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为了求解在出行者(车辆)随机到达交通瓶颈条件下的最优外生通行权发行方式,构建了由等待队列损失与日程延误损失两部分组成的出行者经济损失模型,其中,对实时等待队列长度变化的描述采用了Fokker-Planck方程式。此后,通过设定4种外生通行权发行函数(线性函数、指数函数、幂函数、S形函数)来进行数值试验,求解出各类出行者行为特性组合(等待队列时间价值、风险回避系数、到达瓶颈出行者数量的标准差)下的最优外生通行权发行方式。同时,以线性函数为例分析了通行权发行数量与各时间损失之间的关系。研究结果表明:等待队列损失与日程延误损失之间存在着“此消彼长”的关系;随着通行权发行数量的增加,等待队列损失的期望值与标准差也都随之增加,但日程延误的损失则逐渐减小;当出行者行为特性取值较小时,S形函数为最优外生通行权发行函数;而当特性取值逐渐增大时,最优外生通行权发行函数则由S形函数逐渐向指数函数与线性函数转变;当特性取值较大时,幂函数变为最优外生发行函数。
In order to solve the optimal exogenous distribution method for travelers (vehicles) arriving at traffic bottlenecks, a model of travelers’ economic loss consisting of waiting queue loss and schedule delay loss is constructed, in which real-time waiting queue The description of the change in length uses the Fokker-Planck equation. Afterwards, four kinds of exergy distribution functions (linear function, exponential function, power function, S-shaped function) were set up to carry out numerical experiments, and the combinations of behavioral characteristics of various types of travelers (waiting queue time value, risk aversion coefficient , Standard deviation of the number of bottleneck arrivals reached). At the same time, taking the linear function as an example, this paper analyzes the relationship between the number of passing rights and the time loss. The results show that there is a relationship between waiting queue loss and schedule delay loss. With the increase of the number of passing right, the expected value and standard deviation of waiting queue loss also increase, The loss of schedule delay decreases gradually. When the behavior characteristic of traveler is smaller, the S-shaped function is the optimal distribution function of extermination right. When the characteristic value is gradually increased, the optimal distribution function of exteriors’ The S-shaped function gradually changes to the exponential function and the linear function; when the characteristic value is larger, the exponential function becomes the optimal exogenous distribution function.