Geodesic
Stochastic models of the two unit duel fight
Matematičeskoe modelirovanie i čislennye metody, no. 10 (2016), pp. 69-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

On the basis of the theory of continuous Markov processes we developed models of the two unit duel fight. We obtained computing formulas for calculating the basic fight indicators. Moreover, we found that the pre-emptive strike of one of the units participating in the fight has a significant impact on the fight outcome of the units which are similar in forces. The strike has a negligible impact, if one of the units has a significant advantage. The findings of the research show that the use of model with constant effective firing rates can lead to significant errors in the evaluation of its results. Finally, we found that the pre-emptive strike, coupled with a high degree of effective firing rate growth, can sometimes compensate for more than the double initial superiority of the opponent. We show the possibility of using approximations of the effective firing rate of the fighting units by the different functions of the fight time.
Keywords: Fighting unit, the effective firing rate, duel fight, a fight between two units, correlation of forces parameter, continuous markov process. 
@article{MMCM_2016_10_a4,
     author = {V. U. Chuev and I. V. Dubogray},
     title = {Stochastic models of the two unit duel fight},
     journal = {Matemati\v{c}eskoe modelirovanie i \v{c}islennye metody},
     pages = {69--84},
     year = {2016},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMCM_2016_10_a4/}
}
TY  - JOUR
AU  - V. U. Chuev
AU  - I. V. Dubogray
TI  - Stochastic models of the two unit duel fight
JO  - Matematičeskoe modelirovanie i čislennye metody
PY  - 2016
SP  - 69
EP  - 84
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/MMCM_2016_10_a4/
LA  - ru
ID  - MMCM_2016_10_a4
ER  - 
%0 Journal Article
%A V. U. Chuev
%A I. V. Dubogray
%T Stochastic models of the two unit duel fight
%J Matematičeskoe modelirovanie i čislennye metody
%D 2016
%P 69-84
%N 10
%U http://geodesic.mathdoc.fr/item/MMCM_2016_10_a4/
%G ru
%F MMCM_2016_10_a4
V. U. Chuev; I. V. Dubogray. Stochastic models of the two unit duel fight. Matematičeskoe modelirovanie i čislennye metody, no. 10 (2016), pp. 69-84. http://geodesic.mathdoc.fr/item/MMCM_2016_10_a4/

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

[2] Ilyin V.A., Programme Products and Systems, 2006, no. 1, 23–27

[3] Jaiswal N.K., Military Operations Research: Quantitative Decision Making, Kluwer Academic Publishers, Boston, 1997, 388 pp.

[4] Bretnor R., Decisive Warfare: A Study in Military Theory, Stackpole Books, New York, 1969, 192 pp.

[5] Glushkov I.N., Programme Products and Systems, 2010, no. pp

[6] Taylor J.G., “Force-on-force attrition modeling”, Military Application Section of Operations Research Society of America, 1980, 320

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

[8] Venttsel E.S., Operations research, URSS Publ., Moscow, 2006, 432 pp.

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

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

[11] Chuev Yu.V., Operations research in military art, Voenizdat, Moscow, 1970, 270 pp.

[12] Pashkov N.Yu., Strogalev V.P., Chuev V.Yu., “Oboronnaya tekhnika”, Defense equipment, 2000, no. 9–10, 19–21

[13] Chuev V.Yu., Herald of the Bauman Moscow State Technical University. Series Natural Sciences. Special iss. “Mathematical Modeling”, 2011, 223–232

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

[15] Chuev V.Yu., Dubogray I.V., Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2016, no. 2, 18–24

[16] Chuev V.Yu., Dubogray I.V., “Middle bilateral hostilities models: dynamics models of middle bilateral hostilities of the numerous groups”, LAP Lambert Academic Publ., 2014, 80

[17] Chuev V.Yu., Dubogray I.V., Mathematical Modeling and Computational Methods, 2016, pp