弹性需求下拥挤道路收费的模型与算法研究

Toll Model and Algorithm of Road Jammed with Traffic Based on Elastic Demand

摘要: 拥挤道路收费作为交通需求管理的一种有效措施在许多国家和地区开始提倡。研究了弹性需求下的拥挤道路收费问题, 建立了双层规划模型, 其中上层模型以用户盈余最大化为目标, 下层模型满足弹性需求下的随机用户平衡(SUE)。基于双层模型求解的复杂性, 设计了一个基于步长加速法和惩罚函数法的启发式算法, 实例计算表明该模型与算法是有效的。
- 拥挤道路收费 /
- 弹性需求 /
- 随机用户平衡 /
- 步长加速法 /
- 惩罚函数法
Abstract: Collecting toll for road jammed with traffic as an effective measure was adopted for managing traffic demand in many conutries and areas. The bi level programming model of the toll road was developed. The upper objective is consumer surplus which belongs to economics, while the lower is stochastic user equilibrium with elastic demand.Because of complex property, a heuristic algorithm which is based on step acceleration method and penalty function method is proposed, and a numerical example is given.
- collecting toll for road jammed with traffic /
- elastic demand /
- stochastic user equilibrium /
- step acceleration method /
- penalty function method

图 1 算例网络

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表 1 OD对需求函数的参数数据

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表 2 路段旅行时间函数的参数数据

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表 3 不同的η及δ下的求解结果

η	0.03	0.05	0.06	0.03	0.03	0.05
δ	0.4	0.4	0.4	0.6	0.8	1.0
u (1, 4)	0.4000	0.7312	0.8500	0.6094	1.0000	1.0000
u (1, 5)	0.45000	0	0.20000	0.22500	0.06875	0.50000
u (1, 7)	0.2000	0.4250	0.5063	0.2531	0	0.4453
u (2, 1)	0.5000	0.9500	1.0630	0.7031	1.6000	0.8125
u (2, 6)	0.4000	0.8687	1.2000	0.6000	0.8812	0.5234
u (3, 4)	0.8938	1.5190	1.3440	1.5280	1.8060	1.2580
u (3, 7)	0.7063	1.2560	1.0560	1.0870	0.6625	0.7734
u (4, 7)	0.8500	0.6937	0.6563	0.6563	0	0.5000
u (5, 7)	1.100	1.781	1.656	1.397	1.100	1.250
u (6, 5)	0.8000	0.4000	0.4000	0.6000	0.8438	1.0000
u (6, 7)	0.4500	0.9750	0.8437	0.6000	0.2875	1.0470
Z	-20640	-20660	-206650	-20630	-20610	-20660
q (1, 7)	246.8	238.0	237.1	251.4	256.0	237.8
q (2, 7)	142.3	133.4	131.9	144.1	145.8	135.4
q (3, 7)	186.8	184.1	185.2	184.4	186.3	186.7
q (6, 7)	217.1	213.3	215.1	216.0	217.1	211.7
num.SUE	612	1431	1023	1510	907	663
num.i	2	6	2	2	2	3
注: 在每种情形下, u ⁽⁰⁾ =0, α=1.95, ε=0.01, num.SUE为模型求解过程中SUE的总迭代数, num.i为惩罚迭代次数。

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表 4 OD需求函数参数π_ω变化下的计算结果

π_ω	0.04	0.05	0.06	0.08	0.10
q (1, 7)	287.3	266.6	220.6	175.8	147.0
q (2, 7)	169.00	146.60	128.70	83.37	62.39
q (3, 7)	182.9	173.0	146.0	124.0	107.5
q (4, 7)	186.4	180.2	166.7	140.0	123.9
TD	825.60	766.40	662.00	523.17	440.79
Z	-21910	-15560	-11550	-6875	-4378
注: 在每种情形下, u ⁽⁰⁾ =0, α=1.95, ε=0.08, δ=0.4, TD为网络所有OD对的总实际需求量, 不同OD对的需求函数参数π_ω均相同。

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