IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v153y2012i3d10.1007_s10957-012-9986-8.html
   My bibliography  Save this article

New Average Optimality Conditions for Semi-Markov Decision Processes in Borel Spaces

Author

Listed:
  • Qingda Wei

    (Sun Yat-Sen University)

  • Xianping Guo

    (Sun Yat-Sen University)

Abstract

This paper deals with semi-Markov decision processes under the average expected criterion. The state and action spaces are Borel spaces, and the cost/reward function is allowed to be unbounded from above and from below. We give another set of conditions, under which the existence of an optimal (deterministic) stationary policy is proven by a new technique of two average optimality inequalities. Our conditions are slightly weaker than those in the existing literature, and some new sufficient conditions for the verifications of our assumptions are imposed on the primitive data of the model. Finally, we illustrate our results with three examples.

Suggested Citation

  • Qingda Wei & Xianping Guo, 2012. "New Average Optimality Conditions for Semi-Markov Decision Processes in Borel Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 709-732, June.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-012-9986-8
    DOI: 10.1007/s10957-012-9986-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-9986-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-9986-8?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. A. Jaśkiewicz, 2004. "On the Equivalence of Two Expected Average Cost Criteria for Semi-Markov Control Processes," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 326-338, May.
    2. Anna Jaśkiewicz, 2001. "An approximation approach to ergodic semi-Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 1-19, October.
    3. Federgruen, A. & Hordijk, A. & Tijms, H. C., 1979. "Denumerable state semi-Markov decision processes with unbounded costs, average cost criterion," Stochastic Processes and their Applications, Elsevier, vol. 9(2), pages 223-235, November.
    4. Liuer Ye & Xianping Guo, 2010. "New sufficient conditions for average optimality in continuous-time Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 75-94, August.
    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. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.

    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. C. Drent & S. Kapodistria & J. A. C. Resing, 2019. "Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 269-308, December.
    2. Prasenjit Mondal, 2020. "Computing semi-stationary optimal policies for multichain semi-Markov decision processes," Annals of Operations Research, Springer, vol. 287(2), pages 843-865, April.
    3. L. Jianyong & Z. Xiaobo, 2004. "On Average Reward Semi-Markov Decision Processes with a General Multichain Structure," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 339-352, May.
    4. A. Jaśkiewicz, 2009. "Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 321-347, May.
    5. Xianping Guo & Yi Zhang, 2016. "Optimality of Mixed Policies for Average Continuous-Time Markov Decision Processes with Constraints," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1276-1296, November.
    6. Huang, Yonghui & Guo, Xianping, 2011. "Finite horizon semi-Markov decision processes with application to maintenance systems," European Journal of Operational Research, Elsevier, vol. 212(1), pages 131-140, July.
    7. Ping Cao & Jingui Xie, 2016. "Optimal control of a multiclass queueing system when customers can change types," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 285-313, April.

    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:joptap:v:153:y:2012:i:3:d:10.1007_s10957-012-9986-8. 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.