Markovian Traffic Equilibrium Assignment based on Network Generalized Extreme Value Model

This study establishes a novel framework of 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 in traffic assignment has recently been proposed and enables capturing the path correlation without explicit path enumeration. However, the NGEV equilibrium assignment has never been investigated in the literature, which has limited the practical applicability of the NGEV-based models. We address this gap by providing the necessary development for the NGEV equilibrium assignment. We first show that the NGEV assignment can be formulated and solved under the same path algebra with the Markovian traffic assignment models. We then provide the equivalent optimization formulations to the NGEV equilibrium assignment, from which both primal and dual types of solution algorithms are derived. In particular, we are the first to propose an efficient algorithm based on an accelerated gradient method in the traffic assignment field. The convergence and complementary relationship of the proposed primal-dual algorithms are shown through numerical experiments.