An algorithm for improved delay-scaling in input-queued switches

Abstract

We consider an $n\times n$ input-queued switch with uniform Bernoulli traffic and study the delay (or equivalently, the queue length) in the regime where the size of the switch n and the load (denoted by $\rho$) simultaneously become large. We devise an algorithm with expected total queue length equal to $O((n^{5/4}(1-\rho )^{-1})\log \max (1/\rho ,n))$ for large n and $\rho$ such that $(1-\rho )^{-1} \ge n^{3/4}$. This result improves the previous best queue length bound in the regime $n^{3/4}< (1-\rho )^{-1} < n^{7/4}$. Under same conditions, the algorithm has an amortized time complexity $O(n+(1-\rho )^2 n^{7/2} / \log \max (1/\rho ,n))$. The time complexity becomes O(n) when $(1-\rho )^{-1} \ge n^{5/4}.$