Queueing theoretic analysis of labor and delivery

Matthew Gombolay, Toni Golen, Neel Shah, Julie Shah

Childbirth is a complex clinical service requiring the coordinated support of highly trained healthcare professionals as well as management of a finite set of critical resources (such as staff and beds) to provide safe care. The mode of delivery (vaginal delivery or cesarean section) has a significant effect on labor and delivery resource needs. Further, resource management decisions may impact the amount of time a physician or nurse is able to spend with any given patient. In this work, we employ queueing theory to model one year of transactional patient information at a tertiary care center in Boston, Massachusetts. First, we observe that the M/G/∞ model effectively predicts patient flow in an obstetrics department. This model captures the dynamics of labor and delivery where patients arrive randomly during the day, the duration of their stay is based on their individual acuity, and their labor progresses at some rate irrespective of whether they are given a bed. Second, using our queueing theoretic model, we show that reducing the rate of cesarean section - a current quality improvement goal in American obstetrics - may have important consequences with regard to the resource needs of a hospital. We also estimate the potential financial impact of these resource needs from the hospital perspective. Third, we report that application of our model to an analysis of potential patient coverage strategies supports the adoption of team-based care, in which attending physicians share responsibilities for patients.