Queue length asymptotics for generalized max-weight scheduling in the presence of heavy-tailed traffic
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Tsitsiklis_Queue length.pdf
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Author(s)
Jagannathan, Krishna Prasanna
Markakis, Michail
Modiano, Eytan H.
Tsitsiklis, John N.
Date Issued
June 2011
Journal
2011 Proceedings IEEE INFOCOM
Publisher
Institute of Electrical and Electronics Engineers
Citation
Jagannathan, Krishna et al. “Queue Length Asymptotics for Generalized Max-weight Scheduling in the Presence of Heavy-tailed Traffic.” 2011 Proceedings IEEE INFOCOM. Shanghai, China, 2011. 2318-2326.
Version
Author's final manuscript
Abstract
We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-α scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also shows that the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above `negative' result regarding the max-weight-α policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/INFCOM.2011.5935049
