Discrete Markov ballistic missile defense system modeling

Expected value is a common and useful baseline used to compare different multi-layered missile defense strategies or fire doctrines (number of interceptors fired at one target). However, expected value by itself does not render enough information to the military or national security researchers regarding the probability distribution of the effectiveness of the entire missile defense system. The objective of this paper is to provide relevant probability distribution functions (pdf) for ballistic missile defense (BMD) planning and cost-effective analyzing. To achieve this goal, discrete time Markov process is utilized to model multi-layered BMD system. Most issues of the multi-layered BMD system are covered in this model, including multi-reentry vehicles, discrimination probabilities and accompanying risk and waste of defensive resources, probability to engage all of the hostile objects, and required inventory levels. The effectiveness of a multi-layered BMD system is expressed in the pdf form of the number of warheads or missiles penetrating the BMD system. This paper also suggests that by changing fire doctrines and comparing the resulting effectiveness against cost the BMD system might be optimized. Since Markov process modeling requires initial state, military intelligence and information will be necessary to generate the initial state.