Hyprober: Hybrid Probabilistic Relay Capacity Estimation for Optimized Load Balancing in Tor

The anonymity and performance of Tor depend on accurate relay capacity estimation to ensure balanced traffic distribution across thousands of volunteer relays. Existing estimators, based on bandwidth probing or maximum likelihood approaches, struggle to adapt to Tor's evolving network dynamics and the heterogeneous behaviors of its relays. These limitations often result in suboptimal load balancing, higher latency, and a decreased user experience. To address these challenges, we introduce HyProber, a hybrid framework that integrates statistical profiling with graph-based inference for adaptive relay capacity estimation. HyProber initially classifies relays based on historical load dynamics (high-load, fluctuating, or underloaded) and applies specific estimation techniques. These estimates are further refined using a GNN-inspired model, where iterative message passing adjusts relay estimates according to inter-relay similarity and temporal behavior. Simulation results demonstrate HyProber's superior accuracy and stability compared to stateof-the-art methods. It achieves MAE of 67.1 KB/s, 96.9 KB/s, and 177.2 KB/s under underloaded, normal, and overloaded conditions. Relay capacity estimation errors remain below 1.1% across all categories, and path bandwidth allocation closely tracks the true capacities (≈ 24KB/s). HyProber's hybrid, contextaware design outperforms all existing estimators in terms of precision and computational efficiency, thereby strengthening Tor's overall performance and resilience.