Content deleted Content added
Redefine P(N) because G(-1) was not defined. |
Gareth Jones (talk | contribs) →Marginal distributions, expected number of customers: clarify k=0 situation, remove case k=N as k is already set to N in the expression |
||
Line 27:
The coefficients g(''n'',''m''), computed using Buzen's algorithm, can also be used to compute [[marginal distribution]]s and [[expected value|expected]] number of customers at each node.
::<math>\mathbb P(n_i = k) = \frac{X_i^k}{G(N)}[G(N-k) - X_i G(N-k-1)]\quad\text{ for }k=0,1,\ldots,N-1.</math>
::<math>\mathbb P(n_i = N) = \frac{X_i^N}{G(N)}[G(0)]
the expected number of customers at facility ''i'' by
::<math>\mathbb E(n_i) = \sum_{k=1}^N X_i^k \frac{G(N-k)}{G(N)}.</math>
| |||