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Multi-server accumulating priority queues with heterogeneous servers

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  • Li, Na
  • Stanford, David A.

Abstract

In the present work, we develop a multi-class multi-server queuing model with heterogeneous servers under the accumulating priority queuing discipline, where customers accumulate priority credits as a linear function of their waiting time in the queue, at rates which are distinct to the class to which they belong. At a service completion instant, the customer with the greatest accumulated priority commences service. When the system has more than one idle server, the so-called r-dispatch policy is implemented to determine which of the idle servers is to be selected to serve a newly-arriving customer. We establish the waiting time distribution for each class of customers. We also present a conservation law for the mean waiting time in M/Mi/c systems, and study a cost function in relation to the conservation law to optimize the level of heterogeneity among the service times in M/Mi/2 systems. Numerical investigations through simulation are carried out to validate our model.

Suggested Citation

  • Li, Na & Stanford, David A., 2016. "Multi-server accumulating priority queues with heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 252(3), pages 866-878.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:3:p:866-878
    DOI: 10.1016/j.ejor.2016.02.010
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    References listed on IDEAS

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    1. Laoucine Kerbache & F. S. Q. Alves & H. C. Yehia & L.A.C Pedrosa & F.R.B. Cruz, 2011. "Upper Bounds on Performance Measures of Heterogeneous M/M/c Queues," Post-Print hal-00609498, HAL.
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    4. Thomas L. Saaty, 1960. "Time-Dependent Solution of the Many-Server Poisson Queue," Operations Research, INFORMS, vol. 8(6), pages 755-772, December.
    5. Leonard Kleinrock & Roy P. Finkelstein, 1967. "Time Dependent Priority Queues," Operations Research, INFORMS, vol. 15(1), pages 104-116, February.
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    7. Vijendra P. Singh, 1970. "Two-Server Markovian Queues with Balking: Heterogeneous vs. Homogeneous Servers," Operations Research, INFORMS, vol. 18(1), pages 145-159, February.
    8. Leonard Kleinrock, 1965. "A conservation law for a wide class of queueing disciplines," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(2), pages 181-192, June.
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    Cited by:

    1. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.
    2. 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.
    3. Lien Vanbrabant & Kris Braekers & Katrien Ramaekers, 2021. "Improving emergency department performance by revising the patient–physician assignment process," Flexible Services and Manufacturing Journal, Springer, vol. 33(3), pages 783-845, September.
    4. Li, Na & Stanford, David A. & Sharif, Azaz B. & Caron, Richard J. & Pardhan, Alim, 2019. "Optimising key performance indicator adherence with application to emergency department congestion," European Journal of Operational Research, Elsevier, vol. 272(1), pages 313-323.
    5. Moura, Márcio das Chagas & Santana, João Mateus & Droguett, Enrique López & Lins, Isis Didier & Guedes, Bruno Nunes, 2017. "Analysis of extended warranties for medical equipment: A Stackelberg game model using priority queues," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 338-354.

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