IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i4d10.1007_s11009-018-9647-y.html
   My bibliography  Save this article

Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times

Author

Listed:
  • Ramin Behzad

    (Allameh Tabataba’i University)

  • Mohammad Reza Salehi Rad

    (Allameh Tabataba’i University)

  • Nader Nematollahi

    (Allameh Tabataba’i University)

Abstract

We consider a queueing system where some customers decide to simultaneously wait in two queues, rather than in a single queue, to receive their service. In practice, when there exists a number of queues rendering the same service, the customers may tend to simultaneously wait in more than one queue in order to receive the service sooner and thus scale down their waiting time. In this framework, the customers may abandon one of the queues when they are called to receive the service from the other. We treat this situation as customer reneging or abandonment. We study the customer’s waiting time under this model for the cases of independence and dependence of the waiting time random variables of the queues. In conducting this study, a Copula approach is applied to take into account the dependence structure of the waiting time random variables. We compare the numerical results of the dependence with that of the independence.

Suggested Citation

  • Ramin Behzad & Mohammad Reza Salehi Rad & Nader Nematollahi, 2019. "Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1045-1056, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9647-y
    DOI: 10.1007/s11009-018-9647-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9647-y
    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/s11009-018-9647-y?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. C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging. I," Operations Research, INFORMS, vol. 11(1), pages 88-100, February.
    2. Robert E. Stanford, 1979. "Reneging Phenomena in Single Channel Queues," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 162-178, May.
    3. Chihoon Lee & Jianqiang C. Wang, 2011. "Waiting time probabilities in the M/G/1 + M queue," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 72-83, 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. Pala, Ali & Zhuang, Jun, 2018. "Security screening queues with impatient applicants: A new model with a case study," European Journal of Operational Research, Elsevier, vol. 265(3), pages 919-930.
    2. Katsunobu Sasanuma, 2021. "Asymptotic Analysis for Systems with Deferred Abandonment," Mathematics, MDPI, vol. 9(18), pages 1-11, September.
    3. Li Xiao & Susan H. Xu & David D. Yao & Hanqin Zhang, 2022. "Optimal staffing for ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 309-351, October.
    4. Amina Angelika Bouchentouf & Aicha Messabihi, 2018. "Heterogeneous two-server queueing system with reverse balking and reneging," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 251-267, June.
    5. Veeraruna Kavitha & Jayakrishnan Nair & Raman Kumar Sinha, 2019. "Pseudo conservation for partially fluid, partially lossy queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 255-292, June.
    6. Yong Tan & Kamran Moinzadeh & Vijay S. Mookerjee, 2005. "Optimal Processing Policies for an e-Commerce Web Server," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 99-110, February.
    7. Navid Ghaffarzadegan & Richard C. Larson, 2018. "SD meets OR: a new synergy to address policy problems," System Dynamics Review, System Dynamics Society, vol. 34(1-2), pages 327-353, January.
    8. J. E. Reed & Amy R. Ward, 2008. "Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 606-644, August.
    9. Ivo Adan & Brett Hathaway & Vidyadhar G. Kulkarni, 2019. "On first-come, first-served queues with two classes of impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 113-142, February.
    10. Yoshiaki Inoue & Onno Boxma & David Perry & Shelley Zacks, 2018. "Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 303-350, August.
    11. Amy R. Ward & Sunil Kumar, 2008. "Asymptotically Optimal Admission Control of a Queue with Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 167-202, February.
    12. Roubos, Alex & Jouini, Oualid, 2013. "Call centers with hyperexponential patience modeling," International Journal of Production Economics, Elsevier, vol. 141(1), pages 307-315.
    13. Hayriye Ayhan, 2022. "Server assignment policies in queues with customer abandonments," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 393-395, April.
    14. Baris Ata & Peter W. Glynn & Xiaoshan Peng, 2017. "An equilibrium analysis of a discrete-time Markovian queue with endogenous abandonments," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 141-212, June.
    15. H. Christian Gromoll & Philippe Robert & Bert Zwart, 2008. "Fluid Limits for Processor-Sharing Queues with Impatience," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 375-402, May.
    16. J. G. Dai & Shuangchi He, 2010. "Customer Abandonment in Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 347-362, May.
    17. Asmita Tamuli & Dhruba Das & Amit Choudhury, 2024. "Optimizing the Performance of Multi-server Heterogeneous Queueing Systems with Dynamic Customer Behaviour," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 366-414, November.
    18. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    19. Cheng-Dar Liou, 2015. "Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2165-2182, September.
    20. Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.

    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:21:y:2019:i:4:d:10.1007_s11009-018-9647-y. 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.