A stochastic user equilibrium model solving overlapping path and perfectly rational issues

Abstract

Traffic assignment has been recognized as one of the key technologies in supporting transportation planning and operations. To better address the perfectly rational issue of the expected utility theory (EUT) and the overlapping path issue of the multinomial logit (MNL) model that are involved in the traffic assignment process, this paper proposes a cumulative prospect value (CPV)-based generalized nested logit (GNL) stochastic user equilibrium (SUE) model. The proposed model uses CPV to replace the utility value as the path performance within the GNL model framework. An equivalent mathematical model is provided for the proposed CPV-based GNL SUE model, which is solved by the method of successive averages (MSA). The existence and equivalence of the solution are also proved for the equivalent model. To demonstrate the performance of the proposed CPV-based GNL SUE model, three road networks are selected in the empirical test. The results show that the proposed model can jointly deal with the perfectly rational issue and the overlapping path issue, and additionally, the proposed model is shown to be applicable for large road networks. 交通分配是交通规划和运营的关键技术之一。为了更好地解决交通分配过程中涉及的期望效用 理论(EUT)的完全理性问题和多项式logit(MNL)模型的路径重叠问题, 本文提出了基于累积前景值 (CPV)的广义巢式logit(GNL)随机用户平衡(SUE)模型, 即基于CPV 的GNL SUE 模型。该模型在GNL 模型框架内使用CPV 代替效用值作为路径性能。对于该模型, 给出等价的数学模型, 并使用相继平 均法(MSA)对该数学模型进行求解, 同时模型解的存在性和等价性也被证明。为了展示基于CPV 的 GNL SUE 模型的性能, 选择三个道路网络作为测试实例, 结果表明, 提出的模型可以同时处理完全理 性问题和路径重叠问题, 并且适用于大型道路网络。