运输网络的最优干预
Optimal intervention in transportation networks
摘要：
我们研究了一个网络设计问题（NDP）的规划者的目的是选择最佳的单链路干预交通网络，以尽量减少旅行时间下Wardrop平衡流。我们的第一个结果是，如果延迟函数是仿射的和平衡的支持不修改与干预，NDP可以制定一个相关的电阻网络上计算的电气量。特别是，我们表明，旅行时间的变化对应于一个给定的链接上的干预依赖于链接的端点之间的有效电阻。我们提出了一种方法来近似这样一个有效的电阻，只执行本地计算，并利用它来设计一个有效的算法来解决NDP。在无限大网络的极限下讨论了该方法的最优性，并给出了其最优性的一个充分条件。然后，我们提供了数值模拟，表明我们的算法实现了良好的性能，即使平衡支持度的变化和延迟函数是非线性的。
英文摘要：
We study a network design problem (NDP) where the planner aims at selecting the optimal single-link intervention on a transportation network to minimize the travel time under Wardrop equilibrium flows. Our first result is that, if the delay functions are affine and the support of the equilibrium is not modified with interventions, the NDP may be formulated in terms of electrical quantities computed on a related resistor network. In particular, we show that the travel time variation corresponding to an intervention on a given link depends on the effective resistance between the endpoints of the link. We suggest an approach to approximate such an effective resistance by performing only local computation, and exploit it to design an efficient algorithm to solve the NDP. We discuss the optimality of this procedure in the limit of infinitely large networks, and provide a sufficient condition for its optimality. We then provide numerical simulations, showing that our algorithm achieves good performance even if the equilibrium support varies and the delay functions are non-linear.
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