Markovian Traffic Equilibrium Assignment based on Network Generalized Extreme Value Model

TL;DR

This paper develops a theoretical framework for NGEV-based Markovian traffic equilibrium assignment, enabling efficient solution algorithms and addressing previous limitations in capturing route correlations.

Contribution

It provides the first theoretical analysis and optimization formulations for NGEV equilibrium assignment, including a novel dual algorithm using accelerated gradient methods.

Findings

The NGEV model can be formulated and solved using path algebra.

The dual algorithm with accelerated gradient converges efficiently.

Numerical experiments demonstrate excellent convergence properties.

Abstract

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.