In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], '''Buzen's algorithm''' (or '''convolution algorithm''') is an algorithm for calculating the [[normalization constant]] ''G''(''K'') in the [[Gordon–Newell theorem]]. This method was first proposed by [[Jeffrey P. Buzen]] in 1973.<ref name="buzen-1973">{{cite doi | 10.1145/362342.362345}}</ref> OnceComputing ''G'' is computedrequired theto probability distributions forcompute the network can be found. In contrast,stationary [[meanprobability value analysisdistribution]] isof ana alternativeclosed algorithmqueueing that can also be used to derive some performance measures (such as the mean queue lengths) without having to directly compute the normalization constantnetwork.
The motivation for this algorithm is efficiency:Performing a straightforwardnaïve Gordon-Newellcomputation calculationof wouldthe requirenormalising theconstant requires enumeration of all states. thatFor thea system canwith be''N'' in,jobs resultingand in''M'' astates combinatorialthere explosion.are <math>\tbinom{N+M-1}{M-1}</math> states. Buzen's algorithm is of order ''N''<sup>2</sup>, making the application of the G-N theorem practical, and opening up a large class of queueing systems to accurate modeling.
In the queuing literature Buzen's algorithm is sometimes also referred to as the '''convolution algorithm'''.
