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Is Forecasting Accuracy Enough? A Comparative Study of Traffic Forecasters for Beam-Hopping LEO Satellite Networks

Yekta Demirci, Guillaume Mantelet, Stéphane Martel, Jean-François Frigon, Gunes Karabulut Kurt

arXiv:2609.04662v1eess.SP

TL;DR

The paper asks whether better traffic-forecast accuracy is the right objective for Beam-Hopping LEO networks, where prior allocation methods often assume static or slowly varying demand. It compares diverse forecasters on synthetic self-similar and Wi-Fi traffic, then evaluates them through forecast-driven BH simulation. Accuracy rankings vary across traffic conditions, but these differences have little system-level effect compared with utilization and planning-period choices.

  • Problem

    Existing BH allocation approaches often assume static or slowly varying traffic and lack near-term forecasting integrated into the optimization loop.

  • Method

    The study compares statistical, theoretical, linear, and transformer forecasters using synthetic self-similar traces and Wi-Fi data, evaluating MASE and forecast-driven BH simulation metrics.

  • Results

    Self-similarity-aware forecasters lead on purely self-similar traffic, rankings nearly reverse on raw Wi-Fi data, and accuracy differences do not translate into comparable system-level differences.

  • Takeaways & Limitations

    Optimizing utilization margins and planning periods is likely to yield larger system-level gains than pursuing marginal improvements in raw forecasting accuracy.

Abstract

from arXiv · show

We evaluate diverse models for user traffic demand forecasting in Low Earth Orbit (LEO) satellite networks with Beam Hopping (BH), questioning whether predictive accuracy is the right objective for this task. To capture the complex nature of the user traffic demand, we employ a second-order self-similar traffic model, supplemented by a publicly available Wi-Fi dataset to validate the self-similar model against the empirical traffic patterns. We compare forecasters ranging from classical statistical approaches, such as the optimal forecaster for self-similar data and the optimal linear predictor on the discrete sampling grid, to Fractional Auto-Regressive Integrated Moving Average (FARIMA) models, as well as emerging deep learning architectures. The latter category encompasses foundation and domain-specific transformer models, alongside a lightweight neural network consisting solely of linear layers. We assess these models at two levels: in isolation, through the Mean Absolute Scaled Error (MASE), and in context, through a BH simulator in which the forecast drives the illumination plan. On purely self-similar traffic the three self-similarity aware forecasters perform on par with one another and dominate the learned models, whereas on the raw Wi-Fi trace this ordering nearly reverses. Seasonality violates their stationary increment assumption; removing the periodic component restores their comparative accuracy. Crucially, these accuracy differences barely propagate to the system level. Loss ratio and buffer backlog are affected more by system utilization and the planning period than by the choice of forecaster, with the performance gap between forecasters vanishing entirely below 0.90 utilization. This suggests design efforts are better spent optimizing utilization margins and planning periods rather than chasing marginal gains in raw accuracy.

I. INTRODUCTION

LEO satellite networks are shifting toward regenerative payloads and Beam Hopping to match fluctuating demand, but effective proactive allocation requires forecasting traffic that existing BH optimization often treats as static. This study compares forecasting approaches and evaluates whether predictive accuracy improves system-level performance.

  • Motivation: Beam Hopping dynamically adjusts beam illumination and bandwidth to align satellite resources with nonuniform, time-varying user demand.Unlike equal allocation across beams, BH uses time-division multiplexing and adjustable dwell time.
  • Research gap: Existing BH optimization methods commonly assume static or slowly varying traffic and lack mechanisms for anticipating near-term demand.This creates a gap in integrating traffic forecasting into the BH optimization loop.
  • Traffic modeling: User demand is modeled as self-similar because aggregated, bursty IP traffic fluctuates over millisecond intervals and related networking traces exhibit self-similarity.The paper supplements this model with empirical Wi-Fi data and verifies daily and multi-day demand fluctuations.
  • Evaluation design: The evaluation combines one-step-ahead MASE with a BH simulator that measures the loss ratio and buffer backlog induced by forecast-driven illumination plans.MASE is normalized by persistence, while the simulator tests whether forecast differences affect operational outcomes.
  • Evaluation design: The study compares seven forecasters, spanning theoretical benchmarks, statistical models, lightweight linear networks, and domain-specific and foundation transformers.Models are evaluated on synthetic self-similar traces with varying long-range dependence and an empirical Wi-Fi trace.
  • Main finding: Forecasting accuracy differences barely propagate to system metrics, while system utilization and planning period dominate loss ratio and buffer backlog.The planning period can become the binding constraint when slot-allocation granularity is too rigid.

