Simulation methods for non-stationary queues and value function computation
- The first part of the dissertation is concerned with the challenges that arise in the planning of stochastic simulations of systems in which time-of-day effects, day-of-week effects, or seasonal effects are present. In such simulations, one would like to avoid simulating the system over the entire time horizon of interest, say [0, t]. Since such non-stationary models frequently exhibit a "loss of memory", it is often possible to accurately compute system performance measures by generating paths only over [s, t], provided that s is chosen properly. We propound using reflected Brownian motion (RBM) with time-dependent drift and volatility as a guide to choose s in the setting of such simulations. We develop the first exact simulation method for reflected Brownian motion (RBM) with time-dependent drift and volatility. The running time of generating exact samples of non-stationary RBM at any time t is uniformly bounded. These exact samples can be used for planning simulations of non-stationary complex queueing systems. The second part of the dissertation addresses the estimation, via simulation, of value functions in the context of expected infinite horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate dynamic programming and applied probability in general. One approach is to build an approximation to the value function by estimating the basis coefficients in a linear basis expansion via least squares. Nevertheless, selecting appropriate basis functions is usually challenging. In contrast, we develop a fully nonparametric method to estimate the value function by incorporating "soft information" into the estimation algorithm, such as knowledge of convexity, monotonicity, or Lipchitz constants. In the presence of such information, a nonparametric estimator for the value function can be computed that is provably consistent as the simulated time horizon tends to infinity. As an application, we implement our method on pricing tolling contracts in energy markets.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Mousavi, Seyed Mohammad Hossein
|Stanford University, Department of Management Science and Engineering.
|Glynn, Peter W
|Glynn, Peter W
|Statement of responsibility
|Seyed Mohammad Hossein Mousavi.
|Submitted to the Department of Management Science and Engineering.
|Thesis (Ph.D.)--Stanford University, 2013.
- © 2013 by Seyed Mohammad Hossein Mousavi
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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