Arrivals follow the clock
Most emergency departments see their fewest patients in the early morning and their most from late morning through the evening. The daily total can be steady for months while the hourly shape decides whether patients wait.
That shape is the input most staffing plans leave out. A schedule built from daily volume can have the right number of provider hours and still put them in the wrong places.
Door-to-provider time
Door-to-provider time is how long a patient waits from arrival until a provider first sees them. It drives patients leaving without being seen, and it's the number that changes first when coverage falls behind arrivals. In QSimHealth, the wait reported for each hour is this time: arrival to the start of treatment, averaged over every patient who arrived in that hour across a simulated year.
Same hours, two schedules
Example assumptions, not benchmarks. An ED sees about 81 patients a day, from about 1 an hour before dawn to about 5 an hour at midday. MD visits average 20 minutes and vary from patient to patient. Both schedules use 48 MD hours a day.
- Flat: two MDs around the clock.
- Shaped: one MD from 10pm to 7am, two in the early morning and evening, three from 9am to 6pm.
| Schedule | Average wait | 1am | 5am | 10am | 2pm | 6pm | 10pm |
|---|---|---|---|---|---|---|---|
| Flat | 12.1 min | 2 | 1 | 9 | 17 | 20 | 9 |
| Shaped | 8.9 min | 37 | 13 | 2 | 2 | 7 | 16 |
Hourly columns are average wait in minutes for patients arriving in that hour. Each schedule was run for a simulated year.
Shaping the schedule cuts the daytime wait to a few minutes and lowers the daily average from 12.1 to 8.9 minutes. But the overnight MD now works alone, and the worst hour moves to 1am at 37 minutes. Neither schedule is the answer. The comparison shows where the next change should go: back toward the late evening and the first hours of the night.
A study at an urban ED found the same kind of gain in practice. On the four days of the week where total provider hours didn't change, moving provider hours to match arrivals cut the number of patients who left without being seen by 21.7%, even with 5.5% more arrivals.1
What would happen if volume grows 20%?
We ran the shaped schedule again with every hour's arrivals up 20%, to about 97 patients a day. The daily average wait rises from 8.9 to 11.8 minutes and the worst hour to 40 minutes at 1am. Daytime waits stay short, because three MDs absorb the growth. The strain lands overnight and in the late evening.
That's the kind of answer a growth plan needs before it asks for headcount. For what an added shift would buy, and where, see locum cost vs. patient wait.
Emergency department capacity planning
- Start from arrivals by hour of day, averaged over a season or a year.
- Enter provider coverage by hour, with separate visit times for MDs, PAs and NPs.
- Look at the wait at each hour, not the daily average.
- Test the change you're considering: a moved shift, an added provider, a volume forecast. Compare the scenarios side by side with cost per day.
Sources
- Green LV, Soares J, Giglio JF, Green RA. Using queueing theory to increase the effectiveness of emergency department provider staffing. Academic Emergency Medicine 2006;13(1):61–68. doi:10.1197/j.aem.2005.07.034