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Joint Laser Inter-Satellite Link Matching and Traffic Flow Routing in LEO Mega-Constellations via Lagrangian Duality

Zhouyou Gu, Jihong Park, Jinho Choi

TL;DR

This paper tackles the challenge of maximizing throughput in LEO mega-constellations by jointly optimizing LISL connections and traffic routing while accounting for LCT mechanical limits and non-uniform traffic. It introduces a Lagrangian duality-based decomposition that splits the problem into a maximum weight LISL matching, a weighted shortest-path routing, and a linear-rate allocation subproblem, with a subgradient-descent procedure (DuJo) that guarantees convergence under bounded dual variables. The approach yields substantial throughput gains (up to about 145% over grid-based baselines and 35% over pure high-rate matching) and remains tractable despite the original NP-hard formulation. The framework is validated on Starlink-like constellations with realistic beam, jitter, and gateway constraints, highlighting the practical benefits and outlining avenues for acceleration and enhanced LCT design in future work.

Abstract

Low Earth orbit (LEO) mega-constellations greatly extend the coverage and resilience of future wireless systems. Within the mega-constellations, laser inter-satellite links (LISLs) enable high-capacity, long-range connectivity. Existing LISL schemes often overlook mechanical limitations of laser communication terminals (LCTs) and non-uniform global traffic profiles caused by uneven user and gateway distributions, leading to suboptimal throughput and underused LCTs/LISLs -- especially when each satellite carries only a few LCTs. This paper investigates the joint optimization of LCT connections and traffic routing to maximize the constellation throughput, considering the realistic LCT mechanics and the global traffic profile. The problem is formulated as an NP-hard mixed-integer program coupling LCT connections with flow-rate variables under link capacity constraints. Due to its intractability, we resort to relaxing the coupling constraints via Lagrangian duality, decomposing the problem into a weighted graph-matching for LCT connections, weighted shortest-path routing tasks, and a linear program for rate allocation. Here, Lagrange multipliers reflect congestion weights between satellites, jointly guiding the matching, routing, and rate allocation. Subgradient descent optimizes the multipliers, with provable convergence. Simulations using real-world constellation and terrestrial data show that our methods substantially improve network throughput by up to $35\%$--$145\%$ over existing non-joint approaches.

Joint Laser Inter-Satellite Link Matching and Traffic Flow Routing in LEO Mega-Constellations via Lagrangian Duality

TL;DR

This paper tackles the challenge of maximizing throughput in LEO mega-constellations by jointly optimizing LISL connections and traffic routing while accounting for LCT mechanical limits and non-uniform traffic. It introduces a Lagrangian duality-based decomposition that splits the problem into a maximum weight LISL matching, a weighted shortest-path routing, and a linear-rate allocation subproblem, with a subgradient-descent procedure (DuJo) that guarantees convergence under bounded dual variables. The approach yields substantial throughput gains (up to about 145% over grid-based baselines and 35% over pure high-rate matching) and remains tractable despite the original NP-hard formulation. The framework is validated on Starlink-like constellations with realistic beam, jitter, and gateway constraints, highlighting the practical benefits and outlining avenues for acceleration and enhanced LCT design in future work.

Abstract

Low Earth orbit (LEO) mega-constellations greatly extend the coverage and resilience of future wireless systems. Within the mega-constellations, laser inter-satellite links (LISLs) enable high-capacity, long-range connectivity. Existing LISL schemes often overlook mechanical limitations of laser communication terminals (LCTs) and non-uniform global traffic profiles caused by uneven user and gateway distributions, leading to suboptimal throughput and underused LCTs/LISLs -- especially when each satellite carries only a few LCTs. This paper investigates the joint optimization of LCT connections and traffic routing to maximize the constellation throughput, considering the realistic LCT mechanics and the global traffic profile. The problem is formulated as an NP-hard mixed-integer program coupling LCT connections with flow-rate variables under link capacity constraints. Due to its intractability, we resort to relaxing the coupling constraints via Lagrangian duality, decomposing the problem into a weighted graph-matching for LCT connections, weighted shortest-path routing tasks, and a linear program for rate allocation. Here, Lagrange multipliers reflect congestion weights between satellites, jointly guiding the matching, routing, and rate allocation. Subgradient descent optimizes the multipliers, with provable convergence. Simulations using real-world constellation and terrestrial data show that our methods substantially improve network throughput by up to -- over existing non-joint approaches.
Paper Structure (28 sections, 3 theorems, 43 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 28 sections, 3 theorems, 43 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notations and Paper Organization
  3. System Model of Mega-Constellation
  4. Constellation Model
  5. Satellite Form Factor and LCT Mechanics Models
  6. LCT Beam Model
  7. Traffic Profile Model
  8. Problem Formulation
  9. LCT Connection Constraints
  10. Traffic Serving and Demand Rates Constraints
  11. Traffic Routing Constraints
  12. LISL Maximum Data Rate Constraints
  13. Joint Link Matching and Flow Routing Problem
  14. Joint Link Matching and Flow Routing via Lagrangian Duality
  15. Lagrangian Dual Relaxation
  16. ...and 13 more sections

Key Result

Lemma 1

The distance from the initial Lagrange multipliers to optimal ones and the maximum norm of the dual function's supergradient are both bounded by finite constants, i.e., there exist constants $0<\eta_1<\infty$ and $0<\eta_2<\infty$ such that

Figures (7)

  • Figure 1: Illustration of a) the LEO satellite mega-constellation, and b) the LCT and beam model from one LCT to another.
  • Figure 2: Constellations with $1000$ satellites randomly selected from the Starlink constellation: a) the constellation and LISLs connected in our DuJo scheme; b) and c) the comparison in the flow paths between our DuJo scheme and a non-joint scheme, MRate.
  • Figure 3: The convergence of our method, DuJo: a) the convergence of the subgradient descent, b) throughput using Lagrange multiplier conversion.
  • Figure 4: DuJo vs. baselines for different numbers of satellites $I$.
  • Figure 5: Computing time measurement of steps in our method, DuJo, with legend as follows: steps of dual optimization: link matching \ref{['eq:routine:mwm_given_lambda']}, flow routing \ref{['eq:routine:spf_given_lambda']}, rate allocation \ref{['eq:routine:flow_rate_given_routing_cost']}, subgradient descent step \ref{['eq:routine:dual_variable_update']} (with legend "D. MWM", "D. SPF", "D. FRM" and "D. SG", respectively); steps of conversion of Lagrange multipliers: link matching with given Lagrange multipliers \ref{['eq:rounding:mwm']}, flow routing with given matched LISLs \ref{['eq:rounding:spf']} and rate allocation with matching and routing decisions \ref{['eq:rounding:frm']} (with legend "P. MWM", "P. SPF" and "P. FRM").
  • ...and 2 more figures

Theorems & Definitions (6)

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