Flow optimization process in a transportation network

摘要

Numerous networks, such as transportation, distribution, and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods, such as electricity, water, gas, telephone, and data (Internet), or services as mail, railways, and roads are examples of transportation networks. The optimal design fixes network architecture, including clustering, degree distribution, hierarchy, community structures, and other structural metrics. These networks are specifically designed for efficient transportation, minimizing transit times and costs. All sorts of transportation networks face the same problem: traffic congestion among their channels. In this work, we considered a transportation network model in which we optimize/minimize a cost function for the flow/current at each channel/link of the network. We performed simulations and an analytical study of this problem, focusing on the fraction of used channels and the flow distribution through these channels. In this work we show that, after the initial time, the number of used channels are constant and, remarkably, do not depends on the lattice structure. One can see in our results two different regimes, for high and for small current flows. In the first regime, all channels in the network are used, whereas for the small current flow, surprisingly, the fraction of used channels depends on the square root of the flow.