Mathematical Single-Player Computer Game Model to Reproduce Duel Fight of Tanks

In improving computer games, which reproduce a battle of tanks, two tasks can be distinguished: increasing a collection of game tools to represent virtual prototypes of real tank models and ensuring a realistic game. To solve these problems, a tool is necessary that allows us to compare gaming capabilities of virtual tank brands with combat capabilities of their real prototypes. A mathematical model of a computer game that reproduces a duel battle of tanks can be used as the tool. The specified model satisfies the following requirements: the sequence of operations reproduced in the model is in line with the sequence of operations implemented by the player in the course of the game; the maximum amount of ammunition that a tank can use in a model must correspond to the amount of tank ammunition. The duel lasts until one of the tanks is hit, or until all the gunshots available to hit the enemy are expended. It is necessary to find the probabilities of possible outcomes of a duel battle, the mathematical expectation of its duration, the mathematical expectation of the ammunition consumption of each side.The solution to the problem is obtained by constructing a mathematical model according to the scheme of Markov random process with discrete states and continuous time. It is implemented as a program for a model of a duel battle of tanks and can be used when developing a computer game of the genre of tank simulators to assess the gaming capabilities of the virtual tanks in a duel battle from the data on the amount of their ammunition and on the intensity of the game process transition from one state to another; for selecting the intensity values of the game process transition from one state to another, based on the data on the estimated game capabilities of virtual tanks in a duel battle. Thus, game participants can use this model to conduct their own research. Developers of computer games can use it for setting up the game and setting such intensity values of the game process transition from one state to another, at which the gaming capabilities of virtual tanks will correspond to the combat capabilities of their real prototypes on the battlefield.

Reliability Modeling for Multistate System with Preventive Maintenance under Customer Demand

The performance level of a multistate system (MSS) can vary among different values rather than only two states (perfect functioning and complete failure). To improve the reliability of MSSs, a maintenance strategy has been adopted to satisfy customer demand, and reliability modeling of MSS with preventive maintenance and customer demand is proposed. According to the regular degradation and random failure at each state, based on the Markov random process, the proposed MSS with preventive maintenance can be modeled to satisfy the customer demand in a specific state. This model can also be adapted to compute other reliability indices. Based on this model, the effect of different preventive maintenance actions on the reliability indices can be analyzed and further compared. Two numerical examples have been illustrated to show the validity of the proposed model. The reliability model presented in this study can be used to assess the type of MSS and help reliability engineers to compare different maintenance actions quantitatively and make optimal decisions.

Forecasting macro parameters representing the behavior of an applied multi-agent system

Under consideration is the method of probabilistic forecasting of macro parameters representing general patterns of an applied multi-agent system behavior. This system introduces the game interaction between a set of agents and a target. The behavior dynamics of such a system is described by a discrete-state discrete-time Markov random process and represented in the terms, which are considered convenient for interpretation and practical control of macro parameters. The corresponding calculations are based on common characteristics of the initial conditions. The probabilistic model of behavior of the system is generalized for the case of the mobile target and supplemented with formulas for the dynamical calculation of probabilistic distributions of the target’s defeat by the agents as well as the agent’s defeat by the target.

Using Mathematical Models in Event Analysis from Military History

One of the ways of knowing the events of military history is to reproduce them using mathematical models. Based on the analysis of the fighting operations of the 4th Panzer Brigade of the Red Army in the vicinity of the city of Mtsensk in early October 1941, the capability to provide mathematical modeling of the fragments of these combat operations and the application of the apparatus of Markov random processes for these purposes is substantiated.The effectiveness of tanks depends not only on their technical properties, but also on the ways they are used on the battlefield. At the same time, combat effectiveness of tanks is commonly understood as their effectiveness in conditions when the methods of conducting combat operations by each of the opposing sides are the best.The battle outcome is probabilistic. It has certain regularity, depending on the combat tactics. The battle can be imagined as a multitude of randomly dueling fights between tanks, differing in their location and range of fire. A study of the probability of a system transition from each transient state to the next leads to the construction of mathematical models that allow calculating the ratio of losses of opposing sides.Based on the facts of military history and discovered regularities, the mathematical models are constructed to allow reproducing various fragments of combat according to the scheme of the Markov random process, and on their basis calculations are performed. The dependence of the ratio of the losses of the opposing sides depending on the number of firing positions used by the ambush tanks was established, provided that the change of these positions was made imperceptibly for the enemy.The obtained results can be used to develop tactical methods of using tanks in antiterrorist operations.

Optimization of reliability parameters structure for district heating systems

The problem of reliability parameters distribution on the district heating system's scheme is considered. This is one of important part of the general problem of optimal synthesis of district heating systems and is urgent for both the systems under design and the existing insufficiently reliable systems. The concept of solving the problem is based on the average reliability parameters of components (failure and restoration rates) which determine the first approximation to the optimal solution. This parameters needs for the further distribution its average values among system components. Algorithm and mathematical models for determine of optimal reliability parameters of system components with provide the required level of heat supply reliability and minimal total costs on ensuring this level are developed. The methodology of solving the stated problem is based on the methods of the theory of hydraulic circuits, nodal reliability, indices models of Markov random process and general regularities of heat transfer processes. The methodology also takes into account changes in thermal loads during the heating period and time redundancy of consumers related to heat storage.

Reliability Analysis of Multi-State Engine Units Utilizing Time-Domain Response Data

A novel reliability-based approach has been developed for multi-state engine systems. Firstly, the output power of the engine is discretized and modeled as a discrete-state continuous-time Markov random process. Secondly, the multi-state Markov model is established. According to the observed data, the transition intensity is determined. Thirdly, the proposed method is extended to compute the forced outage rate and the expected engine capacity deficiency based on time response. The proposed method can therefore be used for forecasting and monitoring the reliability of the multi-state engine utilizing time-domain response data. It is illustrated that the proposed method is practicable, feasible and gives reasonable prediction which conforms to the engineering practice.