Adding More Beds to the Emergency Department or Reducing Admitted Patient Boarding Times: Which Has a More Significant Influence on Emergency Department Congestion?

Introduction 

Materials and Methods 

Selection of Participants 

We used patient ED visit data for February 2006 as the base case, which included 5,751 total ED visits coded as a mean of 205 visits per day. We validated the sampled data used for the base case with census and mean length of stay data from earlier months in the same data set, February 2005 and October 2005. Detailed inputs used in the base case model appear in Figure 1 and Table 1.

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Figure 1. The simulated patient flow dodel with the base case values.

Table 1. Observed and simulated values for model elements.

	Process, Location, or Attribute	Observed Values	Source	Simulated Values	Assumptions
	Arrivals	205/day	Census data set	Poisson arrivals, average=205/day	70% of arrivals between noon and midnight
	Triage/ESI category	Percentage breakdown per ESI level: 1=2.4%, 2=25.4%, 3=45.8%, 4=13.2%,5=13.2%	Census data set	Poisson arrivals based on above average and percentage breakdown	Lower ESI values are prioritized throughout the model (ESI 4 seen before ESI 5; ESI 2 seen before ESI 3; ESI 1 seen first).
	Waiting area			No preset limit on how many patients can wait for placement in the main ED.	Patients wait if all ED beds are taken. They are moved to an urgent care or main ED bed on a first come, first served basis within their ESI category.
	Main ED	23 beds	Institutional information	23 beds	Patients in main ED first see a physician and then wait without physician (for diagnostic testing and treatment), then see a physician again before being admitted or discharged. Times are provided in Figure 1.
		3 attending physicians from 6 am to 10 pm		3 attending physicians
		2 attending physicians from 10 pm to 6 am
	Observation unit	1 attending physician, 23 beds	Institutional information	Not modeled	Patients admitted to the observation unit are modeled like those admitted to the hospital.
	Urgent care	7 beds	Institutional information	7 beds	Patients in urgent care first see a physician, then wait without physician, then are discharged. Times are provided in Figure 1.
		1 attending physician from 9 am to 9 pm		1 attending physician
				Always open
	Admission proportion	Percentage admitted per ESI level: 1=55%, 2=57%, 3=31%, 4=1%, 5=1%	Census data set	1=55%, 2=57%, 3=31%, 4=0%, 5=0%	Patient exits ED or is directed to admission according to percentage breakdown.
	Admission processing time	61 admissions per day at a rate of 2.5 patients per h (1 per 24 min)	Census data set+institutional information	Admitted patients are processed one at a time, at an average Poisson rate of 3 patients per h (1 per 20 min).	No ESI 4, 5 patients are admitted.
	Boarding	25 hallway beds	Institutional information.	No preset limit on how many patients can board	Admitted patients wait in boarding area (hallway) for inpatient bed.
	Leave without being seen	3-4%/day	Census data set	25% of ESI 3 leave if not seen by a physician after 90 min; 50% of ESI 4, 5 leave if not seen by a physician after 60 min

To model the flow of patients cared for in the ED, we defined and coded the locations, resources, processes, and routing policies. Second, we focused on the model input requirements as empirical data, estimates, or assumptions based on expert consensus statements.13, 14 Because the main goal of this work is to identify, measure, analyze, and manage our bottlenecks, we made several simplifications when coding the patient flow. For instance, we assumed in the simulation that all urgent care patients are discharged, despite a small number (an average of 2 per day) who were admitted during the study period. These and other assumptions and simplifications are in Figure 1 and Table 1.

Sensitivity Analyses 

To test the robustness of the results to changes in model assumptions and actual institutional data, we performed several univariate sensitivity analyses (Table 2):

•Increasing the number of ED beds from 23 to 33 in increments of 5 beds

•Varying the admitted patient departure rate from 1 patient every 25 minutes to 1 patient every 10 minutes in increments of 2.5 minutes

•Increasing the daily patient census by 15% to 236, following the same patient arrival distribution as in the base case

•Increasing and decreasing triage level proportions of ESI 3 with ESI 4 and 5 by 10%

•Increasing and decreasing treatment times of ESI 2 and 3 by 10%

•Increasing and decreasing admission rates of ESI 2 and 3 by 10%

•Increasing and decreasing left without being seen rates of ESI 3 with ESI 4 and 5 by 10%

