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Stability of JSQ in queues with general server-job class compatibilities

Author

Listed:
  • James Cruise

    (Heriot-Watt University)

  • Matthieu Jonckheere

    (Universidad de Buenos Aires and CONICET)

  • Seva Shneer

    (Heriot-Watt University)

Abstract

We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is routed to the shortest queue among the corresponding vertices. This generalizes many known models such as power-of-d load balancing and JSQ (join the shortest queue) on generic graphs. We prove that stability in this model is achieved if and only if there exists a stable static routing policy. This stability condition is equivalent to that of the JSW (join the shortest workload) policy. We show that some graph topologies lead to a loss of capacity, implying more restrictive stability conditions than in, for example, complete graphs.

Suggested Citation

  • James Cruise & Matthieu Jonckheere & Seva Shneer, 2020. "Stability of JSQ in queues with general server-job class compatibilities," Queueing Systems: Theory and Applications, Springer, vol. 95(3), pages 271-279, August.
    • Handle: RePEc:spr:queues:v:95:y:2020:i:3:d:10.1007_s11134-020-09656-w
    DOI: 10.1007/s11134-020-09656-w
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    References listed on IDEAS

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    1. Alexander L. Stolyar, 2017. "Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 31-65, February.
    2. Matthieu Jonckheere & Balakrishna J. Prabhu, 2018. "Asymptotics of insensitive load balancing and blocking phases," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 243-278, April.
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    Cited by:

    1. Cardinaels, Ellen & Borst, Sem & van Leeuwaarden, Johan S.H., 2024. "Heavy-traffic universality of redundancy systems with assignment constraints," Other publications TiSEM 1ab2791a-b085-466e-8ada-e, Tilburg University, School of Economics and Management.
    2. Xiao-Yue Gong & Vineet Goyal & Garud N. Iyengar & David Simchi-Levi & Rajan Udwani & Shuangyu Wang, 2022. "Online Assortment Optimization with Reusable Resources," Management Science, INFORMS, vol. 68(7), pages 4772-4785, July.

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