Interval-Based Simulation to Model Input Uncertainty in Stochastic Lanchester Models

Abstract

Interval-based simulation (IBS) has been proposed to model input uncertainty in discrete-event simulation. The foundation of this new simulation paradigm is imprecise probability, which models systems under both aleatory and epistemic uncertainties. The statistical distribution parameters in IBS are represented by intervals instead of precise real numbers. This paper discusses how the IBS approach can be applied to stochastic Lanchester models that are used in combat simulation to better account for input parameter uncertainty. The advantages of this approach are explored in comparison with second-order Monte Carlo simulation. Using IBS, an improved estimate of the probability of a team winning a battle is calculated by taking advantage of the interval structure. By resampling from intervals to determine event times, we can separate the effect of parameter uncertainty from random number generator uncertainty to estimate the probability that one team will win for given stream of random numbers used in a single replication. Additionally, we show how our method can be used to improve the reliability of stochastic Lanchester results by accounting for different skill levels within each team, and show how the interval structure can be used to highlight the disproportionate effect of the first few encounters in the battle.