Geodesic
Models of bilateral warfare of numerous groups
Matematičeskoe modelirovanie i čislennye metody, no. 9 (2016), pp. 89-104 Cet article a éte moissonné depuis la source Math-Net.Ru

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Based on the theory of Markov processes the model of "poorly organized" battle was developed. Formulae for calculating its basic parameters at different initial numbers of the opposing sides were obtained. A comparison of the results of modeling a battle using probabilistic and deterministic models was performed. It was found that the dynamics model errors of the average are primarily affected by the balance of forces of the opposing sides in the beginning of the battle. It was shown that in case of military groups of similar forces the first-strike attack is of significant importance. When one of the warring parties at the beginning of the battle has a great advantage, the influence of first-strike attack is negligible. An increase in the influence of first-strike attack on the expected losses of a strong hand, and a reduction of its impact on the expected losses of the weaker party, as the number of groups involved in the fight increases proportionally, is also shown.
Keywords: Combat units, the effective rapidity of fire, markov processes, the balance of forces, the model of bilateral warfare. 
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V. U. Chuev; I. V. Dubogray. Models of bilateral warfare of numerous groups. Matematičeskoe modelirovanie i čislennye metody, no. 9 (2016), pp. 89-104. http://geodesic.mathdoc.fr/item/MMCM_2016_9_a5/

[1] Alekseev O.G., Anisimov V.G., Anisimov E.G., Markovskie modeli boya, Ministerstvo oborony SSSR, Moskva, 1985, 85 pp.

[2] Venttsel E.S., Operation research, URSS Publ., Moscow, 2006, 432 pp.

[3] Venttsel E.S., Probability theory, Vysshaya shkola Publ., Moscow, 1999, 576 pp.

[4] Dubogray I.V., Dyakova L.N., Chuev V.Yu., Engineering Journal: Science and Innovation, 2013, no. 7

[5] Dubogray I.V., Chuev V.Yu., Science and education: Electronic scientific journal, 2013, no. 10

[6] Zarubin V.S., Kuvyrkin G.N., Mathematical Modeling and Computational Methods, 2014, no. 1, 5–17

[7] Tkachenko P.N., Mathematical models of warfare, Sovetskoe radio Publ., Moscow, 1969, 240 pp.

[8] Chuev V.Yu., Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2011, 223–232

[9] Chuev V.Yu., Dubogray I.V, Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2015, no. 2, 53–62

[10] Chuev V.Yu., Operations research in military science, Voenizdat Publ., Moscow, 1970, 270 pp.

[11] Jaiswal N.K., Military Operations Research, Kluwer Academic Publishers, Quantitative Decision Making. Boston, 1997, 388 pp. | MR | Zbl

[12] Lanchester F., Aircraft in Warfare: the Dawn of the Fourth Arm, Constable and Co., London, 1916, 243 pp. | Zbl

[13] Shanahan L., Sen S.., Dynamics of Model Battle: Markovian and strategic cases, Physics Department, New York, 2003, 43 pp.

[14] Chen X., Jing Yu., Li Ch., Li M., “Warfare Command Stratagem Analysis for Winning Based on Lanchester Attrition Models”, J. of Science and Systems Engineering, 21:1 (2012), 94–105 | DOI

[15] Winston W.L., “Operations Research: Applications and Algorithms”, Duxbury Press, 2001, 1–128 | MR