Moment-linear stochastic systems and their applications
Name
54927407-MIT.pdf
Description
Full printable version
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17.76 MB
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06c0df0d4e43959749985e82f1f58f1e
Author(s)
Roy, Sandip, 1978-
Advisor(s)
George C. Verghese.
Date Issued
2003
Publisher
Massachusetts Institute of Technology
Abstract
Our work is motivated by the need for tractable stochastic models for complex network and system dynamics. With this motivation in mind, we develop a class of discrete-time Markov models, called moment-linear stochastic systems (MLSS), which are structured so that moments and cross-moments of the state variables can be computed efficiently, using linear recursions. We show that MLSS provide a common framework for representing and characterizing several models that are common in the literature, such as jump-linear systems, Markov-modulated Poisson processes, and infinite server queues. We also consider MLSS models for network interactions, and hence introduce moment-linear stochastic network (MLSN) models. Several potential applications for MLSN-in such areas as traffic flow modeling, queueing, and stochastic automata modeling-are explored. Fur- ther, we exploit the quasi-linear structure of MLSS and MLSN to analyze their asymptotic dynamics, and to construct linear minimum mean-square-error estimators and minimum quadratic cost controllers. Finally, we study in detail two examples of MLSN, a stochastic automaton called the influence model and an aggregate model for air traffic flows.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.
Includes bibliographical references (p. 263-271).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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