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Computation of Steady-State Probabilities for M / M /1 Priority Queues

Author

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  • Douglas R. Miller

    (The George Washington University, Washington, D.C.)

Abstract

Recursive computational formulas for the steady-state distributions of exponential single-server (preemptive and nonpreemptive) priority queues with two classes of customers are derived using Neuts’ theory of matrix-geometric invariant probability vectors.

Suggested Citation

  • Douglas R. Miller, 1981. "Computation of Steady-State Probabilities for M / M /1 Priority Queues," Operations Research, INFORMS, vol. 29(5), pages 945-958, October.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:5:p:945-958
    DOI: 10.1287/opre.29.5.945
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    Citations

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    Cited by:

    1. Jayaswal, Sachin & Vidyarthi, Navneet, 2013. "Capacitated Multiple Allocation Hub Location with Service Level Constraints for Multiple Consignment Classes," IIMA Working Papers WP2013-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. William Liang & Barış Balcıog̃lu & Robert Svaluto, 2013. "Scheduling policies for a repair shop problem," Annals of Operations Research, Springer, vol. 211(1), pages 273-288, December.
    3. Lars A. Vianen & Adriana F. Gabor & Jan-Kees Ommeren, 2016. "Waiting times in classical priority queues via elementary lattice path counting," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 295-307, December.
    4. Jayaswal, Sachin & Vidyarthi, Navneet, 2023. "Multiple allocation hub location with service level constraints for two shipment classes," European Journal of Operational Research, Elsevier, vol. 309(2), pages 634-655.
    5. Josef Zuk & David Kirszenblat, 2024. "Explicit results for the distributions of queue lengths for a non-preemptive two-level priority queue," Annals of Operations Research, Springer, vol. 341(2), pages 1223-1246, October.
    6. Jayaswal, Sachin & Jewkes, Elizabeth & Ray, Saibal, 2011. "Product differentiation and operations strategy in a capacitated environment," European Journal of Operational Research, Elsevier, vol. 210(3), pages 716-728, May.
    7. Xinlei Liu & Xiuli Xu & Mingxin Liu, 2024. "Strategy Analysis of Retrial Queue with Parallel Customer and Standby Server," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-22, September.
    8. Luyi Yang & Laurens Debo & Varun Gupta, 2017. "Trading Time in a Congested Environment," Management Science, INFORMS, vol. 63(7), pages 2377-2395, July.
    9. Philip A. Ernst & Søren Asmussen & John J. Hasenbein, 2018. "Stability and busy periods in a multiclass queue with state-dependent arrival rates," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 207-224, December.
    10. Amir Rastpour & Armann Ingolfsson & Burhaneddin Sandıkçı, 2022. "Algorithms for Queueing Systems with Reneging and Priorities Modeled as Quasi-Birth-Death Processes," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1693-1710, May.
    11. Jianfu Wang & Opher Baron & Alan Scheller-Wolf, 2015. "M/M/c Queue with Two Priority Classes," Operations Research, INFORMS, vol. 63(3), pages 733-749, June.
    12. Attahiru Sule Alfa & Bin Liu & Qi‐Ming He, 2003. "Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 662-682, September.
    13. van Vianen, L.A. & Gabor, A.F. & van Ommeren, J.C.W., 2016. "Waiting times in classical priority queues via elementary lattice path counting," Econometric Institute Research Papers EI2016-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Drekic, Steve & Woolford, Douglas G., 2005. "A preemptive priority queue with balking," European Journal of Operational Research, Elsevier, vol. 164(2), pages 387-401, July.
    15. William P. Barnett & Daniel A. Levinthal, 2017. "Special Issue Introduction: Evolutionary Logics of Strategy and Organization," Strategy Science, INFORMS, vol. 2(1), pages 1-1, March.
    16. Jori Selen & Brian Fralix, 2017. "Time-dependent analysis of an M / M / c preemptive priority system with two priority classes," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 379-415, December.
    17. Winfried K. Grassmann & Steve Drekic, 2008. "Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 73-83, March.

    More about this item

    Keywords

    698; 705 computation of steady-state probabilities for M/M1/PRI;

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