一类搜索型多对二随机格斗的获胜概率

研究搜索型多对二随机格斗战斗模型。假设格斗开始时A方有m件武器,B方有2件武器,B方处于隐蔽状态,格斗开始后B方可以直接对A方进行射击,A方需先搜索到B方后才能进行射击。双方各为同类武器,都是集火射击,所有开火都是独立的,每件武器开火射击直到毁伤对方才重新射击下一个目标。对搜索时间和毁伤间隔时间都服从一般分布的随机格斗模型,通过分析各状态的特征,利用状态概率分析方法和向后递归时间方法建立状态方程,求出了格斗处在各个状态的概率,并得到双方的获胜概率计算公式。

Winning probabilities of a kind of searching many-versus-two stochastic duel

This paper makes an investigation into a kind of searching many-versus-two stochastic duel model by the state probabilities analysis and the backward recurrence time technique.Suppose that A has many weapons,and B has two weapons but it is under shelter.After the beginning of the duel,B can start shooting directly while A does not begin to shoot until it has found B.When both sides possess the weapons of the same kind,they will use the concentrated fire.Each weapon fires until its target is destroyed and then resumes firing at next target.Thus,it is possible to derive the state probabilities and the formulae of winning probabilities for both sides.