Example conceptual models π©Ίπ§
π― Objectives
This page introduces two models:
- π©Ί Nurse visit simulation: Simple M/M/s queueing model.
- π§ Stroke pathway simulation: Patient flow model based on a published study.
We have developed two example simulation models, each implemented in both Python and R, and openly shared as public repositories.
Each model serves as an illustrative example following the covered concepts in this book, and they are included as examples throughout the book.
π©Ί Nurse visit simulation
This model simulates a clinic where patients arrive randomly, wait to see a nurse, receive care, then leave. It is designed to help analyse resource utilisation and patient wait times.
Code repositories
Process flow diagram
Model summary
Aspect | Description |
---|---|
Type | Discrete-event simulation of a multi-server queue (M/M/s system). |
Arrivals | Patients arrive at random intervals, following a Poisson process (memoryless/inter-arrival times are exponential). |
Service | Each nurse serves one patient at a time; service times are exponentially distributed. Multiple nurses operate in parallel. |
Inputs | Patient arrival rate, nurse service time, number of nurses. |
How it works
This model follows an M/M/s queueing structure - a widely used model in healthcare operations. M/M/s stands for:
- Markovian (Poisson) arrivals
- Markovian (exponential) service times
- s servers (nurses) in parallel
Why Poisson arrivals?
Patients tend to arrive independently and randomly; this is well-represented by a Poisson process, where:
- The number of arrivals in a period follows the Poisson distribution.
- The time between arrivals follows the exponential distribution.
Applications
This model structure can be used for a variety of healthcare and service settings, such as:
Queue | Server/Resource |
---|---|
Patients in a waiting room | Doctor or nurse consultations |
Patients waiting for ICU transfer | ICU beds |
Prescriptions to be processed | Pharmacists |
Further information on M/M/s models
- 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.
π§ Stroke pathway simulation
This model is based on a published study of stroke care. It simulates patient flow through acute stroke and rehabilitation units to support capacity planning and estimate the likelihood of admission delays for different patient groups.
It is described in:
Monks T, Worthington D, Allen M, Pitt M, Stein K, James MA. A modelling tool for capacity planning in acute and community stroke services. BMC Health Serv Res. 2016 Sep 29;16(1):530. doi: 10.1186/s12913-016-1789-4. PMID: 27688152; PMCID: PMC5043535.
The original study implemented the model using SIMUL8 software. Based on the published description of the modelβs logic and parameters, we have recreated it in both Python and R.
Code repositories
Process flow diagram
Model summary
Aspect | Description |
---|---|
Type | Discrete-event simulation of a patient pathway. |
Arrivals | Multiple patient classes (e.g., stroke, TIA, complex neurological, other) each have their own arrival processes to the acute stroke unit and rehabilitation unit, with inter-arrival times drawn from specified distributions. |
Service | Patients experience lengths of stay in each unit based on distributions specific to their class and care type (e.g., lognormal for length of stay). |
Routing | After acute care, patients are routed to rehabilitation, early supported discharge, or exit the system, according to probabilities defined for each patient class. |
Resources | The model assumes infinite capacity for both acute and rehabilitation beds (i.e., no explicit queueing). |