Lu Lili, Wang Jian, Zheng Pengjun, Wang Wei
Faculty of Maritime and Transportation, Ningbo University, Ningbo, China.
National Traffic Management Engineering & Technology Research Centre Ningbo University Sub-center, Ningbo, China.
PLoS One. 2017 Feb 8;12(2):e0171158. doi: 10.1371/journal.pone.0171158. eCollection 2017.
Among different stochastic user equilibrium (SUE) traffic assignment models, the Logit-based stochastic user equilibrium (SUE) is extensively investigated by researchers. It is constantly formulated as the low-level problem to describe the drivers' route choice behavior in bi-level problems such as network design, toll optimization et al. The Probit-based SUE model receives far less attention compared with Logit-based model albeit the assignment result is more consistent with drivers' behavior. It is well-known that due to the identical and irrelevant alternative (IIA) assumption, the Logit-based SUE model is incapable to deal with route overlapping problem and cannot account for perception variance with respect to trips. This paper aims to explore the network capacity with Probit-based traffic assignment model and investigate the differences of it is with Logit-based SUE traffic assignment models. The network capacity is formulated as a bi-level programming where the up-level program is to maximize the network capacity through optimizing input parameters (O-D multiplies and signal splits) while the low-level program is the Logit-based or Probit-based SUE problem formulated to model the drivers' route choice. A heuristic algorithm based on sensitivity analysis of SUE problem is detailed presented to solve the proposed bi-level program. Three numerical example networks are used to discuss the differences of network capacity between Logit-based SUE constraint and Probit-based SUE constraint. This study finds that while the network capacity show different results between Probit-based SUE and Logit-based SUE constraints, the variation pattern of network capacity with respect to increased level of travelers' information for general network under the two type of SUE problems is the same, and with certain level of travelers' information, both of them can achieve the same maximum network capacity.
在不同的随机用户均衡（SUE）交通分配模型中，基于Logit的随机用户均衡（SUE）受到了研究人员的广泛研究。它经常被表述为低层次问题，用于描述双层问题（如网络设计、收费优化等）中驾驶员的路径选择行为。与基于Logit的模型相比，基于Probit的SUE模型受到的关注要少得多，尽管其分配结果与驾驶员的行为更为一致。众所周知，由于相同且不相关替代（IIA）假设，基于Logit的SUE模型无法处理路径重叠问题，也无法考虑行程感知差异。本文旨在探讨基于Probit的交通分配模型下的网络容量，并研究其与基于Logit的SUE交通分配模型的差异。网络容量被表述为一个双层规划问题，其中上层规划是通过优化输入参数（O-D乘法和信号分割）来最大化网络容量，而下层规划是基于Logit或Probit的SUE问题，用于模拟驾驶员的路径选择。详细提出了一种基于SUE问题灵敏度分析的启发式算法来求解所提出的双层规划。使用三个数值示例网络来讨论基于Logit的SUE约束和基于Probit的SUE约束之间网络容量的差异。本研究发现，虽然基于Probit的SUE和基于Logit的SUE约束下的网络容量结果不同，但在两种类型的SUE问题下，一般网络的网络容量随旅行者信息水平增加的变化模式是相同的，并且在一定水平的旅行者信息下，它们都可以达到相同的最大网络容量。
