Improved queue-size scaling for input-queued switches via graph factorization
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This paper studies the scaling of the expected total queue size in an n× n input-queued switch, as a function of both the load ρ and the system scale n. We provide a new class of scheduling policies under which the expected total queue size scales as O( n(1-ρ)^-4/3({1/1-ρ, n})), over all n and ρ<1, when the arrival rates are uniform. This improves over the previously best-known scalings in two regimes: O(n^1.5(1-ρ)^-11/1-ρ) when Ω(n^-1.5) < 1-ρ< O(n^-1) and O(n n/(1-ρ)^2) when 1-ρ≥Ω(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.
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