Abrupt transition to complete congestion on complex networks and control.

Previous works on traffic-flow dynamics on complex networks have mostly focused on continuous phase transition from a free-flow state to a locally congested state as a parameter, such as the packet-generating rate, is increased through a critical value. Above the transition point congestion occurs on a small subset of nodes. Utilizing a conventional traffic-flow model based on the packet birth-death process and more importantly, taking into account the fact that in realistic networks nodes have only finite buffers, we find an abrupt transition from free flow to complete congestion. Slightly below the transition point, the network can support the maximum amount of traffic for some optimal value of the routing parameter. We develop a mean-field theory to explain the surprising transition phenomenon and provide numerical support. Furthermore, we propose a control strategy based on the idea of random packet dropping to prevent/break complete congestion. Our finding provides insights into realistic communication networks where complete congestion can occur directly from a free-flow state without any apparent precursor, and our control strategy can be effective to restore traffic flow once complete congestion has occurred.