Offprint. Foundations and trends in stochastic systems. Vol. 1, no. 1 (2006).
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Includes bibliographical references.
CONTENTS NOTE
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Abstract -- 1. Introduction -- 2. Typical results -- 3. The framework -- 4. Criteria and the environment -- 5. Operators -- 6. Inequalities -- 7. Propagation results -- 8. Monotonicity of control -- 9. Models -- 10. Other state spaces -- 11. Comparing systems -- 12. Conclusions and future research directions -- References.
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SUMMARY OR ABSTRACT
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This paper focuses on monotonicity results for dynamic systems that take values in the natural numbers or in more-dimensional lattices. The results are mostly formulated in terms of controlled queueing systems, but there are also applications to maintenance systems, revenue management, and so forth. We concentrate on results that are obtained by inductively proving properties of the dynamic programming value function. We give a framework for using this method that unifies results obtained for different models. We also give a comprehensive overview of the results that can be obtained through it, in which we discuss not only (partial) characterizations of optimal policies but also applications of monotonicity to optimization problems and the comparison of systems.
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Title
Monotonicity in Markov reward and decision chains.