II. SYSTEM MODEL AND THEORETICAL FRAMEWORK

The paper models aggregated LEO downlink demand as a self-similar process driven by heterogeneous users and validates its empirical setting with aggregated Wi-Fi observations.

  • Traffic model: Aggregated beam-level demand is modeled as a self-similar process because users have varying activity, heterogeneous demands, and aggregate at the beam level.The model defines traffic as A_t and uses a normalized fractional Brownian motion component.
  • Traffic model: The self-similarity component has stationary increments, zero mean, variance scaling with |t|^2H, continuous paths, and Gaussian finite-dimensional distributions.
  • Empirical observation: The CRAWDAD trace aggregates SNMP data into 10-minute intervals, with 359 mean active users and 797 Gbits average downlink demand per interval.

B. Synthetically Generating Self-similar Traffic

Synthetic traffic is generated by superposing independent ON/OFF sources with heavy-tailed durations, while a public Wi-Fi trace provides an empirical proxy for aggregated LEO demand.

  • Synthetic generation: The synthetic process superposes M independent ON/OFF reward sequences and rescales time by T to generate aggregate traffic.ON periods represent packet arrivals, whereas OFF periods represent inactivity.
  • Synthetic generation: Pareto-like heavy-tailed ON/OFF durations produce aggregate behavior that statistically approaches the self-similar traffic model.The construction uses long-tailed durations and large source and time-scaling parameters.
  • Model relationship: The model links the Pareto shape parameter and self-similarity through H = (3 − β)/2, and its functional structure matches the fractional-Brownian formulation.
  • Empirical validation: A high-density Wi-Fi trace is used as a proxy because both Wi-Fi access points and beam-hopped satellites aggregate broadband traffic from many users over wireless last hops.The paper notes that the two access technologies differ, while arguing that their aggregated higher-layer traffic has relevant similarities.
  • Empirical validation: The CRAWDAD fall01 trace covers a campus Wi-Fi network and is processed by aggregating SNMP downlink counters into fixed-length time buckets.The processing handles counter wraparound and splits byte deltas across buckets by temporal overlap.

D. Forecasting Models

The study compares theoretical self-similarity-aware predictors, FARIMA, and deep-learning architectures, including a foundation transformer and a lightweight linear model.

  • Forecasting models: Seven forecasting models span theoretical statistical predictors, FARIMA, domain-specific and foundation transformers, and a decomposition-based linear neural model.
  • Statistical predictors: The Norros forecaster is the mathematically optimal predictor for pure fractional Brownian motion over a continuous observed path.It conditions the forecast on a horizon Δ and a look-back window τ, and is referred to as the Norros forecaster.
  • Statistical predictors: The study includes FARIMA because its non-integer differencing parameter supports modeling processes with asymptotic second-order self-similarity.
  • Deep-learning models: Deep-learning candidates include Informer, Chronos, and DLinear, spanning efficient attention, foundation-model forecasting, and decomposition-based linear prediction.Chronos is described as a time-series foundation model, while DLinear is designed to challenge the need for complex transformer layers.
  • Statistical predictors: The paper notes that the closed-form Norros predictor has little sensitivity to extending the observed history when H > 0.9.For relatively high H, knowing the process over (−Δ, 0) makes relatively little difference compared with knowing it over (−∞, 0).

2) The optimal predictor for discrete stationary processes:

Because measurements provide discrete traffic increments rather than continuous paths, the paper derives the best linear predictor directly on the sampling grid and uses it as a benchmark.

