﻿ 车道占用对城市道路通行能力的影响分析 Analysis on the Line Occupation Effects on Traffic Capacity

Advances in Applied Mathematics
Vol.04 No.01(2015), Article ID:14868,8 pages
10.12677/AAM.2015.41007

Analysis on the Line Occupation Effects on Traffic Capacity

Fei Wang, Chunyan Zhang, Gang Liu, Dashuang Liao, Peng Zheng

School of Mathematical Sciences, Anhui University, Hefei Anhui

Email: 625895943@qq.com

Received: Feb. 7th, 2015; accepted: Feb. 20th, 2015; published: Feb. 25th, 2015

Copyright © 2015 by authors and Hans Publishers Inc.

ABSTRACT

This paper analyzes the line occupation effects on traffic capacity, and establishes ANOVA model and multiple regression model built on differential equations based on the video data [1] [2] [3] , and do qualitative analysis and quantitative calculations for results. Firstly, the data which was associated with road capacity was obtained by observing the video; then through MATLAB, interpolation fitting was done. Secondly, it established variance analysis model, and then explored the impact of different occupied lanes on traffic capacity. Then by using the differential model, the relationship among vehicle queue length, traffic capacity, traffic accident time and traffic flow was obtained. In the end, combining the theory of model with practice, the duration of the actual accident was calculated.

Keywords:Road’s Capacity, Interpolation Fitting, Analysis of Variance, Differential Equations, Traffic Flow

Email: 625895943@qq.com

1. 引言 [4] [5]

2. 问题概况

2.1. 问题概述

2.2. 数据获取及基本假设

2.3. 标准车当量数的折算系数

3. 道路实际通行能力变化分析

3.1. 数据处理

3.2. 插值模型与结果分析 [3] [6] [7]

3.2.1. 插值模型建立

(3.1)

1)

2) 在每个时间段区间是三次多项式，记为

3)上二阶连续可微。

Figure 1. Simple figure about the traffic accident in the first video

Figure 2. Simple figure about the traffic accident in the second video

Table 1. The road traffic capacity duration of the accident in the first video

Table 2. The road traffic capacity duration of the accident in the second video

3.2.2. 模型求解与结果分析

1) 初始阶段(16:42~16:43)：事故刚发生，没有发生堵车，道路通行能力减弱的不是很多；

2) 堵塞阶段(16:44~17:00)：随着事故持续时间的增加，道路开始发生堵塞，车速下降，车辆开始排队。这一段时间道路的通行能力明显降低，直到事故撤离，道路的实际通行能力在一个范围内呈现较小的周期性波动；

3) 撤离阶段(17:00~17:02)：事故撤离后，道路的通行能力明显上升，之后，道路的通行能力恢复正常水平。

3.3. 方差分析模型 [2] [3]

Figure 3. The changing process of the first video traffic capacity

Figure 4. The changing process of the second video traffic capacity

Table 3. Different lanes of the influence for actual capacity of the accident cross section

Table 4. The analysis of variance about different lanes of the influence for actual capacity of the accident cross section

4. 建立实际通行能力微分模型 [3] [8] - [10]

4.1. 微分模型建立流程

4.2. 微分模型建立步骤

(4.1)

(4.2)

(4.3)

(4.4)

Figure 5. Differential equation model modeling ideas

Figure 6. Cross-sectional actual capacity curve fitting

Table 5. The queue length every 30 seconds

4.3. 模型的实际应用

5. 结束语

Analysis on the Line Occupation Effects on Traffic Capacity. 应用数学进展,01,54-62. doi: 10.12677/AAM.2015.41007

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