Hybrid light fidelity (LiFi) and wireless fidelity (WiFi) networks are a promising paradigm of heterogeneous network (HetNet), attributed to the complementary physical properties of optical spectra and radio frequency. However, the current development of such HetNets is mostly bottlenecked by the existing transmission control protocol (TCP), which restricts the user equipment (UE) to connecting one access point (AP) at a time. While the ongoing investigation on multipath TCP (MPTCP) can bring significant benefits, it complicates the network topology of HetNets, making the existing load balancing (LB) learning models less effective. Driven by this, we propose a graph neural network (GNN)-based model to tackle the LB problem for MPTCP-enabled HetNets, which results in a partial mesh topology. Such a topology can be modeled as a graph, with the channel state information and data rate requirement embedded as node features, while the LB solutions are deemed as edge labels. Compared to the conventional deep neural network (DNN), the proposed GNN-based model exhibits two key strengths: i) it can better interpret a complex network topology; and ii) it can handle various numbers of APs and UEs with a single trained model. Simulation results show that against the traditional optimisation method, the proposed learning model can achieve near-optimal throughput within a gap of 11.5%, while reducing the inference time by 4 orders of magnitude. In contrast to the DNN model, the new method can improve the network throughput by up to 21.7%, at a similar inference time level.

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