Stochastic fluctuations can have profound impacts on engineered systems. Nonetheless, we can achieve significant benefits such as cost reduction based uponexpanding our fundamental knowledge of stochastic systems. The primary goal of this thesis is to contribute to our understanding by developing and analyzing stochastic models for specific types of engineered systems. The knowledge gained can helpmanagement to optimize decision making under uncertainty.This thesis has three parts. In Part I, we study many-server queues that model large-scale service systems such as call centers. We focus on the positive recurrence ofpiecewise Ornstein-Uhlenbeck (OU) processes and the validity of using these processes to predict the steady-state performance of the corresponding many-server queues. In Part II, we investigate diffusion processes constrained to the positive orthant under infinitesimal changes in the drift.This sensitivity analysis on the drift helps us understand how changes in service capacities at individual stations in a stochastic network would affect the steady-state queue-length distributions. In Part III, westudy the trading mechanism known as limit order book. We are motivated by a desire to better understand the interplay among order flow rates, liquidity fluctuation, and optimal executions. The goal is to characterize the temporal evolution of orderbook shape on the “macroscopic” time scale.
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Stochastic models for service systems and limit order books
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