Simple templates and example of implementations of DES models in Python and R, within a reproducible analytical pipeline (RAP)
⚠️ Work in progress
TBC. Notes:
- Link to template repositoryes
- Link to STARS.
- Link to relevant publication.
A simulation is a computer model that mimics a real-world system. It allows us to test different scenarios and see how the system behaves. One of the most common simulation types in healthcare is discrete-event simulation (DES).
In DES models, time progresses only when specific events happen (e.g., a patient arriving or finishing treatment). Unlike a continuous system where time flows smoothly, DES jumps forward in steps between events. For example, when people (or tasks) arrive, wait for service, get served, and then leave.
Simple model animation created using web app developed by Sammi Rosser (2024) available at https://github.com/hsma-programme/Teaching_DES_Concepts_Streamlit and shared under an MIT Licence.
One simple example of a DES model is the M/M/s queueing model, which is implemented in this template. In a DES model, we use well-known statistical distributions to describe the behaviour of real-world processes. In an M/M/s model we use:
- Poisson distribution to model patient arrivals - and so, equivalently, use an exponential distribution to model the inter-arrival times (time from one arrival to the next)
- Exponential distribution to model server times.
These can be referred to as Markovian assumptions (hence "M/M"), and "s" refers to the number of parallel servers available.
For this M/M/s model, you only need three inputs:
- Average arrival rate: How often people typically arrive (e.g. patient arriving to clinic).
- Average service duration: How long it takes to serve one person (e.g. doctor consultation time).
- Number of servers: How many service points are available (e.g. number of doctors).
This model could be applied to a range of contexts, including:
| Queue | Server/Resource |
|---|---|
| Patients in a waiting room | Doctor's consultation |
| Patients waiting for an ICU bed | Available ICU beds |
| Prescriptions waiting to be processed | Pharmacists preparing and dispensing medications |
For further information on M/M/s models, see:
- Ganesh, A. (2012). Simple queueing models. University of Bristol. https://people.maths.bris.ac.uk/~maajg/teaching/iqn/queues.pdf.
- Green, L. (2011). Queueing theory and modeling. In Handbook of Healthcare Delivery Systems. Taylor & Francis. https://business.columbia.edu/faculty/research/queueing-theory-and-modeling.
TBC. Notes on:
- View it online
- View it locally
# Clone project
git clone https://github.com/pythonhealthdatascience/rap_des
cd rap_des
# Create conda environment
conda env create --file environment.yaml
| Contributor | ORCID | GitHub |
|---|---|---|
| Amy Heather |  |
https://github.com/amyheather |
This template is licensed under the MIT License.
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This project was developed as part of the project STARS: Sharing Tools and Artefacts for Reproducible Simulations. It is supported by the Medical Research Council [grant number MR/Z503915/1].