In this paper, we characterize the performance of several canonical mobility models in a drone cellular network in which drone base stations (DBSs) serve a set of user equipment (UE) on the ground. In particular, we consider the following four mobility models: (i) straight line (SL), (ii) random stop (RS), (iii) random walk (RW), and (iv) random waypoint (RWP), among which the SL mobility model is inspired by the simulation models used by the third generation partnership project (3GPP) for the placement and trajectory of drones, while the other three are well-known canonical models (or their variants) that offer a useful balance between realism and tractability. Assuming the nearest-neighbor association policy, we consider two service models for the UEs: (i) UE independent model (UIM), and (ii) UE dependent model (UDM). While the serving DBS follows the same mobility model as the other DBSs in the UIM, it is assumed to fly towards the UE of interest in the UDM and hover above its location after reaching there. The main contribution of this paper is a unified approach to characterize the point process of DBSs for all the mobility and service models. Using this, we provide exact mathematical expressions for the average received rate and the session rate as seen by the typical UE. Further, using tools from the calculus of variations, we concretely demonstrate that the simple SL mobility model provides a lower bound on the performance of other general mobility models (including the ones in which drones follow curved trajectories) as long as the movement of each drone in these models is independent and identically distributed (i.i.d.). To the best of our knowledge, this is the first work that provides a rigorous analysis of key canonical mobility models for an infinite drone cellular network and establishes useful connections between them.

中文翻译：

---

无人机蜂窝网络中规范移动模型的性能表征

在本文中，我们描述了无人机蜂窝网络中几种规范移动模型的性能，其中无人机基站 (DBS) 为地面上的一组用户设备 (UE) 提供服务。特别地，我们考虑以下四种移动性模型：（i）直线（SL），（ii）随机停止（RS），（iii）随机游走（RW）和（iv）随机路点（RWP），其中SL 移动模型的灵感来自第三代合作伙伴项目 (3GPP) 用于无人机放置和轨迹的仿真模型，而其他三个是众所周知的规范模型（或其变体），它们在现实主义之间提供了有用的平衡和易处理性。假设最近邻关联策略，我们考虑 UE 的两种服务模型：（i）UE 独立模型（UIM）和（ii）UE 相关模型（UDM）。虽然服务 DBS 遵循与 UIM 中的其他 DBS 相同的移动模型，但假设它飞向 UDM 中感兴趣的 UE，并在到达那里后悬停在其位置上方。本文的主要贡献是一种统一的方法来表征所有移动性和服务模型的 DBS 的点过程。使用它，我们提供了典型 UE 所见的平均接收速率和会话速率的精确数学表达式。此外，我们使用变异演算的工具，具体证明了简单的 SL 移动模型为其他通用移动模型（包括无人机遵循弯曲轨迹的模型）的性能提供了一个下限，只要每个无人机的移动在这些模型中是独立同分布的（iid）。据我们所知，