IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v67y2008i2p323-340.html
   My bibliography  Save this article

Constrained continuous-time Markov decision processes with average criteria

Author

Listed:
  • Lanlan Zhang
  • Xianping Guo

Abstract

In this paper, we study constrained continuous-time Markov decision processes with a denumerable state space and unbounded reward/cost and transition rates. The criterion to be maximized is the expected average reward, and a constraint is imposed on an expected average cost. We give suitable conditions that ensure the existence of a constrained-optimal policy. Moreover, we show that the constrained-optimal policy randomizes between two stationary policies differing in at most one state. Finally, we use a controlled queueing system to illustrate our conditions. Copyright Springer-Verlag 2008

Suggested Citation

  • Lanlan Zhang & Xianping Guo, 2008. "Constrained continuous-time Markov decision processes with average criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 323-340, April.
    • Handle: RePEc:spr:mathme:v:67:y:2008:i:2:p:323-340
    DOI: 10.1007/s00186-007-0154-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-007-0154-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-007-0154-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 461-484, June.
    2. Masayuki Horiguchi, 2001. "Markov decision processes with a stopping time constraint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 279-295, June.
    3. Eugene A. Feinberg, 2000. "Constrained Discounted Markov Decision Processes and Hamiltonian Cycles," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 130-140, February.
    4. Yasemin Serin & Vidyadhar Kulkarni, 2005. "Markov decision processes under observability constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 311-328, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yonghui Huang & Qingda Wei & Xianping Guo, 2013. "Constrained Markov decision processes with first passage criteria," Annals of Operations Research, Springer, vol. 206(1), pages 197-219, July.
    2. Guo, Xianping & Ye, Liuer & Yin, George, 2012. "A mean–variance optimization problem for discounted Markov decision processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 423-429.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guo, Xianping & Zhang, Wenzhao, 2014. "Convergence of controlled models and finite-state approximation for discounted continuous-time Markov decision processes with constraints," European Journal of Operational Research, Elsevier, vol. 238(2), pages 486-496.
    2. Eugene A. Feinberg & Uriel G. Rothblum, 2012. "Splitting Randomized Stationary Policies in Total-Reward Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 129-153, February.
    3. Lauren B. Davis & Thom J. Hodgson & Russell E. King & Wenbin Wei, 2009. "Technical note: A computationally efficient algorithm for undiscounted Markov decision processes with restricted observations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 86-92, February.
    4. Vladimir Ejov & Jerzy A. Filar & Michael Haythorpe & Giang T. Nguyen, 2009. "Refined MDP-Based Branch-and-Fix Algorithm for the Hamiltonian Cycle Problem," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 758-768, August.
    5. Ali Eshragh & Jerzy Filar & Michael Haythorpe, 2011. "A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem," Annals of Operations Research, Springer, vol. 189(1), pages 103-125, September.
    6. Vivek Borkar & Jerzy Filar, 2013. "Markov chains, Hamiltonian cycles and volumes of convex bodies," Journal of Global Optimization, Springer, vol. 55(3), pages 633-639, March.
    7. Ali Eshragh & Jerzy Filar, 2011. "Hamiltonian Cycles, Random Walks, and Discounted Occupational Measures," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 258-270, May.
    8. Yonghui Huang & Qingda Wei & Xianping Guo, 2013. "Constrained Markov decision processes with first passage criteria," Annals of Operations Research, Springer, vol. 206(1), pages 197-219, July.
    9. Ali Eshragh & Jerzy A. Filar & Thomas Kalinowski & Sogol Mohammadian, 2020. "Hamiltonian Cycles and Subsets of Discounted Occupational Measures," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 713-731, May.
    10. Vladimir Ejov & Jerzy A. Filar & Minh-Tuan Nguyen, 2004. "Hamiltonian Cycles and Singularly Perturbed Markov Chains," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 114-131, February.
    11. Nelly Litvak & Vladimir Ejov, 2009. "Markov Chains and Optimality of the Hamiltonian Cycle," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 71-82, February.
    12. Konstantin Avrachenkov & Ali Eshragh & Jerzy A. Filar, 2016. "On transition matrices of Markov chains corresponding to Hamiltonian cycles," Annals of Operations Research, Springer, vol. 243(1), pages 19-35, August.
    13. Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    14. G. Dorini & F. Pierro & D. Savic & A. Piunovskiy, 2007. "Neighbourhood Search for constructing Pareto sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 315-337, April.
    15. Héctor Jasso-Fuentes & Tomás Prieto-Rumeau, 2024. "Constrained Markov Decision Processes with Non-constant Discount Factor," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 897-931, August.
    16. Richard Chen & Eugene Feinberg, 2010. "Compactness of the space of non-randomized policies in countable-state sequential decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 307-323, April.
    17. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:67:y:2008:i:2:p:323-340. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.