  Recent technological advancements in satellite based quantum communication
has made it a promising technology for realizing global scale quantum networks.
Due to better loss distance scaling compared to ground based fiber
communication, satellite quantum communication can distribute high quality
quantum entanglements among ground stations that are geographically separated
at very long distances. This work focuses on optimal distribution of bipartite
entanglements to a set of pair of ground stations using a constellation of
orbiting satellites. In particular, we characterize the optimal
satellite-to-ground station transmission scheduling policy with respect to the
aggregate entanglement distribution rate subject to various resource
constraints at the satellites and ground stations. We cast the optimal
transmission scheduling problem as an integer linear programming problem and
solve it efficiently for some specific scenarios. Our framework can also be
used as a benchmark tool to measure the performance of other potential
transmission scheduling policies.
