日常网络流量动态中的认知层次结构

Minyu Shen, Feng Xiao, Weihua Gu, Hongbo Ye
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引用次数: 0

摘要

在决定路线时,旅行者可能会在一定程度上推测其他人在接下来的一天里会做些什么,从而使昨天最短的路线变得不那么有吸引力。这种现象在最近的虚拟实验中得到了体现,该实验模仿了旅行者每天重复的出行决策过程。遗憾的是,现有的日常交通动力学模型无法忠实地再现其中收集到的流量演变数据。为此,我们提出了一个基于认知层次理论的日常交通行为建模框架,在该框架中,具有不同战略推理能力水平的旅行者在选择路线时会形成自己对低水平旅行者能力的信念。两个被广泛研究的日常模型--网络塔顿过程动态模型和 Logit 动态模型--被扩展到该框架中,并作为实例进行了研究。虚拟实验的校准是使用扩展的 "网络吞吐过程 "动力学模型进行的,该模型与实验数据的拟合程度相当高。我们证明,这两个扩展动力学有多个均衡,其中一个是经典的用户均衡。由于存在多个平衡点,分析全局稳定性并不容易,但我们通过分析和数值实验验证了平衡点附近的局部稳定性。此外,还揭示了关键参数如何影响用户均衡稳定性的一般见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cognitive Hierarchy in Day-to-day Network Flow Dynamics
When making route decisions, travelers may engage in a certain degree of reasoning about what the others will do in the upcoming day, rendering yesterday's shortest routes less attractive. This phenomenon was manifested in a recent virtual experiment that mimicked travelers' repeated daily trip-making process. Unfortunately, prevailing day-to-day traffic dynamical models failed to faithfully reproduce the collected flow evolution data therein. To this end, we propose a day-to-day traffic behavior modeling framework based on the Cognitive Hierarchy theory, in which travelers with different levels of strategic-reasoning capabilities form their own beliefs about lower-step travelers' capabilities when choosing their routes. Two widely-studied day-to-day models, the Network Tatonnement Process dynamic and the Logit dynamic, are extended into the framework and studied as examples. Calibration of the virtual experiment is performed using the extended Network Tatonnement Process dynamic, which fits the experimental data reasonably well. We show that the two extended dynamics have multiple equilibria, one of which is the classical user equilibrium. While analyzing global stability is intractable due to the presence of multiple equilibria, local stabilities near equilibria are developed analytically and verified by numerical experiments. General insights on how key parameters affect the stability of user equilibria are unveiled.
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