基于道路饱和度空间分布的拥挤收费模型研究
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摘要
随着城市交通需求和机动车保有量的不断增加,城市交通的供需矛盾日益突出,交通拥挤现象也越来越严重。城市交通拥挤收费作为交通需求管理的措施之一,可以有效的减少交通拥挤。本文在分析道路饱和度的基础上,建立了基于道路饱和度空间分布的交通拥挤收费模型,为最大程度的减少交通拥挤提供有效的交通拥挤收费方案。
首先,分析了影响拥挤收费费率的因素,利用经济学理论阐述了交通拥挤收费的基本原理,对交通拥挤收费的分类和实施后影响进行了总结分析,并在交通配流理论的基础上,介绍了拥挤收费的双层规划模型。
其次,用路网中道路饱和度的标准差来表征道路饱和度在路网中空间分布的情况。建立了基于道路饱和度空间分布的拥挤收费双层规划模型。上层模型为最小化路网用户的总出行时间,用道路饱和度的标准差的取值范围作为上层模型的约束条件;下层模型为固定需求下的用户平衡问题。在测试分析了函数迭代算法、连续平均算法和Polyak迭代平均算法这三种算法后,选取Polyak算法求解下层模型,运用二元遗传算法求解上层模型问题,因此用Polyak算法和遗传算法的组合算法来求解本文所建立的交通拥挤收费模型。
最后,通过案例分析来验证所建立的交通拥挤收费模型的实用性和模型求解算法的有效性,其中采用的路网是美国南达科他州的苏福尔市的道路网,算法求解是Matlab环境下编程实现的。算例分析了能使路网用户总出行时间最小的最优收费路段和收费水平,结果发现通过增加收费路段的数目,用户总出行时间和道路饱和标准差的就会变得更小。而且道路饱和度标准差达到最小值的收费费率比用户出行时间达到最小是的要高出不少。通过计算得出了在5个道路标准差区间中的最优收费方案供交通管理者选择。
With the growth of urban traffic demands and motor vehicles, the imbalance between supply and demand of urban traffic is obvious day by day. As a measure of traffic demand management, congestion pricing can decrease the traffic congestion effectively. Based on the spatial distribution analysis of road saturation, the congestion pricing model is established, and this can provide effective scheme for decreasing the congestion in greatest degree.
Firstly, factors influencing the traffic congestion toll is analyzed, and the basic principle of congestion pricing is explained from the aspect of economic theory. Based on the analysis of the classification of congestion pricing and the influence after the implement, the bi-level programming model of the congestion pricing is analyzed in combining with the basic theory of traffic assignment.
Secondly, the standard deviation of road saturation is used to describe the spatial distribution, and the traffic mode of private car is in consideration. The bi-level programming model based on the spatial distribution of road saturation is established. The upper level is to minimize the total travel time of users subjecting to the standard deviation of road saturation, while the lower level is the user equilibrium under fixed demand. The Genetic Algorithm combined with Polyak algorithm is selected to solve the model after the contrast of function iteration algorithm, method of successive averages algorithm, and Polyak iterate averaging algorithm.
Lastly, the road network of the Sioux Falls City,South Dakota is taken as a case to validate the practicability of the model and the validity of the algorithm, and the algorithm is realized by Matlab software. Case analysis shows the optimal toll locations and toll levels, and the result also shows that the total travel time can be decreased with the increase of number of toll links. The best toll scheme is determined for the traffic managers from the 5 road deviations.
首先,分析了影响拥挤收费费率的因素,利用经济学理论阐述了交通拥挤收费的基本原理,对交通拥挤收费的分类和实施后影响进行了总结分析,并在交通配流理论的基础上,介绍了拥挤收费的双层规划模型。
其次,用路网中道路饱和度的标准差来表征道路饱和度在路网中空间分布的情况。建立了基于道路饱和度空间分布的拥挤收费双层规划模型。上层模型为最小化路网用户的总出行时间,用道路饱和度的标准差的取值范围作为上层模型的约束条件;下层模型为固定需求下的用户平衡问题。在测试分析了函数迭代算法、连续平均算法和Polyak迭代平均算法这三种算法后,选取Polyak算法求解下层模型,运用二元遗传算法求解上层模型问题,因此用Polyak算法和遗传算法的组合算法来求解本文所建立的交通拥挤收费模型。
最后,通过案例分析来验证所建立的交通拥挤收费模型的实用性和模型求解算法的有效性,其中采用的路网是美国南达科他州的苏福尔市的道路网,算法求解是Matlab环境下编程实现的。算例分析了能使路网用户总出行时间最小的最优收费路段和收费水平,结果发现通过增加收费路段的数目,用户总出行时间和道路饱和标准差的就会变得更小。而且道路饱和度标准差达到最小值的收费费率比用户出行时间达到最小是的要高出不少。通过计算得出了在5个道路标准差区间中的最优收费方案供交通管理者选择。
With the growth of urban traffic demands and motor vehicles, the imbalance between supply and demand of urban traffic is obvious day by day. As a measure of traffic demand management, congestion pricing can decrease the traffic congestion effectively. Based on the spatial distribution analysis of road saturation, the congestion pricing model is established, and this can provide effective scheme for decreasing the congestion in greatest degree.
