This study proposes a novel flexible bus dispatching system in which a fleet of fully automated modular bus units, together with conventional buses, serves the passenger demand. These modular bus units can either operate individually or combined (forming larger modular buses with a higher passenger capacity). This provides enormous flexibility to manage the service frequencies and vehicle allocation, reducing thereby the operating cost and improving passenger mobility.

We develop an optimization model used to determine the optimal composition of modular bus units and the optimal service frequency at which the buses (both conventional and modular) should be dispatched across each bus line. We explicitly account for the dynamics of traffic congestion and complex interactions between the modes at the network level based on the recently proposed three-dimensional macroscopic fundamental diagram (3D-MFD). To the best of our knowledge, this is the first application of the 3D-MFD and modular bus units for the frequency setting problem in the domain of bus operations.

Numerical results show the improvements in the total system cost made by adjusting the number of combined modular bus units and their dispatching frequencies to the evolution of both, the car and the bus passenger demand. A comparison with the commonly used approach that considers only the bus system (neglecting the complex multimodal interactions and congestion propagation) reveals the value of the proposed modeling framework. Finally, a sensitivity analysis of the effect of the operating unit cost of modular bus units, the size of the bus network, and the size of the bus fleet sheds light on the robustness of the proposed optimization framework.

这项研究提出了一种新颖的灵活的公交车调度系统，在该系统中，一组全自动的模块化公交车单元以及常规公交车可以满足乘客的需求。这些模块化总线单元可以单独运行，也可以组合运行（形成具有更高载客量的更大模块化总线）。这为管理服务频率和车辆分配提供了极大的灵活性，从而降低了运营成本并提高了乘客的机动性。

我们开发了一种优化模型，用于确定模块化总线单元的最佳组成以及应在每条总线上分配总线（常规总线和模块化总线）的最佳服务频率。我们基于最近提出的三维宏观基本图（3D-MFD），在网络级别上明确说明了流量拥塞的动态以及模式之间的复杂交互。据我们所知，这是3D-MFD和模块化总线单元在总线操作领域中频率设置问题的首次应用。

数值结果表明，通过调整组合式模块化公交车单元的数量及其调度频率以适应汽车和公交车乘客需求的变化，可以改善总系统成本。与仅考虑总线系统（忽略复杂的多模式交互和拥塞传播）的常用方法的比较揭示了所提出的建模框架的价值。最后，对模块化公交车的运营成本，公交网络的规模以及公交车队规模的影响进行了敏感性分析，这为所提出的优化框架的稳健性提供了启示。