Controlled Stochastic Dynamical Systems
Final rept. 1 Feb 2005-31 Jan 2007
IOWA STATE UNIV AMES
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In section 1, we describe our results on optimal control of a long term average cost rate problem. A new method, an Abelian limit approach is developed to solve this singular control problem. Abelian limit relations between three types of value functions are also developed. Results on two singular control problems arising from queueing networks in heavy traffic are described in section 2. There we derive an optimal buffer size for the singular control problem and it will yield asymptotically optimal buffer lengths for the corresponding queueing networks in heavy traffic. In section 3, the results on a combined control and stopping problem is described. Novelty feature here is that the diffusion coefficient is controlled and it is allowed to take the value zero. A martingale characterization is derived. Also, an explicit optimal strategy is obtained when the drift coefficient is linear. A stochastic differential game with degenerate variance control is described.
- Statistics and Probability
- Operations Research