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.

中文翻译：

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基于网络广义极值模型的马尔可夫流量均衡分配

本研究基于网络广义极值（NGEV）模型建立了马尔可夫交通均衡分配的新框架，我们称之为NGEV均衡分配。最近提出了在流量分配中使用 NGEV 模型，并且无需显式路径枚举即可捕获路径相关性。然而，文献中从未研究过 NGEV 平衡分配，这限制了基于 NGEV 的模型的实际适用性。我们通过为 NGEV 平衡分配提供必要的发展来解决这一差距。我们首先表明 NGEV 分配可以在与马尔可夫交通分配模型相同的路径代数下制定和解决。然后我们为 NGEV 平衡分配提供等效的优化公式，原始和对偶类型的求解算法均从中派生出来。特别是，我们在交通分配领域率先提出了一种基于加速梯度法的高效算法。通过数值实验表明了所提出的原始对偶算法的收敛性和互补关系。