Using queueing theory to determine operating room staffing needs

Area of Science:

• Healthcare Operations Research
• Trauma Surgery Management
• Applied Mathematics in Medicine

Background:

• Level I and II trauma centers require 24/7 in-house operating room (OR) staff per American College of Surgeons standards.
• Hospital OR staffing needs fluctuate based on emergency case volume, particularly during night shifts.
• Queueing theory offers an objective method for analyzing historical data to optimize service delivery and minimize waiting times.

Purpose of the Study:

• To determine the necessity of activating a backup OR team during night shifts at a verified Level II trauma center.
• To apply queueing theory to assess OR staffing requirements during off-peak hours.
• To optimize the utilization of surgical resources in trauma centers.

Main Methods:

• Applied basic queueing theory formulas for a single-phase, single-channel system to OR patient needs.
• Calculated mean arrival rate by dividing annual cases by 2,920 night hours (8 hours/night x 365 days).
• Determined mean service rate by averaging the duration of actual OR cases and used simulation to validate queueing model results.

Main Results:

• Analyzed 62 OR cases occurring between 11 PM and 7 AM over one year.
• Calculated an average arrival rate (λ) of 0.0212 patients/hour and a mean service rate (μ) of 0.7427 patients/hour.
• Queueing theory predicted a probability of less than 0.1% (0.0008) for two or more simultaneous night OR cases.

Conclusions:

• Activation of a second OR team is deemed unnecessary when the primary team is engaged, given the low probability of concurrent cases.
• Queueing theory is a valuable tool for determining staffing needs across various hospital departments.
• Trauma centers should leverage mathematical modeling, such as queueing theory, to optimize operational resources.