Table 2. Sensitivity analysis for selected elements.⁎

	Process/Location	Data	Origin	Simulation Input/Sensitivity Analysis
	Arrivals, total	205/day	Census data set	Base: Assumed to follow a Poisson distribution, with average of 205/day
				Base+15%: Poisson with average=236/day
	Arrivals per ESI Category	Percentage breakdown per ESI level: 1=2.4%, 2=25.4%, 3=45.8%, 4=13.2%, 5=13.2%	Census data set	5% And 10% shifts between ESI=3 and ESI=4, 5: Base: 1=2.4%, 2=25.4%, 3=45.8%, 4=13.2%, 5=13.2% Base−5%: 1=2.4%, 2=25.4%, 3=43.6%, 4=14.3%, 5=14.3% Base−10%: 1=2.4%, 2=25.4%, 3=41.3%, 4=15.5%, 5=15.5% Base+5%: 1=2.4%, 2=25.4%, 3=48.2%, 4=12.0%, 5=12.00% Base+10%: 1=2.4%, 2=25.4%, 3=50.5%, 4=10.9%, 5=10.9%
	Main ED (number of beds)	23 beds	Institutional information	Base: 23 beds Base+5 beds: 28 beds Base+10 beds: 33 beds
	Main ED (treatment and evaluation times)	ESI 1: 15+90+10=115 min	Institutional information	5% And 10% shift in treatment and evaluation times for ESI 2 and 3
		ESI 2: 15+90+10=115 min ESI 3: 15+150+10=175 min ESI 4, 5: 15+90=105 min		Base treatment and waiting times in minutes for ESI 1=90, 2=90, 3=150, 4=90, 5=90 Base−5%: 1=90, 2=86, 3=143, 4=90, 5=90 Base−10%: 1=90, 2=81, 3=135, 4=90, 5=90 Base+5%: 1=90, 2=95, 3=158, 4=90, 5=90 Base+10%: 1=90, 2=99, 3=165, 4=90, 5=90
	Admission proportion	Percentage admitted per ESI level: 1=55%, 2=57%, 3=31%, 4=1%, 5=1%	Census data set	5% And 10% shift for ESI 2 and 3 admission rates Base: 1=55%, 2=57%, 3=31%, 4=1%, 5=1% Base−5%: 1=55%, 2=54%, 3=29%, 4=0%, 5=0% Base−10%: 1=55%, 2=51%, 3=28%, 4=0%, 5=0% Base+5%: 1=55%, 2=60%, 3=33%, 4=0%, 5=0% Base+10%: 1=55%, 2=63%, 3=34%, 4=0%, 5=0%
	Admission processing time	61 admissions per day=23.6 min per admission	Census data set	Base: Poisson distribution, average of 20 min per admission Analyzed: 10, 12.5, 15, 17.5, 20, 22.5 and 25 min per admission
	Leave without being seen	3-4%/day	Census data set and expert opinion	Where (x, y) is the probability of x that the patient leaves after waiting y minutes or more for placement into an ED or urgent care bed
				Base: (0.25, 90) for ESI=3 and (0.5, 60) for ESI=4, 5
				0%: (0, 90) for ESI=3 and (0, 60) for ESI=4, 5
				25%: (0.25, 90) for ESI=3 and (0.25, 60) for ESI=4, 5
				75%: (0.75, 90) for ESI=3 and (0.75, 60) for ESI=4, 5
				100%: (1.0, 90) for ESI=3 and (1.0, 60) for ESI=4, 5
				Base−66.7%: (0.25, 30) for ESI=3 and (0.5, 20) for ESI=4, 5
				Base−33.3%: (0.25, 60) for ESI=3 and (0.5, 40) for ESI=4, 5
				Base+33.3%: (0.25, 120) for ESI=3 and (0.5, 60) for ESI=4, 5
				Base+66.7%: (0.25, 150) for ESI=3 and (0.5, 80) for ESI=4, 5

⁎ The base case values are in bold.

Results 

We validated the model by comparing model length of stay with actual institution length of stay. Table 3 displays the similarity between daily census and length of stay when comparing the model to 3 months of actual institutional data: February 2006 (base case), October 2005, and February 2005. ED census was similar across each of the 3 months, with the greatest difference being 4 patients, or a 2.0% difference. Model length of stay was also similar to each month's length of stay, with the greatest difference being 33 minutes, or a 12.1% difference.

