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TD-STGT: A Spatio-Temporal Graph Transformer for Mobile Traffic Demand Forecasting

Mohamad Alkadamani, Halim Yanikomeroglu

arXiv:2609.06636v1eess.SYcs.AIcs.LG

TL;DR

Mobile traffic demand forecasting needs fine-grained spatial and temporal signals for network planning, but operator traffic data are generally inaccessible for research. This paper builds a population-scaled proxy from crowdsourced measurements and daytime population, then uses TD-STGT to forecast grid-level demand changes. Across the evaluated settings, TD-STGT achieves the best reported baseline performance, with ΔR2 = 0.462 and ΔRMSE of 0.050, while its computational cost remains practical for offline planning.

  • Problem

    Mobile traffic demand forecasting supports planning decisions, while direct operator traffic data are generally inaccessible for research.

  • Method

    The method constructs a population-scaled crowdsourced demand proxy and forecasts its grid-level changes with a spatio-temporal graph transformer.

  • Results

    ΔR2 = 0.462 and ΔRMSE of 0.050 are reported for TD-STGT, which achieves the best performance among evaluated baselines.

  • Takeaways & Limitations

    The framework can help identify areas with increasing demand pressure and support proactive capacity-planning decisions.

  • Takeaways & Limitations

    TD-STGT is the most expensive advanced model, although its cost remains practical for offline planning.

Abstract

from arXiv · show

Fine-grained mobile traffic demand forecasting is essential for long-term planning of 5G and future 6G networks, including radio upgrades, site densification, backhaul expansion, and spectrum activation. This paper proposes the Traffic Demand Spatio-Temporal Graph Transformer (TD-STGT), a graph neural forecasting framework for predicting changes in wireless mobile traffic demand across fine geographic grids. The framework uses a population-scaled demand proxy developed from crowdsourced mobile measurements and daytime population information. Experiments across five Canadian metropolitan regions show that TD-STGT achieves the best performance in forecasting grid-level demand changes, reaching a $ΔR^2$ of 0.462 and reducing $Δ$RMSE by 5.7\% relative to the strongest baseline. The proposed model provides a practical tool for identifying areas with increasing demand pressure and prioritizing future mobile-network capacity upgrades.

I. INTRODUCTION

The paper addresses fine-grained mobile traffic-demand forecasting despite limited access to proprietary operator data. It constructs a population-scaled crowdsourced proxy and forecasts grid-level demand changes with a spatio-temporal graph transformer.

  • Motivation: Crowdsourced mobile measurements provide repeated spatial-temporal observations because direct operator traffic data are generally inaccessible for research.The measurements are time-stamped and geo-located user-side data collected through application SDKs, but do not represent complete operator-carried traffic.
  • Research gap: Prior work often focuses on spatial estimation or relies on proprietary counters and short observation windows, leaving limitations for mobile traffic forecasting.
  • Proposed framework: TD-STGT uses local graph attention, global spatial self-attention, temporal convolution, and temporal self-attention to forecast grid-level demand changes.
  • Evaluation scope: The assessment covers five Canadian metropolitan regions and evaluates demand-change patterns in urban and suburban planning scenarios.
  • Proxy construction: The proposed proxy combines observed mobile data usage per crowdsourced observation with daytime population to represent grid-level peak-demand potential.
  • Proxy construction: The forecasting target is the one-period change in the log-transformed proxy, computed at weekly and monthly resolutions.Monthly aggregation is the main planning-level target because it smooths sampling variability and aligns with MNO capacity-planning cycles.

C. Proxy Behavior and Validation

The proxy exhibits heterogeneous temporal and spatial behavior across grids, motivating grid-level spatio-temporal forecasting. Independent validation compares the proxy with deployed network bandwidth.

  • Proxy behavior: Temporal proxy behavior differs across metropolitan regions and among high-demand Toronto grids, showing heterogeneous local trajectories.This heterogeneity supports grid-level rather than purely aggregate city-level prediction.
  • Proxy behavior: Toronto grids show spatially heterogeneous growth when colored by the annualized trend of their monthly log-proxy series.
  • Validation: The proxy is independently assessed through its spatial association with deployed bandwidth assigned to the same grid.The validation rationale is that persistent demand pressure should be associated with greater provisioned capacity.

