 Pollaczek-Khinchine formula

ID: pollaczek-khinchine-formula

For a stable first-come first-served M/G/1 queue, write

ρ = λ E S < 1

and

S (s) = E e^{- s S}

. The stationary waiting-time Laplace transform is

W_{q} (s) = \frac{( 1 - ρ ) s}{s - λ + λ S ( s )} .

With finite second service moment, differentiating at zero gives the Pollaczek-Khinchine mean formula. These are the transform and mean forms of the same queueing identity.

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