Combining Stylized Models and Simulation Models for Metamodeling and Simulation Optimization with Applications in Queueing Systems

In the field of operations research and management sciences (OR/MS), mathematicalmodels are often built to understand the system behaviors and to make decisions. Thesemodels have a wide spectrum of fidelity, from highly stylized models to complicatedsimulation models. Stylized models are often built on overly-simplified assumptions andadmit elegant analytical formula. They are useful in understanding how systems workon a high level, in developing managerial insights and in making qualitative decisions.But they often perform poorly in predicting system performances and in makingquantitative decisions. Simulation models, on the other hand, incorporate many detailsand often deliver credible predictions. But they are typically slow to run and, thus, it isdifficult to construct the response surface (i.e., metamodeling) and conduct optimization(i.e., simulation optimization).In this project we propose to incorporate stylized models into stochastic kriging method,which is a popular and powerful tool for simulation metamodeling, and use the newcombined model for prediction and optimization. Our preliminary results show that theidea works well for simple queueing simulation models. For the idea to work for morerealistic problems, there are a number of research questions that need to be answered.In this project we will design hypothesis test to test whether the inclusion of stylizedmodels improve the fitting quality, create indicators that measure the goodness of fit,develop algorithms for fast metamodeling so it may be used in simulation optimizationalgorithms, and study the convergence and rate of convergence of the new algorithms.We will also consider how to apply the new methods in queueing simulation problems,which include applications in manufacturing, supply chains and healthcare management.In particular, we will study how to develop appropriate stylized models for typicalqueueing situations and consider how to generate stylized models automatically incommercial simulation software packages such as Arena and Simio.?