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Probabilistic selfish routing in parallel batch and single-server queues

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  • A. Wang

    (The University of Auckland)

  • I. Ziedins

    (The University of Auckland)

Abstract

We consider a network of parallel queues, operating under probabilistic routing, where users can choose to join either a batch service queue, or one of several FIFO single-server queues. Afimeimounga et al. (Queueing Syst 49:321–334, 2005) considered the 2-queue case, which is known to exhibit the Downs–Thomson paradox, where delays may increase as capacity is increased. We show that in larger parallel systems, with multiple single-server queues, the user equilibrium is always unique when the batch size is sufficiently large relative to the number of queues; no more than three equilibria exist; Braess paradox may appear when adding extra queues.

Suggested Citation

  • A. Wang & I. Ziedins, 2018. "Probabilistic selfish routing in parallel batch and single-server queues," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 389-407, April.
    • Handle: RePEc:spr:queues:v:88:y:2018:i:3:d:10.1007_s11134-017-9558-6
    DOI: 10.1007/s11134-017-9558-6
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    References listed on IDEAS

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    Cited by:

    1. Ayane Nakamura & Tuan Phung-Duc, 2023. "Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size," Mathematics, MDPI, vol. 11(18), pages 1-22, September.
    2. Melia, Dr Steve, 2019. "Why did UK governments cut road building in the 1990s and expand it after 2010?," Transport Policy, Elsevier, vol. 81(C), pages 242-253.
    3. Yusei Koyama & Ayane Nakamura & Tuan Phung-Duc, 2024. "Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers," Mathematics, MDPI, vol. 12(18), pages 1-27, September.
    4. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.

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