IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v22y2022i5d10.1007_s12351-022-00712-2.html
   My bibliography  Save this article

On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study

Author

Listed:
  • Carlos Chaves

    (Boeing, Inc.)

  • Abhijit Gosavi

    (Missouri University of Science and Technology)

Abstract

We consider the multi-server, single-channel queue, i.e., a G/G/k queue with k identical servers in parallel, under the first-come-first-served discipline in which the inter-arrival process is non-Poisson, the service time has any given distribution, and traffic is of medium intensity. Such queues are common in factories, airports, and hospitals, where the inter-arrival times and service times are typically not exponentially distributed, but rather have double-tapering distributions whose probability density functions taper on both sides, e.g., gamma, triangular etc. For these conditions, a new closed-form approximation based on only the mean and variance of the two inputs, the inter-arrival and service times, is presented. Determining distributions of inputs typically requires additional human effort in terms of histogram-fitting and running a goodness-of-fit test, which is avoided here. The new approximation is tested on a variety of scenarios and its performance is benchmarked against simulation. Further, the new approximation is also implemented on a ventilator case study from the recent COVID-19 pandemic to demonstrate its utility in optimizing server capacity. The approximation provides errors typically in the range 1–15% and 31% in the worst case. In systems where data change rapidly and decisions must be made quickly, this approximation will be particularly useful.

Suggested Citation

  • Carlos Chaves & Abhijit Gosavi, 2022. "On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study," Operational Research, Springer, vol. 22(5), pages 5205-5229, November.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00712-2
    DOI: 10.1007/s12351-022-00712-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-022-00712-2
    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/s12351-022-00712-2?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. Rabta, Boualem, 2013. "A hybrid method for performance analysis of G/G/m queueing networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 38-49.
    2. Saif Benjaafar & Joon-Seok Kim & N. Vishwanadham, 2004. "On the Effect of Product Variety in Production–Inventory Systems," Annals of Operations Research, Springer, vol. 126(1), pages 71-101, February.
    3. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    4. Lawrence W. Robinson & Rachel R. Chen, 2011. "Estimating the Implied Value of the Customer's Waiting Time," Manufacturing & Service Operations Management, INFORMS, vol. 13(1), pages 53-57, February.
    5. Toshikazu Kimura, 1986. "A Two-Moment Approximation for the Mean Waiting Time in the GI/G/s Queue," Management Science, INFORMS, vol. 32(6), pages 751-763, June.
    6. A. E. Eckberg, 1977. "Sharp Bounds on Laplace-Stieltjes Transforms, with Applications to Various Queueing Problems," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 135-142, May.
    7. A. Azadeh & M. S. Naghavi lhoseiny & V. Salehi, 2018. "Optimum alternatives of tandem G/G/K queues with disaster customers and retrial phenomenon: interactive voice response systems," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 68(3), pages 535-562, July.
    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. Lyons, Andrew Charles & Um, Juneho & Sharifi, Hossein, 2020. "Product variety, customisation and business process performance: A mixed-methods approach to understanding their relationships," International Journal of Production Economics, Elsevier, vol. 221(C).
    2. Wouter van Eekelen & Dick den Hertog & Johan S.H. van Leeuwaarden, 2022. "MAD Dispersion Measure Makes Extremal Queue Analysis Simple," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1681-1692, May.
    3. Freeman, Mark C. & Groom, Ben, 2016. "How certain are we about the certainty-equivalent long term social discount rate?," Journal of Environmental Economics and Management, Elsevier, vol. 79(C), pages 152-168.
    4. Konstantinos S. Boulas & Georgios D. Dounias & Chrissoleon T. Papadopoulos, 2023. "A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines," Journal of Intelligent Manufacturing, Springer, vol. 34(2), pages 823-852, February.
    5. Korporaal, R. & Ridder, A.A.N. & Kloprogge, P. & Dekker, R., 1999. "Capacity planning of prisons in the Netherlands," Econometric Institute Research Papers EI 9909-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Lot sizing and lead time decisions in production/inventory systems," International Journal of Production Economics, Elsevier, vol. 155(C), pages 351-360.
    7. Menezes, Mozart B.C. & Jalali, Hamed & Lamas, Alejandro, 2021. "One too many: Product proliferation and the financial performance in manufacturing," International Journal of Production Economics, Elsevier, vol. 242(C).
    8. Dhouib, K. & Gharbi, A. & Landolsi, N., 2009. "Throughput assessment of mixed-model flexible transfer lines with unreliable machines," International Journal of Production Economics, Elsevier, vol. 122(2), pages 619-627, December.
    9. George Liberopoulos & George Kozanidis & Panagiotis Tsarouhas, 2007. "Performance Evaluation of an Automatic Transfer Line with WIP Scrapping During Long Failures," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 62-83, December.
    10. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    11. Wen-Ya Wang & Diwakar Gupta, 2011. "Adaptive Appointment Systems with Patient Preferences," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 373-389, July.
    12. Sumi Kim & Seongmoon Kim, 2015. "Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing," Annals of Operations Research, Springer, vol. 230(1), pages 35-55, July.
    13. Eser Gemikonakli & Enver Ever & Glenford Mapp & Orhan Gemikonakli, 2017. "Admission control and buffer management of wireless communication systems with mobile stations and integrated voice and data services," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 65(4), pages 663-675, August.
    14. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Modelling complex assemblies as a queueing network for lead time control," European Journal of Operational Research, Elsevier, vol. 174(1), pages 150-168, October.
    15. Kong, Qingxia & Lee, Chung-Yee & Teo, Chung-Piaw & Zheng, Zhichao, 2016. "Appointment sequencing: Why the Smallest-Variance-First rule may not be optimal," European Journal of Operational Research, Elsevier, vol. 255(3), pages 809-821.
    16. Papadopoulos, H. T. & Vidalis, M. I., 2001. "Minimizing WIP inventory in reliable production lines," International Journal of Production Economics, Elsevier, vol. 70(2), pages 185-197, March.
    17. Michael Freeman & Nicos Savva & Stefan Scholtes, 2017. "Gatekeepers at Work: An Empirical Analysis of a Maternity Unit," Management Science, INFORMS, vol. 63(10), pages 3147-3167, October.
    18. Tan, Bar[iota]s, 1999. "Variance of the output as a function of time: Production line dynamics," European Journal of Operational Research, Elsevier, vol. 117(3), pages 470-484, September.
    19. Belmansour, Ahmed-Tidjani & Nourelfath, Mustapha, 2010. "An aggregation method for performance evaluation of a tandem homogenous production line with machines having multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1193-1201.
    20. Robert N. Boute & Marc R. Lambrecht & Benny Van Houdt, 2007. "Performance evaluation of a production/inventory system with periodic review and endogenous lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 462-473, 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:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00712-2. 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.