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Waiting-Time Distribution of a Multi-Server, Priority Queuing System

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  • Richard H. Davis

    (Stanford Research Institute, Menlo Park, California)

Abstract

An explicit formula is given for the waiting-time distribution of any number of parallel, negative-exponential servers subject to Poisson demands from any number of priority classes. The demand rates may be different for the priority classes, but the service rate is the same for all classes. The queue discipline is first-come-within-priority class sequence.

Suggested Citation

  • Richard H. Davis, 1966. "Waiting-Time Distribution of a Multi-Server, Priority Queuing System," Operations Research, INFORMS, vol. 14(1), pages 133-136, February.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:1:p:133-136
    DOI: 10.1287/opre.14.1.133
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    Citations

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    Cited by:

    1. A. Baykal Hafızoğlu & Esma S. Gel & Pınar Keskinocak, 2013. "Expected Tardiness Computations in Multiclass Priority M / M / c Queues," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 364-376, May.
    2. Hideaki Takagi, 2016. "Waiting time in the M/M/ $$ m $$ m LCFS nonpreemptive priority queue with impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 257-289, 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. 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.
    5. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    6. Constantinos Maglaras & Assaf Zeevi, 2005. "Pricing and Design of Differentiated Services: Approximate Analysis and Structural Insights," Operations Research, INFORMS, vol. 53(2), pages 242-262, April.
    7. 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.
    8. Mor Harchol-Balter & Takayuki Osogami & Alan Scheller-Wolf & Adam Wierman, 2005. "Multi-Server Queueing Systems with Multiple Priority Classes," Queueing Systems: Theory and Applications, Springer, vol. 51(3), pages 331-360, December.
    9. 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.
    10. Gabor, A.F. & van Vianen, L.A. & Yang, G. & Axsäter, S., 2016. "Enabling customer satisfaction and stock reduction through service differentiation with response time guarantees," Econometric Institute Research Papers EI2016-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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