# Markovian Traffic Equilibrium Assignment based on Network Generalized Extreme Value Model

arXiv: https://arxiv.org/abs/2009.02033 · HTML: https://mlsanity.com/paper/2009.02033/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Capturing positive network attributes during the estimation of recursive logit models: A prism-based approach](https://mlsanity.com/paper/2204.01215/) (2022)
- [Global path preference and local response: A reward decomposition approach for network path choice analysis in the presence of locally perceived attributes](https://mlsanity.com/paper/2307.08646/) (2023)
- [Cost-augmented Schr"odinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned control](https://mlsanity.com/paper/2610.02195/) (2026)

## Abstract (arXiv)

This study establishes Markovian traffic equilibrium assignment based on the network generalized extreme value (NGEV) model, which we call NGEV equilibrium assignment. The use of the NGEV model for route choice modeling has recently been proposed, and it enables capturing the path correlation without explicit path enumeration. However, the theoretical properties of the model in traffic assignment have yet to be investigated in the literature, which has limited the practical applicability of the NGEV model in the traffic assignment field. This study addresses the research gap by providing the theoretical developments necessary for the NGEV equilibrium assignment. We first show that the NGEV assignment can be formulated and solved under the same path algebra as the traditional Markovian traffic assignment models. Moreover, we present the equivalent optimization formulations to the NGEV equilibrium assignment. The formulations allow us to derive both primal and dual types of efficient solution algorithms. In particular, the dual algorithm is based on the accelerated gradient method that is for the first time applied in the traffic assignment. The numerical experiments showed the excellent convergence and complementary relationship of the proposed primal-dual algorithms.