  • Discrete formulation: Fractional Brownian motion has stationary increments, so unit-interval sampling yields a stationary fractional Gaussian noise sequence with lag-dependent autocovariance.
  • Discrete formulation: The best linear predictor projects a target variable onto recent observations using their means, covariance vector, and covariance matrix.
  • Discrete formulation: The discrete predictor uses the T most recent increments to forecast demand accumulated over the next h intervals.
  • Comparison with Norros: The resulting Linear predictor is a strict lower bound on attainable error after discretization because the Norros forecaster is also linear in the same T increments.Any performance gap between the two predictors is attributed solely to discretizing the continuous-path predictor.
  • Comparison models: FARIMA generalizes ARIMA by allowing the differencing parameter d to take non-integer values.

3) FARIMA:

FARIMA is specified through fractional differencing, with coefficients expressed using the Gamma function and stationarity governed by autoregressive-polynomial roots.

  • The fractional differencing operator (1 − B)^d is defined through a binomial series for d ∈ (−1/2, 1/2).
  • The differencing coefficients a_j are determined using Gamma-function expressions.
  • Stationarity and invertibility depend on the autoregressive polynomial having no common roots with the relevant polynomials.

4) Informer:

Informer reduces vanilla Transformer attention costs by selecting the most informative queries and estimating their importance efficiently.

  • Informer uses ProbSparse attention to mitigate the quadratic time and memory complexity of vanilla self-attention.
  • Query importance is measured through divergence between each attention distribution and a uniform distribution.
  • The model approximates the sparsity measurement with Log-Sum-Exp rather than computing the full KL divergence.
  • Randomly sampling keys maintains O(L log L) complexity while extracting informative long-range temporal dependencies.

5) DLinear:

DLinear is a lightweight forecasting baseline that decomposes the input into trend-cyclical and seasonal-remainder components, then maps them directly to the forecast horizon.

  • DLinear decomposes the input sequence into trend-cyclical and seasonal-remainder components using a moving-average kernel.
  • Separate linear layers regress each component directly to the future horizon, avoiding recursive step-by-step forecasting errors.
  • The model shares weights across variates instead of explicitly modeling spatial or inter-variate relationships.
  • DLinear is included as a benchmark because its simple architecture has outperformed Transformer-based solutions in some domains.

B. Investigating Self-Similarity in the Wifi Dataset

The Wi-Fi analysis supports self-similar modeling after deseasonalization, while highlighting a resolution limitation and evaluating forecasting models on synthetic and empirical traffic.

  • The CRAWDAD series is deseasonalized using nested daily and weekly additive components before self-similarity analysis.
  • H = 0.84 was estimated for the deseasonalized data, within H ∈ [0.78, 0.90], while KPSS produced p = 0.1.
  • The 10-minute Wi-Fi resolution prevents direct verification of scale invariance at the finer timescales used later.
  • Synthetic forecasting results vary β across Tables II–IV, with each entry averaged over 10 seeds and reported with a 95% confidence interval.
  • Chronos was evaluated in zero-shot and fine-tuned forms, using the smallest chronos-bolt-tiny variant for resource-constrained satellite settings.
  • Informer and chronos-bolt-tiny use approximately 11.3M and 8.6M trainable parameters, whereas DLinear uses 150–3,000.

D. Performance Metrics

The study evaluates forecasting accuracy with one-step-ahead MASE on synthetic self-similar and empirical Wi-Fi traffic. Self-similarity-aware forecasters dominate synthetic traces, while seasonality reverses the ranking on raw Wi-Fi data and preprocessing restores their advantage.

  • Accuracy metric: MASE equals 1 for persistence, while values below 1 indicate improvement over repeating the last observation.The denominator is the mean absolute one-step change of the ground truth, and forecasts use the 48 most recent demand samples.
  • Synthetic traffic: As β increases from 1.04 to 1.44, long-range dependency decreases, but MASE comparisons must be interpreted as relative gains over persistence.Strong long-range dependency can make persistence highly accurate because of positive autocorrelation.
  • Synthetic traffic: Linear, Norros, and FARIMA occupy the top three ranks at every β, with overlapping confidence intervals; at β = 1.44, Linear and FARIMA both reach MASE 0.8393.The three methods estimate the same optimal linear predictor through different routes, making them interchangeable on purely self-similar traffic.
  • Synthetic traffic: Chronos* remains outside the top three, Informer ranks fourth or fifth, and DLinear is weakest on synthetic traces.Fine-tuning makes Chronos* competitive relative to zero-shot Chronos, but not among the leading forecasters.
  • Wi-Fi traffic: On raw Wi-Fi traffic, DLinear is most accurate while Linear and Norros become the worst performers because seasonality violates their stationary-increment assumption.The time-of-day and day-of-week profile produces an ordering close to the reverse of the synthetic ranking.
  • Wi-Fi traffic: After deseasonalization, FARIMA becomes best overall at MASE 0.9665, with gains concentrated in self-similarity-aware forecasters.Classical models require periodic components to be removed, whereas deep models absorb part of the seasonality internally.
  • Efficiency: Informer and Chronos* impose greater computational costs than lightweight or classical alternatives.Informer has large model size and O(L log L) runtime, while Chronos* requires fine-tuning on representative traffic.

