IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i1d10.1007_s11009-019-09701-z.html
   My bibliography  Save this article

Fluctuation Analysis in Parallel Queues with Hysteretic Control

Author

Listed:
  • Jewgeni H. Dshalalow

    (Florida Institute of Technology)

  • Ahmed Merie

    (Florida Institute of Technology)

  • Ryan T. White

    (Florida Institute of Technology)

Abstract

We study an enhanced hysteretic control system, with primary and secondary queues and random batch service. When the primary queue down-crosses r, the server operates on two parallel lines, servicing them asynchronously until the primary line of remaining units is processed or the number of serviced secondary units is at least S, whichever comes first. The server then waits until the primary queue length reaches N (if needed) before returning to primary service. The server capacity of primary units is limited by R with two options: r ≤ R ≤ N and R > N. Using fluctuation analysis we obtain closed-form distributions of available units during key periods of time and the steady state distribution of the primary queue. We illustrate analytical tractability by numerous analytical and computational examples.

Suggested Citation

  • Jewgeni H. Dshalalow & Ahmed Merie & Ryan T. White, 2020. "Fluctuation Analysis in Parallel Queues with Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 295-327, March.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:1:d:10.1007_s11009-019-09701-z
    DOI: 10.1007/s11009-019-09701-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09701-z
    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/s11009-019-09701-z?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. Alexander Dudin & Srinivas Chakravarthy, 2002. "Optimal Hysteretic Control for the BMAP/G/ 1 System with Single and Group Service Modes," Annals of Operations Research, Springer, vol. 112(1), pages 153-169, April.
    2. Jewgeni H. Dshalalow, 1997. "On the level crossing of multi-dimensional delayed renewal processes," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-7, January.
    3. Alexander N. Dudin & Shoichi Nishimura, 2000. "Optimal hysteretic control for a B M A P / S M / 1 / N queue with two operation modes," Mathematical Problems in Engineering, Hindawi, vol. 5, pages 1-23, January.
    4. 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, March.
    5. Jau-Chuan Ke, 2006. "An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 357-369, May.
    6. Kostia Avrachenkov & Efrat Perel & Uri Yechiali, 2016. "Finite-buffer polling systems with threshold-based switching policy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 541-571, October.
    7. Carri W. Chan & Mor Armony & Nicholas Bambos, 2016. "Maximum weight matching with hysteresis in overloaded queues with setups," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 315-351, April.
    8. Jelmer P. Gaast & Ivo J. B. F. Adan & René B. M. Koster, 2017. "The analysis of batch sojourn-times in polling systems," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 313-335, April.
    9. Jianyu Cao & Weixin Xie, 2017. "Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 117-147, February.
    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. Jewgeni H. Dshalalow & Ahmed Merie, 2018. "Fluctuation analysis in queues with several operational modes and priority customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 309-333, July.
    2. Sem Borst & Onno Boxma, 2018. "Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 335-369, October.
    3. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    4. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    5. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    6. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    7. Houyuan Jiang & Zhan Pang & Sergei Savin, 2012. "Performance-Based Contracts for Outpatient Medical Services," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 654-669, October.
    8. Shan Gao & Zaiming Liu & Qiwen Du, 2014. "Discrete-Time Gix/Geo/1/N Queue With Working Vacations And Vacation Interruption," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-22.
    9. Wee Meng Yeo & Xue-Ming Yuan & Joyce Mei Wan Low, 2017. "On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement," Annals of Operations Research, Springer, vol. 248(1), pages 553-578, January.
    10. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    11. 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.
    12. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    13. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Dmitry Kozyrev, 2021. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation," Mathematics, MDPI, vol. 9(4), pages 1-29, February.
    14. Srinivas R. Chakravarthy & Serife Ozkar, 2016. "Crowdsourcing and Stochastic Modeling," Business and Management Research, Business and Management Research, Sciedu Press, vol. 5(2), pages 19-30, June.
    15. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    16. Veena Goswami & Gopinath Panda, 2024. "Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-27, June.
    17. Jewgeni H. Dshalalow & Hend Aljahani, 2023. "Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information," Mathematics, MDPI, vol. 11(16), pages 1-27, August.
    18. A. D. Banik & M. L. Chaudhry, 2017. "Efficient Computational Analysis of Stationary Probabilities for the Queueing System BMAP / G /1/ N With or Without Vacation(s)," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 140-151, February.
    19. Jewgeni H. Dshalalow & Ryan T. White, 2022. "Fluctuation Analysis of a Soft-Extreme Shock Reliability Model," Mathematics, MDPI, vol. 10(18), pages 1-33, September.
    20. Kuo-Hsiung Wang & Cheng-Dar Liou & Ya-Lin Wang, 2014. "Profit optimisation of the multiple-vacation machine repair problem using particle swarm optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1769-1780, August.

    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:metcap:v:22:y:2020:i:1:d:10.1007_s11009-019-09701-z. 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.