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The purpose of the Buzen algorithm is to numerically compute values of G.
==Marginal distributions, expected number of customers==
The general G-N distribution given above is mainly of theoretical interest. However, expressions for a number of useful performance measures can be derived from it. Buzen showed that the probability that there are exactly k customers at facility i is given by:
:<math>P(n_i = k) = \frac{X_i^k}{G(N)}[G(N-k) - X_i G(N-k-1)]</math>
and the expected number of customers at facility i by:
:<math>E[n_i] = \sum_{k=1}^N X_i^k \frac{G(N-k)}{G(N)}</math>
Note that these expressions also involve G. It is in the evaluation of these expressions that the algorithm is useful.
==Derivation==
''G''(''N'') = ''g''(''M'', ''N'')
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