Using queueing theory to determine operating room staffing needs

To meet American College of Surgeons criteria, Level I and II trauma centers are required to have in-house operating room (OR) staff 24 hours per day. According to the number of emergency cases occurring, hospitals may have varying needs for OR staffing during the night shift. Queueing theory, the analysis of historic data to provide optimal service while minimizing waiting, is an objective method of determining staffing needs during any time period. This study was done to determine the need to activate a backup OR team during the night shift at a designated, verified Level II trauma center.

The basic queueing theory formula for a single-phase, single-channel system was applied to patients needing the services of the OR. The mean arrival rate was determined by dividing the number of actual cases by 2,920 hours in a year (8 hours per night x 365). The mean service rate is determined by averaging the length of the actual cases during the period studied. Using the mean arrival rate and the mean service rate, the probability of two or more patients needing the OR at the same time was determined. This probability was used to reflect the likelihood of needing to activate the backup OR team. Simulation was then used to calculate the same probability and validate the results obtained from the queueing model.

All OR cases (n = 62) beginning after 11 PM and before 7 AM from July 1, 1996, through June 30, 1997, were analyzed. During the study period, the average arrival rate (A) was one patient every 5.9 days (0.0212 patient every hour), with an average service rate (mu) of 80.79 minutes per patient (0.7427 patients per hour). According to queueing theory, lambda = 0.0212 patients per hour, mu = 0.7427 patients per hour, lambda/mu = 0.0285, the probability of no patients being in the system (P0) = 0.9714, P1 = 0.0278, P> or =2 = 1 - (0.0278 + 0.9714) = 0.0008. The probability of two or more cases occurring simultaneously on the night shift is less than 0.1%.

In our institution, activation of a second OR team is unnecessary when the first team is busy with a case on the night shift because the likelihood of two cases occurring concurrently is less than one in a thousand. Queueing theory can be a valuable tool to use in determining the staffing needs of many hospital departments. Trauma centers should apply this mathematical model in optimizing the use of their operational resource.