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Matching queues with reneging: a product form solution

Author

Listed:
  • Francisco Castro

    (University of California)

  • Hamid Nazerzadeh

    (University of Southern California)

  • Chiwei Yan

    (University of Washington)

Abstract

Motivated by growing applications in two-sided markets, we study a parallel matching queue with reneging. Demand and supply units arrive to the system and are matched in an FCFS manner according to a compatibility graph specified by an N-system. If they cannot be matched upon arrival, they queue and may abandon the system as time goes by. We derive explicit product forms of the steady-state distributions of this system by identifying a partial balance condition.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:96:y:2020:i:3:d:10.1007_s11134-020-09662-y
    DOI: 10.1007/s11134-020-09662-y
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    References listed on IDEAS

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    1. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    2. 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.
    3. 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.
    4. 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.
    5. Ivo Adan & Gideon Weiss, 2012. "Exact FCFS Matching Rates for Two Infinite Multitype Sequences," Operations Research, INFORMS, vol. 60(2), pages 475-489, April.
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    7. Rishi Talreja & Ward Whitt, 2008. "Fluid Models for Overloaded Multiclass Many-Server Queueing Systems with First-Come, First-Served Routing," Management Science, INFORMS, vol. 54(8), pages 1513-1527, August.
    8. Philipp Afèche & Adam Diamant & Joseph Milner, 2014. "Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks," Operations Research, INFORMS, vol. 62(5), pages 1179-1201, October.
    9. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
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    Cited by:

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    3. Angelos Aveklouris & Amber L. Puha & Amy R. Ward, 2024. "A fluid approximation for a matching model with general reneging distributions," Queueing Systems: Theory and Applications, Springer, vol. 106(3), pages 199-238, April.
    4. Ausseil, Rosemonde & Ulmer, Marlin W. & Pazour, Jennifer A., 2024. "Online acceptance probability approximation in peer-to-peer transportation," Omega, Elsevier, vol. 123(C).
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    6. Gideon Weiss, 2020. "Directed FCFS infinite bipartite matching," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 387-418, December.
    7. 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.

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