# 考虑用户异质性和瓶颈处停车换乘的交通定价模型研究The Pricing Model of Parking and Transit Fare Considering Park-and-Ride Facilities and User Heterogeneity

DOI: 10.12677/MSE.2019.84034, PDF, HTML, XML, 下载: 283  浏览: 409

Abstract: This paper extends the bottleneck model and develops a bi-level programming model to study the traffic charge problem between two companies, one of which operates buses and park-and-ride (P&R) parking lots simultaneously, while the other of which owns central parking lots. Therefore, commuters can get their destination by either auto or P&R mode. The proposed model analyzes two game scenarios: perfect competition and market regulation and considers heterogeneous users who are distinguished by their valuation of travel time. Specifically, in the upper level, the objective of operators is to maximize their own net profit; in the lower level, the followers would choose the optimal travel plans given the traffic charge rules. Finally, numerical examples are provided to illustrate the effectiveness of the developed models; furthermore, the result shows that when the proportion of commuters with higher value of time (VOT) is increasing, the gap of total social costs between two game scenarios becomes larger.

1. 引言

2. 模型建立

2.1. 模型背景及参数说明

Figure 1. A one-to-one bi-modal transportation system

$\begin{array}{l}{\alpha }_{w}>{\alpha }_{b},\text{}{\beta }_{w}<{\beta }_{b},\text{}\frac{{\gamma }_{w}}{{\beta }_{w}}=\frac{{\gamma }_{b}}{{\beta }_{b}}=\eta \\ {\theta }_{w}>{\theta }_{b}\\ {\alpha }_{w}/{\theta }_{w}>{\alpha }_{b}/{\theta }_{b}\end{array}$ (1)

Table 1. List of other notations involved in the model

2.2. 上层交通定价优化目标

$\mathrm{max}T{R}_{P}={p}_{2}{N}^{A}-{c}_{2}N$ (2)

$\mathrm{max}T{R}_{Q}=\left({p}_{1}+P\left(l\right)-a\right){N}^{T}-{c}_{1}N-F$ (3)

$\mathrm{max}TR={p}_{2}{N}^{A}+\left({p}_{1}+P\left(l\right)\right){N}^{T}-a{N}^{T}-\underset{i=w,b}{\sum }\left[{N}_{i}^{A}\left(M{C}_{i}^{A}\right)+{N}_{i}^{T}\left(M{C}_{i}^{T}\right)\right]-\left({c}_{1}+{c}_{2}\right)N-F$ (4)

2.3. 下层交通出行广义出行费用

2.3.1. 全程自驾出行费用

${C}_{i}^{A}\left(t\right)={\alpha }_{i}T\left(t\right)+{\beta }_{i}\mathrm{max}\left\{0,{t}^{*}-t-T\left(t\right)\right\}+{\gamma }_{i}\mathrm{max}\left\{0,t+T\left(t\right)-{t}^{*}\right\}+{p}_{2},\text{}i=w,b$ (5)

2.3.2. P&R出行费用

${C}_{i}^{T}\left(l\right)={\alpha }_{i}\left(\frac{L}{{v}_{1}}+\frac{l}{{v}_{2}}+T\right)+{\theta }_{i}{N}^{T}+P\left(l\right)+{p}_{1}\text{,}i=w,b$ (6)

3. 用户出行均衡状态分析

3.1. 人均交通出行成本分析

Figure 2. The auto commuting equilibrium traffic pattern

$M{C}_{w}^{A}=\frac{{\delta }_{w}{N}^{A}}{s}+{\alpha }_{w}\frac{L+l}{{v}_{1}}+{p}_{2}$ (7)

$M{C}_{b}^{A}=\frac{{\delta }_{b}{N}_{b}^{A}}{s}+\frac{{\alpha }_{b}}{{\alpha }_{w}}\frac{{\delta }_{w}{N}_{w}^{A}}{s}+{\alpha }_{b}\frac{L+l}{{v}_{1}}+{p}_{2}$ (8)

$M{C}_{w}^{T}={\alpha }_{w}\left(\frac{L}{{v}_{1}}+\frac{l}{{v}_{2}}+T\right)+{\theta }_{w}{N}^{T}+P\left(l\right)+{p}_{1}$ (9)

$M{C}_{b}^{T}={\alpha }_{b}\left(\frac{L}{{v}_{1}}+\frac{l}{{v}_{2}}+T\right)+{\theta }_{b}{N}^{T}+P\left(l\right)+{p}_{1}$ (10)

3.2. 交通出行模式组合概览

Table 2. Nine possible traffic patterns

${N}^{A}=\frac{{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+\left(P\left(l\right)+{p}_{1}-{p}_{2}\right)s+{\theta }_{w}sN}{{\delta }_{w}+s{\theta }_{w}}$ (11)

${N}^{T}=\frac{{\delta }_{w}N-{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)-\left(P\left(l\right)+{p}_{1}-{p}_{2}\right)s}{{\delta }_{w}+s{\theta }_{w}}$ (12)

