Paper 06: Phase Transitions: Why Overloaded Systems Freeze Instead of Slowing Down

Thu, 02 Jul 2026 00:00:00 +0000

I. Abstract #

Linear intuition predicts that 10% more load costs roughly 10% more latency. Landau’s classification of phase transitions, Kleinrock’s queueing divergence, and the physics of traffic flow predict something else: a loaded system crosses a load-driven transition with three measurable signatures. First, a goodput cliff — useful output does not degrade, it drops discontinuously. Second, capacity drop — the jammed state delivers less than the system did right before jamming, and that state sustains itself. Third, critical slowing down — the variance and lag-1 autocorrelation of latency rise well before the mean does, which makes the collapse observable in advance. The engineering consequences: define sustainable capacity at the knee of the latency curve rather than at the benchmark peak, aim monitoring at second-order statistics rather than means, and when the system is already jammed, shed load far below nominal capacity instead of trimming it by degrees.

Queueing Theory on VinhMDev

Paper 06: Phase Transitions: Why Overloaded Systems Freeze Instead of Slowing Down

I. Abstract #