Using queueing theory to determine operating room staffing needs

Background: To meet American College of Surgeons criteria, Level I and II t rauma centers are required to have in-house operating room (OR) staff 24 ho urs per day. According to the number of emergency cases occurring, hospital s may have varying needs for OR staffing during the night shift. Queueing t heory, the analysis of historic data to provide optimal service while minim izing waiting, is an objective method of determining staffing needs during any time period. This study was done to determine the need to activate a ba ckup OR team during the night shift at a designated, verified Level II trau ma center. Methods: The basic queueing theory formula for a single-phase, single-chann el 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 determ ined 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 p robability was used to reflect the likelihood of needing to activate the ba ckup OR team. Simulation was then used to calculate the same probability an d validate the results obtained from the queueing model. Results: All OR cases (n = 62) beginning after II PM and before 7 AM from J uly 1, 1996, through June 30, 1997, were analyzed. During the study period, the average arrival rate (lambda) was one patient every 5.9 days (0.0212 p atient 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 (P-0) = 0.9714, P-1 = 0.0278, P >(2) = 1 - (0.0278 + 0.9714)= 0.0008. The probability of two or m ore cases occurring simultaneously on the night shift is less than 0.1%. Conclusion: In our institution, activation of a second OR team is unnecessa ry when the first team is busy with a case on the night shift because the l ikelihood of two cases occurring concurrently is less than one in a thousan d. Queueing theory can be a valuable tool to use in determining the staffin g needs of many hospital departments. Trauma centers should apply this math ematical model in optimizing the use of their operational resource.