Balance function of a flow-level network ($n_r{x}_r(n)=\Phi (n-e_r)/\Phi (n)$)

A positive balance function $\Phi$ expresses each active route's aggregate service as this ratio. With independent Poisson arrivals and exponential document sizes, detailed balance yields stationary weights $\Phi (n){\prod }_r{\rho }_r^{n_r}$, provided their sum is finite.