  We introduce the discrete Green's function to elucidate how resource
fluctuations determine flow fluctuations in a network optimizing a global cost
function. To enhance the robustness of the network against fluctuations, we
develop the schemes of optimal bandwidth allocation in links and optimal
resource adjustment in nodes. With the total bandwidth of the network fixed,
the approach of optimal bandwidth allocation is to increase the bandwidth in
links such that the number of overloaded links or the amount of excess flows in
networks under fluctuations can be minimized. Similarly, the approach of
optimal resource adjustment is to minimize the number of overloaded links in
networks under fluctuations with the total resource change in the network
fixed. Compared with the conventional approach of proportionate bandwidth
assignment or resource reduction, it is found that the optimized bandwidth
allocation or resource adjustment can highly enhance the stability of the
networks against fluctuations. The changes of loads and currents prescribed by
the optimal bandwidth allocation and resource adjustment schemes are correlated
with each other, except for some nodes that exhibit relay effects.
