On Queue-Size Scaling for Input-Queued Switches

TL;DR

This paper advances understanding of queue-size scaling in input-queued switches by proposing new scheduling policies that improve bounds on expected total queue size, especially near full load conditions.

Contribution

It introduces a new class of scheduling policies that achieve better queue-size bounds, moving closer to the conjectured optimal scaling for various load regimes.

Findings

Expected total queue size scales as O(n^{1.5}(1-ρ)^{-1} log(1/(1-ρ))) under the new policies.

Improves bounds from O(n^3) to O(n^{2.5} log n) for the case ρ = 1 - 1/n.

Progress towards the conjectured optimal queue-size scaling for input-queued switches.

Abstract

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 $\Theta (n/(1-\rho))$. In a recent work, 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 $O(n^{1.5}(1-\rho)^{-1}\log(1/(1-\rho)))$ 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 $O(n^{2.5}\log n)$.