﻿ 基于移动属性的车队与路侧单元连通度分析

# 基于移动属性的车队与路侧单元连通度分析Analysis of the Connectivity for Platoon-Based Vehicle-to-RSU by Traffic Property

Abstract: In view of the connection between vehicles and the roadside units in the Vehicular Ad Hoc Net-work, taking the platoon as the research unit, by studying the traffic property of the vehicles ar-riving on the road, the connectivity probability analysis had transformed into the probability cal-culation of the arrived platoon length. This paper proposed that when vehicles are driving in a platoon, the headways of vehicles were subject to a lognormal distribution, in the case of large traffic flow, and then deduced the probability model of the platoon length by convolution formula, and the results verified the correctness of the proposed probability model.

1. 引言

2. 连通模型

Figure 1. Model of the connectivity for vehicle-to-RSU

3. 车队长度概率模型

3.1. 车头时距分布特性

$P\left(n\right)=\frac{{\left(\lambda t\right)}^{n}{\text{e}}^{-\lambda t}}{n!}$ (1)

$f\left(h (2)

$f\left(t\right)=\left\{\begin{array}{l}\lambda {\text{e}}^{-\lambda \left(t-\Delta \right)},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{\hspace{0.17em}}t\ge \Delta \\ 0,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}t<\Delta \end{array}$ (3)

$f\left(t\right)=\frac{1}{\sigma \sqrt{2\pi }t}{\text{e}}^{-{\left(\frac{\mathrm{ln}t-\mu }{2\sigma }\right)}^{2}}$ (4)

${f}_{d}\left(d\right)=f\left(t\cdot v\right)=\frac{1}{\sigma \sqrt{2\pi }t\cdot v}{\text{e}}^{-{\left[\frac{\mathrm{ln}t\cdot v-\mu }{2\sigma }\right]}^{2}}$ (5)

3.2. 车队长度概率

${f}_{k}\left(x\right)=A\mathrm{sin}\left(\omega \cdot t\cdot v\right)$ (6)

$f\left({d}_{2}\right)={f}_{d}\ast {f}_{k}={\int }_{{d}_{\mathrm{min}}}^{{d}_{\mathrm{max}}}{f}_{d}\left({d}_{2}\right){f}_{k}\left({d}_{2}-x\right)\text{d}{d}_{2}$ (7)

$\left\{\begin{array}{l}{d}_{\mathrm{min}}=\stackrel{¯}{l}+\alpha \\ {d}_{\mathrm{max}}=\stackrel{¯}{l}+\beta \end{array}$ (8)

$f\left({d}_{n}\right)={\int }_{{d}_{\mathrm{min}}}^{{d}_{\mathrm{max}}}\cdots {\int }_{{d}_{\mathrm{min}}}^{{d}_{\mathrm{max}}}{f}_{d}\left({d}_{2}\right){f}_{d}\left({d}_{3}\right)\cdots {f}_{d}\left({d}_{n}\right){f}_{k}\left(x-{d}_{2}-{d}_{3}-\cdots -{d}_{n}\right)\text{d}{d}_{2}\text{d}{d}_{3}\cdots \text{d}{d}_{n}$ (9)

3.3. 连接概率

${P}_{n}=1-\left[{\int }_{0}^{L-{l}_{n}}{f}_{e}\left(y\right){\int }_{0}^{{l}_{n}}{f}_{{d}_{n}}\left(x\right){f}_{k}\left(L-x\right)\text{d}x\text{d}y+{\int }_{L-{l}_{n}}^{L}{f}_{e}\left(y\right){\int }_{0}^{{l}_{n}}{f}_{{d}_{n}}\left(x\right){f}_{k}\left(L-x\right)\text{d}x\text{d}y\right]$ (10)

$\Delta {P}_{n}\left({l}_{n},L\right)={P}_{n}\left({l}_{n}+\frac{\Delta }{2},L\right)-{P}_{n}\left({l}_{n}-\frac{\Delta }{2},L\right)$ (11)

4. 实例分析

4.1. 车辆移动属性分析

Figure 2. Distribution fitting of headway

4.2. 车队与路侧单元连通度分析

Figure 3. Comparison of practical and theoretical results of connectivity

5. 结语

(1) 一般运行状态下的车辆到达间隔分布并不符合车队中车辆间隔的分布，分析得出车辆在密集行驶状态下的车头时距符合对数正态分布的结论。

(2) 本文结合提出的车头时距分布，利用卷积公式建立了车队长度概率模型，采用平衡更新理论描述车队中车辆的间隔，在提出的模型中考虑了车辆跟驰行为特性对车辆间隔的扰动，将车队与路侧单元的连通概率计算转化为车队长度概率计算，并通过实例分析验证了模型计算结果与实际基本一致，该研究结果可对路侧单元的部署间隔提供一定的参考依据。

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