随机等分组合条件下轮流对抗的Markov链模型

首先,分析了红蓝双方将各自兵器随机等分组合后,轮流进行火力对抗的状态。然后,推导了对抗过程中状态转移的概率矩阵。从而,建立了随机等分组合条件下轮流对抗的离散Markov链模型。在上述基础上,得出了各方获胜概率及平均对抗次数的计算公式,结合公式内部递归关联的特点,提出了计算上述公式的计算机递归算法。最后,结合歼击机与轰炸机进行火力对抗的实例,介绍了该模型的应用方法。供进一步研究参考。

The Markov Chains Model of Firing Antagonism by Turn in the Manner of Even Combination at Random

This paper provides a firing antagonism model-Markov chains,which describes the process of the firing antagonism by turn in the manner of even combination at random,and brings forward a recursion method with computer to solve the relative problems.Firstly,the state of the antagonism is analyzed.After red side and Blue side deploying their arms and assigning each arm's target as equally as possible,the firing antagonism occurs.But how describes the process?The state of the antagonism is necessary.Secondly,possibility matrix describing the relation between the states of the antagonism is deduced.Therefore,the model is established.Based on the model,the formula and a recursion method with computer to calculate the possibility of the winner and the antagonism number both are brought forward.Finally,an instance of the antagonism between a killer and a bomber is provided to exemplify how to use the model.The model and the method mentioned in this paper can be used for the further research.