Erlang fixed point approximation

The Erlang fixed point approximation treats resource blocking as independent and applies the Erlang loss formula to traffic screened by other resources. Its self-consistency equations have a unique fixed point under fixed routing, but can have several under alternative routing.

For unit resource requirements in a loss network, the effective offered traffic to resource $j$ is $a_j={\sum }_{r:j\in r}{\alpha }_r{\prod }_{k\in r\setminus \{j\}}(1-B_k)$, where $B_k$ are approximate resource blocking probabilities. The resource being modeled is excluded from its own screening product.