Pollaczek-Khinchine formula

From Wikipedia, the free encyclopedia

The Pollaczek-Khinchine formula is used in queuing theory determine average flow time in a single server situation with arrivals distributed according to a Poisson distribution. The formula was developed by Felix Pollaczek and Aleksandr Khinchin.

[edit] Formula

The formula states that the average flow time in the queue is given by:
$F_q=\frac{1}{\lambda_s}\times \frac{\rho}{1-\rho}\times\frac{1+C_s^2}{2}$
The average time in the system, F, is given by:
$F=F_q+\frac{1}{\lambda_s}$
In the above equations, the variables are defined as:
$λ s$ =rate of service
$λ a$ =rate of arrival
$\rho=\frac{\lambda_a}{\lambda_s}$ , which is called "traffic intensity," and is average demand in number of servers
$C s = λ s σ s$ , where $C s = 0$ for constant service time and $C s = 1$ when service times follow an Exponential distribution