Moment-linear stochastic systems and their applications

• Main Author: Roy, Sandip, 1978-
• Other Authors: George C. Verghese.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2014
• Subjects: Electrical Engineering and Computer Science.
• Online Access: http://hdl.handle.net/1721.1/87904

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003. === Includes bibliographical references (p. 263-271). === 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. === by Sandip Roy. === Ph.D.