Firstly, factors influencing the traffic congestion toll is analyzed, and the basic principle of congestion pricing is explained from the aspect of economic theory. Based on the analysis of the classification of congestion pricing and the influence after the implement, the bi-level programming model of the congestion pricing is analyzed in combining with the basic theory of traffic assignment.
Secondly, the standard deviation of road saturation is used to describe the spatial distribution, and the traffic mode of private car is in consideration. The bi-level programming model based on the spatial distribution of road saturation is established. The upper level is to minimize the total travel time of users subjecting to the standard deviation of road saturation, while the lower level is the user equilibrium under fixed demand. The Genetic Algorithm combined with Polyak algorithm is selected to solve the model after the contrast of function iteration algorithm, method of successive averages algorithm, and Polyak iterate averaging algorithm.
Lastly, the road network of the Sioux Falls City,South Dakota is taken as a case to validate the practicability of the model and the validity of the algorithm, and the algorithm is realized by Matlab software. Case analysis shows the optimal toll locations and toll levels, and the result also shows that the total travel time can be decreased with the increase of number of toll links. The best toll scheme is determined for the traffic managers from the 5 road deviations.
引文
1 Albert Cheung, Graham Bodell.曼谷的交通问题——对上海的教训.畅达新世纪的城市交通.同济大学出版社. 1999, 11: 43~53
2 Bruno De Borger, Kurt Van Dender.Transport tax reform, commuting, and endogenous values of time. Journal of Urban Economics. 2003, 53(3): 510~530
3胡欣,江小群.城市经济学.上海:立信会计出版社. 2005: 18~36
4 Small K. A. Special issue:congestion pricing. Transportation. 1992, 19:287~291
5 Pigou A.C. the economics of welfare. Macmillan. 1920: 5~10
6 Knight F. H. Some fallacies in the interpretation of social cost. Quarterly Journal of Economics. 1924, 38(August): 582~606
7 Button K. J, Verhoef E. Road Pricing, Traffic Congestion and the Environment: Issues of Efficiency and Social Feasibility. Edward Elgar, Aldershot. 1998: 156~194
8 Gibbons E. O'Mahony M. External cost internalisation of urban transport: a case study of Dublin. Journal of Environmental Management. 2002, 64(4): 401~410
9 Werner Rothengatter. How good is first best? Marginal cost and other pricing principles for user charging in transport. Transport Policy. 2003, 10:121~130
10 John R. Meyer, JoséA. Gómez-Ibá?ez, William B. Tye, Clifford Winston. Essays in transportation economics and policy. Brookings institution press. Washington, D.C. 1999: 99~102
11 Richard H. M. Emmerink. Information and pricing in road transportation. Springer. 1998: 35~57
12 Vickrey W. S. Congestion theory and transport investment. American Economic Review. 1969, 59: 251~261
13 Arnott R., de Palma A., Lindsey R. Economics of bottleneck. Journal of Urban Economics. 1990, 27: 11~30
14 Arnott R., de Palma A., Lindsey R. Departure time and route choice for the morning commute. Transportation Research Part B. 1990, 24: 209~228
15 Laih C. H. Queuing at a bottleneck with single- and multi-step tolls. Transportation Research Part A. 1994, 28: 197~208
16 Liu,N.L., McDonald, J.E. Economics efficiency of second-best congestionpricing schemes in urban highway systems. Transportation Research Part B. 1999, 33: 157~188
17 Liu, N.L, McDonald, J.E. Efficient congestion tolls in the presence of unPriced congestion:A peak and off-peak simulation model. Journal of Urban Economics. 1998, 44: 352~366
18 Liu, N.L, Boyce, D.E. Variational inequality formulation of the system-optimal travel choice problem and efficient congestion tolls for a general transportation network with multiple time periods. Regional Science and Urban Economics. 2002, 32: 627~650
