IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v36y2019i01ns0217595919500039.html
   My bibliography  Save this article

Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule

Author

Listed:
  • Qingqing Ma

    (School of Economics and Management, Shanxi University, Taiyuan 030006, P. R. China)

  • Yiqiang Q. Zhao

    (School of Mathematics and Statistics, Carleton University, Ottawa K1V 5B6, Canada)

  • Weiqi Liu

    (Institute of Management and Decision, Shanxi University, Taiyuan 030006, P. R. China4Faculty of Finance and Banking, Shanxi University of Finance and Economics, Taiyuan 030006, P. R. China)

  • Jihong Li

    (Institute of Management and Decision, Shanxi University, Taiyuan 030006, P. R. China)

Abstract

This study considers a single-server Markovian working vacation queuing system with Bernoulli vacation interruptions. Based on a linear reward-cost structure, the customer strategic joining behavior is analyzed under different information levels available to the arriving customers, namely fully observable, almost unobservable, and fully unobservable. For these cases, we first obtain the system stationary distribution. Thereafter, we determine the customer equilibrium strategies and compare them numerically with socially optimal strategies.

Suggested Citation

  • Qingqing Ma & Yiqiang Q. Zhao & Weiqi Liu & Jihong Li, 2019. "Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-26, February.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:01:n:s0217595919500039
    DOI: 10.1142/S0217595919500039
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595919500039
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595919500039?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. Jie Liu & Jinting Wang, 2017. "Strategic joining rules in a single server Markovian queue with Bernoulli vacation," Operational Research, Springer, vol. 17(2), pages 413-434, July.
    2. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, December.
    4. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    5. Guo, Pengfei & Hassin, Refael, 2012. "Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 222(2), pages 278-286.
    6. Wei Sun & Shiyong Li, 2014. "Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 694-715, July.
    7. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    8. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    Full references (including those not matched with items on IDEAS)

    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. Zhongbin Wang & Yunan Liu & Lei Fang, 2022. "Pay to activate service in vacation queues," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2609-2627, June.
    2. Economou, Antonis & Logothetis, Dimitrios & Manou, Athanasia, 2022. "The value of reneging for strategic customers in queueing systems with server vacations/failures," European Journal of Operational Research, Elsevier, vol. 299(3), pages 960-976.
    3. Gopinath Panda & Veena Goswami & Abhijit Datta Banik, 2016. "Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-34, October.
    4. Wang, Jinting & Zhang, Feng, 2013. "Strategic joining in M/M/1 retrial queues," European Journal of Operational Research, Elsevier, vol. 230(1), pages 76-87.
    5. Xianyue Shi & Liwei Liu, 2023. "Equilibrium Joining Strategies in the Retrial Queue with Two Classes of Customers and Delayed Vacations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
    6. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.
    7. Apostolos Burnetas & Antonis Economou & George Vasiliadis, 2017. "Strategic customer behavior in a queueing system with delayed observations," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 389-418, August.
    8. Jie Liu & Jinting Wang, 2017. "Strategic joining rules in a single server Markovian queue with Bernoulli vacation," Operational Research, Springer, vol. 17(2), pages 413-434, July.
    9. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    10. Ziani, Sofiane & Rahmoune, Fazia & Radjef, Mohammed Said, 2015. "Customers’ strategic behavior in batch arrivals M2/M/1 queue," European Journal of Operational Research, Elsevier, vol. 247(3), pages 895-903.
    11. Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.
    12. Bountali, Olga & Economou, Antonis, 2017. "Equilibrium joining strategies in batch service queueing systems," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1142-1151.
    13. Zhen Wang & Liwei Liu & Yiqiang Q. Zhao, 2022. "Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and N-policy," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 870-908, May.
    14. Lan Lu & Zheng Zhu & Pengfei Guo & Qiao‐Chu He, 2022. "Service Operations for Mixed Autonomous Paradigm: Lane Design and Subsidy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1595-1612, April.
    15. Gopinath Panda & Veena Goswami, 2022. "Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1439-1466, September.
    16. Wei Sun & Shiyong Li, 2014. "Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 694-715, July.
    17. Wang, Jinting & Zhang, Xuelu & Huang, Ping, 2017. "Strategic behavior and social optimization in a constant retrial queue with the N-policy," European Journal of Operational Research, Elsevier, vol. 256(3), pages 841-849.
    18. Dimitrakopoulos, Y. & Burnetas, A.N., 2016. "Customer equilibrium and optimal strategies in an M/M/1 queue with dynamic service control," European Journal of Operational Research, Elsevier, vol. 252(2), pages 477-486.
    19. Opher Baron & Antonis Economou & Athanasia Manou, 2022. "Increasing social welfare with delays: Strategic customers in the M/G/1 orbit queue," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2907-2924, July.
    20. Olga Bountali & Apostolos Burnetas & Lerzan Örmeci, 2022. "Join, balk, or jettison? The effect of flexibility and ranking knowledge in systems with batch arrivals," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3505-3524, September.

    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:wsi:apjorx:v:36:y:2019:i:01:n:s0217595919500039. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.