  In recent years, LEO satellite constellations have become envisioned as a
core component of the next-generation wireless communication networks. The
successive establishment of mega satellite constellations has triggered further
demands for satellite communication advanced features: high reliability and low
latency. In this article, we first establish a multi-objective optimization
problem that simultaneously maximizes reliability and minimizes latency, then
we solve it by two methods. According to the optimal solution, ideal upper
bounds for reliability and latency performance of LEO satellite routing can be
derived. Next, we design an algorithm for relay satellite subset selection,
which can approach the ideal upper bounds in terms of performance. Furthermore,
we derive analytical expressions for satellite availability, coverage
probability, and latency under the stochastic geometry (SG) framework, and the
accuracy is verified by Monte Carlo simulation. In the numerical results, we
study the routing performance of three existing mega constellations and the
impact of different constellation parameter configurations on performance. By
comparing with existing routing strategies, we demonstrate the advantages of
our proposed routing strategy and extend the scope of our research.
