Finite-Time Queue Peak Laws in Stochastic Networks: Logarithmic Scaling After Geometric Thresholds

arXiv:2606.18218v2 Announce Type: replace-cross Abstract: We study finite-horizon queue peaks in generalized switches, a standard stochastic-network model in which many queues share constrained service resources. Arrivals may be dependent, nonstationary, and responsive to the system history; the only load condition is uniform interior slack, meaning the conditional mean arrival vector stays in a fixed contraction of the capacity region. We show that this slack reshapes the finite-time peak law for drift-minimizing scheduling policies such as MaxWeight. The square-root envelope that is sharp wi