III. PROBLEM FORMULATION

The problem is to forecast one-period changes in grid-level mobile traffic demand using a population-scaled proxy and spatio-temporal features. The formulation evaluates whether models can identify demand trajectories that change beyond persistence across 10,250 grids.

  • III. PROBLEM FORMULATION: The target is the one-period change in log-transformed, population-scaled mobile traffic demand rather than its persistent level.This tests whether the model can identify changes beyond simple persistence.
  • III. PROBLEM FORMULATION: The grid-time panel contains 10,250 grids across five metropolitan regions.
  • III. PROBLEM FORMULATION: Inputs include historical proxy values, previous changes, lagged peak-hour sample counts, exposure-normalized byte indicators, and daytime population descriptors.
  • III. PROBLEM FORMULATION: The model uses an input window from t −L to t −1 to predict future proxy changes over forecast horizon H, with the main task using H = 1.Evaluation reports ∆R2, ∆RMSE, and ∆MAE on the change target.

IV. PROPOSED TD-STGT METHODOLOGY

TD-STGT combines spatial, temporal, and prediction modules over a graph whose nodes are grid cells and whose edges encode adjacency and distance-based proximity. The architecture integrates graph attention, global spatial attention, temporal convolution, and temporal transformer blocks.

  • IV. PROPOSED TD-STGT METHODOLOGY: The spatial graph represents grid cells as nodes and encodes adjacency and distance-based proximity through its edges.Self-loops preserve each grid’s history, and the default graph connects eight nearest grids.
  • IV. PROPOSED TD-STGT METHODOLOGY: TD-STGT contains spatial, temporal, and prediction modules combining GAT, global spatial attention, TCN, and temporal transformer blocks.
  • IV. PROPOSED TD-STGT METHODOLOGY: The input window is projected into a d-dimensional representation before subsequent spatio-temporal processing.

D. Local Spatial Graph Attention Branch

The local spatial branch updates each grid from its spatial neighbors using graph attention, while the global spatial branch uses self-attention to capture longer-range relationships. Their attention mechanisms use learned projections and multi-head representations.

  • D. Local Spatial Graph Attention Branch: For each time step, graph attention updates grid i using information from its spatial neighbors.
  • D. Local Spatial Graph Attention Branch: The normalized coefficient ατij weights the contribution from neighbor j to grid i.The attention score is unnormalized before normalization.
  • D. Local Spatial Graph Attention Branch: The graph-attention computation uses a learnable attention vector, projection matrix, grid embeddings, concatenation, and nonlinear activation.Multi-head attention concatenates or averages head-specific outputs.
  • D. Local Spatial Graph Attention Branch: The spatial transformer adds positional encodings and applies multi-head self-attention to capture long-range spatial relationships.The attention uses query, key, and value matrices across multiple heads.

MSSA( ˜H) + ˜H

TD-STGT fuses local and global spatial representations with a learned gate, then models temporal dependencies using causal dilated convolution and temporal self-attention. The architecture overview summarizes these components.

  • MSSA( ˜H) + ˜H: The learned fusion gate combines local GAT and global spatial-transformer outputs at each grid and timestamp.It determines whether local or global spatial context is more informative.
  • MSSA( ˜H) + ˜H: The temporal module uses causal dilated convolutions and residual TCN blocks to model local temporal dependencies.The blocks capture local temporal changes in deployment and demand.
  • MSSA( ˜H) + ˜H: Temporal positional encodings are added before temporal multi-head self-attention is applied along the time dimension for each grid.The temporal branch uses temporal query, key, and value matrices with an output projection.
  • MSSA( ˜H) + ˜H: Fig. 3 provides an overview of the TD-STGT architecture.

LN(MTSA(˜Z) + ˜Z)

TD-STGT maps temporal representations to a forecast horizon and trains with a composite objective. The objective combines change-forecasting accuracy with spatial and temporal smoothness regularization.

