  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.
