Tucker J B, Barone J E, Cecere J, Blabey R G, Rha C K
Stamford Hospital/Columbia University College of Physicians and Surgeons, CT 06904, USA.
J Trauma. 1999 Jan;46(1):71-9. doi: 10.1097/00005373-199901000-00012.
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.
为符合美国外科医师学会的标准，一级和二级创伤中心需要每天24小时配备内部手术室（OR）工作人员。根据急诊病例的数量，医院在夜班期间对手术室人员配备可能有不同的需求。排队论是一种通过分析历史数据来提供最佳服务并尽量减少等待时间的方法，是确定任何时间段人员配备需求的一种客观方法。本研究旨在确定在指定的、经过验证的二级创伤中心夜班期间激活备用手术室团队的必要性。
将单相、单通道系统的基本排队论公式应用于需要手术室服务的患者。平均到达率通过将实际病例数除以一年中的2920小时（每晚8小时×365天）来确定。平均服务率通过对研究期间实际病例的时长求平均值来确定。利用平均到达率和平均服务率，确定两个或更多患者同时需要手术室的概率。该概率用于反映激活备用手术室团队的可能性。然后使用模拟来计算相同的概率并验证从排队模型获得的结果。
分析了1996年7月1日至1997年6月30日期间晚上11点之后和早上7点之前开始的所有手术室病例（n = 62）。在研究期间，平均到达率（A）为每5.9天有一名患者（每小时0.0212名患者），平均服务率（μ）为每名患者80.79分钟（每小时0.7427名患者）。根据排队论，λ = 每小时0.0212名患者，μ = 每小时0.7427名患者，λ/μ = 0.0285，系统中无患者的概率（P0） = 0.9714，P1 = 0.0278，P≥2 = 1 - （0.0278 + 0.9714） = 0.0008。夜班期间两个或更多病例同时发生的概率小于0.1%。
在我们机构，当第一个手术室团队在夜班期间忙于一个病例时，激活第二个手术室团队是不必要的，因为两个病例同时发生的可能性小于千分之一。排队论可以是确定许多医院科室人员配备需求的一个有价值的工具。创伤中心应应用此数学模型来优化其运营资源的使用。
