In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], '''Buzen's 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 journaldoi | 10.1145/362342.362345}}</ref> Once ''G'' is computed the probability distributions for the network can be found. In contrast, [[mean value analysis]] is an alternative algorithm that can also be used to derive some performance measures (such as the mean queue lengths) without having to directly compute the normalization constant.
| first = Jeffrey
| last = Buzen
| authorlink = Jeffrey P. Buzen
| year = 1973
| month = September
| title = Computational algorithms for closed queueing networks with exponential servers
| journal = Communications of the ACM
| volume = 16
| issue = 9
| doi = 10.1145/362342.362345
| pages = 527
}} [http://www-unix.ecs.umass.edu/~krishna/ece673/buzen.pdf]</ref> Once ''G'' is computed the probability distributions for the network can be found. In contrast, [[mean value analysis]] is an alternative algorithm that can also be used to derive some performance measures (such as the mean queue lengths) without having to directly compute the normalization constant.
The motivation for this algorithm is efficiency: a straightforward Gordon-Newell calculation would require the enumeration of all states that the system can be in, resulting in a combinatorial explosion. 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.
