519.8 Stochastic models of bilateral hostilities of numerous groups while linear dependence of military units’ effective firing rate on the duration of the battle

Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)

CONTINUOUS MARKOV PROCESS, PROBABILISTIC MODEL OF BILATERAL HOSTILITIES, COMBAT UNIT, THE EFFECTIVE FIRING RATE, THE PARAMETER OF THE INITIAL BALANCE OF FORCES


doi: 10.18698/2309-3684-2018-2-122132


The article presents developed on the basis of the theory of Markov’s processes the models of bilateral hostilities with the linear dependence of effective firing rate of military units on the time of the battle. Developed the algorithm allows to calculate the main indicators of the battle of numerous groups. Fulfilled the comparison with the results of a battle simulation, received on the basis of probabilistic models of the battle with constant effective firing rate and the deterministic model of a combat with a linear dependency of effective firing rate on the time of the battle. The range of the last models applicability presented.


[1] Aleksandrov А.А., Dimitrienko Yu.I. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1 (1), pp. 3–4.
[2] Zarubin V.S., Kuvyrkin G.N. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 5–17.
[3] Chuev Yu.V. Issledovanie operatsiy v voennom dele [Investigation of military operations]. Moscow, Voenizdat Publ., 1970, 270 p.
[4] Venttsel E.S. Issledovanie operatsiy: zadachi, printsipy i metodologiya [Research operations: tasks, principles and methodology]. Moscow, URSS Publ., 2006, 432 p.
[5] Glushkov I.N. Programnye produkty i sistemy – Software and systems, 2010. №1. P. 1 – 9.
[6] Ilin V.A. Programnye produkty i sistemy – Software and systems, 2006, № 1, с. 23–27.
[7] Hillier F.S., Lieberman G.J. Introduction to operations research. New York, MeGrew-Hill, 2005, 998 p.
[8] Winston W.L. Operations research: applications and algorithms. Belmont, Duxbury Press, 2001, 128 p.
[9] Chen X., Jing Y., Li C., Li M. Warfare command stratagem analysis for winning based on Lanchester attrition models. Journal of Science and Systems Engineering, 2012, vol. 21 (1), pp. 94–105.
[10] Tkachenko P.N. Matematicheskie modeli boevykh deystviy [Mathematical models of military operations]. Moscow, Sovetskoe radio Publ., 1969, 240 p.
[11] Jaswall N.K. Military Operations research: quantitative decision making. Boston, Kluwer Academic Publishers, 1997, 388 p.
[12] Shamahan L. Dynamics of model battles. New York, Physics Department, State University of New York, 2005, pp. 1–43.
[13] Alekseev O.G., Anisimov V.G., Anisimov E.G. Markovskie modeli boya [Markov's combat models]. Moscow, the USSR Ministry of Defense, 1985, 85 p.
[14] Venttsel E.S. Teoriya veroyatnostey [Probability Theory]. Moscow, KnoRus, 2016, 658 p.
[15] Chuev V.Yu. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki. Spets. vypusk “Matematicheskoe modelirovanie” — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, Spec. issue “Mathematical Modeling”, 2011, pp. 223–232.
[16] Chuev V.Yu., Dubogray I.V. Matematicheskoe modelirovanie i chislennye metody – Mathematical Modeling and Computational Methods, 2016, no. 1, pp. 89–104.
[17] Chuev V.Yu., Dubogray I.V., Dyakova L.N. Matematicheskoe modelirovanie i chislennye metody – Mathematical Modeling and Computational Methods, 2017, no. 1, pp. 91–101.
[18] Chuev V.Yu., Dubogray I.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2016, no. 2 (10), pp. 69–84.
[19] Chuev V.Yu., Dubogray I.V. Modeli dinamiki srednikh dvukhstoronnikh boevykh deystviy mnogochislennykh gruppirovok [Dynamics models of the average bilateral military operations of numerous groupings]. Saarbryukken, LAP LAMBERT Academic Publishing, 2014, 72 p.
[20] Chuev V.Yu., Dubogray I.V. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki. Spets. vypusk “Matematicheskoe modelirovanie” — Herald of the Bauman Moscow State Technical University., 2017, no 4, pp. 16–25.


Чуев В.Ю., Дубограй И.В. Стохастические модели двухсторонних боевых тдействий многочисленных группировок при линейных зависимостях эффективнх скорострельностей боевых единиц сторон от времени боя. Математическое моделирование и численные методы, 2018, № 2, с. 122–132.



Download article

Количество скачиваний: 480