Table 3. Model validation.⁎

	Model	February 2006	October 2005	February 2005
	Daily patient census	205	209	204
	Actual LOS, min	273	251	259
	Model LOS, min	240	249	237
	% Difference in LOS from actual	−12.1%	−0.8%	−8.6%

LOS, Length of stay.

⁎ Comparison of model outputs with 3 separate months of institutional data. Bolded area indicates the month on which model inputs and census were developed.

Table 4A, Table 4B displays results of the 4 simulations. When keeping the departure rate constant at 1 patient per 20 minutes and increasing ED beds from 23 to 28, mean length of stay increased from 240 to 247 minutes (95% CI 0.8-12.6 minutes). When keeping the departure rate constant at 1 patient per 15 minutes and increasing ED beds from 23 to 28, there was an increase in mean length of stay from 218 to 225 minutes (95% CI 2.3 to 11.3 minutes).

Table 4A. Length of stay with varying the number of ED beds.

	Departure Rate/min	23 Beds, min	28 Beds, min	Difference, min	95% CI
	1 Patient/20	240 min	247 min	+7	0.8–12.6⁎
	1 Patient/15	218 min	225 min	+7	2.3–11.3⁎

⁎ Significant: 95% CI for the pairwise differences does not include 0.

Table 4B. Length of stay with varying the admitted patient departure rate.

	Departure Rate, No. Beds	1 Patient/20 min	1 Patient/15 min	Difference, min	95% CI
	23	240 min	218 min	−22	16.8–26.2⁎
	28	247 min	225 min	−22	15.8–27.1⁎

⁎ Significant: 95% CI for the pairwise differences does not include 0.

When keeping the number of beds constant at 23 and increasing the departure rate from 1 patient every 20 minutes to 1 every 15 minutes, there was a reduction in the mean length of stay (Δ 22 minutes; 95% CI 16.8 to 26.2 minutes). When keeping the number of ED beds constant at 28 and increasing the departure rate from 1 patient every 20 minutes to 1 every 15 minutes, there was a reduction in the mean length of stay (Δ 22 minutes; 95% CI 15.8 to 27.1 minutes).

Figure 2 is the sensitivity analysis of the ED length of stay for a set of ED admitted patient departure rates for an ED census of 205. It also depicts a variation in ED beds (23, 28, and 33 beds) and shows the decrease in length of stay as departure rate increases, regardless of the number of beds. Beyond the results in Table 4A, Table 4B, there were no other differences in length of stay observed from varying the number of beds. With a daily census of 205, there was a reduction in mean length of stay when increasing the admitted patient departure rate from 1 every 25 minutes to 1 every 15 minutes in increments of 2.5 minutes for 23-, 28-, and 33-bed settings.

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Figure 2. ED length of stay over a set of ED admitted patient departure rates and a variation in ED beds for an ED census of 205.

We conducted several other sensitivity analyses to evaluate the effect of altering 4 model inputs on length of stay (Figure 3). The figures show that when altering the daily patient census, admission proportions, acuity levels, treatment times, and there was an ongoing reduction in length of stay when increasing the admitted patient departure rate from 1 every 25 minutes to 1 every 15 minutes in a 23-bed setting across the sensitivity analyses. The same is true for the analysis with an increased ED patient census to 236 when increasing the admitted patient departure rate from 1 every 25 minutes to 1 every 17.5 minutes for 23-, 28-, and 33-bed settings.

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Figure 3. Sensitivity analysis. Effect of length of stay on altering model inputs over different number of beds and a range of patient departure rates.

Table 5A, Table 5B shows the results where the sensitivity analysis testing was the same as the base case analysis, but with a 15% increase in daily patient volume to 236 inputted into the model. The results demonstrate no differences in overall ED length of stay.

Table 5A. Length of stay with varying the number of ED beds at a 15% increase in daily patient census.

	Departure Rate/min	23 Beds	28 Beds	Difference, min	95% CI
	1 Patient/20	482 min	504 min	+22	−22.3to66.4
	1 Patient/15	404 min	422 min	+18	−59.8to24.1

Table 5B. Length of stay with varying the admitted patient departure rate at a 15% increased daily patient census.

