Pollaczek-Khinchine formula

Pollaczek-Khinchine formula

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.

Formula

The formula states that the average flow time in the queue is given by:
F_q=frac{1}{lambda_s} imes frac{ ho}{1- ho} imesfrac{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:
lambda_s=rate of service
lambda_a=rate of arrival
ho=frac{lambda_a}{lambda_s}, which is called "traffic intensity," and is average demand in number of servers
C_s=lambda_ssigma_s, where C_s=0 for constant service time and C_s=1 when service times follow an Exponential distribution


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