Fatigue-aware nurse staffing in emergency departments with state-dependent service rates

Existing staffing models for emergency department (ED) nurses typically treat service rates as fixed and therefore miss an important feature of overloaded emergency care: nurse efficiency may deteriorate as workload rises. This paper studies ED nurse staffing in a stochastic queueing system with state-dependent service rates that capture fa-tigue-induced capacity loss. Using fluid and diffusion asymptotics, we show that fa-tigue can fundamentally alter system dynamics, generating bistability and a fatigue trap in which modest demand shocks or staffing shortfalls lead to disproportionate congestion. The analysis also explains why the benchmark square-root staffing rule be-comes vulnerable in fatigue-prone environments: the conventional diffusion-scale safety buffer can be offset by fatigue-induced service decay. Motivated by this mecha-nism, we derive a revised staffing rule that combines a structural fatigue premium with a risk-adjusted forecast correction. Discrete-event simulation results show that RAFD reduces collapse exposure and upper-tail congestion relative to the square-root bench-mark, while producing a cost–risk trade-off relative to uniformly conservative staffing. More broadly, the results suggest that when service capacity is endogenous to work-load, staffing decisions should account for robustness as well as efficiency.