Duality-Guided Graph Learning for Real-Time Joint Connectivity and Routing in LEO Mega-Constellations

TL;DR

This work tackles real-time joint LISL connectivity, routing, and flow-rate allocation in time-varying LEO mega-constellations. It introduces DeepLaDu, a Lagrangian duality-guided graph learning framework that predicts edge-wise congestion prices with a graph neural network, enabling one-shot joint decisions instead of iterative dual updates. By tying max-weight LISL matching, shortest-path routing, and linear programming-based flow allocation to learned prices, DeepLaDu achieves up to 20% throughput gains over baselines while meeting real-time constraints within the constellation’s coherent time. The approach scales polynomially with constellation size and is validated on Starlink-like scenarios with realistic LCT mechanics and traffic distributions.

Abstract

Laser inter-satellite links (LISLs) of low Earth orbit (LEO) mega-constellations enable high-capacity backbone connectivity in non-terrestrial networks, but their management is challenged by limited laser communication terminals, mechanical pointing constraints, and rapidly time-varying network topologies. This paper studies the joint problem of LISL connection establishment, traffic routing, and flow-rate allocation under heterogeneous global traffic demand and gateway availability. We formulate the problem as a mixed-integer optimization over large-scale, time-varying constellation graphs and develop a Lagrangian dual decomposition that interprets per-link dual variables as congestion prices coordinating connectivity and routing decisions. To overcome the prohibitive latency of iterative dual updates, we propose DeepLaDu, a Lagrangian duality-guided deep learning framework that trains a graph neural network (GNN) to directly infer per-link (edge-level) congestion prices from the constellation state in a single forward pass. We enable scalable and stable training using a subgradient-based edge-level loss in DeepLaDu. We analyze the convergence and computational complexity of the proposed approach and evaluate it using realistic Starlink-like constellations with optical and traffic constraints. Simulation results show that DeepLaDu achieves up to 20\% higher network throughput than non-joint or heuristic baselines, while matching the performance of iterative dual optimization with orders-of-magnitude lower computation time, suitable for real-time operation in dynamic LEO networks.

Figures (16)

• Figure 1: DeepLaDu for joint connectivity and routing in a mega-constellation.
• Figure 2: Illustration of the LCT and beam model from one LCT to another.
• Figure 3: A constellation graph at a time instance $t$: (a) a network of four satellites, each equipped with two LCTs; (b) its LCT connectivity graph $\mathcal{G}^{\text{LCT}}(t)$; and (c) the satellite adjacency graph $\mathcal{G}^{\text{SAT}}(t)$.
• Figure 4: The percentage of lost connectable LCT pairs over time in a Starlink-like constellation with different numbers of satellites where each satellite carries $N'=2$ LCTs and has a FOR of $\theta=60$ deg (detailed constellation parameters are provided in Section \ref{['sec:simulation_results']}).
• Figure 5: The constellation graph $\mathcal{G}^\text{LCT}$ indicating the connectable LCT pairs at the starting ($0$ s) and different ending time ($1$ s, $10$ s, $100$ s) when $I=1000$. Blue lines indicate the connectable LCT pairs, while red lines indicate the LCT pairs that are no longer connectable due to the satellite movement (detailed constellation parameters are provided in Section \ref{['sec:simulation_results']}).

Theorems & Definitions (7)

• Lemma 1
• proof
• Theorem 1
• proof
• Corollary 1
• proof
• proof