Nurse Staffing in Medical Units: A Queueing Perspective

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Abstract
In this paper, we present a closed queueing model to determine efficient nurse staffing policies. We explicitly model the workload experienced by s nurses within a single medical unit with n homogeneous patients as a closed M/M/s//n queueing system, where each patient alternates between requiring assistance and not. The performance of the medical unit is based on the probability of excessive delay, the relative frequency with which the delay between the onset of patient neediness and the provision of care from a nurse exceeds a given time threshold. Using new many-server asymptotic results, we find that effective staffing policies should deviate from threshold-specific nurse-to-patient ratios by factors that take into account the total number of patients present in the unit. In particular, our staffing rule significantly differs from California Bill AB 394, legislation that mandates fixed nurse-to-patient staffing ratios. Simulations show that our results are robust to delay-dependent service times, generally distributed service times, and nonhomogeneous patients, i.e., those with different acuity levels.

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