Improve the efficiency in the Emergency Department with Queueing Modeling and Simulation

Qing Meng, Megan Song, Alex VanderEls

December 6th, 2016

IntroductionBackground 4,176

1995 2005

115.3 million

96.5 million 3795

The Emergency Department Visits

The Number of Hospitals

IntroductionProblem: 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

Queueing Theory in the Emergency Department

Emergency Department

Doctor/Nurse

Queueing ModelingINPUT

λ = mean arrival rate = 1/ interarrival timeμ = mean service rate = 1/ service time s = number of servers# of Priority ClassDistribution 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

Data IntroductionParameter 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 hoursthe door-to-exit time - 3.73 hoursService time - 2.76 hours

0.36/hr 1/2.76= 0.36

Servers 6.5/hr new arrivals2.76 hours length of stay

20 6.5*2.76= 17.94

Priority Class 5 5

Data IntroductionDistribution 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

Data IntroductionDistribution 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%

M/M/s model resultsMean arrival rate = 6.5 patients / hrMean service rate = 0.36 patients/ hrServers = 20

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

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

Average length of stay of each priority

Queueing Model vs. SimulationWaiting 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

Simulation● Design custom processes by defining:

○ Activities

○ Resources

○ Inputs

Scenario 1

Scenario 2

Output (Scenario 2)

Key Output: Scenario 1 Vs Scenario 2

RecommendationLabor 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

Thanks!Q&A