两类交通网络的随机用户均衡研究

发布时间：2018-11-23 19:42

【摘要】：均衡的失效率研究是交通科学和计算机科学等领域的研究热点之一。在交通网络中,均衡的失效率是指,网络处于均衡状态时的最大总出行时间成本与网络的最优总出行时间成本之比。当假设网络用户掌握精确的出行时间信息,并以最小化自身出行时间为目标时,相应的均衡是一个确定性用户均衡。而当假设网络用户对出行时间有感知偏差,以最小化自身的感知出行时间为目标时,相应的均衡是一个随机用户均衡。本文的研究目的是比较上述两类均衡的失效率,以此考察网络用户在具备更多信息时的出行选择是否可能降低网络效率。本文首先定义均衡的相对失效率比为随机用户均衡的失效率与确定性用户均衡的失效率之比,并给出了一般网络中相对失效率比的上下界。其次,在两条平行弧网络中,假设其中一条弧的通行时间成本为常数,本文研究了此类网络中随机用户均衡的性质,得到随机用户均衡的失效率为1的充要条件。定义使两条弧的通行时间成本相等的弧流量为交汇点,本文证明了当网络的总流量在交汇点附近时,相对失效率比小于1;而当网络的总流量为交汇点的二倍时,相对失效率比等于1。同时,本文得到了该类网络中相对失效率比的最小值及其取最小值时网络的参数,并说明相对失效率比的下界是紧的。接着,本文将两条平行弧网络中的结论拓展至具有两类出行成本函数的多条平行弧网络中,给出了相对失效率比等于1和小于1的充分条件,并证明了相对失效率比的下界在此类网络中仍然是紧的。最后,在单起点多讫点的环形网络中,本文研究了该类网络的随机用户均衡的性质,得到一个相对失效率比小于1的充分条件,并分别对三种具体的网络结构分析了相对失效率比。本文的主要创新与贡献是:(1)首次比较了随机用户均衡与确定性用户均衡的失效率,在两类平行弧网络及单起点多讫点环形网络中给出了完全出行信息会降低网络效率的条件;(2)在含有一条常数弧的两条平行弧网络中得到了相对失效率比的最小值;(3)验证了相对失效率比下界的紧性。
[Abstract]:The study of equilibrium failure rate is one of the hotspots in traffic science and computer science. In traffic networks, the equilibrium failure rate refers to the ratio between the maximum total travel time cost and the optimal total trip time cost of the network when the network is in equilibrium state. When it is assumed that network users have accurate travel time information and aim at minimizing their travel time, the corresponding equilibrium is a deterministic user equilibrium. When it is assumed that the network user has a perception bias to travel time and the goal is to minimize the perceived travel time, the corresponding equilibrium is a random user equilibrium. The purpose of this study is to compare the failure rates of the above two types of equilibrium, so as to investigate whether the travel choices of network users with more information may reduce the network efficiency. In this paper, we first define the relative failure rate ratio of equilibrium as the ratio of the failure rate of random user equilibrium to that of deterministic user equilibrium, and give the upper and lower bounds of relative failure rate ratio in general networks. Secondly, in two parallel arc networks, assuming that the travel time cost of one of the arcs is constant, this paper studies the properties of stochastic user equilibrium in this kind of networks, and obtains a sufficient and necessary condition for the failure rate of stochastic user equilibrium to be 1. In this paper, it is proved that the relative failure rate ratio is less than 1 when the total flow of the network is near the intersection point. When the total flow of the network is twice that of the intersection, the relative failure rate is equal to 1. 5%. At the same time, the minimum value of the ratio of relative failure rate and the parameters of the network are obtained, and it is shown that the lower bound of the ratio of relative failure rate is compact. Then, the conclusion of two parallel arc networks is extended to multiple parallel arc networks with two kinds of trip cost functions, and the sufficient conditions for the relative failure rate ratio to be equal to or less than 1 are given. It is proved that the lower bound of the relative failure rate ratio is still tight in this kind of networks. Finally, in this paper, we study the properties of random user equilibrium for a single starting point multi-point ring network, and obtain a sufficient condition for the ratio of relative failure rate to be less than 1. The relative failure rate ratio is analyzed for three specific network structures. The main innovations and contributions of this paper are as follows: (1) the failure rates of random user equilibrium and deterministic user equilibrium are compared for the first time. In two kinds of parallel arc networks and single-starting point multi-point ring networks, the condition that complete trip information can reduce the network efficiency is given. (2) in two parallel arc networks with a constant arc, the minimum value of the relative failure rate ratio is obtained, and (3) the compactness of the lower bound of the relative failure rate ratio is verified.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U491

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