We study the effect of random removal of nodes in networks on the maximum capability to deliver information in communication processes. Measuring the changes on the onset of congestion, we observe different behaviors depending on the network structure, governed by the distribution of the algorithmic betweenness (number of paths traversing a node given a communication protocol) of the nodes, and particularly by the node with the highest betweenness. We also compare the robustness of networks from a topological and dynamical point of view. We find that for certain values of traffic load, after suffering a random failure, the network can be physically connected but the nodes are unable to communicate due congestion. These results highlight the necessity to include dynamical considerations in studies about resilience of complex networks.