Max-Weight Scheduling in Queueing Networks With Heavy-Tailed Traffic
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Author(s)
Markakis, Michail
Modiano, Eytan H
Tsitsiklis, John N
Date Issued
March 2013
Journal
IEEE/ACM Transactions on Networking
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Markakis, Mihalis G., et al. “Max-Weight Scheduling in Queueing Networks With Heavy-Tailed Traffic.” IEEE/ACM Transactions on Networking, vol. 22, no. 1, Feb. 2014, pp. 257–70.
Version
Original manuscript
Abstract
We consider the problem of scheduling in a single-hop switched network with a mix of heavy-tailed and light-tailed traffic and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric, we use the delay stability of traffic flows: A traffic flow is delay-stable if its expected steady-state delay is finite, and delay-unstable otherwise. First, we show that a heavy-tailed traffic flow is delay-unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay-unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can become delay-unstable, even when it does not conflict with heavy-tailed traffic. Delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies. We show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
https://doi.org/10.1109/TNET.2013.2246869
