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.

Utilizing a game-theoretic model, this study distinguishes between privacy-protecting and privacy-disclosing consumers, examining the impact of digital privacy on manufacturers’ channel strategies, including no encroachment, encroachment, and shifting. The results indicate that when consumers prefer privacy disclosure, manufacturers consistently opt for the shifting strategy. In contrast, when privacy protection is prioritized, the outcome depends on the intensity of consumer preferences. Specifically, weak preferences lead to encroachment, whereas strong preferences favor no-encroachment. This contingency framework illustrates how privacy preference thresholds shape channel strategy selection. From a practical perspective, the findings offer actionable guidance for manufacturers. First, a win-win outcome depends on the manufacturer’s cost-efficiency in channel-shifting operations, suggesting that firms should assess their operational capabilities before implementation. Second, consumer benefits under encroachment imply manufacturers can adopt this strategy for competitive advantage while addressing privacy concerns. These insights equip practitioners with a decision-making toolkit for balancing privacy compliance, channel efficiency, and stakeholder value creation in digital transformation initiatives.