Abstract: The tile-based approach is widely adopted in adaptive 360-degree video streaming systems, due to its efficiency in managing limited bandwidth resources. However, the inherent uncertainty of users' viewports, making viewport prediction difficult, has posed limitations on the performance of tile-based bitrate adaptive streaming. In this paper, we introduce a Multi-window and Stochastic Viewport Prediction approach to address the uncertainty in viewport changes. In particular, considering our goal of maximizing the expectation of future Quality of Experience (QoE), we investigate a viewport distribution prediction model, to cope with the inherent randomness. Additionally, to accommodate the varying gap between the playback and the downloading process, we explore the multiple-windows viewport prediction model to capture different prediction windows. Even with the utilization of distributional prediction and multi-window models, predicting viewports far into the future is still inherently challenging. Accordingly, we propose a patience pattern temporarily suspending the download process, allowing for the accumulation of additional head movement trajectory data. Finally, within the framework of Model Prediction Control (MPC)-based rate adaptation, we introduce a multi-window Probabilistic view-port prediction-based Tile-level Bitrate Adaptation Streaming (PTBAS) algorithm. Extensive experiments, utilizing real-world traces and user head movement trajectories, demonstrate that PTBAS outperforms state-of-the-art methods, improving overall QoE performance by 15.96%.