28 - Using Queuing Theory to Determine Optimal NICU Bed Numbers

Poster Number: 28
Publication Number: 28.338

Scott D. Duncan, University of Louisville, Louisville, KY, United States; Liza M. Creel, University of Louisville School of Public Health and Information Sciences, Louisville, KY, United States; Sagnik Bhadury, University of Louisville School of Medicine, Louisville, KY, United States; Caroline N. Jackson, University of Louisville School of Medicine, Louisville, KY, United States; Kahir S. Jawad, University of Louisville School of Medicine, Louisville, KY, United States; Yana Feygin, University of Louisville School of Medicine, Louisville, KY, United States; Maiying Kong, University of Louisville, Louisville, KY, United States

Background: Queuing theory has multiple applications in healthcare, including utilization analysis for clinical operations at the level of service delivery and state-wide healthcare planning. Kentucky is a certificate of needs state and requires a utilization of 80% of capacity for additional NICU beds to be considered.

Objective: This analysis uses simulated admission rates and determines optimal bed numbers using queuing theory.

Design/Methods: Public data published in the 2019 Kentucky Annual Hospital Utilization and Services Report was examined. Data was analyzed by area developmental district (ADD) and state, including number of births, NICU patient days and NICU beds. NICU admissions were estimated at 12.5% of total births. The Erlang-C formula, based on a M/M/c queuing model, was applied to generate the probability of a non-zero wait time, given the current number of NICU beds and 80% utilization of beds. A sensitivity analysis determined the number of beds required to ensure the probability of a delay to be < 10%, < 5% and < 1%. Average wait times were calculated for all simulations.

Results: Current capacity utilization ranged from 10.8 to 83.2% across the ADDs, with state utilization of 65.9%. With the current number of beds, probability of positive wait times was typically < 1%, except for ADD 5 and 10, with a probability of non-zero wait times of 12.3% and 42.9%, respectively. Further evaluation demonstrated few beds available in ADD 5 (n=6) and a reported level III bed utilization more than 500% in ADD 10. Table 1 displays current capacity and utilization. Only ADD 6 and 10 shows utilization approaching 80%. Table 2 shows bed numbers based on utilization or probability of delays, with average wait times. When calculating bed numbers based on 80% utilization, probability of wait is unacceptably high in some ADDs; wait times may exceed 10 hours. With a < 1% probability of delay, wait times range from 2-40 min.Conclusion(s): This analysis demonstrates varying need for NICU beds in the ADDs and state. Through the utilization of queuing theory, there is potential to impact public policy, where capacity could be adjusted based on calculated need assessment. At the hospital level, such calculations can be used to assess and adjust staffing needs. Detailed modeling utilizing queuing theory may be useful in determining need and access, including the impact of differing levels of care. Applying queuing theory as part of operations research can shape policy and operations in caring for the neonate.
Erlang-C Formula
NICU Capacity and UtilizationTable 1