In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue. The formula is the product of three terms which depend on utilization (U), variability (V) and service time (T). It was first published by John Kingman in his 1961 paper ''The single server queue in heavy traffic''. It is known to be generally very accurate, especially for a system operating close to saturation.

Statement of formula

Kingman's approximation states are equal to :

\mathbb E(W_q) \approx \left( \frac \right) \left( \frac\right) \tau

where ''τ'' is the mean service time (i.e. ''μ'' = 1/''τ'' is the service rate), ''λ'' is the mean arrival rate, ''ρ'' = ''λ''/''μ'' is the utilization, ''c_a'' is the

coefficient of variation In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as ...

for arrivals (that is the standard deviation of arrival times divided by the mean arrival time) and ''c_s'' is the coefficient of variation for service times.

References

{{Queueing theory Single queueing nodes