On the Theory of Network Architectures in the Solar System Internet

Delay Tolerant Networking (DTN) is maturing into a viable enabling technology for the so-called Solar System Internet (SSI). The focus of SSI is shifting towards modern network architectures and scalability, which goes beyond the underlying protocol suite of DTN. Following a record-setting experiment campaign on the International Space Station (ISS), there is a wealth of operational experience and lessons-learned based on the advent of service-provider oriented architectures available to propel humanity's ability to network in space to new levels. However, deeper understandings of extending these architectures to the solar-system level are not fully explored. In this paper, we combine this new information with previous theoretical advances to open new doors in DTN network modeling with an eye on practical means to designing, creating, and operating future space networks. The primary purpose of networking is scalability, however sim-ply using DTN does not give this for free. Indeed, having a protocol suite does not inform the user on its best practices; in the case of DTN, best practices are not known. In particular, the ISS experiments illustrated the difficulty of uniting DTN network areas across project and programmatic boundaries. In traditional DTN routing, all nodes have the same schedule of contacts - known as a contact graph - and it is expected that these data are globally consistent. Approaches depending on omniscience neither scale nor generalize well, yet alternatives remain elusive as there is no standard temporospatial network modeling approach. We investigate the capability of various mathematical models of dynamic heterogeneous networks to capture critical features such as routing, data flow optimization, and network hierarchy detection for the Near Space Network's upcoming real-mission deployment including LunaNet. To better encapsulate the multifaceted nature of space communications, we first explore sheaf constructions on hypergraphs and more accurately model time variation in our network using the theory of topos and moduli spaces. For algorithmic directions, we develop a framework for automated community and bottleneck detection using Ollivier-Ricci curvature and persistence homology, so we can either bypass or exploit the detected bottlenecks using network coding. In establishing solid mathematical frameworks to model space communications, we will be able to better standardize more efficient and scalable network services for the upcoming Near-Space Network and design the architecture of the eventual Solar System Internet. Examples are given in the context of the ISS network experiment with a discussion on how these tools can be used in more general settings. Finally, we conclude with future research directions.