= Product-form stationary distribution of a loss network
{title2=$\pi(n)\propto\prod_r\alpha_r^{n_r}/n_r!$}
= Product-form stationary distributions of loss networks
{synonym}
For a <loss network> with feasible occupancies $An\leq C$, its <stationary distribution> is proportional to $\prod_r\alpha_r^{n_r}/n_r!$. It is the law of independent <Poisson random variables> conditioned on the resource constraints. With exponential holding times, <detailed balance for a continuous-time Markov chain> proves the formula directly.
Back to article page
