#### 519.8 “Mixed” probabilistic models of bilateral military operations of numerous groups

##### Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University), Dyakova L. N. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2017-1-91101

The purpose of this work was to develop "mixed" probabilistic models of bilateral military operations according to the theory of continuous Markov processes. In our research we obtained calculation formulas for estimating the main combat indices of groups small in number. Moreover, we developed a numerical algorithm to calculate the main combat indices of numerous groupings and made a comparison with the results of combat simulation using a deterministic model of two-way combat operations, the model being developed according to themean-value method dynamics. Findings of the research show that the correlation of the forces of the opposing sides, rather than their initial numbers, affects the errors in the mean-value method dynamics.

Chuev V., Dubogray I., Dyakova L. “Mixed” probabilistic models of bilateral military operations of numerous groups. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 91-101

#### 519.8 “Mixed” stochastic models of reciprocal hostilities for the case of one belligerent performing a pre-emptive strike

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

doi: 10.18698/2309-3684-2017-2-107123

We used the theory of continuous-time Markov processes as the basis for developing our stochastic “mixed” models of reciprocal hostilities and a numerical algorithm that makes it possible to compute main combat metrics for large forces. We show that a pre-emptive strike performed by one of the belligerents significantly affects the outcome and main metrics of combat between forces that are sufficiently similar in strength. We determine that it is not the initial numerical strengths of the two belligerents but their balance of power that affects errors shown by the method of dynamics of mean values; moreover, the errors increase with increasing the time to a pre-emptive strike.

Chuev V. Yu., Dubogray I.V. “Mixed” stochastic models of reciprocal hostilities for the case of one belligerent performing a pre-emptive strike. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 107-123

#### 519.8 Models of bilateral warfare of numerous groups

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

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.

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

#### 519.8 Probability model of meeting an attack of different types of weapon

##### Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University), Anisova T. L. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2018-1-9097

On the basis of the continuous Markov processes theory we have developed a probabilistic model of the two-way battle of one combat unit against two enemy units of different types. The authors have obtained calculation formulas for computing current and final states under various firing tactics of the unit. We have determined the applicability areas for different combat tactics of the unit. The study shows that the right choice of the firing tactics can considerably increase the probability of the victory in the battle. The developed model of the two-way battle may be used for estimating the combat effectiveness of the multipurpose weaponry units.

Чуев В.Ю., Дубограй И.В., Анисова Т.Л. Вероятностная модель отражения атаки разнотипных средств. Математическое моделирование и численные методы, 2018, № 1, с. 90-97

#### 519.8 Stochastic models of bilateral hostilities of numerous groups while linear dependence of military units’ effective firing rate on the duration of the battle

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

doi: 10.18698/2309-3684-2018-2-122132

The article presents developed on the basis of the theory of Markov’s processes the models of bilateral hostilities with the linear dependence of effective firing rate of military units on the time of the battle. Developed the algorithm allows to calculate the main indicators of the battle of numerous groups. Fulfilled the comparison with the results of a battle simulation, received on the basis of probabilistic models of the battle with constant effective firing rate and the deterministic model of a combat with a linear dependency of effective firing rate on the time of the battle. The range of the last models applicability presented.

Чуев В.Ю., Дубограй И.В. Стохастические модели двухсторонних боевых тдействий многочисленных группировок при линейных зависимостях эффективнх скорострельностей боевых единиц сторон от времени боя. Математическое моделирование и численные методы, 2018, № 2, с. 122–132.

#### 519.8 Stochastic models of the two unit duel fight

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

doi: 10.18698/2309-3684-2016-2-6984

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.

Chuev V., Dubogray I. Stochastic models of the two unit duel fight. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 69-84