Waiting lines & capacity · M/M/1 and M/M/c · utilisation, wait time and queue length. Drag the arrival rate up toward capacity and watch the wait time explode.
Queues explode nonlinearly as utilisation nears 100% - the core law of service systems.
Arrival and service rates set utilisation rho; waiting time grows like 1/(1-rho).
Keep planned utilisation below ~85%; the last 15% of capacity is your buffer against chaos.