	Departure Rate	1 Patient/20 min	1 Patient/15 min	Difference, min	95% CI
	23 Beds	482 min	404 min	−78	33.3–121.1⁎
	28 Beds	504 min	422 min	−82	36.9–125.8⁎

⁎ Significant: 95% CI for the pairwise differences does not include 0.0

Finally, we completed a sensitivity analysis on patients leaving without being seen. We varied both the threshold wait time at which ESI 3 and ESI 4 and 5 patients would wait before leaving the waiting room and the proportion of patients who left without being seen at the base threshold wait time. We found that varying these parameters has little effect on overall length of stay. Holding the threshold wait times at which patients will leave without being seen constant at 90 minutes for ESI 3 patients and 60 minutes for ESI 4 and 5 patients while increasing the proportion who will leave without being seen at those times from 0% to 100% reduced mean length of stay by only 10 minutes (4.1%). Holding the proportion of patients who left without being seen at a given threshold wait time constant at 25% for ESI 3 patients and 50% for ESI 4 and 5 patients increased the mean length of stay by only 8.3 minutes (3.5%).

Limitations 

A computer simulation model is a theoretical instrument based on rules, generalizations, and assumptions. The ability to predict actual outcomes depends on the validity of the assumptions made. We used inputs and assumptions based on institutional data and expert physician experience. These data and assumptions may not be valid in other settings. However, other work supports these assumptions. For example, there is a correlation between waiting room times and ED congestion and leaving without being seen.15, 16

We also made generalizations and simplifications to the actual institution experience when developing the model. We treated all patients admitted to the observation unit as if they were admitted to the hospital. The model was developed with as much actual institutional data as possible but, for example, during the study time period patient boarding times were not captured. Therefore, in the model we used total ED length of stay as a marker for congestion and an indirect indicator of boarding time. We also used the admitted patient departure rate as an indirect method of changing the amount of time that patients board in the ED. We presumed that by increasing the rate at which admitted patients depart the ED we are decreasing the boarding times. While necessary for modeling a complex environment, these generalizations, simplifications, and indirect measures may limit the scope of our results.

When making model generalizations and simplifications, one must remember that the model is not a perfect fit to the actual ED: there was a 33-minute or 12.1% difference in length of stay between modeled and observed data. We still believe the model allows estimation of effects even if discrete values vary from actual.

Although the results presented here are based on institutional data, our model is based on 1 ED. Other sites may experience different characteristics and require specific inputs to measure results in their institution.

Discussion 

Our simulation allows the effect of ED bottleneck intervention to be assessed. In this ED, the admitted patient departure rate is the key bottleneck. If alterations are made in other areas first, ED length of stay and congestion will likely be only marginally affected. Recent data confirm the paradox that a bigger ED alone did not improve—and actually worsened—ED length of stay and admitted patient boarding times.17

Understandably, many concepts in operations research seem counterintuitive. On first glance, it would seem that adding ED beds would allow a department to treat more patients quickly by decreasing waiting room times. However, when increasing the number of patients processed through the ED without increasing the rate at which patients depart the ED, length of stay remains the same or increases. In an analogous manner, one can imagine the ED to be a pipe and patients as water passing through the pipe. If we enlarge the diameter of the middle of the pipe but leave the end the same, we analogously have increased the number of ED beds without improving the departure rate.

Researchers have proposed methods that coordinate hospital census and drivers of inpatient congestion with ED patient outflow. Litvak et al proposed that the artificial variability of elective surgery scheduling and elective inpatient admissions affect inhospital congestion, and a decrease in this variability would improve ED output and subsequently ED congestion.18 Others have reinforced these concepts by showing a correlation between hospital occupancy and ED length of stay,19 as well as a correlation between increased scheduled elective surgeries and ED length of stay.20 Some have proposed that boarding admitted patients outside the confines of the ED, in the inpatient hallways, would be a better solution to long inpatient boarding times in the ED.21, 22 All aforementioned strategies decrease the amount of time patients spend boarding in the ED, decrease ED length of stay, and free ED bed space to treat new patients in need of care, an opportunity lost otherwise.23

By modeling our ED through computer simulation, we show that improving the rate at which admitted patients depart the ED produced an improvement in ED length of stay and therefore congestion, whereas increasing the number of ED beds did not.