论文标题
非均质通勤者走廊问题的队列替换原则
Queue replacement principle for corridor problems with heterogeneous commuters
论文作者
论文摘要
这项研究调查了出发时间选择问题的理论特性，考虑到通勤者在走廊网络的时间表延迟的价值方面的异质性。具体而言，我们开发了一种分析方法来解决动态系统最佳（DSO）和动态用户平衡（适当）问题。为了得出DSO解决方案，我们首先证明了基于瓶颈的分解属性，即，DSO问题可以分解为多个单个瓶颈问题。随后，我们通过将最佳运输理论应用于每个分解的问题并得出最佳拥塞价格来获得分析解决方案，以实现DSO状态。为了得出应有的解决方案，我们证明了队列替换原则（QRP），随着时间变化的最佳拥塞价格等于每个瓶颈的应有状态排队延迟。该原理使我们能够基于DSO解决方案得出封闭形式的应有解决方案。此外，作为QRP的应用，我们证明可以通过分析获得各种策略下的平衡解决方案（例如，跨度计量，坡度定价及其部分实施）。最后，我们将这些平衡与DSO状态进行了比较。
This study investigates the theoretical properties of a departure time choice problem considering commuters' heterogeneity with respect to the value of schedule delay in corridor networks. Specifically, we develop an analytical method to solve the dynamic system optimal (DSO) and dynamic user equilibrium (DUE) problems. To derive the DSO solution, we first demonstrate the bottleneck-based decomposition property, i.e., the DSO problem can be decomposed into multiple single bottleneck problems. Subsequently, we obtain the analytical solution by applying the theory of optimal transport to each decomposed problem and derive optimal congestion prices to achieve the DSO state. To derive the DUE solution, we prove the queue replacement principle (QRP) that the time-varying optimal congestion prices are equal to the queueing delay in the DUE state at every bottleneck. This principle enables us to derive a closed-form DUE solution based on the DSO solution. Moreover, as an application of the QRP, we prove that the equilibrium solution under various policies (e.g., on-ramp metering, on-ramp pricing, and its partial implementation) can be obtained analytically. Finally, we compare these equilibria with the DSO state.
