Considering the flow governed by the natural laws to model distributed flow, and using a realistic load-capacity relation for network nodes, a cascading model with a tunable weight parameter was proposed. According to new measures to the robustness of a network, Cascading dynamics on weighted scale-free model networks and real-world network was further investigated. The simulation results show that the existence of an optimal weighting strategy for which the network under distributed flows exhibits a maximum degree of robustness against cascading failures. Furthermore, the optimal weighting st...