IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v168y2017icp128-135.html
   My bibliography  Save this article

Analysis of an optimal stopping problem for software rejuvenation in a deteriorating job processing system

Author

Listed:
  • Machida, Fumio
  • Miyoshi, Naoto

Abstract

Software rejuvenation is the proactive maintenance operation for software systems that experience software aging causing degradations in system performance and reliability. The normal system performance can be recovered by software rejuvenation, which restarts the software system to clear all the internal error states due to software aging. Since software rejuvenation drops all the jobs in the system, a trigger for software rejuvenation needs to be carefully determined in consideration of such costs. In this paper, we theoretically derive the optimal policy that minimizes the cost of decision for software rejuvenation in a deteriorating job processing system, which is modeled as an M/M/1 queue with infinite buffer size. In our model, the number of queued jobs is used to represent the system state and the decision of rejuvenation is made upon the completion of a foreground job. We formulate the problem as an optimal stopping problem to analytically derive the optimal policy for the rejuvenation decision. The analytical results show that the optimal stopping policy is determined by the service degradation rate, the costs of dropped jobs and delayed jobs, and it does not depend on the number of queued jobs. This indicates that whether to trigger rejuvenation can be decided immediately when the system confirms the level of service degradation, regardless of the number of queued jobs at that time instant.

Suggested Citation

  • Machida, Fumio & Miyoshi, Naoto, 2017. "Analysis of an optimal stopping problem for software rejuvenation in a deteriorating job processing system," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 128-135.
    • Handle: RePEc:eee:reensy:v:168:y:2017:i:c:p:128-135
    DOI: 10.1016/j.ress.2017.05.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016305841
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2017.05.019?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. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    3. Chen, Dongyan & Trivedi, Kishor S., 2005. "Optimization for condition-based maintenance with semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 25-29.
    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. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    2. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2020. "Cost minimization of real-time mission for software systems with rejuvenation," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Levitin, Gregory & Xing, Liudong & Huang, Hong-Zhong, 2019. "Optimization of partial software rejuvenation policy," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 289-296.
    4. Wu, Shaomin & Do, Phuc, 2017. "Editorial," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 1-3.
    5. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2020. "Optimizing software rejuvenation policy for tasks with periodic inspections and time limitation," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. Levitin, Gregory & Xing, Liudong & Ben-Haim, Hanoch, 2018. "Optimizing software rejuvenation policy for real time tasks," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 202-208.

    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. Andriotis, C.P. & Papakonstantinou, K.G., 2019. "Managing engineering systems with large state and action spaces through deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    2. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    3. Shuyuan Gan & Bolun Wang & Zhifang Song, 2021. "A Combined Maintenance Strategy Considering Spares, Buffer, and Quality," Journal of Risk and Reliability, , vol. 235(3), pages 431-445, June.
    4. Zheng, Meimei & Ye, Hongqing & Wang, Dong & Pan, Ershun, 2021. "Joint Optimization of Condition-Based Maintenance and Spare Parts Orders for Multi-Unit Systems with Dual Sourcing," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    5. Pierre Bernhard & Marc Deschamps, 2017. "Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter," Working Papers 2017-10, CRESE.
    6. Jones, Randall E. & Cacho, Oscar J., 2000. "A Dynamic Optimisation Model of Weed Control," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123685, Australian Agricultural and Resource Economics Society.
    7. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    8. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    9. Pam Norton & Ravi Phatarfod, 2008. "Optimal Strategies In One-Day Cricket," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(04), pages 495-511.
    10. Aghayi, Nazila & Maleki, Bentolhoda, 2016. "Efficiency measurement of DMUs with undesirable outputs under uncertainty based on the directional distance function: Application on bank industry," Energy, Elsevier, vol. 112(C), pages 376-387.
    11. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    12. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    13. Azizi, Fariba & Salari, Nooshin, 2023. "A novel condition-based maintenance framework for parallel manufacturing systems based on bivariate birth/birth–death processes," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    14. Crutchfield, Stephen R. & Brazee, Richard J., 1990. "An Integrated Model of Surface and Ground Water Quality," 1990 Annual meeting, August 5-8, Vancouver, Canada 271011, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    16. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    17. Schön, Cornelia & König, Eva, 2018. "A stochastic dynamic programming approach for delay management of a single train line," European Journal of Operational Research, Elsevier, vol. 271(2), pages 501-518.
    18. Eric D. Gould, 2008. "Marriage and Career: The Dynamic Decisions of Young Men," Journal of Human Capital, University of Chicago Press, vol. 2(4), pages 337-378.
    19. KarabaÄŸ, Oktay & Eruguz, Ayse Sena & Basten, Rob, 2020. "Integrated optimization of maintenance interventions and spare part selection for a partially observable multi-component system," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    20. Lange, Rutger-Jan, 2024. "Bellman filtering and smoothing for state–space models," Journal of Econometrics, Elsevier, vol. 238(2).

    More about this item

    Statistics

    Access and download statistics

    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:eee:reensy:v:168:y:2017:i:c:p:128-135. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.