The document discusses using queueing modeling and simulation to improve efficiency in the emergency department. It presents a queueing model to analyze patient wait times and length of stay with different staffing levels. A simulation is also created to model patient flow more realistically. The simulation shows that a team approach to triage leads to better outcomes than staffing with only nurses. Key recommendations include adjusting staffing levels based on patient arrival patterns and utilizing teams of doctors and nurses for triage.

1. Improve the efficiency in the Emergency Department
with Queueing Modeling and Simulation
Qing Meng, Megan Song, Alex VanderEls
December 6th, 2016

2. Introduction
Background
4,176
1995 2005
115.3 million
96.5 million 3795
The Emergency Department Visits
The Number of Hospitals

3. Introduction
Problem:
Reduce the waiting time and length of stay in the Emergency Room
1. How much labor should be arranged during different time of a day
2. Who should staff the triage area
Model: Queueing Model
Simulation : More processes and Roles
Recommendation

4. Queueing Theory in the Emergency Department
Emergency Department
Doctor/Nurse

5. Queueing Modeling
INPUT
λ = mean arrival rate
= 1/ interarrival time
μ = mean service rate
= 1/ service time
s = number of servers
# of Priority Class
Distribution of Priority
Class
OUTPUT
Wq = waiting time in queue
(excludes service time) for
each individual
Length of stay
M/M/s
- All patients are
treated equally
- Number of visits per
hour is a constant
M/M/s
nonpreemptive
priorities

6. Data Introduction
Parameter Original Data Data in Our Model Rationale
Arrival Rate 155/day 6.5/hr 155/24=6.5
Service Rate door-to-doctor time (waiting time) - 0.97 hours
the door-to-exit time - 3.73 hours
Service time - 2.76 hours
0.36/hr 1/2.76= 0.36
Servers 6.5/hr new arrivals
2.76 hours length of stay
20 6.5*2.76= 17.94
Priority Class 5 5

7. Data Introduction
Distribution of Arrivals in Hours
Time (am) 1 2 3 4 5 6 7 8 9 10 11 12
Arrivals 4.2 3.5 3.4 3.2 3 3 3.2 3.5 4.2 6.6 8.3 9.8
Time (pm) 1 2 3 4 5 6 7 8 9 10 11 12
Arrivals 10.2 9.3 9.3 9.5 9.3 9 8.6 8.6 7 7 6.7 5.6

8. Data Introduction
Distribution of Priority Classes
Immediate Emergency Urgent Semi-Urgent Nonurgent Discharge
A Nurse For Triage
1.2% 11% 43.3% 36.3% 8.2% 0
A Group (A Doctor and A Nurse) For Triage
0.6% 5.6% 22.1% 18.5% 4.2% 48.9%

9. M/M/s model results
Mean arrival rate = 6.5 patients / hr
Mean service rate = 0.36 patients/ hr
Servers = 20

10. M/M/s model Results
Patients : Servers ~ 1 : 3
Mean arrival rate
(patients/hr)
Mean service rate
(patients/hr)
Servers Length of stay
(min)
Waiting time (min)
6.5 0.36 20 215 48
3 0.36 10 215 49
4 0.36 13 210 43
8 0.36 24 225 58

11. Average waiting time of M/M/s and
nonpreemptive priority M/M/s models
Mean arrival rate = 6.5 / hr
Mean service rate = 0.36 / patients/ hr
Servers = 20, 20, 12

12. Average length of stay of each priority

13. Queueing Model vs. Simulation
Waiting time = door-to-doctor time
Service time = doctor-to-exit time
Doctors and nurses are equally
One doctor/nurse serve one patient
at a time
Different steps for service
Waiting time and service time at
each step
Doctors and nurses engage in
different activities
One doctor/nurse serve multiple
patients at mean time

14. Simulation
● Design custom processes by defining:
○ Activities
○ Resources
○ Inputs

15. Scenario 1

16. Scenario 2

17. Output (Scenario 2)

18. Key Output: Scenario 1 Vs Scenario 2

19. Recommendation
Labor Arrangement
- When 3-4 patients arrive per hour in the midnight, a labor capacity of 10-13 servers
should be assigned to keep waiting time less than 60 minutes
- When 8 patients arrive per hour in the afternoon, a labor capacity of 24 servers should
be assigned to keep waiting time less than 60 minutes
- Most labor force should be in the time period of 11am - 11pm, instead of a traditional
8am-5:30 pm shift
Resource Allocation - A Team of Doctor and A Nurse Vs A Nurse Role in the triage process
- Teamwork wins
- Opportunity for crosstraining

20. Thanks!
Q&A