F. Beam Hopping Simulation Scenarios

The BH simulator tests whether forecasting differences affect loss and backlog under varied utilization, planning periods, traffic burstiness, and user asymmetry. System conditions generally matter more than forecaster choice.

  • Simulation setup: The simulator models three cells sharing one beam, 1 ms slots, 1 MiB per-cell buffers, and self-similar demand from 1500 Pareto ON/OFF sources.Arrivals exceeding buffer capacity are dropped, and loss ratio is measured alongside backlog metrics.
  • Simulation setup: Each illumination plan uses one-step-ahead forecast demand plus current buffer occupancy, with slots allocated proportionally by largest-remainder apportionment.The scheduler clips forecast demand at zero before computing cell weights.
  • Simulation setup: The evaluation compares Linear and DLinear on identical traffic realizations across loss ratio, mean backlog, and maximum mean per-cell backlog.Each scenario uses ten independent replicates with two-hour testing windows.
  • Scenario design: Five scenarios vary utilization, forecasting period, source counts, and Hurst parameter while retaining three cells sharing one beam.The scenario configuration covers utilization and granularity sweeps, self-similarity changes, and symmetric or asymmetric users.
  • System-level effects: Across scenarios, utilization and forecasting granularity dominate system metrics, and forecaster choice becomes effectively irrelevant under low utilization.Higher utilization naturally increases loss ratio, while accuracy gaps do not produce significant differences in loss or backlog.
  • Planning period: Below 150 ms, the two forecasters are indistinguishable; at 60 s, mean backlog rises to 1.26 Mb and loss ratio grows by two orders of magnitude.The loss ratio is essentially flat below 150 ms, while mean backlog is minimized at 150 ms.
  • Traffic characteristics: Forecaster differences narrow as self-similarity decreases, becoming similar by H = 0.78, while asymmetric users reduce loss ratio below 0.1 ppm.Backlog metrics remain indistinguishable under asymmetric user counts, with or without varying self-similarity.

IV. CONCLUSION

The paper compares statistical and deep-learning forecasters in isolation and within a BH simulator. Self-similarity-aware methods lead on synthetic traffic, preprocessing changes empirical rankings, and system performance depends more on utilization and planning granularity than forecasting accuracy.

  • Approach: The study evaluates statistical and deep-learning forecasters using one-step-ahead MASE on synthetic self-similar and empirical Wi-Fi traces, then embeds them in a BH simulator.The simulator evaluates the forecast through the illumination plan rather than predictive accuracy alone.
  • Forecasting results: Linear, Norros, and FARIMA rank highest on purely self-similar traffic, while DLinear leads on raw Wi-Fi traffic and FARIMA leads after deseasonalization at MASE 0.9665.Removing seasonality makes statistical and deep-learning models comparably effective.
  • System-level results: Across five scenarios, the accuracy gap between Linear and DLinear does not produce comparable differences in loss ratio, mean backlog, or worst-cell backlog.System utilization and forecasting granularity dictate performance more strongly than forecaster choice.
  • Implication: Optimizing utilization margins and planning periods is likely to yield larger system-level gains than deploying a more accurate forecasting model.This conclusion shifts design emphasis from raw predictive accuracy toward operating conditions.
  • Scope boundary: The simulator currently abstracts away dynamic channel conditions, joint power and bandwidth allocation, and full-constellation effects.Future work also targets power consumption, memory usage, and scalability.
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