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Original Articles

Denumerable continuous-time Markov decision processes with multiconstraints on average costs

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Pages 576-585 | Received 14 Dec 2009, Accepted 16 Jun 2010, Published online: 28 Sep 2010

References

  • Alidrisi , MM . 1990 . Optimal Control of the Service Rate of an Exponential Queuing Network using Markov Decision Theory . International Journal of Systems Science , 21 : 2553 – 2563 .
  • Anderson , WJ . 1991 . Continuous-time Markov Chains , New York : Springer-Verlag .
  • Aso , H and Kimura , M . 1973 . An Application of Markov Potential Theory to Markovian Decision Processes . International Journal of Systems Science , 4 : 907 – 932 .
  • Bertsekas , DP and Shreve , SE . 1996 . Stochastic Optimal Control: The Discrete-time Case , Belmont, MA : Athena Scientific .
  • Chen , MF . 2004 . From Markov Chains to Non-equilibrium Particle Systems , Singapore : World Scientific .
  • Feller , W . 1940 . On the Integro-differential Equations of Purely Discontinuous Markoff Processes . Transactions of the American Mathematical Society , 48 : 488 – 515 .
  • Guo , XP . 2007a . Constrained Optimisation for Average Cost Continuous-time Markov Decision Processes . IEEE Transactions on Automatic Control , 52 : 1139 – 1143 .
  • Guo , XP . 2007b . Continuous-time Markov Decision Processes with Discounted Rewards: the Case of Polish Spaces . Mathematics of Operations Research , 32 : 73 – 87 .
  • Guo , XP and Hernández-Lerma , O . 2003a . Drift and Monotonicity Conditions for Continuous-time Controlled Markov Chains with an Average Criterion . IEEE Transactions on Automatic Control , 48 : 236 – 245 .
  • Guo , XP and Hernández-Lerma , O . 2003b . Constrained Continuous-time Markov Control Processes with Discounted Criteria . Mathematics of Operations Research , 67 : 323 – 340 .
  • Guo , XP and Hernández-Lerma , O . 2003c . Continuous-time Controlled Markov Chains with Discounted Criteria . Actaied Applications Mathematics , 79 : 195 – 216 .
  • Guo , XP and Hernández-Lerma , O . 2009 . Continuous-time Markov Decision Processes: Theory and Applications , New York : Springer .
  • Hernández-Lerma , O and González-Hernández , J . 2000 . Constrained Markov Control Processes in Borel Spaces: the Discounted Case . Mathematics of Operations Research , 52 : 271 – 285 .
  • Hernández-Lerma , O , González-Hernández , J and López-Martínez , R . 2003 . Constrained Average Cost Markov Control Processes in Borel Spaces . SIAM Journal on and Control Optimization , 42 : 442 – 468 .
  • Hernández-Lerma , O and Lasserre , JB . 1996 . Discrete-time Markov Control Processes , New York : Springer-Verlag .
  • Hernández-Lerma , O and Lasserre , JB . 2002 . Further Topics on Discrete-tIme Markov Control Processes , New York : Springer-Verlag .
  • Prieto-Rumeau , T and Hernández-Lerma , O . 2008 . Ergodic Control of Continuous-time Markov Chains with Pathwise Constraints . SIAM Journal on and Control Optimization , 47 : 1888 – 1908 .
  • Puterman , ML . 1996 . Markov Decision Processes: Discrete Stochastic Dynamic Programming , New York : John Willy Sons .
  • Tang , H , Xi , HS and Yin , BQ . 2003 . Performance Optimisation of Continuous Time Markov Control Processes Based on Performance Potentials . International Journal of Systems Science , 34 : 63 – 71 .
  • Ye , LE , Guo , XP and Hernández-Lerma , O . 2008 . Existence and Regularity of a Nonhomogeneous Transition Matrix Under Measurablity Conditions . Journal of Theoretical Probability , 21 : 604 – 627 .
  • Zhang , LL and Guo , XP . 2008 . Constrained Continuous-time Markov Decision Processes with Average Criteria . Mathematics of Operations Research , 67 : 323 – 340 .
  • Zhu , QX . 2008 . Average Optimality for Continuous-time Markov Decision Processes with a Policy Iteration Approach . Journal of Mathematical Analysis and Applications , 339 : 691 – 704 .
  • Zhu , QX and Prieto-Rumeau , T . 2008 . Bias and Overtaking Optimality for Continuous-time Jump Markov Decision Processes in Polish Spaces . Journal of Applications Probability , 45 : 417 – 429 .
  • Zhu , QX , Yang , XS and Huang , CX . 2009 . Policy Iteration for Continuous-time Average Reward Markov Decision Processes in Polish Spaces . Abstract and Applied Analysis , 2009 doi:10.1155/2009/103723

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