Combining Response Surface Methodology with Numerical Methods for Optimization of Markovian Models

In general, decision support is one of the main purposes of model-based analysis of systems. Response surface methodology (RSM) is an optimization technique that has been applied frequently in practice, but few automated variants are currently available. In this paper, we show how to combine RSM with numerical analysis methods to optimize continuous time Markov chain models. Among the many known numerical solution methods for large Markov chains, we consider a Gauss-Seidel solver with relaxation that relies on a hierarchical Kronecker representation as implemented in the APNN Toolbox. To effectively apply RSM for optimizing numerical models, we propose three strategies which are shown to reduce the required number of iterations of the numerical solver. With a set of experiments, we evaluate the proposed strategies with a model of a production line and apply them to optimize a class-based queuing system