IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v94y2020i1d10.1007_s11134-019-09620-3.html
   My bibliography  Save this article

Admission control in a two-class loss system with periodically varying parameters and abandonments

Author

Listed:
  • Gabriel Zayas-Cabán

    (University of Wisconsin)

  • Mark E. Lewis

    (Cornell University)

Abstract

Motivated by service systems, such as telephone call centers and emergency departments, we consider admission control for a two-class multi-server loss system with periodically varying parameters and customers who may abandon from service. Assuming mild conditions for the parameters, a dynamic programming formulation is developed. We show that under the infinite horizon discounted problem, there exists an optimal threshold policy and provide conditions for a customer class to be preferred for each fixed time, extending stationary results to the non-stationary setting. We approximate the non-stationary problem by discretizing the time horizon into equally spaced intervals and examine how policies for this approximation change as a function of time and parameters numerically. We compare the performance of these approximations with several admission policies used in practice in a discrete-event simulation study. We show that simpler admission policies that ignore non-stationarity or abandonments lead to significant losses in rewards.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:94:y:2020:i:1:d:10.1007_s11134-019-09620-3
    DOI: 10.1007/s11134-019-09620-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-019-09620-3
    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/s11134-019-09620-3?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. 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. MILLER, Bruce L., 1969. "A queueing reward system with several customer classes," LIDAM Reprints CORE 41, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    4. Sergei V. Savin & Morris A. Cohen & Noah Gans & Ziv Katalan, 2005. "Capacity Management in Rental Businesses with Two Customer Bases," Operations Research, INFORMS, vol. 53(4), pages 617-631, August.
    5. Bruce L. Miller, 1969. "A Queueing Reward System with Several Customer Classes," Management Science, INFORMS, vol. 16(3), pages 234-245, November.
    6. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    7. Gabriel Zayas-Cabán & Jingui Xie & Linda V. Green & Mark E. Lewis, 2016. "Dynamic control of a tandem system with abandonments," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 279-293, December.
    8. Arie Hordijk & Martin L. Puterman, 1987. "On the Convergence of Policy Iteration in Finite State Undiscounted Markov Decision Processes: The Unichain Case," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 163-176, February.
    9. Linda V. Green & Peter J. Kolesar, 1995. "On the Accuracy of the Simple Peak Hour Approximation for Markovian Queues," Management Science, INFORMS, vol. 41(8), pages 1353-1370, August.
    10. Linda V. Green & Peter J. Kolesar, 1997. "The Lagged PSA for Estimating Peak Congestion in Multiserver Markovian Queues with Periodic Arrival Rates," Management Science, INFORMS, vol. 43(1), pages 80-87, January.
    11. Qingda Wei & Xianping Guo, 2012. "New Average Optimality Conditions for Semi-Markov Decision Processes in Borel Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 709-732, June.
    12. Martin L. Puterman & Moon Chirl Shin, 1978. "Modified Policy Iteration Algorithms for Discounted Markov Decision Problems," Management Science, INFORMS, vol. 24(11), pages 1127-1137, July.
    13. 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.
    14. Armann Ingolfsson & Elvira Akhmetshina & Susan Budge & Yongyue Li & Xudong Wu, 2007. "A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 201-214, May.
    15. Michael C. Fu & Steven I. Marcus & I-Jeng Wang, 2000. "Monotone Optimal Policies for a Transient Queueing Staffing Problem," Operations Research, INFORMS, vol. 48(2), pages 327-331, April.
    16. Alex Roubos & Sandjai Bhulai & Ger Koole, 2017. "Flexible Staffing for Call Centers with Non-stationary Arrival Rates," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. van Dijk (ed.), Markov Decision Processes in Practice, chapter 0, pages 487-503, Springer.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barış Ata & Xiaoshan Peng, 2020. "An Optimal Callback Policy for General Arrival Processes: A Pathwise Analysis," Operations Research, INFORMS, vol. 68(2), pages 327-347, March.

    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. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    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. Samantha L. Zimmerman & Alexander R. Rutherford & Alexa Waall & Monica Norena & Peter Dodek, 2023. "A queuing model for ventilator capacity management during the COVID-19 pandemic," Health Care Management Science, Springer, vol. 26(2), pages 200-216, June.
    4. Huh, Woonghee Tim & Lee, Jaywon & Park, Heesang & Park, Kun Soo, 2019. "The potty parity problem: Towards gender equality at restrooms in business facilities," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    5. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    6. Pazour, Jennifer A. & Roy, Debjit, 2012. "Minimizing Customer Waiting Costs for Rental Vehicle Providers using Threshold Reservation Policies," IIMA Working Papers WP2012-12-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    7. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    8. Leon Yang Chu & Zhixi Wan & Dongyuan Zhan, 2018. "Harnessing the Double-edged Sword via Routing: Information Provision on Ride-hailing Platforms," Working Papers 18-04, NET Institute.
    9. Xufeng Yang & Wen Jiao & Juliang Zhang & Hong Yan, 2022. "Capacity management for a leasing system with different equipment and batch demands," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3004-3020, July.
    10. Wall, A.D. & Worthington, D.J., 2007. "Time-dependent analysis of virtual waiting time behaviour in discrete time queues," European Journal of Operational Research, Elsevier, vol. 178(2), pages 482-499, April.
    11. 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.
    12. Apurva Jain & Kamran Moinzadeh & Aussadavut Dumrongsiri, 2015. "Priority Allocation in a Rental Model with Decreasing Demand," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 236-248, May.
    13. 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.
    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. Xufeng Yang & Juliang Zhang & Wen Jiao & Hong Yan, 2023. "Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers," Management Science, INFORMS, vol. 69(3), pages 1468-1485, March.
    16. Alnowibet, Khalid Abdulaziz & Perros, Harry, 2009. "Nonstationary analysis of the loss queue and of queueing networks of loss queues," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1015-1030, August.
    17. Felix Papier & Ulrich W. Thonemann, 2010. "Capacity Rationing in Stochastic Rental Systems with Advance Demand Information," Operations Research, INFORMS, vol. 58(2), pages 274-288, April.
    18. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    19. Noah Gans & Sergei Savin, 2007. "Pricing and Capacity Rationing for Rentals with Uncertain Durations," Management Science, INFORMS, vol. 53(3), pages 390-407, March.
    20. Kyle Y. Lin, 2003. "Decentralized admission control of a queueing system: A game‐theoretic model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 702-718, October.

    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:queues:v:94:y:2020:i:1:d:10.1007_s11134-019-09620-3. 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.