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Stability and convergence in dynamic models

Thursday, September 26th, 2024

Tessa Hayman
Product Specialist, Aimsun
Gavin Bailey
Regional Head of Business Development, Aimsun

As previewed at the Aimsun User Day, held earlier this month in Manchester, we are very happy to present the new guidance from Aimsun on stability and convergence in dynamic models. The guidance has been written with the support of the UK Department for Transport (DfT). 

Overview

Dynamic assignment is a powerful tool that can provide detailed predictions of travel time across a network over time. However, non-conformance with the DfT’s Transport Appraisal Guidance (TAG), specifically regarding convergence, stability, and robustness, has largely restricted the application of dynamic assignment to operational modelling, development planning and event planning.  

This document outlines a method that ensures dynamic assignment models can reach more stable results. The aim is to provide principles and best practice for practitioners to follow when developing dynamic assignment models, particularly in relation to model stability and convergence. 

Summary of recommendations

In summary, we advise practitioners to carry out the following tasks when developing dynamic models to ensure that models converge and provide stable, robust results:  

  • Remove sources of stochasticity where not needed 
  • Monitor stability, sensitivity and sensibility 
  • Target RGap matrix  
  • Calculate the relative gap using probability that a path is chosen not the number of vehicles assigned 
  • Use Instantaneous or Time-Dependent Shortest-Path (TDSP) costs averaged over multiple replications and analytical functions for low flow links 
  • Use a warm start from the base model in dynamic assignment changing the assignment step size when paths go through the scheme area or have a high rgap 
  • Use path assignment skims for outputs  

Document

Read the document for a complete explanation of the points above, including a full illustration using a test model of Barnsley.  

View document

For further information or if you have any questions, please contact Tessa Hayman or Gavin Bailey.  

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