Hospital Emergency Department Flow: Triage, Priority Queue…

Queueing Networks in Healthcare

A queueing network is a mathematical model used to describe the behavior of systems with multiple queues. In an emergency department (ED), patients arrive at random intervals, are triaged based on severity, and then wait for treatment or imaging before being discharged. This system can be modeled as a queueing network where each node represents a stage in the patient’s journey through the ED.

Queueing theory helps healthcare administrators understand how to allocate resources efficiently, minimize waiting times, and improve overall patient satisfaction.

Key Components of the Model

The model includes several key components: Poisson arrivals represent the random nature of patient arrival times; a triage desk sorts patients into priority levels; a priority waiting room ensures that higher-priority patients are treated first; treatment bays where doctors provide care; an imaging door for diagnostic procedures; and finally, discharge. Each component interacts with others to form a complex network.

By tuning the number of bays and staff, the simulation allows users to explore how these changes affect patient flow and overall performance metrics.

live demo · related simulation● LIVE

Mathematical Foundations

The model is grounded in several key mathematical concepts. Erlang C is used to calculate the probability that a patient will have to wait for service, given the number of servers (doctors) and the arrival rate of patients. Little’s law relates the average number of patients in the system to the arrival rate and the average time spent by each patient in the system.

Cobham’s priority formula helps determine the optimal allocation of resources based on patient priorities.

Real-World Applications

Understanding these models can help hospitals design more efficient ED layouts, optimize staffing levels, and reduce wait times. For instance, by adjusting the number of treatment bays or imaging doors, hospitals can better manage patient flow during peak hours.

Moreover, insights from queueing theory can inform policy decisions on resource allocation and emergency response strategies.

Frequently asked questions

What is Erlang C used for in this model?

Erlang C is used to determine the probability that a patient will have to wait for service, which helps in understanding how many doctors are needed to keep wait times manageable.

How does Little’s law apply to an emergency department?

Little’s law states that the average number of patients in the system is equal to the arrival rate multiplied by the average time spent in the system, which helps in estimating patient flow and resource utilization.

Why is triage important in this model?

Triage ensures that higher-priority patients are treated first, reducing wait times for critical cases and improving overall patient care.

How can hospitals use these models to improve their EDs?

Hospitals can use the insights gained from these models to optimize staffing levels, adjust resource allocation, and design more efficient layouts that reduce wait times and enhance patient satisfaction.

Try it live

Everything above runs in your browser — open Hospital Emergency Department Flow: Triage, Priority Queue, Treatment Bays and Imaging Door-to-Doctor Lab and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Hospital Emergency Department Flow: Triage, Priority Queue, Treatment Bays and Imaging Door-to-Doctor Lab simulation