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Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview

Author

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  • Kristen Gardner

    (Amherst College)

  • Rhonda Righter

    (University of California, Berkeley)

Abstract

In recent years, a number of models involving different compatibilities between jobs and servers in queueing systems, or between agents and resources in matching systems, have been studied, and, under Markov assumptions and appropriate stability conditions, the stationary distributions have been shown to have product forms. We survey these results and show how, under an appropriate detailed description of the state, many existing product-form results are corollaries of similar results for the Order Independent queue. We also discuss how to use the product-form results to determine distributions for steady-state response times.

Suggested Citation

  • Kristen Gardner & Rhonda Righter, 2020. "Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 3-51, October.
    • Handle: RePEc:spr:queues:v:96:y:2020:i:1:d:10.1007_s11134-020-09668-6
    DOI: 10.1007/s11134-020-09668-6
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    References listed on IDEAS

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    1. Itay Gurvich & Ward Whitt, 2009. "Queue-and-Idleness-Ratio Controls in Many-Server Service Systems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 363-396, May.
    2. Kristen Gardner & Samuel Zbarsky & Sherwin Doroudi & Mor Harchol-Balter & Esa Hyytiä & Alan Scheller-Wolf, 2016. "Queueing with redundant requests: exact analysis," Queueing Systems: Theory and Applications, Springer, vol. 83(3), pages 227-259, August.
    3. Ivo Adan & Gideon Weiss, 2012. "Exact FCFS Matching Rates for Two Infinite Multitype Sequences," Operations Research, INFORMS, vol. 60(2), pages 475-489, April.
    4. 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.
    5. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    6. Ivo Adan & Ana Bušić & Jean Mairesse & Gideon Weiss, 2018. "Reversibility and Further Properties of FCFS Infinite Bipartite Matching," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 598-621, May.
    7. A. E. Krzesinski, 2011. "Order Independent Queues," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 0, pages 85-120, Springer.
    8. Itai Gurvich & Ward Whitt, 2010. "Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing," Operations Research, INFORMS, vol. 58(2), pages 316-328, April.
    9. Dimitris Bertsimas & Daisuke Nakazato, 1995. "The Distributional Little's Law and Its Applications," Operations Research, INFORMS, vol. 43(2), pages 298-310, April.
    10. Itay Gurvich & Ward Whitt, 2009. "Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 237-253, June.
    11. Youri Raaijmakers & Sem Borst & Onno Boxma, 2019. "Redundancy scheduling with scaled Bernoulli service requirements," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 67-82, October.
    12. Kristen Gardner & Mor Harchol-Balter & Alan Scheller-Wolf & Mark Velednitsky & Samuel Zbarsky, 2017. "Redundancy-d: The Power of d Choices for Redundancy," Operations Research, INFORMS, vol. 65(4), pages 1078-1094, August.
    13. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.
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    Cited by:

    1. 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.
    2. Céline Comte & Jan-Pieter Dorsman, 2021. "Pass-and-swap queues," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 275-331, August.
    3. Gideon Weiss, 2022. "Parallel multi-type many server conjecture," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 269-271, April.
    4. Gideon Weiss, 2020. "Directed FCFS infinite bipartite matching," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 387-418, December.
    5. Kristen Gardner & Rhonda Righter, 2022. "The cost of collaboration," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 7-40, February.
    6. Neil Walton, 2022. "Queueing: a perennial theory," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 557-559, April.
    7. Jocelyn Begeot & Irène Marcovici & Pascal Moyal, 2023. "Stability regions of systems with compatibilities and ubiquitous measures on graphs," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 275-312, April.
    8. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.

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