Reducing parameter uncertainty for stochastic systems

Abstract

The design of many production and service systems is informed by stochastic model analysis. But the parameters of statistical distributions of stochastic models are rarely known with certainty, and are often estimated from field data. Even if the mean system performance is a known function of the model's parameters, there may still be uncertainty about the mean performance because the parameters are not known precisely. Several methods have been proposed to quantify this uncertainty, but data sampling plans have not yet been provided to reduce parameter uncertainty in a way that effectively reduces uncertainty about mean performance. The optimal solution is challenging, so we use asymptotic approximations to obtain closed-form results for sampling plans. The results apply to a wide class of stochastic models, including situations where the mean performance is unknown but estimated with simulation. Analytical and empirical results for the M/M/1 queue, a quadratic response-surface model, and a simulated critical care facility illustrate the ideas.