4. 交通定价策略优化分析

4.1. 企业P和企业Q净利润最大(自由竞争模式)

$\mathrm{max}T{R}_{P}=\frac{-{\left({p}_{2}\right)}^{2}s+{p}_{2}\left[{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+\left(P\left(l\right)+{p}_{1}\right)s+{\theta }_{w}sN\right]}{{\delta }_{w}+s{\theta }_{w}}-{c}_{2}N$ (13)

$\begin{array}{l}\mathrm{max}T{R}_{Q}=\frac{-{\left(P\left(l\right)+{p}_{1}\right)}^{2}s+\left(P\left(l\right)+{p}_{1}\right)\left[{\delta }_{w}N-{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+{p}_{2}s+as\right]}{{\delta }_{w}+s{\theta }_{w}}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\left[a\frac{{\delta }_{w}N-{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+{p}_{2}s}{{\delta }_{w}+s{\theta }_{w}}+{c}_{1}N+F\right]\end{array}$ (14)

${p}_{2}=\frac{P\left(l\right)+{p}_{1}+{\alpha }_{w}\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+{\theta }_{w}N}{2}$ (15)

$P\left(l\right)+{p}_{1}=\frac{1}{2}\left[\frac{{\delta }_{w}N}{s}-{\alpha }_{w}\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+{p}_{2}+a\right]$ (16)

${p}_{2}=\frac{2{\theta }_{w}N}{3}+\frac{1}{3}\left(\frac{{\delta }_{w}N}{s}+a-{\alpha }_{w}\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)\right)$ (17)

$P\left(l\right)+{p}_{1}=\frac{1}{3}\left[{\theta }_{w}N-{\alpha }_{w}\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)\right]+\frac{2}{3}\left(\frac{{\delta }_{w}N}{s}+a\right)$ (18)

4.2. 社会净收益最大(政府干预模式)

$\begin{array}{l}\mathrm{min}TC={N}_{w}^{A}\left(\frac{{\delta }_{w}{N}^{A}}{s}+{\alpha }_{w}\frac{L+l}{{v}_{1}}\right)+{N}_{b}^{A}\left(\frac{{\delta }_{b}{N}_{b}^{A}}{s}+\frac{{\alpha }_{b}}{{\alpha }_{w}}\frac{{\delta }_{w}{N}_{w}^{A}}{s}+{\alpha }_{b}\frac{L+l}{{v}_{1}}\right)\\ \text{}+{N}_{w}^{T}\left[{\alpha }_{w}\left(\frac{L}{{v}_{1}}+\frac{l}{{v}_{2}}+T\right)+{\theta }_{w}{N}^{T}\right]+{N}_{b}^{T}\left[{\alpha }_{b}\left(\frac{L}{{v}_{1}}+\frac{l}{{v}_{2}}+T\right)+{\theta }_{b}{N}^{T}\right]\\ \text{}+a{N}^{T}+F+\left({c}_{1}+{c}_{2}\right)N\end{array}$ (19)

$\begin{array}{l}\mathrm{min}TC=\left({\alpha }_{w}{N}_{w}+{\alpha }_{b}{N}_{b}\right)\left(\frac{L}{{v}_{1}}+\frac{l}{{v}_{2}}+T\right)+{N}^{T}\left({\theta }_{w}{N}_{w}+{\theta }_{b}{N}_{b}\right)\\ \text{}+\left(N-{N}^{T}\right)\left(P\left(l\right)+{p}_{1}-{p}_{2}\right)+a{N}^{T}+F+\left({c}_{1}+{c}_{2}\right)N\end{array}$ (20)

$P\left(l\right)+{p}_{1}-{p}_{2}=\frac{a-\left[{N}_{b}\left({\theta }_{w}-{\theta }_{b}\right)+{\alpha }_{w}\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)\right]}{2}$ (21)

${N}^{A}=\frac{as+{N}_{b}s\left({\theta }_{w}+{\theta }_{b}\right)+{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)+2{\theta }_{w}s{N}_{w}}{2\left({\delta }_{w}+s{\theta }_{w}\right)}$ (22)

${N}^{T}=\frac{2{\delta }_{w}N-{\alpha }_{w}s\left(\frac{l}{{v}_{2}}-\frac{l}{{v}_{1}}+T\right)-as+{N}_{b}s\left({\theta }_{w}-{\theta }_{b}\right)}{{\delta }_{w}+s{\theta }_{w}}$ (23)

5. 算例分析

5.1. 停车换乘时间和通行能力变化

Figure 3. The prices of company p and company Q versus T with different s

Figure 4. The net profit of company p and company Q versus T with different s

Figure 5. The total social cost versus T with different s

Figure 6. The percentage of P&R versus T with different s

5.2. 两类出行者所占比例对系统总成本的影响

Figure 7. The total cost with or without government intervention versus different Nw

6. 结语

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