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Steady-state analysis of shortest expected delay routing

Author

Listed:
  • Jori Selen

    (Eindhoven University of Technology
    Eindhoven University of Technology)

  • Ivo Adan

    (Eindhoven University of Technology)

  • Stella Kapodistria

    (Eindhoven University of Technology)

  • Johan Leeuwaarden

    (Eindhoven University of Technology)

Abstract

We consider a queueing system consisting of two nonidentical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with nonidentical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product forms that can be determined recursively. The resulting series expression is directly amenable to numerical calculations and it also provides insight into the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.

Suggested Citation

  • Jori Selen & Ivo Adan & Stella Kapodistria & Johan Leeuwaarden, 2016. "Steady-state analysis of shortest expected delay routing," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 309-354, December.
    • Handle: RePEc:spr:queues:v:84:y:2016:i:3:d:10.1007_s11134-016-9497-7
    DOI: 10.1007/s11134-016-9497-7
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    References listed on IDEAS

    as
    1. Blanc, J.P.C., 2009. "Bad luck when joining the shortest queue," European Journal of Operational Research, Elsevier, vol. 195(1), pages 167-173, May.
    2. Ward Whitt, 1986. "Deciding Which Queue to Join: Some Counterexamples," Operations Research, INFORMS, vol. 34(1), pages 55-62, February.
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    Cited by:

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    2. Jing Dong & Elad Yom-Tov & Galit B. Yom-Tov, 2019. "The Impact of Delay Announcements on Hospital Network Coordination and Waiting Times," Management Science, INFORMS, vol. 67(5), pages 1969-1994, May.
    3. Siddharth Prakash Singh & Mohammad Delasay & Alan Scheller‐Wolf, 2023. "Real‐time delay announcement under competition," Production and Operations Management, Production and Operations Management Society, vol. 32(3), pages 863-881, March.
    4. Jazeem Abdul Jaleel & Sherwin Doroudi & Kristen Gardner, 2024. "Queue-length-aware dispatching in large-scale heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 125-184, October.
    5. Nur Sunar & Yichen Tu & Serhan Ziya, 2021. "Pooled vs. Dedicated Queues when Customers Are Delay-Sensitive," Management Science, INFORMS, vol. 67(6), pages 3785-3802, June.
    6. Merino, S. & Sánchez, F.J. & Sidrach de Cardona, M. & Guzmán, F. & Guzmán, R. & Martínez, J. & Sotorrío, P.J., 2018. "Optimization of energy distribution in solar panel array configurations by graphs and Minkowski’s paths," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 48-58.

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