  In this paper, we characterize the performance of several canonical mobility
models in a drone cellular network in which drone base stations (DBSs) serve
user equipments (UEs) 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 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.
