Flow controllers are needed to avoid congestion in different types of networks. The dynamics of such networks, however, can usually be represented by infinite-dimensional models, which are either based on partial-differential equations or delay-differential equations. An optimal H-infinity flow controller design approach has recently been proposed for networks whose dynamics involve multiple and uncertain time-varying time delays. In the present paper, performance level and stability margins of controllers designed by this approach are analyzed. It is shown that, by choosing certain controller design parameters large, stability margins can be improved; while choosing them small improves performance levels. Therefore, there is a clear trade-off between robustness and performance.