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.[1] Computing G(N) is required to compute the stationary probability distribution of a closed queueing network.



Performing a naï ve computation of the normalising constant requires enumeration of all states. For a system with N jobs and M states there are \tbinom{N+M-1}{M-1} states. Buzen s algorithm "computes G(1), G(2), ..., G(N) using a total of NM multiplications and NM additions." This is a significant improvement and allows for computations to be performed with much larger networks.