Unified Geometric--Kinematic Laws of Mobility in 3D Cellular Networks
Abstract
Mobility in three-dimensional (3D) cellular networks induces frequent handovers and random sojourn times for aerial users. Analyzing these events is challenging because they jointly depend on user trajectories and random service-boundary geometry. This paper develops a unified geometric--kinematic framework in which service regions form a stationary random tessellation, their boundaries constitute a random closed set, and user motion follows a cruise--turn mobility model. Under the stated stationarity, isotropy, and independence conditions, the handover rate satisfies the exact law H=(SV/2)v̅, where SV is the specific surface area and v̅ is the long-run mean speed. The forward boundary-distance distribution provides the local geometric input to an effective-traversal approximation for the mean remaining sojourn time. These results link global and local geometric descriptors to complementary mobility metrics. Combining the handover law with link coverage yields a handover-aware effective spectral efficiency for base station (BS) density selection and service-architecture comparison. We then specialize the framework to Poisson--Voronoi single-BS service and Poisson--Delaunay four-BS coordinated multi-point service; under both models, the handover rate scales as λ1/3v̅. Numerical results corroborate the exact handover expressions, assess the sojourn-time approximations, and show how user speed and interruption duration affect the preferred density and architecture.
Versions
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BibTeX
@misc{shi2026unified,
title = {{Unified Geometric--Kinematic Laws of Mobility in 3D Cellular Networks}},
author = {Tian Shi and Minghua Xia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23075},
eprint = {2610.23075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23075},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Unified Geometric--Kinematic Laws of Mobility in 3D Cellular Networks
AU - Tian Shi
AU - Minghua Xia
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23075
UR - https://arxiv.org/abs/2610.23075
AB - Mobility in three-dimensional (3D) cellular networks induces frequent handovers and random sojourn times for aerial users. Analyzing these events is challenging because they jointly depend on user trajectories and random service-boundary geometry. This paper develops a unified geometric--kinematic framework in which service regions form a stationary random tessellation, their boundaries constitute a random closed set, and user motion follows a cruise--turn mobility model. Under the stated stationarity, isotropy, and independence conditions, the handover rate satisfies the exact law H=(S_V/2)v̅, where S_V is the specific surface area and v̅ is the long-run mean speed. The forward boundary-distance distribution provides the local geometric input to an effective-traversal approximation for the mean remaining sojourn time. These results link global and local geometric descriptors to complementary mobility metrics. Combining the handover law with link coverage yields a handover-aware effective spectral efficiency for base station (BS) density selection and service-architecture comparison. We then specialize the framework to Poisson--Voronoi single-BS service and Poisson--Delaunay four-BS coordinated multi-point service; under both models, the handover rate scales as λ^1/3v̅. Numerical results corroborate the exact handover expressions, assess the sojourn-time approximations, and show how user speed and interruption duration affect the preferred density and architecture.
ER -