Blocking partition ratio for a loss network ($B_r=1-Z(C-A_r)/Z(C)$)

Let $Z(C)$ sum the unnormalized occupancy weights ${\prod }_r{\rho }_r^{n_r}/n_r!$ over feasible counts. The states admitting another type-$r$ call are exactly those feasible under capacities $C-A_r$. Poisson arrivals see time averages therefore gives the displayed blocking probability. Take $Z$ to be zero when the reduced capacities make its feasible set empty.