Sampling Distributed Schedulers for Resilient Space Communication

Abstract

We consider routing in delay-tolerant networks like satellite constellations with known but intermittent contacts, random message loss, and resource-constrained nodes. Using a Markov decision process model, we seek a forwarding strategy that maximises the probability of delivering a message given a bound on the network-wide number of message copies. Standard probabilistic model checking would compute strategies that use global information, which are not implementable since nodes can only act on local data. In this paper, we propose notions of distributed schedulers and good-for-distributed-scheduling models to formally describe an implementable and practically desirable class of strategies. The schedulers consist of one sub-scheduler per node whose input is limited to local information; good models additionally render the ordering of independent steps irrelevant. We adapt the lightweight scheduler sampling technique in statistical model checking to work for distributed schedulers and evaluate the approach, implemented in the Modest Toolset, on a realistic satellite constellation and contact plan.

A Modest Approach to Markov Automata

“…The scheduler sampling implementation in modes further complements the abilities of mcsta where the latter fails due to state space explosion. It provides significantly more useful results than other tools that have to rely on a single scheduler such as the uniform randomised one, and can in this way, e.g., disprove safety or provide implementable strategies [29] where other tools cannot. Still, it is important to keep its limitations, in particular, the inability to quantify the optimality of the sampled scheduler and thus, e.g., prove safety, in mind.…”

Routing in the Space Internet: A contact graph routing tutorial

“…Initial CGR reliability studies followed in 2017. Dr. Juan Fraire et al showed how CGR behaved under uncertain contact plans [87], [88], for which reliable CGR variations based on state-of-the-art computer science models were introduced [89]- [91]. As discussed in Section VII, scalability as well as uncertain and opportunistic CGR extensions are among the most active and promising research lines in CGR.…”

“…Recent studies have proposed formal methods to model these probabilistic routing and copy-based forwarding questions [90]. The probabilistic contact plan may be modeled as a Markov Decision Process (MDP), from which optimal copybased routing policies can be obtained [91].…”

A Review of Verification and Validation for Space Autonomous Systems

“…Experiments were performed with a CubETH nanosatellite [22] and low Earth orbit observation satellite show that this incrementally-built model can reduce the number of testing required in later stages of the design. Some examples of probabilistic verification are [23][24][25]. In [23], a realistic use case of routing in a Walker satellite constellation (i.e., in circular orbits and with the same period and inclination) in low Earth orbit is verified using probabilistic model checking.…”

“…Some examples of probabilistic verification are [23][24][25]. In [23], a realistic use case of routing in a Walker satellite constellation (i.e., in circular orbits and with the same period and inclination) in low Earth orbit is verified using probabilistic model checking. The approach consists of using distributed schedulers that can only make use of local data.…”