Before revision:  For the equal-weights case, the upper and lower bounds coincide, which implies the heavy-traffic insensitivity of the expectation of the total number of flows .
After revision:  Our approach is Lyapunov-drift based, which is different from the widely used diffusion approximation approach. A key technique we develop is to construct a novel inner product in the state space, which then allows us to obtain a multiplicative type of state-space collapse in steady state .