Business Process Simulation (BPS) refers to techniques designed to replicate the dynamic behavior of a business process. Many approaches have been proposed to automatically discover simulation models from historical event logs, reducing the cost and time to manually design them. However, in dynamic business environments, organizations continuously refine their processes to enhance efficiency, reduce costs, and improve customer satisfaction. Existing techniques to process simulation discovery lack adaptability to real-time operational changes. In this paper, we propose a streaming process simulation discovery technique that integrates Incremental Process Discovery with Online Machine Learning methods. This technique prioritizes recent data while preserving historical information, ensuring adaptation to evolving process dynamics. Experiments conducted on four different event logs demonstrate the importance in simulation of giving more weight to recent data while retaining historical knowledge. Our technique not only produces more stable simulations but also exhibits robustness in handling concept drift, as highlighted in one of the use cases.