and Computational Methods

doi: 10.18698/2309-3684-2016-1-89104

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.

[1] Alekseev O.G, Anisimov V.G, Anisimov Е.G. Markovskie modeli boya [Markov models of a battle]. Moscow, Ministry of defense of the USSR Publ., 1985, 85 p.

[2] Venttsel E.S. Issledovanie operatsiy [Operation research]. Moscow, URSS Publ., 2006, 432 p.

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

[4] Dubogray I.V., Dyakova L.N., Chuev V.Yu. Inzhenernyi zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2013, no. 7. Available at: http://enggournal.ru/catalog/mathmodel/hidden/842.html

[5] Dubogray I.V., Chuev V.Yu. Nauka i obrazovanie: elektronnoe nauchnotekhnicheskoe izdanie — Science and education: Electronic scientific journal, October 2013, no. 10. DOI 10.7463/1013.0617171

[6] Zarubin V. S., Kuvyrkin G. N. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 5–17.

[7] Tkachenko P.N. Matematicheskie modeli boevykh deystviy [Mathematical models of warfare]. Moscow, Sovetskoe radio Publ., 1969, 240 p.

[8] Chuev V.Yu. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2011, Spetsialnyi vypusk “Matematicheskoe modelirovanie” [Special issue “Mathematical modeling”], pp. 223–232.

[9] Chuev V. Yu., Dubogray I.V. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2015, no. 2, pp. 53–62.

[10] Chuev V.Yu. Issledovanie operatsiy v voennom dele [Operations research in military science]. Moscow, Voenizdat Publ., 1970, 270 p.

[11] Jaswal N. K. Military Operations Rescarch. Quantitative Decision Making. Kluwer Academic Publishers, 2000, 388 p.

[12] Lanchester F. Aircraft in Warfare: the Dawn of the Fourth Arm. London, Constable And Co., 1916, 243 р.

[13] Shamahan L. Dynamics of Model Battles. N.Y., Phisics Department, State University of New York Publ., 2003, pp. 1–43.

[14] Chen X., Jing Yu., Li Ch., 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.

[15] Winston W.L. Operations Research: Applications and Algorithms. Duxbury Press, 2001, 128 p.

Chuev V., Dubogray I. Models of bilateral warfare of numerous groups. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 89-104

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