A fast approximation of homogeneous stochastic combat

The stochastic combat model with arbitrary interkilling time distribution is more general than the deterministic Lanchester model or the exponent model. Unfortunately, the exact analytical solution of the more general combat model requires a huge amount of computation time, which makes it practically impossible to use for battles beyond 4 on 4. An approximation solution for a class of homogeneous stochastic combats with arbitrary interkilling time distribution is developed in this study. A large number of randomly generated battles from a very general population have been used to evaluate the approximation algorithm for accuracy and computation time. The results indicate that the approximation algorithm is highly accurate and its computation speed is about 100 to 1000 times faster than the corresponding simulation to reach the same level of accuracy.