Optimization of Jump Stochastic Systems

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9500746 Feinberg This research is focused on the optimization of continuous time jump stochastic systems. In particular, the research is aimed at developing new methods for analyzing stochastic syqtems: (1) study the structure of optimal control strategies, (2) develop algorithms to compute optimal strategies, and (3) develop structural and computational results for optimal strategies in production/inventory and telecommunications systems. The investigator is proposing a new method of analysis for jump stochastic systems. The potential for the research work is that it will provide a unified framework for the analysis of both the Continuous Time Markov Decision Processes with piecewise constant trajectories and Semi-Markov Decision Processes. By using the new framework and some other modeling and analysis techniques, including finite and infinite-dimensional linear programming, the research will pursue to develop structural results and efficient algorithms for the solution of continuous time problems, including problems with multiple criteria and constraints. The results of this project will provide analytical methods and computational tools for dynamic optimization of a wide range of natural and man-made systems whose behavior can be described by stochastic processes with piecewise constant trajectories. Knowledge of how to control dynamic stochastic systems beyond Markovian systems is in its infancy. This research will advance the frontier toward a better understanding and control of generalized Semi-Markov Processes. Stochastic models that can adjust based on real time data are needed. This work paves the way toward the realization of such a goal.