Data-Driven Bed Capacity Planning Using $M_t/G_t/\infty$ Queueing Models with an Application to Neonatal Intensive Care Units

Hospitals face challenges in long-term intensive care unit (ICU) capacity planning under uncertain demand. Admission rates fluctuate over time, and LOS distributions vary with patient heterogeneity, hospital location, case mix, and clinical practice. Common approaches rely on steady-state queueing models or heuristic rules with fixed parameters, which often fail to capture real occupancy dynamics. The widely used 85% occupancy rule, for example, recommends keeping average utilization below this level to preserve responsiveness, yet it is grounded in stationary assumptions and may lack resilience in time-varying systems. Our analysis shows that even when long-run utilization targets are satisfied, daily occupancy often exceeds 100% capacity. We propose a data-driven framework to estimate ICU bed occupancy using an $M_t/G_t/\infty$ queueing model with time-varying arrival rates and empirically fitted LOS distributions. The approach combines statistical decomposition and parametric fitting to capture temporal patterns in admissions and LOS, and is applied to multi-year data from neonatal ICUs (NICUs) in Calgary. We evaluate capacity scenarios including average-based thresholds and Poisson-based surge estimates. Results show that static heuristics are inadequate under fluctuating demand and underscore the importance of modeling LOS variability when estimating bed needs. Although the case study focuses on NICUs, the framework has potential applicability to other ICU settings and provides interpretable, data-informed support for systems facing rising demand and constrained capacity.