Time-varying capacity design holds an opportunity to reduce the energy consumption of urban mass transit systems, e.g., urban rail transits, bus rapid transits, modular autonomous vehicles. In this paper, we investigate the joint design of dispatch headway and vehicle capacity for one to one shuttle systems with oversaturated traffic to achieve the optimal tradeoff between general vehicle dispatching cost (mainly comprised of vehicle energy consumption) and customer waiting cost. We propose a continuum approximation model from a macroscopic point of view to reveal fundamental analytical insights into the optimal design. By introducing the concept of a preferred virtual arrival demand curve at the origin station, we prove that the investigated problem with possibly oversaturated traffic can be equivalently solved with a simpler revised problem where only unsaturated traffic is present. With this property, we decompose the original problem into a set of independent unit-time revised unsaturated problems that can be analytically solved in each neighborhood across the operational horizon. With two sets of numerical experiments, we show that the CA model offers near-optimum solutions with negligible errors very efficiently and we also verify the theoretical properties. Also, the effectiveness of time-varying vehicle capacity design is demonstrated in shuttle systems under both saturated and unsaturated traffic. Overall, the proposed CA model contributes to the CA methodology literature by extending the CA method for traditional transit dispatching problems with unsaturated traffic to the joint design of dispatch headway and vehicle capacity considering oversaturated traffic, adjustable vehicle capacities and other factors (e.g. minimum dispatch headway).

时变容量设计为减少城市公共交通系统（例如城市轨道交通，快速公交，模块化自动驾驶汽车）的能耗提供了机会。在本文中，我们研究了过饱和交通的一对一穿梭系统的调度进度和车辆容量的联合设计，以实现一般车辆调度成本（主要包括车辆能耗）与客户等待成本之间的最佳折衷。我们从宏观的角度提出了一种连续近似模型，以揭示对最佳设计的基本分析见解。通过引入首选虚拟到达需求曲线在始发站的概念，我们证明，所研究的可能具有过度饱和流量的问题可以通过仅存在非饱和流量的更简单的修正问题来等效解决。利用此属性，我们将原始问题分解为一组独立的单位时间修正的不饱和问题，可以在整个运营范围内的每个邻域中进行分析解决。通过两组数值实验，我们证明了CA模型非常有效地提供了几乎可以忽略不计的误差的最佳解决方案，并且我们还验证了理论性质。同样，时变车辆容量设计的有效性在饱和和非饱和交通的穿梭系统中得到了证明。总体，