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Redundancy scheduling with scaled Bernoulli service requirements

Author

Listed:
  • Youri Raaijmakers

    (Eindhoven University of Technology)

  • Sem Borst

    (Eindhoven University of Technology
    Nokia Bell Labs)

  • Onno Boxma

    (Eindhoven University of Technology)

Abstract

Redundancy scheduling has emerged as a powerful strategy for improving response times in parallel-server systems. The key feature in redundancy scheduling is replication of a job upon arrival by dispatching replicas to different servers. Redundant copies are abandoned as soon as the first of these replicas finishes service. By creating multiple service opportunities, redundancy scheduling increases the chance of a fast response from a server that is quick to provide service and mitigates the risk of a long delay incurred when a single selected server turns out to be slow. The diversity enabled by redundant requests has been found to strongly improve the response time performance, especially in the case of highly variable service requirements. Analytical results for redundancy scheduling are unfortunately scarce however, and even the stability condition has largely remained elusive so far, except for exponentially distributed service requirements. In order to gain further insight in the role of the service requirement distribution, we explore the behavior of redundancy scheduling for scaled Bernoulli service requirements. We establish a sufficient stability condition for generally distributed service requirements, and we show that, for scaled Bernoulli service requirements, this condition is also asymptotically nearly necessary. This stability condition differs drastically from the exponential case, indicating that the stability condition depends on the service requirements in a sensitive and intricate manner.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:1:d:10.1007_s11134-019-09621-2
    DOI: 10.1007/s11134-019-09621-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Youri Raaijmakers & Sem Borst & Onno Boxma, 2023. "Fork–join and redundancy systems with heavy-tailed job sizes," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 131-159, February.
    2. Jonatha Anselmi, 2022. "Replication vs speculation for load balancing," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 389-391, April.
    3. Kristen Gardner, 2022. "Correlation in redundancy systems," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 197-199, April.
    4. Kristen Gardner & Rhonda Righter, 2022. "The cost of collaboration," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 7-40, February.
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    6. 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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