Moment-linear stochastic systems and their applications

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. Further, 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. Thesis Supervisor: George C. Verghese Title: Professor of Electrical Engineering and Computer Science Thesis Supervisor: Bernard C. Lesieutre Title: Staff Scientist, Lawrence Berkeley National Laboratory