基于累积前景理论的动态交通流演化博弈模型

An Evolutionary Game Model for the Dynamic Traffic Flow Based on Cumulative Prospect Theory

交通流演化的内在动力机制是出行者的适应性学习及其诱发的路径选择行为的持续改变,当选择行为趋于稳定时交通系统也将达到或接近均衡状态。首先基于累积前景理论建立了一个用户均衡模型及其等价的变分不等式,在一定约束条件下对模型解的性质进行了讨论;然后将累积前景理论与演化博弈论相结合,利用复制子动态来刻画出行者日常路径选择的博弈学习行为,建立了一个动态交通系统模型,结合稳定性分析证明了当满足一定条件时系统演化能够实现用户均衡;最后通过算例在不同初始状态和不同参照点更新规则下分别展示了交通流的动态演化与用户均衡的实现过程,对相关研究结论进行了验证。本文拓展了传统交通分配模型完全理性假设和均衡分析方法的局限,更加真实、全面的刻画了动态交通系统长期运行特征和规律。

Most existing traffic assignment models are usually based on Expected Utility Theory and Wardropian User Equilibrium （UE） Principle.Due to complete rationality assumptions and the limitations of equilibrium analysis method,these models are unable to capture the long-term operation characteristics and regulations of the dynamical traffic system,such as travelers＇ day-to-day route choices and dynamic traffic evolution.According to previous researches of behavior sciences,such as psychology and behavioral economics,traffic system typically contains uncertainty,under which travelers＇ decision behaviors appear to be bounded rational.Several empirical researches show travellers＇ behaviors under uncertainty,especially in the choices of departure time and route.Risk appetite coincides with the fundamental assumptions of Prospect Theory （PT）,proposed by Kahneman and Tversky.These are often used to deal with bounded rational decision-making problems.The inherent dynamical mechanism of traffic evolution arises from travelers＇ adaptive learning as well as the resulting route adjustment.Once adjustment stabilizes,a dynamical system will also be at or close to equilibrium.In order to explore the interactions between travelers＇ day-to-day route choice behaviors and the dynamic traffic equilibration and evolution within the frame of bounded rationality,this paper attempts to model dynamic traffic evolution based on Cumulative Prospect Theory （CPT,an extension of PT）.Firstly,a UE model and its equivalent variational inequality are formulated based on CPT,and a proof for the uniqueness of link-flow solution of the UE model is given under three constraints.These three constrains are：（1） travel demand between any of the OD pairs is fixed ; （2） there is no correlation between the mean and variance of the travel time on any of the links; and （3） travelers with the same OD possess the same reference point.Secondly,the replicator dynamic is introduced to describe travelers＇ day-to-day route choice behaviors and integrated with CPT to establish a dynamical traffic system.According to stability analysis,it is indicated that the dynamical system can evolve to UE eventually when there are no unused routes at the initial time and its equilibrium points are interior points of the feasible route flow set.Finally,we illustrate the processes of achieving UE through a numerical experiment under different initial states and by distinct reference point updating rules.In summary,this paper not only improves and expands traditional traffic assignment model within the frame of bounded rationality by an integration of equilibrium and evolution analysis,but also presents a reasonable explanation for the achievement of UE.The model formulated in this paper characterizes the long-term operation characterics and regulations of the dynamical traffic system more practically and comprehensively.The model and conclusions create a theoretical basis for traffic demand forecasting,transportation planning,traffic network design,ATIS construction,and the establishment of travel demand management strategies （e.g.congestion pricing and regional traffic control）.In addition,several directions for future research are identified.Firstly,some findings of this study need to be further verified by gradually relaxing some constraints in this study.Secondly,parameter estimation of the route prospect function and analysis on reference point update regulations with field survey or experimental data are required for further investigation.Thirdly,seeking for more plausible evolutionary dynamics in conformity with travellers＇ actual behaviors is also a research ovjective.Lastly,it is still challenging to apply the model to analyzing real traffic network in consideration of travelers ‘ decision characteristics and traffic system＇ s operation performance.