Quantum key distribution from satellites becomes particularly valuable when it can be used on a large network and on-demand to provide a symmetric encryption key to any two nodes. A constellation model is described which enables QKD-derived encryption keys to be established between any two ground stations with low latency. This is achieved through the use of low earth orbit trusted-node QKD satellites which create a buffer of keys with the ground stations they pass over, and geostationary relay satellites to transfer secure combinations of the keys to the ground stations. Regional and global network models are considered and the use of inter-satellite QKD links for balancing keys is assessed.