Transformer-Based Next-Step Prediction for Queue Length Distribution

Traditional approaches to model queueing dynamics from real-world setting rely on model selection, parameter estimation, and simulation. These methods struggle with complexities like time-varying arrivals, customer abandonment, and routing interactions, while parameter estimation errors and time-consuming simulations further limit their predictive accuracy and increase their costs. We propose a data-driven alternative that learns queueing dynamics directly from historical data using decoder-only Transformers. Our approach uses the autoregressive nature of queueing systems, where future states depend causally on past sequences through recursions. We treat queue evolution as a sequence prediction problem: inputting queue length distributions and predicting next-step distributions. Experiments on synthetic data demonstrate that our Transformer-based model successfully reproduces queueing dynamics across different queueing models and outperforms traditional sequence models like Recurrent Neural Networks (RNNs). This model-free approach eliminates the need for explicit model specification and parameter estimation while maintaining accuracy in capturing complex system behaviors. Future work will validate this methodology on real-world ride-hailing datasets.