Kingman's formula

Kingman's formula

Kingman's formula is a bound for G/G/1 queues and sates that the mean queue length is given by

:mathbb{E}(X) = holeft( 1 + frac{ ho(c_a^2 + c_s^2)}{2(1 ho)} ight)

and was first published by John Kingman in his 1966 paper "On the Algebra of Queues." It is known to be generally very accurate [Harrison, P.G. and Patel, N.M. "Performance Modelling of Communication Networks and Computer Architectures" ISBN 0201544199 p. 336]

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