【摘要】：均衡的失效率研究是交通科學(xué)和計算機科學(xué)等領(lǐng)域的研究熱點之一。在交通網(wǎng)絡(luò)中,均衡的失效率是指,網(wǎng)絡(luò)處于均衡狀態(tài)時的最大總出行時間成本與網(wǎng)絡(luò)的最優(yōu)總出行時間成本之比。當假設(shè)網(wǎng)絡(luò)用戶掌握精確的出行時間信息,并以最小化自身出行時間為目標時,相應(yīng)的均衡是一個確定性用戶均衡。而當假設(shè)網(wǎng)絡(luò)用戶對出行時間有感知偏差,以最小化自身的感知出行時間為目標時,相應(yīng)的均衡是一個隨機用戶均衡。本文的研究目的是比較上述兩類均衡的失效率,以此考察網(wǎng)絡(luò)用戶在具備更多信息時的出行選擇是否可能降低網(wǎng)絡(luò)效率。本文首先定義均衡的相對失效率比為隨機用戶均衡的失效率與確定性用戶均衡的失效率之比,并給出了一般網(wǎng)絡(luò)中相對失效率比的上下界。其次,在兩條平行弧網(wǎng)絡(luò)中,假設(shè)其中一條弧的通行時間成本為常數(shù),本文研究了此類網(wǎng)絡(luò)中隨機用戶均衡的性質(zhì),得到隨機用戶均衡的失效率為1的充要條件。定義使兩條弧的通行時間成本相等的弧流量為交匯點,本文證明了當網(wǎng)絡(luò)的總流量在交匯點附近時,相對失效率比小于1;而當網(wǎng)絡(luò)的總流量為交匯點的二倍時,相對失效率比等于1。同時,本文得到了該類網(wǎng)絡(luò)中相對失效率比的最小值及其取最小值時網(wǎng)絡(luò)的參數(shù),并說明相對失效率比的下界是緊的。接著,本文將兩條平行弧網(wǎng)絡(luò)中的結(jié)論拓展至具有兩類出行成本函數(shù)的多條平行弧網(wǎng)絡(luò)中,給出了相對失效率比等于1和小于1的充分條件,并證明了相對失效率比的下界在此類網(wǎng)絡(luò)中仍然是緊的。最后,在單起點多訖點的環(huán)形網(wǎng)絡(luò)中,本文研究了該類網(wǎng)絡(luò)的隨機用戶均衡的性質(zhì),得到一個相對失效率比小于1的充分條件,并分別對三種具體的網(wǎng)絡(luò)結(jié)構(gòu)分析了相對失效率比。本文的主要創(chuàng)新與貢獻是:(1)首次比較了隨機用戶均衡與確定性用戶均衡的失效率,在兩類平行弧網(wǎng)絡(luò)及單起點多訖點環(huán)形網(wǎng)絡(luò)中給出了完全出行信息會降低網(wǎng)絡(luò)效率的條件;(2)在含有一條常數(shù)弧的兩條平行弧網(wǎng)絡(luò)中得到了相對失效率比的最小值;(3)驗證了相對失效率比下界的緊性。
[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.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：U491

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