Enhancing emergency department forecasting accuracy through detailed time-based modelling in discrete event simulation

Emergency Department (ED) overcrowding and long waiting time are major healthcare challenges caused by increasing demand and limited resources (He et al. 2011). Accurate short-term forecasting of patient arrivals and discharges is essential for operational planning. This study develops and validates three discrete event simulation (DES) models for shortterm ED forecasting using data from Rambam Hospital, Israel (January 2004 to October 2007) (Armony et al. 2015).

The models differ in detailed time based, the Slot-Based Arrival model uses two daily time slots with weekday specific length of stay (LOS) and Hourly-LOS model adds hourly-weekday LOS distributions while the third model Hourly Arrival implements detailed weekday-hour arrivals with weekday specific LOS. This approach systematically evaluates how time based detail affects forecasting.

Performance was evaluated using 30-day non-overlapping rolling-window validation across 40 periods with 100 replications per window. Accuracy was measured using Mean Absolute Percentage Error (MAPE) and Median Absolute Percentage Error (MdAPE), which is more robust to outliers (Moreno et al. 2013). Statistical testing employed Friedman tests and pairwise Wilcoxon signed-rank tests (Demˇsar 2006).

Results show detailed arrival modelling significantly outperforms simpler approaches. The Hourly Arrival model achieved MdAPE below 8% for arrivals (5.657%) and discharges (7.638%), exceeding the 10% accuracy threshold (Moreno et al. 2013). Other two models showed similar performance (MdAPE ≈ 9.8%), indicating enhanced LOS complexity alone does not improve forecasts. Statistical tests confirmed Hourly Arrival’s superiority across all windows.

These findings demonstrate that capturing time based variability in arrivals is more important than LOS complexity for short-term forecasting for this data set. The study provides a robust validation framework combining rolling-window testing with formal statistics, addressing gaps in simulation research. This approach can support more informed decisions in ED staffing, capacity planning and surge management.

References
Armony, Mor et al. (June 2015). “On Patient Flow in Hospitals: A Data-Based QueueingScience Perspective”. In: Stochastic Systems 5 (1), pp. 146–194. issn: 1946-5238. doi: 10.1287/14-ssy153.
Demˇsar, Janez (2006). Statistical Comparisons of Classifiers over Multiple Data Sets. Tech. rep., pp. 1–30.
He, Jun et al. (2011). “Demand for hospital emergency departments: a conceptual understanding”. In: World Journal of Emergency Medicine 2 (4), p. 253. issn: 1920-8642. doi: 10.5847/wjem.j.1920-8642.2011.04.002.
Moreno, Juan Jos´e Monta˜no et al. (2013). “El ´ındice R-MAPE como medida resistente del ajuste en la previsio´nn”. In: Psicothema 25 (4), pp. 500–506. issn: 02149915. doi: 10.7334/psicothema2013.