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2016 On queue-size scaling for input-queued switches
D. Shah, J. N. Tsitsiklis, Y. Zhong
Stoch. Syst. 6(1): 1-25 (2016). DOI: 10.1214/14-SSY151


We study the optimal scaling of the expected total queue size in an $n\times n$ input-queued switch, as a function of the number of ports $n$ and the load factor $\rho$, which has been conjectured to be $\Theta(n/{(}1-\rho{)})$ (cf. [15]). In a recent work [16], the validity of this conjecture has been established for the regime where $1-\rho=O(1/n^{2})$. In this paper, we make further progress in the direction of this conjecture. We provide a new class of scheduling policies under which the expected total queue size scales as $O\big(n^{1.5}(1-\rho)^{-1}\log\big(1/(1-\rho)\big)\big)$ when $1-\rho=O(1/n)$. This is an improvement over the state of the art; for example, for $\rho=1-1/n$ the best known bound was $O(n^{3})$, while ours is $O(n^{2.5}\log n)$.


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D. Shah. J. N. Tsitsiklis. Y. Zhong. "On queue-size scaling for input-queued switches." Stoch. Syst. 6 (1) 1 - 25, 2016.


Received: 1 May 2014; Revised: 20 May 2015; Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1355.60118
MathSciNet: MR3580996
Digital Object Identifier: 10.1214/14-SSY151

Primary: 60K20, 68M12
Secondary: 68M20

Rights: Copyright © 2016 INFORMS Applied Probability Society


Vol.6 • No. 1 • 2016
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