Question 2. Emergency Department Boarding

Crowding in hospitals is a nationwide problem that can result in emergency department (ED) boarding. ED boarding is the practice of holding patients in the ED when there are no inpatient beds available. It occurs when patients present to the ED (either walk-in or by ambulance), and the decision is made to admit them to the hospital, but no inpatient beds are immediately available, thus they continue staying in the ED. ED boarding often results in poor patient outcomes and higher hospital length of stay.

A major hospital in Cleveland has hired you to help them develop a simulation model of their ED and hospital with the goal of studying the ED boarding issue. In Phase I of the project, you only need to develop a simulation model in Arena. In Phase II, you will use the model to compare multiple strategies to mitigate the ED boarding problem. Given the limited time in this exam, I only ask you to work on Phase I of the project (i.e., develop the model in Arena).

Arrivals to the ED occur either by ambulance or walk-in. The interarrival time for walk-ins follows an exponential distribution with a mean of 15 minutes. The interarrival time for ambulance arrivals follows an exponential distribution with a mean of 18 minutes. Once patients arrive at the ED (walk-in or by ambulance), they will be treated similarly. First, they will go through the triage process to determine the severity of their condition. This process is done by one of the 3 nurses at check-in, which takes between 5 to 10 minutes, uniformly distributed. Patients will be assigned a three-level severity index, with 1 being the most severe and 3 being the least severe. Historical data suggest that 20% of patients are assigned severity 1, 50% are assigned severity 2, and 30% are assigned severity 3, on average.

Next, they will wait in the waiting area until a room becomes available in the ED. The ED has 12 rooms in total. Once a room is available, patients will be transferred to the room and get treated according to their severity index (i.e., patients with severity 1 will be served first, then severity 2, and finally severity 3). The treatment time for each patient follows an exponential distribution with a mean of 55 minutes for severity 1, 45 minutes for severity 2, and 35 minutes for severity 3 patients.

After the treatment, severity 2 and 3 patients are discharged and leave the system. However, 67% of severity 1 patients are admitted to the hospital for further observation and treatment, while the remaining 33% are discharged and leave the system. If no inpatient bed is immediately available, these patients have to wait somewhere in the ED (e.g., in the hallways), resulting in ED boarding. Assume that the hospital has dedicated 30 inpatient beds to accommodate patients admitted to the hospital from the ED. The length of stay in the hospital follows an exponential distribution with a mean of 24 hours, after which the patients are discharged and leave the system.

We need to create a simulation model in Arena for Phase I of this project.