Computing call-blocking probabilities in LEO satellite networks: The single-orbit case

We study the problem of carrying voice calls over a low-earth-orbit satellite network and present an analytical model for computing call-blocking probabilities for a single orbit of a satellite constellation. We have devised a method to solve the corresponding Markov process efficiently for orbits of up to five satellites. For orbits consisting of a larger number of satellites, we have developed an approximate decomposition algorithm to compute the call-blocking probabilities by decomposing the system into smaller subsystems and iteratively solving each subsystem in isolation using the exact Markov process. Our approach can capture blocking due to handoffs for both satellite-fixed and earth-fixed constellations. Numerical results demonstrate that our method is accurate for a wide range of traffic patterns and for orbits with a number of satellites that is representative of commercial satellite systems.