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A policy iteration algorithm for Markov decision processes skip-free in one direction

Authors: Joke Lambert, Benny van Houdt, and Chris Blondia

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

In this paper we present a new algorithm for policy iteration for Markov decision processes (MDP) skip-free in one direction. This algorithm, which is based on matrix analytic methods, is in the same spirit as the algorithm of White (Stochastic Models, 21:785-797, 2005) which was limited to matrices that are skip-free in both directions. Optimization problems that can be solved using Markov decision processes arise in the domain of optical buffers, when trying to improve loss rates of fibre delay line (FDL) buffers. Based on the analysis of such an FDL buffer we present a comparative study between the different techniques available to solve an MDP. The results illustrate that the exploitation of the structure of the transition matrices places us in a position to deal with larger systems, while reducing the computation times.

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Joke Lambert, Benny van Houdt, and Chris Blondia. A policy iteration algorithm for Markov decision processes skip-free in one direction. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{lambert_et_al:DagSemProc.07461.3,
  author =	{Lambert, Joke and van Houdt, Benny and Blondia, Chris},
  title =	{{A policy iteration algorithm for Markov decision processes skip-free in one direction}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.3},
  URN =		{urn:nbn:de:0030-drops-14032},
  doi =		{10.4230/DagSemProc.07461.3},
  annote =	{Keywords: Markov Decision Process, Policy Evaluation, Skip-Free, Optical buffers, Fibre Delay Lines}
}

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A policy iteration algorithm for Markov decision processes skip-free in one direction

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