Advances in Modeling Solar System Internet Structures and their Data Flows

With an ever-increasing presence in space, there is also an increasing burden on existing communications infrastructure. We are heading towards an inflection point where the traditional approach of scheduled, single-path communications for space will no longer be viable. One answer is Delay Tolerant Networking (DTN), which takes the once disparate system of point-to-point links and unifies them in a networked architecture, thereby making communications more scalable. However, much work remains for discovering and harnessing the under-lying theory of DTN. For example, in the terrestrial setting the interplay between routing domains is well-understood, however this is not the case in DTNs. In this paper, we build up the fundamental foundations of DTN, with an emphasis on modeling time-varying networks and data flows across them, with examples of cross-domain routing in a DTN. A lofty goal of DTN is to enable the so-called Solar System Internet (SSI), which implies a standardized and robust suite of protocols. These protocols include routing across disconnected networks using store, carry, and forward mechanisms, which is necessary due to the disconnections, delays, and mobility intrinsic to space networks. Due to these factors, each of which generalize traditional networking, there is a deep and rich theory of DTNs. Here we build off of past successes to broaden this theory while striving to keep actionable results a goal for future implementations and operations. The approach includes modeling the unicast, broadcast, and multicast communications using the language of hypergraphs, which capture the geometric properties of such networked communications algebraically. Also inherent to these networks is their time-varying nature, particularly given mobility, and hence we also cultivate modeling techniques that respect this time dependence. This leads us to develop models using tools from category theory and algebraic geometry, which provide a language well-suited to describing synchronization and optimization over such networks. We also introduce and study a novel generalization of curvature applicable to time-evolving networks, which provides quantitative controls on diffusion processes on the network. Because an interplanetary network would feature links with propagation delays the preclude discovery (feedback) mechanisms, they will always feature a scheduled component. However, it is beneficial to support discovery where possible. While DTNs do not yet have strong definitions for their analogues of autonomous systems or network areas, we show how to join dynamic and schedule-based routing domains, using the language of sheaves, which marks progress towards such definitions. We conclude with a discussion of the progress made, as well as suggestions for future work.