Traffic dynamics on coupled spatial networks

With the rapid development of modern traffic, various means of transportation systems make it more convenient and diversified for passengers to travel out. In this paper, we establish a two-layered spatial network model where the low-speed lower layer is a regular lattice and the high-speed upper layer is a scale-free network embedded in the lattice. Passengers will travel along the path with the minimal travel time, and they can transfer from one layer to the other, which will induce extra transfer cost. We extensively investigate the traffic process on these coupled spatial networks and focus on the effect of the parameter α, the speed ratio between two networks. It is found that, as α grows, the network capacity of the coupled networks increases in the early stage and then decreases, indicating that cooperation between the coupled networks will induce the highest network capacity at an optimal α. We then provide an explanation for this non-monotonous dependence from a micro-scope point of view. The travel time reliability is also examined. Both in free-flow state and congestion state, the travel time is linearly related to the Euclidean distance. However, the variance of travel time in the congestion state is remarkably larger than that in the free-flow state, namely, people have to set aside more redundant time in an unreliable traffic system.