Optimal control of stochastic bandwidth-sharing networks is typically
difficult. In order to facilitate the analysis, deterministic analogues of
stochastic bandwidth-sharing networks, the so-called fluid models, are often
taken for analysis, as their optimal control can be found more easily. The
tracking policy translates the fluid optimal control policy back to a control
policy for the stochastic model, so that the fluid optimality can be achieved
asymptotically when the stochastic model is scaled properly. In this work we
study the efficiency of the tracking policy, that is, how fast the fluid
optimality can be achieved in the stochastic model with respect to the scaling
parameter. In particular, our result shows that, under certain conditions, the
tracking policy can be as efficient as feedback policies.