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Optimal heavy-traffic queue length scaling in an incompletely saturated switch

Author

Listed:
  • Siva Theja Maguluri

    (Georgia Institute of Technology)

  • Sai Kiran Burle

    (University of Illinois at Urbana-Champaign)

  • R. Srikant

    (University of Illinois at Urbana-Champaign)

Abstract

We consider an input-queued switch operating under the MaxWeight scheduling algorithm. This system is interesting to study because it is a model for Internet routers and data center networks. Recently, it was shown that the MaxWeight algorithm has optimal heavy-traffic queue length scaling when all ports are uniformly saturated. Here we consider the case when an arbitrary number of ports are saturated (which we call the incompletely saturated case), and each port is allowed to saturate at a different rate. We use a recently developed drift technique to show that the heavy-traffic queue length under the MaxWeight scheduling algorithm has optimal scaling with respect to the switch size even in these cases.

Suggested Citation

  • Siva Theja Maguluri & Sai Kiran Burle & R. Srikant, 2018. "Optimal heavy-traffic queue length scaling in an incompletely saturated switch," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 279-309, April.
    • Handle: RePEc:spr:queues:v:88:y:2018:i:3:d:10.1007_s11134-017-9562-x
    DOI: 10.1007/s11134-017-9562-x
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    Citations

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    Cited by:

    1. Saulius Minkevičius & Igor Katin & Joana Katina & Irina Vinogradova-Zinkevič, 2021. "On Little’s Formula in Multiphase Queues," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    2. Daniela Hurtado-Lange & Siva Theja Maguluri, 2022. "A load balancing system in the many-server heavy-traffic asymptotics," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 353-391, August.

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