|

Stochasticism and Determinism in Simulation Bilateral Warfare

Authors: Chuev V.Yu., Dubogray I.V. Published: 26.07.2017
Published in issue: #4(73)/2017  
DOI: 10.18698/1812-3368-2017-4-16-28

 
Category: Mathematics and Mechanics | Chapter: Probability Theory and Mathematical Statistics  
Keywords: bilateral warfare model, combat unit, effective rapidity of fire, parameter of co-relation of forces, continuous Markov process

According to the theory of continuous Markov processes we developed stochastic models of the "highly organized" combat action. The model made it possible to calculate the main indicators of the combat of numerous groups. We made a comparison with the results obtained on the basis of a deterministic model of bilateral warfare, the model being built by the mean value dynamics method. Findings of the research show that the errors of the mean value dynamics method primarily result from the co-relation of forces of rival groups, but not their force level at the beginning of the combat. We also made a comparison with simulation results of the "poorly organized" combat.

References

[1] Zarubin V.S., Kuvyrkin G.N. Special features of mathematical modeling of technical instruments. Matematicheskoe modelirovanie i chislennye metody, 2014, no. 1, pp. 5-17 (in Russ.). DOI: 10.18698/2309-3684-2014-1-517

[2] Venttsel’ E.S. Issledovanie operatsiy: zadachi, printsipy i metodologiya [Research on operations: Problems, principles, methodology]. Moscow, URSS Publ., 2006. 432 p.

[3] Glushkov I.N. Choice of the mathematical scheme at construction models of operations. Programmnye produkty i sistemy, 2010, no. 1, pp. 1-9 (in Russ.).

[4] Il’in V.A. Modeling of the Navy forces fighting. Programmnye produkty i sistemy, 2006, no. 1, pp. 23-27 (in Russ.).

[5] Chuev Yu.V. Issledovanie operatsiy v voennom dele [Research of operations in military affairs]. Moscow, Voenizdat Publ., 1970. 256 p.

[6] Tkachenko P.N. Matematicheskie modeli boevykh deystviy [Mathematical models of combat operations]. Moscow, Sovetskoe Radio Publ., 1969. 240 p.

[7] Chuev V.Yu., Dubogray I.V. Modeli dinamiki srednikh dvukhstoronnikh boevykh deystviy mnogochislennykh gruppirovok [Dynamics models of mid-intensity bilateral battlefield of numerous groups]. Saarbryukken, LAP LAMBERT Academic Publishing, 2014. 80 p.

[8] Bretnor R. Decisive warfare - a study in military theory. New York, Stackpole Books, 1989. 192 p.

[9] Lanchester F. Aircraft in warfare: The dawn of the fourth arm. London, Constable and Co., 1916. 243 p.

[10] Taylor J.G. Dependence of the parity-condition parameter on the combat - intensity parameter for Lanchester-type equations of modern warfare. OR Spectrum, 1980, vol. 1, no. 3, pp. 199-205. DOI: 10.1007/BF01719341 Available at: http://link.springer.com/article/10.1007/BF01719341

[11] Taylor J.G. Force-on-force attrition modeling. Military Applications Section of Operations Research Society of America, 1980. 320 p.

[12] Xiangyong Chen, Yuanwei Jing, Chunji Li, Mingwei Li. Warfare command stratagem analysis for winning based on Lanchester attrition models. Journal of Science and Systems Engineering, 2012, vol. 21, no. 1, pp. 94-105. DOI: 10.1007/s11518-011-5177-7 Available at: http://link.springer.com/article/10.1007/s11518-011-5177-7

[13] Venttsel’ E.S. Teoriya veroyatnostey [Probability theory]. Moscow, KnoRus Publ., 2016. 664 p.

[14] Dubogray I.V., D’yakova L.N., Chuev V.Yu. Pre-emptive attack consideration when duel combat operations simulating. Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation], 2013, no. 7 (in Russ.). DOI: 10.18698/2308-6033-2013-7-842 Available at: http://engjournal.ru/catalog/mathmodel/hidden/842.html

[15] Alekseev O.G., Anisimov V.G., Anisimov E.G. Markovskie modeli boya [Markov models of combat actions]. Moscow, USSR Ministry of Defence Publ., 1985. 85 p.

[16] Hillier F.S., Lieberman G.J. Introduction to operations research. New York, McGraw-Hill, 2005. 998 p.

[17] Jaswall N.K. Military operations research: Quantitative decision making. Kluwer Academic Publishers, 1997. 388 p.

[18] Shamahan L. Dynamics of model battles. New York, Physics Department, State University of New York, 2005, pp. 1-43.

[19] Winston W.L. Operations research: Applications and algorithms. Duxbury Press, 2001. 128 p.

[20] Chuev V.Yu., Dubogray I.V. Models of bilateral warfare of numerous groups. Matematicheskoe modelirovanie i chislennye metody, 2016, no. 1, pp. 89-104 (in Russ.). DOI: 10.18698/2309-3684-2016-1-89104

[21] Venttsel’ E.S., Ovcharov V.Ya. Teoriya sluchaynykh protsessov i ee inzhenernye prilozheniya [Random processes theory and its engineering applications]. Moscow, KnoRus Publ., 2015. 448 p.

[22] Dubogray I.V., Chuev V.Yu. Stochastic model of both-sided battle actions during the pre-emptive attack by one of warring parties. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Bauma-na, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2015, no. 2, pp. 53-62 (in Russ.). DOI: 10.18698/1812-3368-2015-2-53-62