LIBRARIES 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, us-ing 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 con-sider MLSS models for network interactions, and hence introduce moment-linear stochas-tic 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 stochasti