异质通勤者走廊问题的排队替代原理
Queue replacement principle for corridor problems with heterogeneous commuters
AI总结：
本研究针对走廊网络中异质通勤者的出发时间选择问题，提出了一种解析方法来求解动态系统最优（DSO）和动态用户均衡（DUE）问题，并证明了排队替代原理（QRP）以推导闭式DUE解及多种政策下的均衡解。
摘要：
本研究调查了在走廊网络中考虑通勤者关于计划延误价值的异质性时的出发时间选择问题的理论性质。具体而言，我们开发了一种解析方法来求解动态系统最优（DSO）和动态用户均衡（DUE）问题。为了推导DSO解，我们首先证明了基于瓶颈的分解性质，即DSO问题可以分解为多个单瓶颈问题。随后，我们通过对每个分解问题应用最优运输理论获得解析解，并推导出实现DSO状态的最优拥堵定价。为了推导DUE解，我们证明了排队替代原理（QRP），即时变最优拥堵定价等于DUE状态下每个瓶颈处的排队延误。该原理使我们能够基于DSO解推导出闭式DUE解。此外，作为QRP的应用，我们证明了在各种政策（例如，匝道控制、匝道定价及其部分实施）下的均衡解可以通过解析方法获得。最后，我们将这些均衡与DSO状态进行了比较。
英文摘要：
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.
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