## 5 Discussion  
This study demonstrates how the integration of process mining with simulation enables the identification, application, and evaluation of tailored management interventions, such as fast-track pathways, to reduce length of stay (LOS) in emergency departments (EDs). The findings highlight that age, triage level, and reason for consultation are critical predictors of prolonged LOS, consistent with prior research in this area [17; 19; 20]. The proposed fast-track pathway specifically addresses the needs of complex patients, who represent a high-impact group within EDs. By prioritising these patients, the pathway ensures that limited resources are directed where they are most needed, improving both clinical outcomes and operational efficiency. Although the term 'fast track' is traditionally associated with less complex cases, we intentionally used it to describe the expedited pre-admission process for complex patients. This terminology underscores the critical time saved during their triage and early management, which is essential for improving outcomes in this high-risk population. We acknowledge that this could lead to some confusion, as these patients often require longer stays overall, but the emphasis is on the swift initial intervention. Unlike traditional flow management strategies, such as separation by severity level or FT referrals for low-acuity patients, this approach offers a novel alternative. By leveraging process mining on historical and real-time data, the study identified a targeted subset of patients, representing only 20-30% of visits but consuming the majority of ED resources and LOS. This Pareto-type methodology shifts focus from patient volume to the drivers of congestion, prioritising interventions based on their impact on care delivery. The predictive formula, activated at triage by nursing staff, anticipates the needs of high-risk and vulnerable patients, particularly those aged 65 years and older. This population is at increased risk of complications, such as delirium, which is closely associated with prolonged waiting times, overstimulation, and fragmented care. Early intervention not only improves clinical outcomes but also mitigates costs associated with extended stays, readmissions, and institutionalisation. From an economic perspective, unnecessary ED occupancy incurs substantial direct and opportunity costs [76]. This formula optimises resource utilisation by identifying patients who stand to benefit most from accelerated care, thereby balancing resource allocation and reducing inefficiencies. Furthermore, the operational flexibility of the model facilitates adaptation to varying healthcare pressures and available resources. Simulation results show that even minimal interventions, such as allocating five beds to the FT pathway, lead to a 21% reduction in average LOS and a 35% decrease in overall ED saturation. These benefits scale proportionally as additional resources are allocated, providing managers with a scalable and adaptable tool. The predictive formula was developed using clinically relevant variables, including age >65 years; frequent ED visits; triage levels II and III; referrals from residential care; and specific reasons for consultation such as poor general condition, dyspnea, and abdominal pain. Validated through simulation, the formula demonstrates predictive performance comparable to other studies [77]. Unlike complex machine learning models, this transparent and traceable tool is easily integrated into existing workflows without requiring sophisticated IT systems, ensuring its applicability even in resource-limited settings. Nonetheless, this approach has limitations. This study is a proof of concept to evaluate the feasibility and potential applicability of implementing this approach in other hospitals. Thus, the study was conducted in a single centre, necessitating adaptations for broader generalisation.