On the Theory of Network Architectures in the Solar System Internet

Networked communications in space are necessary to achieve scalability in terms of the number of communicating nodes but also in terms of the overall system complexity. A key component to such a system is the ability to synchronize clocks, which is the focus of this paper. The so-called Solar System Internet (SSI) will be built upon Delay Tolerant Networking (DTN), which, in analogy to the Internet Protocol (IP), can be considered a suite of protocols necessary for networking in the space domain. Therefore, our goal is to extend this suite to include a DTN clock synchronization capability, analogous to the Network Time Protocol (NTP) used in the Internet. A motivating example of a network in space is NASA’s LunaNet, a vision for a multi-hop multi-path network extending to the moon wherein not all nodes will have direct connections to
an authoritative reference clock. In this paper, we propose a general clock synchronization methodology and algorithm that could be used for LunaNet as well as more elaborate time-varying networks.

In recent years, DTN has benefited from modeling efforts founded on the mathematical tool of sheaves. Here we continue this work to provide an approach to clock synchronization. Due to the time-varying nature of space networks, absolute consensus is not possible. However, the sheaf Laplacian provides a practical, distributed approach to approximating consensus by allowing data to diffuse through the network. In particular, the sheaf Laplacian is readily computable, lending our approach to implementation.

Our approach is well suited to handle the difficulties of space networks. For instance, differences in clock accuracy mean certain nodes are more authoritative than others; we can account for these differences through hierarchies in the network, generalizing the strata in NTP. Furthermore, just as error estimation is an integral part of NTP, we are able to give concrete error bounds for our approach. Indeed, different applications (e.g., communications schedules, pointing, navigation, distributed science) will have different requirements, hence it is necessary to maintain clocks within a given tolerance. We outline some of the necessary steps to turn our approach into a practical network protocol that could be used in DTN, and we conclude the paper with suggestions for future research.