Intelligent systems play an increasingly central role in healthcare systems worldwide. Nonetheless, operational friction represents an obstacle to full utilization of scarce resources and improvement of service standards. In this paper we address the challenge of developing data-driven models of complex workflow systems - a prerequisite for harnessing intelligent technologies for workflow improvement. We present a proof-of-concept model parametrized using real-world data and constructed based on domain knowledge from the Royal Infirmary of Edinburgh, demonstrating how off-the-shelf process mining, machine learning and stochastic process modeling tools can be combined to build predictive models that capture complex control flow, constraints, policies and guidelines.