Buzen's algorithm

In queueing theory, a discipline within the mathematical theory of probability, Buzen's algorithm (or convolution algorithm) is an algorithm for calculating the normalization constant G(N) in the Gordon–Newell theorem. This method was first proposed by Jeffrey P. Buzen in 1973. Computing G(N) is required to compute the stationary probability distribution of a closed queueing network.

Performing a naïve computation of the normalising constant requires enumeration of all states. For a system with N jobs and M states there are