Interval additive piecewise polynomial time operation model of human-operator in a quasi-functional environment. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol. 15, no. 2, pp. 329–337. (In Russian). doi: 10.17586/2226-1494-2015-15-2-329-337
4. Vunder N.A., Dudarenko N.A., Serzhantova M.V., Ushakov A.V. Additive interval model functional activities antropo component in quasistatic environment. Trudy XII Vserossiiskogo soveshchaniya po problemam upravleniya [Proc. XII All-Russian Conference on Control Problems]. Moscow, 2014, no. 1, pp. 6372-6383. (In Russian)
5. Sharyi S.P. Konechnomernyi Interval'nyi Analiz [The Finite Interval Analysis]. Moscow, XYZ Publ., 2007, 700 p.
6. Shipilov A.I, Shipilova O.A. Vysokaya rabotosposobnost' personala – zabota kadrovika [High availability of staff - care personnel officer]. Kadry Predpriyatiya, 2003, no. 3, pp. 7–15.
7. What is Systems Biology. Available at: www.systemsbiology.org/about-systems-biology (accessed 20.01.2015).
8. Gaohua L., Kimura H. A mathematical model of brain glucose homeostasis. Theoretical Biology and Medical Modelling, 2009, vol. 6, no. 26. doi: 10.1186/1742-4682-6-26
9. Doyle III F.J., Bequette B.W., Middleton R., Ogunnaike B., Paden B., Parker R.S., Vidyasagar M. Control in biological systems. In: The Impact of Control Technology. Eds. T. Samad, A.M. Annaswamy. IEEE Control Systems Society, 2011.
10. Mindell D.A. Between Human and Machine: Feedback, Control, and Computing before Cybernetics. Baltimore, Johns Hopkins University Press, 2002, 456 p.
11. Mindell D.A. Digital Apollo. Human and Machine in Spaceflight. Cambridge, MIT Press, 2008, 376 p.
12. Kemeny J.G., Snell J.L., Knapp A.W., Griffeath D.S. Denumerable Markov Chains. NY-Berlin, Springer-Verlag, 1976, 483 p. doi: 10.1007/978-1-4684-9455-6
13. 13.Astrom K.J. Optimal control of Markov decision processes with incomplete state estimation. Journal Mathematical Analysis and Applications, 1965, vol. 10, no. 1, pp. 174–205. doi: 10.1016/0022-247X(65)90154-X
14. Howard R.A. Comments on the origin and application of Markov decision processes. Operations Research, 2002, vol. 50, no. 1, pp. 100–102. doi: 10.1287/opre.18.104.22.16888
15. Lancaster P. The Theory of Matrices. NY: Academic Press, 1969.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License