Traffic dynamics on two-layer complex networks with limited delivering capacity

The traffic dynamics of multi-layer networks has attracted a great deal of interest since many real networks are comprised of two or more layers of subnetworks. Due to its low traffic capacity, the average delivery capacity allocation strategy is susceptible to congestion with the wildly used shortest path routing protocol on two-layer complex networks. In this paper, we introduce a delivery capacity allocation strategy into the traffic dynamics on two-layer complex networks and focus on its effect on the traffic capacity measured by the critical point Rc of phase transition from free flow to congestion. When the total nodes delivering capacity is fixed, the delivering capacity of each node in physical layer is assigned to the degree distributions of both the physical and logical layers. Simulation results show that the proposed strategy can bring much better traffic capacity than that with the average delivery capacity allocation strategy. Because of the significantly improved traffic performance, this work may be useful for optimal design of networked traffic dynamics.