IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1957-d615561.html
   My bibliography  Save this article

The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

Author

Listed:
  • Hong Zhang

    (School of Economics and Management, Changzhou Institute of Technology, Changzhou 213032, China)

  • Saviour Worlanyo Akuamoah

    (Department of Mathematics and Statistics, Ho Technical University, Ho Volta Region P.O. Box HP 217, Ghana)

  • Wilson Osafo Apeanti

    (Faculty of Science, University of Education, Winneba P.O. Box 25, Ghana)

  • Prince Harvim

    (Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada)

  • David Yaro

    (Department of Mathematics and Statistics, School of Applied Sciences and Technology, Cape Coast Technical University, Cape Coast P.O. Box DL 50, Ghana)

  • Paul Georgescu

    (Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506 Iaşi, Romania)

Abstract

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.

Suggested Citation

  • Hong Zhang & Saviour Worlanyo Akuamoah & Wilson Osafo Apeanti & Prince Harvim & David Yaro & Paul Georgescu, 2021. "The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1957-:d:615561
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1957/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1957/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Terekhov, Daria & Christopher Beck, J., 2009. "An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers," European Journal of Operational Research, Elsevier, vol. 198(1), pages 223-231, October.
    2. S R Agnihothri & A K Mishra & D E Simmons, 2003. "Workforce cross-training decisions in field service systems with two job types," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 410-418, April.
    3. Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments," Management Science, INFORMS, vol. 55(10), pages 1729-1742, October.
    4. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2010. "Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(6), pages 563-582, September.
    5. Burdzy, Krzysztof & Kang, Weining & Ramanan, Kavita, 2009. "The Skorokhod problem in a time-dependent interval," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 428-452, February.
    6. Dungey, Mardi & Gajurel, Dinesh, 2015. "Contagion and banking crisis – International evidence for 2007–2009," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 271-283.
    7. E. Morozov & B. Steyaert, 2013. "Stability analysis of a two-station cascade queueing network," Annals of Operations Research, Springer, vol. 202(1), pages 135-160, January.
    8. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.
    9. Mohammed-Aminu Sanda, 2011. "Using ATMs as Workload Relievers for Ghanaian Bank Tellers: The Customer Behavioral Challenge," Journal of Economics and Behavioral Studies, AMH International, vol. 3(1), pages 13-21.
    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. E. Morozov & B. Steyaert, 2013. "Stability analysis of a two-station cascade queueing network," Annals of Operations Research, Springer, vol. 202(1), pages 135-160, January.
    2. Pham, Tho & Talavera, Oleksandr & Tsapin, Andriy, 2018. "Shock contagion, asset quality and lending behavior," BOFIT Discussion Papers 21/2018, Bank of Finland Institute for Emerging Economies (BOFIT).
    3. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    4. Rouba Ibrahim & Ward Whitt, 2011. "Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity," Operations Research, INFORMS, vol. 59(5), pages 1106-1118, October.
    5. Herradi, Mehdi El & Leroy, Aurélien, 2022. "The rich, poor, and middle class: Banking crises and income distribution," Journal of International Money and Finance, Elsevier, vol. 127(C).
    6. Sewraj, Deeya & Gebka, Bartosz & Anderson, Robert D.J., 2018. "Identifying contagion: A unifying approach," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 55(C), pages 224-240.
    7. Qiuping Yu & Gad Allon & Achal Bassamboo, 2017. "How Do Delay Announcements Shape Customer Behavior? An Empirical Study," Management Science, INFORMS, vol. 63(1), pages 1-20, January.
    8. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    9. T. Flavin & M.Dongey & L. Sheenan, 2020. "Banks and Sovereigns: Did adversity bring them closer?," Economics Department Working Paper Series n307-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    10. Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Okhrin, Yarema, 2019. "Tail event driven networks of SIFIs," Journal of Econometrics, Elsevier, vol. 208(1), pages 282-298.
    11. Imen Ghadhab, 2021. "Cross-listing and crisis," Journal of Asset Management, Palgrave Macmillan, vol. 22(7), pages 539-558, December.
    12. G M Campbell, 2011. "A two-stage stochastic program for scheduling and allocating cross-trained workers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1038-1047, June.
    13. Do, A. & Powell, R. & Yong, J. & Singh, A., 2020. "Time-varying asymmetric volatility spillover between global markets and China’s A, B and H-shares using EGARCH and DCC-EGARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    14. Terekhov, Daria & Christopher Beck, J., 2009. "An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers," European Journal of Operational Research, Elsevier, vol. 198(1), pages 223-231, October.
    15. Rami Atar & Anup Biswas & Haya Kaspi, 2015. "Fluid Limits of G / G /1+ G Queues Under the Nonpreemptive Earliest-Deadline-First Discipline," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 683-702, March.
    16. Li, Jingyu & Yao, Yanzhen & Li, Jianping & Zhu, Xiaoqian, 2019. "Network-based estimation of systematic and idiosyncratic contagion: The case of Chinese financial institutions," Emerging Markets Review, Elsevier, vol. 40(C), pages 1-1.
    17. Corbet, Shaen & Larkin, Charles & Lucey, Brian & Meegan, Andrew & Yarovaya, Larisa, 2020. "Cryptocurrency reaction to FOMC Announcements: Evidence of heterogeneity based on blockchain stack position," Journal of Financial Stability, Elsevier, vol. 46(C).
    18. Atar, Rami & Biswas, Anup & Kaspi, Haya, 2018. "Law of large numbers for the many-server earliest-deadline-first queue," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2270-2296.
    19. Bara Kim & Jeongsim Kim, 2023. "Stability of a cascade system with multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 53-64, June.
    20. Raddant, Matthias & Kenett, Dror Y., 2021. "Interconnectedness in the global financial market," Journal of International Money and Finance, Elsevier, vol. 110(C).

    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:gam:jmathe:v:9:y:2021:i:16:p:1957-:d:615561. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.