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Queue length asymptotics for generalized max-weight scheduling in the presence of heavy-tailed traffic

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4 Author(s)
Jagannathan, K. ; Massachusetts Inst. of Technol., Cambridge, MA, USA ; Markakis, M. ; Modiano, E. ; Tsitsiklis, J.N.

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.

Published in:

INFOCOM, 2011 Proceedings IEEE

Date of Conference:

10-15 April 2011