Journal of Emergencies, Trauma, and Shock

: 2019  |  Volume : 12  |  Issue : 4  |  Page : 225--226

What's new in emergencies, trauma and shock? Using queuing theory to optimize the emergency department triage process

Leon D Sanchez, Joshua W Joseph 
 Department of Emergency Medicine, Beth Israel Deaconess Medical Center, Boston, MA, USA

Correspondence Address:
Dr. Leon D Sanchez
Department of Emergency Medicine, Beth Israel Deaconess Medical Center, Boston, MA

How to cite this article:
Sanchez LD, Joseph JW. What's new in emergencies, trauma and shock? Using queuing theory to optimize the emergency department triage process.J Emerg Trauma Shock 2019;12:225-226

How to cite this URL:
Sanchez LD, Joseph JW. What's new in emergencies, trauma and shock? Using queuing theory to optimize the emergency department triage process. J Emerg Trauma Shock [serial online] 2019 [cited 2020 Jul 11 ];12:225-226
Available from:

Full Text

The article “Application of Queuing Theory to Optimize the Triage Process in a Tertiary Emergency Care ('ER') Department” is both a clear introduction to queuing theory and an excellent example of its application to emergency department (ED) operations. Many ED processes are amenable to queuing analysis and understanding these concepts and can help ED providers and administrators make resource allocation decisions in a way that maximizes the utility of limited resources.

The triage process examined by Carrillo AM et al. is a good starting point for applying queuing theory for several reasons. Most EDs will have high-quality data from triage with all of the elements necessary for a queuing analysis (number of triage nurses, patient arrivals, and process length). The triage process itself is short, discrete, and reproducible and has a limited number of inputs, which means that it resembles many of the classic applications of queuing theory, such as network connections or customer service times. Triage itself also tends to have a fairly predictable length of time with limited variability. While many EDs do not measure the time patients spend waiting before triage, this is not logistically difficult to do and may provide valuable information beyond that required for the queuing analysis itself.[1]

Another benefit of understanding and applying queuing theory is the ability to predict when and to what extent waiting times will exceed a particular threshold, which a less nuanced view of staffing will tend to underestimate substantially. It is a commonly held belief that staffing toward an average rate of patient arrivals will tend to “even out” over time, as periods of decreased capacity are matched by periods of excess capacity relative to demand. However, queuing theory forces us to confront the fact that periods of excess capacity simply represent wasted time if there are no new patients to be seen. Similarly, during times when patient arrivals exceed the rate at which patients are triaged, additional arrivals will not result in a linear increase in waiting times but will instead increase exponentially unless arrivals slow or capacity increases.

For example, in an ED in which triage takes 5 min on average, and where about 12 patients arrive per hour, many administrators might assign only one triage nurse per hour, reasoning that this means that patients will have no waiting time and will not require any excess staffing. However, because patients do not arrive at fixed intervals and instead tend to follow a Poisson process, waiting times will start to increase very quickly once the utilization rate reaches 80%, well below the predicted 12 patients per hour. Furthermore, in the event that several patients come in quick succession, as is common after a motor vehicle collision, if the triage nurses do not have reserve capacity, waiting times in such a system will quickly spiral out of control.

While there have been a number of successful applications of queuing theory to processes within the ED,[2],[3] Carrillo AM et al. have provided an example that is relatively straightforward for readers to replicate at their own institution. Their calculations are clearly explained and are not contingent on the use of expensive software or private consulting services. For those interested in exploring the use of queuing theory, there are a number of online and open-source calculators available that allow you to input different values for the key variables (servers, patients, and process time) and can output waiting times and the distribution of the number of people waiting in the queue.[4],[5]

As ED providers and administrators become more facile with queuing theory, they can more easily identify bottlenecks where allocating additional resources can lead to the greatest benefit. While the operations of an entire ED are a complex system, involving the interaction of many different interlocking queues, queuing theory provides the fundamental building blocks from which more sophisticated models, such as discrete event simulations, can be built. Queuing models can also be used to examine the discrepancies between the predicted performance of a process modeled by a queue and real-life performance, which can reveal human factors such as fatigue and cognitive load, which can have significant effects on throughput.[6],[7],[8]

Ultimately, the article by Carrillo AM et al. represents a substantial achievement – not only by demonstrating an immediate, measurable improvement in the delivery of care but also by highlighting the importance of queuing theory for future improvements in ED operations.


1Houston C, Sanchez LD, Fischer C, Volz K, Wolfe R. Waiting for triage: Unmeasured time in patient flow. West J Emerg Med 2015;16:39-42.
2Green LV, Soares J, Giglio JF, Green RA. Using queueing theory to increase the effectiveness of emergency department provider staffing. Acad Emerg Med 2006;13:61-8.
3Wiler JL, Bolandifar E, Griffey RT, Poirier RF, Olsen T. An emergency department patient flow model based on queueing theory principles. Acad Emerg Med 2013;20:939-46.
4Available from: [Last accessed on 2019 Jun 11].
5Available from: [Last accessed on 2019 Jun 11].
6Joseph JW, Henning DJ, Strouse CS, Chiu DT, Nathanson LA, Sanchez LD. Modeling hourly resident productivity in the emergency department. Ann Emerg Med 2017;70:185-90.
7Joseph JW, Davis S, Wilker EH, Wong ML, Litvak O, Traub SJ, et al. Modelling attending physician productivity in the emergency department: A multicentre study. Emerg Med J 2018;35:317-22.
8Westbrook JI, Coiera E, Dunsmuir WT, Brown BM, Kelk N, Paoloni R, et al. The impact of interruptions on clinical task completion. Qual Saf Health Care 2010;19:284-9.