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A Queueing System with General-Use and Limited-Use Servers

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  • Linda Green

    (Columbia University, New York, New York)

Abstract

We consider a queueing system with two types of servers and two types of customers. General-use servers can provide service to either customer type while limited-use servers can be used only for one of the two. Though the apparent Markovian state space of this system is five-dimensional, we show that an aggregation results in an exact two-dimensional representation that is also Markovian. Matrix geometric theory is used to obtain approximations for the mean delay times and other measures of interest for each customer type. We illustrate the methodology by applying it to analyze a token discount policy used by the Triborough Bridge and Tunnel Authority.

Suggested Citation

  • Linda Green, 1985. "A Queueing System with General-Use and Limited-Use Servers," Operations Research, INFORMS, vol. 33(1), pages 168-182, February.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:1:p:168-182
    DOI: 10.1287/opre.33.1.168
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    Cited by:

    1. Carri W. Chan & Linda V. Green & Suparerk Lekwijit & Lijian Lu & Gabriel Escobar, 2019. "Assessing the Impact of Service Level When Customer Needs Are Uncertain: An Empirical Investigation of Hospital Step-Down Units," Management Science, INFORMS, vol. 65(2), pages 751-775, February.
    2. Elvin Coban & Aliza Heching & Alan Scheller‐Wolf, 2019. "Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 788-809, April.
    3. Heng-Li Liu & Quan-Lin Li, 2023. "Matched Queues with Flexible and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    4. Aksin, O. Zeynep & Harker, Patrick T., 2003. "Capacity sizing in the presence of a common shared resource: Dimensioning an inbound call center," European Journal of Operational Research, Elsevier, vol. 147(3), pages 464-483, June.
    5. Lee, Seung-Yup & Chinnam, Ratna Babu & Dalkiran, Evrim & Krupp, Seth & Nauss, Michael, 2021. "Proactive coordination of inpatient bed management to reduce emergency department patient boarding," International Journal of Production Economics, Elsevier, vol. 231(C).
    6. Marina Milenković & Miloš Nikolić & Draženko Glavić, 2022. "Optimization of toll road lane operation: Serbian case study," Operational Research, Springer, vol. 22(5), pages 5297-5322, November.
    7. 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.
    8. Serguei Netessine & Gregory Dobson & Robert A. Shumsky, 2002. "Flexible Service Capacity: Optimal Investment and the Impact of Demand Correlation," Operations Research, INFORMS, vol. 50(2), pages 375-388, April.
    9. P S Ansell & K D Glazebrook & C Kirkbride, 2003. "Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 379-389, April.
    10. Francisco Castro & Hamid Nazerzadeh & Chiwei Yan, 2020. "Matching queues with reneging: a product form solution," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 359-385, December.
    11. Noah Gans & Yong-Pin Zhou, 2007. "Call-Routing Schemes for Call-Center Outsourcing," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 33-50, May.
    12. Dongyuan Zhan & Gideon Weiss, 2018. "Many-server scaling of the N-system under FCFS–ALIS," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 27-71, February.
    13. Edieal J. Pinker & Robert A. Shumsky, 2000. "The Efficiency-Quality Trade-Off of Cross-Trained Workers," Manufacturing & Service Operations Management, INFORMS, vol. 2(1), pages 32-48, July.
    14. Hyun-Soo Ahn & Mark E. Lewis, 2013. "Flexible Server Allocation and Customer Routing Policies for Two Parallel Queues When Service Rates Are Not Additive," Operations Research, INFORMS, vol. 61(2), pages 344-358, April.
    15. Winfried K. Grassmann, 2003. "The Use of Eigenvalues for Finding Equilibrium Probabilities of Certain Markovian Two-Dimensional Queueing Problems," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 412-421, November.
    16. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.
    17. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.

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    Keywords

    802 two levels of servers;

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