The immediate motivation of this paper is California Bill AB 394, legislation which mandates fixed nurse-to-patient staffing ratios as a means to address the current crisis in the quality of health care delivery. Modeling medical units as closed queueing systems, we seek to determine whether or not ratio policies are effective at managing nurse workload. Our many-server asymptotic results suggest that ratio policies cannot provide consistently high service quality across medical units of different sizes. As a remedy, we recommend policies that deviate from the restrictive linear nature of ratio policies, employing the 'square root rule' commonly used to staff large service systems. Under some quality of care assumptions, our policies exhibit a type of 'super' pooling effect, in which, for large systems, the requisite workforce is significantly smaller than the nominal patient load.
queueing system health care public policy nursing staffing manyserver limit theorems