Hypercongestion is the situation where a certain traffic flow occurs at a combination of low speed and high density, while a more favorable combination of these could produce the same flow. The macroscopic fundamental diagram (MFD) can describe hypercongestion, but does not explicitly explain the dynamic process that leads to hypercongestion. Earlier studies of hypercongestion on single links have, however, confirmed that these processes are important to consider. The bathtub model is a model that can be used to investigate how hypercongestion can arise in urban areas, when drivers choose their departure times optimally. This paper investigates equilibrium outcomes and user costs under the realistic assumption that there is finite capacity to exit the bathtub, without which it would be hard to explain why hypercongestion would not dissolve through shockwaves originating from the bathtub exit. We find that when the exit capacity of the bathtub is lower than the attempted equilibrium exit flow from the bathtub, no additional inefficiencies arise due to hypercongestion in the bathtub. This is because the travel time losses incurred by travelers in the bathtub are exactly offset by the reductions in travel time losses in exit queues, and thus the capacity of the full system is not affected. In contrast, when the exit capacity is higher than the equilibrium exit flows from the bathtub in the central part of the peak period, hypercongestion in the bathtub produces the additional inefficiencies known from the conventional textbook description. Our results thus show that the mere observation of hypercongested speeds does not necessarily mean that there is an efficiency loss from capacity drop at the level of the full system.

超拥塞是在低速和高密度的组合下发生某种交通流的情况，而更有利的组合可以产生相同的流量。宏观基本图（MFD）可以描述超拥塞，但没有明确解释导致超拥塞的动态过程。然而，早期对单链路超拥塞的研究证实，这些过程很重要。浴缸模型是一种模型，可用于研究当驾驶员选择最佳出发时间时城市地区如何出现超拥堵。本文研究了在离开浴缸的能力有限的现实假设下的均衡结果和用户成本，没有它，就很难解释为什么超拥塞不会通过源自浴缸出口的冲击波消散。我们发现，当浴缸的出口容量低于浴缸的平衡出口流量时，不会由于浴缸中的过度拥挤而导致额外的低效率。这是因为在浴缸中的旅客所遭受的旅行时间损失正好被出口队列中旅行时间损失的减少所抵消，因此整个系统的容量不受影响。相比之下，当出口容量高于高峰期中心部分浴缸的平衡出口流量时，浴缸中的超拥塞会产生传统教科书描述中已知的额外低效率。