Computing call-blocking probabilities in LEO satellite constellations

We present an analytical model for computing call-blocking probabilities in a low Earth orbit (LEO) satellite network that carries voice calls. Both satellite-fixed and Earth-fixed constellations with interorbit links and handoffs are considered. We assume a single beam per satellite. Also, we assume that call arrivals are Poisson with a fixed arrival rate that is independent of the geographic area. The model is analyzed approximately by decomposing it into subsystems. Each subsystem is solved in isolation exactly using a Markov process and the individual results are combined together through an iterative method. Numerical results demonstrate that our method is accurate for a wide range of traffic patterns. We also derive an upper and lower bound for the link-blocking probabilities that can be computed efficiently. These bounds can be used for constellations of realistic size where each satellite has multiple beams.