Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Chaos. 2009 Sep;19(3):033106. doi: 10.1063/1.3184539.
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.
先前关于复杂网络上交通流动力学的研究主要集中在参数（如包生成率）从自由流状态连续过渡到局部拥挤状态上，当参数通过一个临界点时就会发生拥塞。在过渡点以上，拥塞会发生在一小部分节点上。利用基于包生灭过程的传统交通流模型，更重要的是，考虑到在现实网络中节点的缓冲区是有限的，我们发现从自由流到完全拥塞会发生突然的转变。在过渡点略低的位置，网络可以在路由参数的最优值下支持最大的流量。我们开发了一个平均场理论来解释这一令人惊讶的转变现象，并提供了数值支持。此外，我们还提出了一种基于随机丢包思想的控制策略，以防止/打破完全拥塞。我们的发现为现实中的通信网络提供了一些见解，在这些网络中，完全拥塞可以直接从自由流状态发生，而没有任何明显的前兆，我们的控制策略可以在完全拥塞发生后有效地恢复流量。
