Modeling of Attrition in a Barrier Penetration Process with Evenly Spaced Barrier Elements

摘要

The paper examines a class of combat processes where one side's resources are evenly distributed along a barrier and the other side attempts to penetrate that barrier. Starting from a set of straightforward assumptions, the paper derives exact or approximate expressions for the expected numbers of resources destroyed, the expected number of shots fired at a target, and in some cases, the probability distribution of the number of shots fired at a target. The derivations combine and extend several concepts used in previous attrition models, including having resources situated on a barrier, letting each attacker engage several targets, and the use of the Poisson approximation to the binomial when there are several types of targets. Several different firing rules (attack protocols) are considered. Some of the equations developed here have been used in the Institute for Defense Analyses' NAVMOD naval model to model attrition when a task force or group of ships crosses a hostile submarine barrier.