Service-capacity allocation in an open migration process
= Service-capacity allocation in an open migration process
{title2=$\phi_j-\alpha_j\propto\sqrt{\alpha_j}$}
For positive traffic rates in single-server colonies, a total service budget $F>\sum_j\alpha_j$ minimizes the stationary mean population when the spare rates $\phi_j-\alpha_j$ are proportional to $\sqrt{\alpha_j}$. The <Cauchy-Schwarz inequality> proves the optimum directly.