[1] The formula was first published by Felix Pollaczek in 1930[2] and recast in probabilistic terms by Aleksandr Khinchin[3] two years later.
[6] The formula states that the mean number of customers in system L is given by[7] where For the mean queue length to be finite it is necessary that
"Traffic intensity," ranges between 0 and 1, and is the mean fraction of time that the server is busy.
The variance term enters the expression due to Feller's paradox.
Using Little's law, which states that where so We can write an expression for the mean waiting time as[9] Writing π(z) for the probability-generating function of the number of customers in the queue[10] where g(s) is the Laplace transform of the service time probability density function.
nth moments can be obtained by differentiating the transform n times, multiplying by (−1)n and evaluating at s = 0.