The traffic density of small aerial vehicles operating within urban environments is expected to increase significantly in the near future. This urban environment is highly constrained due to being limited to the low-altitude airspace directly above the existing road network. Multiple studies have addressed factors influencing the capacity of urban airspace. These have used simulations of aircraft, yet the empirical nature of these simulations limits their use beyond the specific conditions that have been tested. Analytical models would not have this limitation, but they are only developed for general airspace, while the emergent patterns in constrained urban airspace are different than in general, unconstrained conditions. For instance, queuing and local congestion are patterns that are unique to the heavily-constrained environment. Therefore, in this paper, we derive an analytical model for air traffic in a confined airspace to find the influencing factors for its capacity. By means of a simulation of aerial vehicles, we verify the analytical model and show a relationship between the mean flow rate and mean density in a two-dimensional orthogonal grid network airspace. Results show that the entire airspace can become unstable when the maximum capacity of just one intersection is reached. Furthermore, the maximum airspace density is found to be unaffected by cruise speed. The results demonstrate how the derived analytical model provides an effective tool to predict the effect of several design parameters on the capacity of constrained urban airspace. Moreover, this model can form the basis for further extensions, including the altitude dimension and non-orthogonal or non-four-way intersections.

在不久的将来，预计在城市环境中运行的小型飞行器的交通密度将显着增加。由于仅限于现有道路网络正上方的低空空域，这种城市环境受到高度限制。多项研究已经解决了影响城市空域容量的因素。这些已经使用了飞机模拟，但这些模拟的经验性质限制了它们的使用超出了已测试的特定条件。分析模型不会有这种限制，但它们只是为一般空域开发的，而受限城市空域中出现的模式与一般的、不受限制的条件不同。例如，排队和局部拥塞是严重受限环境所特有的模式。所以，在本文中，我们推导了一个受限空域空中交通的分析模型，以找出影响其容量的因素。通过飞行器仿真，我们验证了分析模型并显示了二维正交网格空域中平均流量和平均密度之间的关系。结果表明，当仅一个十字路口达到最大容量时，整个空域都会变得不稳定。此外，发现最大空域密度不受巡航速度的影响。结果证明了导出的分析模型如何提供一种有效的工具来预测多个设计参数对受限城市空域容量的影响。此外，该模型可以构成进一步扩展的基础，