519.8 Stochastic model of repelling of attacks made by different types of means with a preemptive strike by one of the parties

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

CONTINUOUS MARKOV PROCESS, COMBAT UNIT, EFFECTIVE RATE OF FIRE, PREEMPTIVE STRIKE, TACTICS OF FIRE.

doi: 10.18698/2309-3684-2019-1-5464

On the basis of the theory of continuous Markov processes, it was developed a stochastic model of reflection by the combat unit of the attack of two different types of enemy units with a preemptive strike of one of the opposing sides. The calculation formulas for calculating the current and final status are obtained. It is shown that the choice of the defending unit of tactics of firing does not depend on which of the opposing sides causes a preemptive strike, but it’s correct choice can significantly increase the probability of it’s victory. The model of two-way combat developed in this article can be used for estimation of the multi-purpose weapons systems combat effectiveness.

[1] Alexandrov A.A., Dimitrienko Yu.I. Matematicheskoe modelirovanie i chislennye metody — Mathematical modeling and Computational Methods, 2014, no. 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] Venttsel E.S. Issledovanie operatsiy: zadachi, printsipy, metodologiya [Operations research: objectives, principles, methodology]. Moscow, URSS Publ., 2006, 432 p.
[4] Chuev Yu.V. Issledovanie operatsiy v voennom dele [Operations research in military arts]. Moscow, Voenizdat Publ., 1970, 270 p.
[5] Bretnor R. Decisive warfare: a study in military theory. New York, Stackpole Books, 1969, p. 192.
[6] Hillier F.S., Lieberman G.J. Introduction to Operations Research. New York, McGraw-Hill, 2005, 998 p.
[7] Shamahan L. Dynamics of Model Battles. New York, Physics Department, State University of New York, 2005, pp. 1–43.
[8] Taylor J.G. Force-on-force attrition modeling. Military Applications Section of Operations Research Society of America, 1980, 320 p.
[9] Alekseev O.G., Anisimov V.G., Anisimov E.G. Markovskie modeli boya [Mar-kov’s battle models]. Moscow, the USSR Ministry of Defense Publ., 1985, 85 p.
[10] Venttsel E.S. Teoriya veroyatnostey [Probability theory]. Moscow, KnoRus Publ., 2016, 658 p.
[11] Venttsel E.S., Ovcharov L.A. Teoriya sluchaynykh protsessov i ee inzhenernye prilozheniya [The theory of random processes and its engineering applications]. Moscow, Knorus Publ., 2015, 448 p.
[12] Chuev V.Yu., Dubogray I.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical modeling and Computational Methods, 2016, no. 1, pp. 89–104.
[13] Chuev V.Yu., Dubogray I.V. Vestnik MGTU im. N.E. Baumana. Ser. Estestven-nye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2017, no. 4, pp. 16–25.
[14] Chuev V.Yu., Dubogray I.V. Modeli dinamiki srednikh dvukhstoronnikh boevykh deystviy mnogochislennykh gruppirovok [Dynamics models of the average bilateral military operations of numerous forces]. Saarbryukken, LAP LAMBERT Academic Publishing, 2014, 72 p.
[15] Chuev V.Yu., Dubogray I.V., Anisova T.L. Matematicheskoe modelirovanie i chislennye metody — Mathematical modeling and Computational Methods, 2018, no. 1, pp. 90–97.

Чуев В.Ю., Дубограй И.В. Стохастическая модель отражения атаки разнотип-ных средств при упреждающем ударе одной из сторон. Математическое модели-рование и численные методы, 2019, № 1, с. 54–64.