[Paper] Optimal Oblivious Load-Balancing for Sparse Traffic in Large-Scale Satellite Networks

Source: arXiv - 2601.02537v1

Overview

This paper tackles oblivious load‑balancing—routing traffic on a fixed set of paths without knowing the actual demand—in the context of large‑scale low‑Earth‑orbit (LEO) satellite constellations, which can be abstracted as an (N\times N) torus network. The authors focus on the sparse traffic regime (only a few source‑destination pairs are active at any time) and prove tight bounds on how well any oblivious scheme can perform, while also presenting an optimal routing construction that meets those bounds.

Key Contributions

• Fundamental lower bounds on the worst‑case link load for oblivious routing on a torus under sparse traffic:
  • (\approx \frac{\sqrt{2k}}{4}) when the number of active pairs (k) satisfies (1<k\le N^{2}/2).
  • (\frac{N}{4}) when (N^{2}/2 \le k \le N^{2}).
• Proof that Valiant Load Balancing (VLB)—the classic oblivious scheme—fails to achieve these bounds in the sparse regime.
• Construction of an optimal oblivious routing algorithm that attains the lower bound for every admissible (k).
• Quantification of the oblivious vs. adaptive gap: a multiplicative factor of (\sqrt{2}) separates the best possible oblivious load from the optimal (non‑oblivious) load.
• Extension to rectangular tori ((N\times M)) and to heterogeneous link capacities (different vertical/horizontal bandwidth).

Methodology

1. Network model – The satellite constellation is modeled as a 2‑dimensional torus graph where each node represents a satellite and each edge a inter‑satellite link.
2. Traffic model – Sparse traffic means at most (k) source‑destination (s‑d) pairs are active simultaneously; the exact pairs are unknown to the routing algorithm.
3. Linear‑program formulation – The authors encode the oblivious routing problem as a linear program that minimizes the maximum link load over all possible demand matrices respecting the sparsity constraint.
4. Analytical lower‑bound derivation – By constructing worst‑case demand patterns and applying cut‑based arguments, they derive the (\frac{\sqrt{2k}}{4}) and (\frac{N}{4}) lower bounds.
5. Algorithm design – They design a deterministic routing scheme that spreads each s‑d flow uniformly over a carefully chosen set of intermediate nodes, ensuring that no link exceeds the derived lower bound.
6. Gap analysis – A comparison with the optimal (adaptive) routing solution, obtained via a separate LP, yields the (\sqrt{2}) factor.
7. Generalization – The same LP and proof techniques are adapted to non‑square tori and to the case where vertical and horizontal links have different capacities.

Results & Findings

• The optimal oblivious scheme exactly meets the theoretical lower bound for every feasible (k).
• The classic Valiant scheme, while simple and robust, can be up to a factor of (\sqrt{2}) worse in the sparse regime.
• The (\sqrt{2}) gap between oblivious and fully adaptive routing shows that even the best oblivious approach cannot completely close the performance gap, but the loss is bounded and modest.

Practical Implications

1. Satellite network operators can adopt the proposed routing tables (pre‑computed, static) to guarantee near‑optimal link utilization when traffic is bursty and localized (e.g., hotspot regions during emergencies).
2. Reduced control‑plane overhead – Because routes are oblivious, there is no need for real‑time traffic measurement or dynamic path computation, which is valuable given the limited processing capabilities and high latency of inter‑satellite links.
3. Scalable provisioning – The scheme scales with the constellation size ((N)) and automatically adapts to different sparsity levels ((k)) without re‑optimizing the network.
4. Hardware‑friendly implementation – The routing rule can be expressed as a small lookup table or a deterministic hash function, making it easy to embed in satellite firmware or ground‑station software.
5. Design guidance for future constellations – The lower‑bound formulas provide a quick sanity check: if a planned constellation’s link capacity is below (\frac{\sqrt{2k}}{4}) (or (\frac{N}{4}) for dense traffic), the operator knows that no oblivious scheme can avoid congestion, prompting either capacity upgrades or more adaptive routing mechanisms.

Limitations & Future Work

• Assumption of a perfect torus topology – Real LEO constellations have irregularities (polar gaps, varying inter‑satellite distances) that may deviate from the ideal torus model.
• Static traffic sparsity – The analysis assumes a hard cap of (k) active s‑d pairs; in practice, (k) can fluctuate rapidly, and the optimal oblivious scheme may need to be recomputed for different (k) regimes.
• Uniform link capacities – While the authors extend results to unequal vertical/horizontal capacities, they do not address more general heterogeneous bandwidths (e.g., due to antenna pointing constraints).
• No consideration of latency or jitter – The focus is purely on load balance; latency‑sensitive applications might require different trade‑offs.

Future directions suggested by the authors include:

• Extending the framework to dynamic sparsity models where (k) follows a stochastic process.
• Incorporating fault tolerance (satellite or link failures) into the oblivious design.
• Exploring hybrid schemes that blend oblivious routing with limited, low‑overhead adaptivity to further narrow the (\sqrt{2}) gap.

Bottom line: For developers building routing software or network‑control systems for massive satellite constellations, this work delivers a provably optimal, low‑complexity oblivious routing strategy tailored to the sparse, hotspot‑driven traffic patterns that dominate real‑world LEO operations. Implementing the scheme can shave off unnecessary congestion while keeping the control plane simple—a win‑win for both performance and operational reliability.

Authors

• Rudrapatna Vallabh Ramakanth
• Eytan Modiano

Paper Information

• arXiv ID: 2601.02537v1
• Categories: cs.NI, cs.DC
• Published: January 5, 2026
• PDF: Download PDF