An Analytically Tractable Cox Point-Process Model for LEO Mega-Constellation Mobility Management

With the rapid proliferation of low Earth orbit (LEO) satellite constellations, mobility management has become a critical challenge for maintaining seamless connectivity. Simulation-based tools such as satellite tool kit (STK) provide accurate assessments of satellite motion but are computationally intensive for large constellations, while conventional analytical models often treat satellite positions as static and fail to capture the dynamic visibility geometry inherent in mobility scenarios. To address these limitations, this work develops a Cox point process-based analytical framework that jointly models the random distribution of orbital planes and the along-track movement of satellites. This dual-layer stochastic geometry captures both the spatial hierarchy and temporal dynamics of LEO constellations, enabling tractable analysis of mobility behavior. Closed-form expressions are derived for key metrics, including access probability, service-time distribution, and handover probability, revealing how orbital altitude, constellation density, and elevation constraints jointly determine link continuity and handover frequency. Analytical results closely match high-fidelity STK simulations while reducing computational complexity by more than two orders of magnitude, demonstrating that the proposed Cox framework provides an effective and scalable foundation for mobility management analysis in next-generation LEO mega-constellations.