Obstetric operating room staffing and operating efficiency using queueing theory

Abstract

Introduction: Strategies to achieve efficiency in non-operating room locations have been described, but emergencies and competing priorities in a birth unit can make setting optimal staffing and operation benchmarks challenging. This study used Queuing Theory Analysis (QTA) to identify optimal birth center operating room (OR) and staffing resources using real-world data.

Methods: Data from a Level 4 Maternity Center (9,626 births/year, cesarean delivery (CD) rate 32%) were abstracted for all labor and delivery operating room activity from July 2019-June 2020. QTA has two variables: Mean Arrival Rate, λ and Mean Service Rate µ. QTA formulas computed probabilities: P₀ = 1-(λ/ µ) and P_n = P₀ (λ/µ)ⁿ where n = number of patients. P_0…n is the probability there are zero patients in the queue at a given time. Multiphase multichannel analysis was used to gain insights on optimal staff and space utilization assuming a priori safety parameters (i.e., 30 min decision to incision in unscheduled CD; ≤ 5 min for emergent CD; no greater than 8 h for nil per os time). To achieve these safety targets, a < 0.5% probability that a patient would need to wait was assumed.

Results: There were 4,017 total activities in the operating room and 3,092 CD in the study period. Arrival rate λ was 0.45 (patients per hour) at peak hours 07:00-19:00 while λ was 0.34 over all 24 h. The service rate per OR team (µ) was 0.87 (patients per hour) regardless of peak or overall hours. The number of server teams (s) dedicated to OR activity was varied between two and five. Over 24 h, the probability of no patients in the system was P₀ = 0.61, while the probability of 1 patient in the system was P₁ = 0.23, and the probability of 2 or more patients in the system was P_≥2 = 0.05 (P₃ = 0.006). However, between peak hours 07:00-19:00, λ was 0.45, µ was 0.87, s was 3, P₀ was 0.48; P₁ was 0.25; and P_≥2 was 0.07 (P₃ = 0.01, P₄ = 0.002, P₅ = 0.0003).

Conclusion: QTA is a useful tool to inform birth center OR efficiency while upholding assumed safety standards and factoring peaks and troughs of daily activity. Our findings suggest QTA is feasible to guide staffing for maternity centers of all volumes through varying model parameters. QTA can inform individual hospital-level decisions in setting staffing and space requirements to achieve safe and efficient maternity perioperative care.

Keywords: Anesthesia; Efficiency; Obstetric; Operating room; Queueing; Staffing.

Fig. 1

Conceptual diagram of queueing theory nodes and characteristics. Patients arrive at rate = λ, then await service for time = w, over queue length = L. Server teams are specified in analysis, with service time (s) defined as time required for treatment provided at service rate per server team = µ. Service nodes are varied in analysis to identify system performance for wait times and utilization. After service, patients then depart the system. Six distinct parameters are shown: 1) the arrival process; 2) the service and departure process; 3) the number of servers available; 4) the queueing discipline (in obstetric operations, the discipline is priority queue); 5) the queue/system capacity; 6) and the size of the client population

Fig. 2

Characteristics of obstetric operating room activities by time of day and duration of overlaps. A Frequency distribution of 2 or more simultaneous operating room activities by time of day. B The same data depicted as frequency distribution of overlapping operating room activities by duration of overlap in minutes

Fig. 3

Poisson distribution of duration of operating room time in minutes