IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2811-d672915.html
   My bibliography  Save this article

Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation

Author

Listed:
  • Sergey Stepanov

    (Department of Communication Networks and Commutation Systems, Moscow Technical University of Communications and Informatics, 8A, Aviamotornaya str., 111024 Moscow, Russia)

  • Mikhail Stepanov

    (Department of Communication Networks and Commutation Systems, Moscow Technical University of Communications and Informatics, 8A, Aviamotornaya str., 111024 Moscow, Russia)

Abstract

The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probability that a customer repeats the call. Such models are seen in the modeling of various telecommunication systems such as emergency information services, call and contact centers, access nodes, etc., functioning in overloading situations. The stationary behavior of the system is described by the infinite-state Markov process. It is shown that stationary characteristics of the model can be calculated with the help of an auxiliary model of the same class but without call repetitions due to losses occurring before and after the occupation of a free server and the aging of transmitted information. The performance measurements of the auxiliary model are calculated by solving a system of state equations using a recursive algorithm based on the concept of the truncation of the used state space. This approach allows significant savings of computer resources to be made by ignoring highly unlikely states in the process of calculation. The error caused by truncation is estimated. The presented numerical examples illustrate the use of the model for the elimination of the negative effects of emergency information service overload based on the filtering of the input flow of calls.

Suggested Citation

  • Sergey Stepanov & Mikhail Stepanov, 2021. "Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation," Mathematics, MDPI, vol. 9(21), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2811-:d:672915
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2811/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/21/2811/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Linda Green & Peter Kolesar, 1991. "The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals," Management Science, INFORMS, vol. 37(1), pages 84-97, January.
    2. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    3. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
    4. Avishai Mandelbaum & Sergey Zeltyn, 2009. "Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers," Operations Research, INFORMS, vol. 57(5), pages 1189-1205, October.
    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. Tevfik Aktekin & Tahir Ekin, 2016. "Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 460-478, September.
    2. Heemskerk, M. & Mandjes, M. & Mathijsen, B., 2022. "Staffing for many-server systems facing non-standard arrival processes," European Journal of Operational Research, Elsevier, vol. 296(3), pages 900-913.
    3. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    4. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    5. Xi Chen & Dave Worthington, 2017. "Staffing of time-varying queues using a geometric discrete time modelling approach," Annals of Operations Research, Springer, vol. 252(1), pages 63-84, May.
    6. Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    7. A. J. E. M. Janssen & J. S. H. van Leeuwaarden & Bert Zwart, 2011. "Refining Square-Root Safety Staffing by Expanding Erlang C," Operations Research, INFORMS, vol. 59(6), pages 1512-1522, December.
    8. O. Zeynep Akc{s}in & Francis de Véricourt & Fikri Karaesmen, 2008. "Call Center Outsourcing Contract Analysis and Choice," Management Science, INFORMS, vol. 54(2), pages 354-368, February.
    9. Ran Liu & Xiaolan Xie, 2018. "Physician Staffing for Emergency Departments with Time-Varying Demand," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 588-607, August.
    10. Yue Zhang & Martin L. Puterman & Matthew Nelson & Derek Atkins, 2012. "A Simulation Optimization Approach to Long-Term Care Capacity Planning," Operations Research, INFORMS, vol. 60(2), pages 249-261, April.
    11. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    12. Barth, Wolfgang & Manitz, Michael & Stolletz, Raik, 2008. "Analysis of Two-Level Support Systems with Time-Dependent Overflow - A Banking Application," Hannover Economic Papers (HEP) dp-399, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    13. Long He & Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2017. "Service Region Design for Urban Electric Vehicle Sharing Systems," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 309-327, May.
    14. J. G. Dai & Pengyi Shi, 2017. "A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management," Operations Research, INFORMS, vol. 65(2), pages 514-536, April.
    15. Brandon M McConnell & Thom J Hodgson & Michael G Kay & Russell E King & Yunan Liu & Greg H Parlier & Kristin Thoney-Barletta & James R Wilson, 2021. "Assessing uncertainty and risk in an expeditionary military logistics network," The Journal of Defense Modeling and Simulation, , vol. 18(2), pages 135-156, April.
    16. Yunan Liu & Ward Whitt & Yao Yu, 2016. "Approximations for heavily loaded G/GI/n + GI queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 187-217, April.
    17. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.
    18. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    19. Itay Gurvich & Mor Armony & Constantinos Maglaras, 2009. "Cross-Selling in a Call Center with a Heterogeneous Customer Population," Operations Research, INFORMS, vol. 57(2), pages 299-313, April.
    20. James Dong & Ward Whitt, 2015. "Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 664-685, December.

    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:21:p:2811-:d:672915. 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.