  • Prediction head: The prediction head maps the temporal representation to the forecast horizon of proxy changes.Its output uses two 1 × 1 convolutional layers, ReLU activation, and a fully connected projection.
  • Training objective: The training loss combines change-forecasting error, spatial smoothness, and temporal smoothness.Spatial and temporal regularization strengths are controlled by λs and λt.
  • Loss components: L∆ penalizes forecasting error, LS penalizes discontinuities between connected grids, and LT regularizes abrupt oscillations across multi-step forecasts.The objective therefore constrains both spatial consistency and temporal behavior in predicted changes.

V. EXPERIMENTAL SETUP, RESULTS, AND DISCUSSION

The experiments use leakage-controlled chronological evaluation, with additional spatial and spatio-temporal holdout protocols for robustness. The main setup forecasts one future proxy-change step from approximately four years of history.

  • Dataset split: Chronological splitting uses earlier periods for training, an intermediate period for validation, and the most recent periods for testing.Validation and test inputs contain only historical context from preceding periods.
  • Robustness protocols: Blocked spatial splits hold out contiguous grid regions, while the strictest protocol tests future periods in spatially held-out regions.The main results use chronological testing; spatial and spatio-temporal splits support robustness analysis.
  • Forecast setup: The main configuration uses an input window of approximately four years and H = 1 forecast step.This corresponds to next-period proxy-change forecasting at the selected weekly or monthly granularity.
  • Configuration tables: The evaluation setup includes a TD-STGT model-configuration table and a separate table of baseline-model hyperparameters.These tables organize the selected experimental configurations.

B. Model Configuration

The study evaluates TD-STGT against persistence, tabular, recurrent, convolutional, and graph-based baselines using change-focused metrics and multiple robustness analyses. TD-STGT performs best in the reported forecasting comparisons and shows stable error behavior across seeds.

  • Baseline models: Seven baselines span linear autoregression, RF, XGBoost, LSTM, GRU, CNN-LSTM, and STGCN.The baselines cover interpretable time-series, nonlinear tabular, recurrent, Euclidean spatio-temporal, and graph-based approaches.
  • Evaluation metrics: Performance is evaluated with ∆R2, ∆RMSE, and ∆MAE on the one-period change target.These metrics avoid overstating skill from the high persistence of proxy levels.
  • Proxy validation: The population-scaled peak-demand proxy reaches median Pearson correlation of 0.71 and OLS R2 of 0.66 with deployed bandwidth.It has the strongest association among the alternative proxy variants.
  • Forecasting results: TD-STGT achieves the highest ∆R2 and lowest ∆RMSE and ∆MAE, reducing ∆RMSE from 0.053 for STGCN to 0.050, a 5.7% reduction.STGCN is the strongest non-proposed baseline in the one-step comparison.
  • Error distributions: TD-STGT has the lowest median absolute delta error and one of the tightest error spreads, while recurrent models show larger dispersion.STGCN is identified as the strongest baseline in the distribution comparison.
  • Robustness: Across 20 random seeds, TD-STGT has the narrowest ∆RMSE and ∆MAE distributions, indicating the most consistent convergence.LSTM, GRU, and CNN-LSTM have wider spreads, whereas STGCN is more stable.
  • Additional analyses: The sensitivity and ablation analyses are presented as additional evaluations of TD-STGT configuration and components.The supplied table labels identify these analyses but do not report their findings.

F. Sensitivity Analysis

Sensitivity analysis evaluates hyperparameters, component contributions, and computational cost for TD-STGT. The model’s strongest configuration and accuracy gains come with higher computational expense that remains practical for offline planning.

  • Hyperparameter sensitivity: Sensitivity analysis varies learning rate, attention heads, batch size, and embedding dimension.
  • Hyperparameter sensitivity: The best operating point uses learning rate 10^-3, four heads, batch size 32, and embedding dimension 128.
  • Ablation study: Removing the spatial module causes the largest degradation, while proxy simplification also reduces accuracy.The ablation study removes one TD-STGT component at a time under the same training protocol.
  • Model complexity and computational cost: TD-STGT is the most expensive advanced model, but its computational cost remains practical for offline planning and is justified by the accuracy gain.The comparison considers parameter count, training time, inference time, and ΔRMSE.
  • Overall result: TD-STGT achieves ΔR2 = 0.462 and ΔRMSE of 0.050 while supporting identification of areas with increasing demand pressure.The framework uses a crowdsourced population-scaled proxy for grid-level mobile traffic demand changes.
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