| Modeling and control of large-scale physical systems is a central concern in both industry and academia for obvious reasons. In this dissertation, we develop a framework for modeling and control of complex stochastic networks, which are typically modeled either via the queueing model, or the flow model. For concreteness, we use manufacturing systems as examples of physical systems modeled via queueing models, and the power transmission networks as examples of physical systems modeled via flow models. For both types of networks, we identify structural properties of the optimal policy, and show that they are similar. Based on the structural properties, we construct easily computable, effective control policies.; One major obstacle in the modeling of large networks has been complexity. The traditional modeling approach of detailed statistical characterization quickly leads to intractable models for networks of moderate size. In this dissertation, we develop two model reduction techniques that dramatically reduce the problem's dimension, and elucidate the structural properties of the optimal policy.; For manufacturing systems, we develop a variety of control policies. In addition to the conventional optimality criteria, we also develop control policies that are time-optimal, and can be easily adapted to take into account a range of issues that arise in a realistic, dynamic environment.; For power transmission networks, we characterize the optimal amount of generation capacity to hold in reserve. The optimal solution indicates precisely how reserves must be adjusted according to environmental factors including the variability of power demand, and the ramping-rate constraints on generation. |
