Queue waiting time explodes non-linearly as utilisation approaches capacity, and variability magnifies the effect.
Kingman's 1961 approximation puts mean queueing time at the utilisation factor, times the average of the squared coefficients of variation of arrivals and service, times mean service time. Where that variability factor is 1, 90% utilisation gives about nine service times of queueing and 95% about nineteen. Running an emergency department or a road network near full capacity is what produces the queue.
In practice
- An emergency department running at 85% of capacity has short waits; at 96% the same department has four-hour waits with the same staff.
- A team where every engineer is fully allocated cannot absorb one sick day, and a fortnight of slippage follows.
- Further reading
- Wikipedia
- Subject
- Design & Systems
- Essay
- Why systems behave against intuition