Queue peaks in loaded networks exhibit a phase transition from square-root to logarithmic growth, with the transition point determined by network geometry—this matters for predicting buffer sizes and scheduling in real systems.
This paper analyzes how queue sizes grow over finite time horizons in stochastic networks with constrained resources. When the system has enough slack (spare capacity), queue peaks follow a surprising two-phase pattern: they grow like a square root initially, then switch to logarithmic growth.