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Monotonicity in Markov Reward and Decision Chains: Theory and Applications
Foundations and Trends® in
Stochastic Systems
Volume 1 Issue 1
DOI: 10.1561/0900000002
Monotonicity in Markov Reward and Decision Chains: Theory and Applications
Ger Koole
Department of Mathematics, VU University Amsterdam, De Boelelaan 1081a, Amsterdam, 1081 HV, The Netherlands, koole@few.vu.nl
Abstract
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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