Linear Analytical Model for Static Traffic Assignment: Explicit Formulation of OD Travel Times and Link Flows
Abstract
This paper introduces an analytical model for predicting static traffic assignment (STA) based on network characteristics and origin-destination (OD) demand. The model provides an explicit analytical solution to the STA problem, avoiding iterative procedures, relying on two key elements: (i) a projection of path flows onto auxiliary flows, and (ii) a linearization of the link performance function that relates travel time to link flow. The analytical model is validated against a Method-of-Successive-Averages (MSA) reference solution on a small synthetic network, the Sioux Falls benchmark, and the real-scale road network of Lyon, France (8,140 links, 4,128 nodes, up to 33,258 OD pairs) with a R 2 ≈ 0.99 on OD travel time prediction. Beyond its computational advantages, the framework supports a backcastingoriented approach, making it suitable for integration into broader planning models.
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BibTeX
@misc{leroux2026linear,
title = {{Linear Analytical Model for Static Traffic Assignment: Explicit Formulation of OD Travel Times and Link Flows}},
author = {Baptiste Leroux and Antonio Sciarretta and Milos Balac},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05742643v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear Analytical Model for Static Traffic Assignment: Explicit Formulation of OD Travel Times and Link Flows
AU - Baptiste Leroux
AU - Antonio Sciarretta
AU - Milos Balac
PY - 2026
DA - 2026/09/08
PB - HAL
UR - https://hal.science/hal-05742643v1
AB - This paper introduces an analytical model for predicting static traffic assignment (STA) based on network characteristics and origin-destination (OD) demand. The model provides an explicit analytical solution to the STA problem, avoiding iterative procedures, relying on two key elements: (i) a projection of path flows onto auxiliary flows, and (ii) a linearization of the link performance function that relates travel time to link flow. The analytical model is validated against a Method-of-Successive-Averages (MSA) reference solution on a small synthetic network, the Sioux Falls benchmark, and the real-scale road network of Lyon, France (8,140 links, 4,128 nodes, up to 33,258 OD pairs) with a R 2 ≈ 0.99 on OD travel time prediction. Beyond its computational advantages, the framework supports a backcastingoriented approach, making it suitable for integration into broader planning models.
ER -