Convergence behavior for traffic assignment characterization metrics

Abstract

Traffic assignment is used for infrastructure planning, based on metrics like total system travel time (TSTT), vehicle-miles traveled (VMT) and link or path flows. Algorithms for traffic assignment converge to an equilibrium solution over multiple iterations, but these metrics converge at different rates. Current guidance indicates that freeway link flows stabilize at a relative gap of roughly ${10}^{-4}$. This study generalizes this guidance by testing additional networks and metrics, in more experimental settings. Our results reveal that aggregate metrics (VMT and TSTT) stabilize earlier (relative gap ${10}^{-4}$) than link flows (relative gap ${10}^{-5}$), which in turn stabilize slightly before the set of most likely used paths and flows on these paths (relative gap ${10}^{-6}$). These results are stable across the TAPAS and Algorithm B methods for solving assignment. Our results also show strong linear correlations between alternative gap measures, allowing for the translation of stabilization results across other gap definitions as well.

Keywords:

• Traffic assignment
• convergence criteria
• network optimization

Acknowledgments

This research was partly supported by the National Science Foundation (Grant Nos. 1254921 and 1562291) and the Data-Supported Transportation Operations and Planning Center. The authors would like to thank Rishabh Thakkar for his help with multi-class TAP code.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 This is the commonly used Bureau of Public Roads function with standard values for its shape parameters Bureau of Public Roads (1964).

Additional information

Funding

This research was partly supported by the National Science Foundation [grant number 1254921] and [grant number 1562291] and the Data-Supported Transportation Operations and Planning Center.