Latency Analysis of LEO Satellite Relay Communication: An Application of Conditional Contact Angle Distribution

This article investigates the transmission delay of a Low Earth Orbit (LEO) satellite communication system in a bent pipe structure. By employing a stochastic geometry framework, satellites are modeled as spherical binomial point processes (BPP). A suboptimal satellite relay selection strategy is proposed, which achieves optimal conditions through theoretical analysis and numerical exploration. We derive the distance distributions for the uplink and downlink links, and provide corresponding analytical expressions for the transmission delays.