Number 10/Networks & contagion/Operations
The Queue Sensitivity
The quantity
The derivative of waiting time with respect to utilisation, evaluated near capacity. It measures how sharply delay explodes as a system fills.
01Why it matters
It separates systems that degrade gracefully from those that fail suddenly, at the same nominal capacity margin.
02Expected value
A sharp rise above utilisation of roughly 0.85, steeper where service-time variance is higher.
03How it would be measured
Waiting-time data against utilisation is routine in most service systems.
04What would refute it
Linear delay growth would make the sensitivity constant and the concern unfounded.