Robust Input Sampling Strategies for Stochastic Simulations with Uncertain Input Model

Abstract

A computer simulation model is often used as a surrogate model of a complex and dynamic real-world system. We employ simulation models to analyze the characteristics of system behavior. Generally, a model with high fidelity generates highly accurate output while requiring large computational complexity. Therefore, an efficient allocation of computing resources is crucial for reliable system analysis within a limited budget. The design of an estimator or simulation procedure takes account of the characteristics of the simulation model. If imprecise or uncertain model information is only in hand, we may run simulations in a manner that has a risk of achieving poor performance for the true model. In this dissertation, we focus on the efficient input sampling strategies for a stochastic simulation model that possesses input uncertainty. Traditionally, various variance reduction techniques have been developed to overcome the inefficiency of naı̈ve Monte Carlo sampling. Those conventional approaches assume that the simulation input model is precisely known and fixed. However, situations where the true input model is unknown and only imprecise or uncertain information is in hand of- ten occur in practice. For example, only limited observation of historical data may be available, and the input model could sometimes possess non-stationarity in practice—e.g., wind speed of a specific location or inter-arrival time of customers. Such input model uncertainty can significantly affect the simulation output. Regarding this issue, we develop estimation procedures by extending the conventional variance reduction approaches while also taking the input uncertainty into account. Specifically, we propose a robust version of the stratified sampling and importance sampling methods, namely distributionally robust stratification (DR-Strat) and distributionally robust stochastic importance sampling (DR-SIS). In common, our approaches model the determination of the input sampling strategy as a min-max problem by employing a perspective of distributionally robust optimization (DRO). The objective function is considered as an estimator variance within a nested simulation framework. However, our objective function does not possess certain structural characteristics that enable the DRO problem to be tractable as in conventional approaches. Hence, we develop an alternative solution procedure to solve the proposed min-max problems, generally by iteratively solving each stage of the two-stage problems. For meaningful analysis, we consider various problem settings—e.g., whether the input variable is discrete or continuous, and whether the metamodel is readily available or not—and propose separate solution methods regarding the specific setting.