519.8 Probabilistic models of bilateral combat operations with linear dependencies of effective rates of fire of combat units of the parties on the time of the battle with a preemptive strike of one of them

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

CONTINUOUS MARKOV PROCESS, PROBABILISTIC MODELS OF BILATERAL MILITARY OPERATIONS, EFFECTIVE RATE OF FIRE, PREEMPTIVE STRIKE.

doi: 10.18698/2309-3684-2019-2-8498

On the basis of the theory of continuous Markov processes the models of bilateral military operations with linear dependences of effective rates of fire of combat units of the parties on the time of battle with a preemptive strike of one of them are developed. The algorithm allowing to calculate the main indicators of fight is developed. A comparison with the simulation results obtained on the basis of probabilistic models of combat with constant effective rates of fire and the model of the dynamics of the average with linear dependencies of effective rates of fire on the time of battle. The influence of a preemptive strike of one of the warring parties on the outcome and the main indicators of the battle is studed.

[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] Chuev Yu.V. Issledovanie operatsiy v voennom dele [Operations research in military arts]. Moscow, Voenizdat Publ., 1970, 270 p.
[4] Venttsel E.S. Issledovanie operatsiy: zadachi, printsipy, metodologiya [Operations research: objectives, principles, methodology]. Moscow, URSS Publ., 2006, 432 p.
[5] Glushkov I.N. Programmnye produkty i sistemy — Software & systems, 2010, no. 1, pp. 1–9.
[6] Ilyin V.А. Programmnye produkty i sistemy — Software & systems, 2006, no. 1, pp. 23–27.
[7] Hillier F.S., Lieberman G.J. Introduction to Operations Research. New York, McGraw-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 Systems Science and Systems Engineering, 2012, vol. 21 (1), pp. 94–105.
[10] Tkachenko P.N. Matematicheskie modeli boevykh deistviy [Mathematical
models of combat operations]. Moscow, Sovetskoe radio, 1969, 240 p.
[11] Jaiswal N.K. Military Operations Research: Quantitative Decision Making. Boston, Kluwer Academic Publishers, 1997, 388 p.
[12] Alekseev O.G., Anisimov V.G., Anisimov E.G. Markovskie modeli boya [Markov’s battle models]. Moscow, the USSR Ministry of Defense Publ., 1985, 85 p.
[13] Venttsel E.S. Teoriya veroyatnostey [Probability theory]. Moscow, KnoRus Publ., 2016, 658 p.
[14] Chuev V.Yu. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki, 2011. Spets. vyp. “Matematicheskoe modelirovanie” — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2011. Spec. issue “Mathematical modeling”, pp. 223–232.
[15] Chuev V.Yu., Dubogray I.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical modeling and Computational Methods, 2016, no. 1, pp. 89–104.
[16] Chuev V.Yu., Dubogray I.V. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2015, no. 2, pp. 53–62.
[17] Chuev V.Yu., Dubogray I.V. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2017, no. 4, pp. 16–25.
[18] Chuev V.Yu., Dubogray I.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical modeling and Computational Methods, 2016, no. 2, pp. 69–84.
[19] Dubogray I.V., Ryabtsev R.A., Chuev V.Yu. Izvestiya rossijskoj akademii raketnyh i artillerijskih nauk — Proceedings of the russian academy of rocket and artillery sciences, 2017, no. 4 (99), pp. 37–46.
[20] 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.

Чуев В.Ю., Дубограй И.В. Вероятностные модели двухсторонних боевых действий с линейными зависимостями эффективных скорострельностей боевых единиц сторон от времени боя при упреждающем ударе одной из них. Математическое моделирование и численные методы, 2019, № 2, с. 84–98.