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Fluid Approximations to Markov Decision Processes with Local Transitions

  • Alexey PiunovskiyEmail author
  • Yi Zhang
Chapter
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

In this chapter we indicate that when it is scaled properly, an absorbing Markov decision process (MDP) model with an expected total undiscounted cost can be approximated by two of its deterministic and continuous analogues, namely, the standard fluid model and the refined fluid model, at least when the scaling parameter \(n = 1,2,\ldots \) grows large. We obtain the level of accuracy of such fluid approximations by showing that the absolute difference between the objective function of the scaled MDP model and the one of the (standard and refined) fluid model goes to zero as fast as \(\frac{1} {n}.\) Under some extra conditions, we obtain that given a particular type of policy solving the refined fluid model, it can be translated into a policy, which is nearly optimal for the scaled MDP model.

Notes

Acknowledgements

Mr. Mantas Vykertas kindly helped us improve the English presentation of this chapter. We thank the referee for valuable comments, too.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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