1 results
Improved queue-size scaling for input-queued switches via graph factorization
- Part of
-
- Journal:
- Advances in Applied Probability / Volume 52 / Issue 3 / September 2020
- Published online by Cambridge University Press:
- 24 September 2020, pp. 798-824
- Print publication:
- September 2020
-
- Article
- Export citation
-
This paper studies the scaling of the expected total queue size in an
$n\times n$ input-queued switch, as a function of both the load 
$\rho$ and the system scale n. We provide a new class of scheduling policies under which the expected total queue size scales as 
$O\big( n(1-\rho)^{-4/3} \log \big(\!\max\big\{\frac{1}{1-\rho}, n\big\}\big)\big)$, over all n and 
$\rho<1$, when the arrival rates are uniform. This improves on the best previously known scalings in two regimes: 
$O\big(n^{1.5}(1-\rho)^{-1} \log \frac{1}{1-\rho}\big)$ when 
$\Omega\big(n^{-1.5}\big) \le 1-\rho \le O\big(n^{-1}\big)$ and 
$O\big(\frac{n\log n}{(1-\rho)^2}\big)$ when 
$1-\rho \geq \Omega(n^{-1})$. A key ingredient in our method is a tight characterization of the largest k-factor of a random bipartite multigraph, which may be of independent interest.