19 S. Proost, K.Van Dender, et al. How large is the gap between present and efficient transport prices in Europe? Transport Policy. 2002, 9: 41~57
20 Andréde Palma, Robin Lindsey, Emile Quinet. Time-varying road pricing and choice of toll locations. Research in Transportation Economics. 2004, 9: 107~131
21 David A. Hensher, Sean M. Puckett. Road user charging: The global relevance of recent developments in the United Kingdom. Transport Policy. 2005, 12: 377~383
22 Stef Proost, Ahksaya Sen. Urban transport pricing reform with two levels of government: A case study of Brussels. Transport Policy. 2006, 13:127~139
23 Stef Proost, Kurt Van Dender. Optimal urban transport pricing in the presence of congestion, economies of density and costly public funds. Transportation Research Part A. 2008, 42: 1220~1230
24 Xuegang (Jeff) Ban, Henry X. Liu. A Link-Node Discrete-Time Dynamic Second Best Toll Pricing Model with a Relaxation Solution Algorithm. Networks and Spatial Economics. 2009, 9(2): 243~267
25 JoséHolguín-Veras, Mecit Cetin. Optimal tolls for multi-class traffic: Analytical formulations and policy implications. Transportation Research Part A. 2009, 43: 445~467
26 Kwang Sik Kim, Keeyeon Hwang. An Application of Road Pricing Schemes to Urban Expressways in Seoul.Cities. 2005, 22(1): 43~53
27 Jan Rouwendal, Erik T.Verhoef. Basic Economic Principles of Road Pricing: from Theory to Applications. Transport Policy. 2006, 13(2):106~114
28 Se-il Mun, Ko-ji Konishi, Kazuhiro Yoshikawa. Optimal cordon pricing in a non-monocentric city. Transportation Research Part A. 2005, 39: 723~736
29 David Levinson. Micro-Foundations of Congestion and Pricing: A Game Theory Perspective. Transportation Research Part A. 2005, 39: 691~704
30 Byung-Wook Wie. Dynamic Stackelberg Equilibrium Congestion Pricing. Transportation Research Part C. 2007, 15: 154~174
31 Christelle Viauroux. Structural estimation of congestion costs. European Economic Review. 2007, 51: 1~25
32 Yang H., Lam W. H. K.. Optimal road tolls under conditions of queuing and congestion. Transportation Research Part A. 1996, 30: 319~332
33 Yang H., Michael G. H. Bell. Traffic restraint, road pricing and network equilibrium. Transportation Research Part B. 1997, 31: 303~314
34 Yang H., Huang H-J. Principle of marginal cost pricing: How does it work in a general road work. Transportation Research Part A. 1998, 32 (1): 45~54
35 Yang H., Xu W., He B. S., Meng Q. Road pricing for congestion control with unknown demand and cost functions. Transportation Research Part C. 2010, 18 (2): 157~175
36黄海军, Michael G. H. Bell,杨海.公共与个体竞争交通系统的定价研究.管理科学学报. 1998, 1(2): 17~23
37晏克非,张国强,覃煜.基与车辆动态导航的拥挤定价.交通运输工程学报. 2001, 1(3): 74~76
38王健.道路拥挤定价下的公共交通收费问题研究.哈尔滨工业大学博士学位论文. 2003: 1~19
39王健,安实,赵泽斌.基于财政补贴的拥挤定价下公交收费策略研究.管理工程学报. 2006, 20(2): 84~88
40王健,田禹,安实.基于环境保护的拥挤定价下公交收费策略研究.系统工程学报. 2006, 21(2): 211~215
41唐毓敏,冯苏苇.政策博弈下的道路交通拥挤定价.管理科学学报. 2008, 11(4): 67~82
42张中安,冯苏苇.公务车与私家车博弈下的交通拥挤收费效果研究.交通运输系统工程与信息. 2008, 8(2): 85~90
43朱广芹,佟光霁,代磊磊.城市道路交通拥挤收费的博弈分析.系统工程理论与实践. 2009, 29(7): 147~152
44刘南,陈达强.多时段城市路网拥挤定价收费的效率分析.系统管理学报. 2007, 16(5): 477~482
45钟绍鹏,邓卫.动态多用户类型和多模式拥挤收费模型.东南大学学报(自然科学版). 2008, 38(5): 866~872
46姚红云,张小宁,孙立军.弹性需求下多类型用户拥挤收费模型.中国公路学报. 2008, 21(6): 102~108
47李志纯,谷强,史峰.弹性需求下拥挤道路收费的模型与算法研究.交通运输工程学报. 2001, 9: 81~85
48史峰,李志纯.网络扩容和拥挤道路使用收费的组合模型及求解算法.中国公路学报. 2003, 2: 90~94
49张华歆,周溪召.多模式交通网络的拥挤道路收费双层规划模型.系统工程理论方法应用. 2005, 6: 546~551
50陈来荣,张岚.基于双层规划的拥挤定价模型及算法.北京工业大学学报. 2006, 6: 526~529
51 Walters , A. A. The theory and measurement of private and social cost of highway congestion. Econometrica. 1961, 29: 676~699
52 Dafermos , S. C. , Sparrow , F. T. Optimal resource allocation and toll patterns in ues-optimized transportation network. Journal of Transportation Economics and Policy. 1971, 5: 198~200
53 Dafermos , S. C. Toll patterns for multiclass-user transportation networks. Transportation Sciences. 1973, 7: 211~223
54 Smith , M. J. The marginal cost taxation of a transportation network. Transportation Research. 1979, 13B: 237~242
55 Button , K. J. Transport Economics (2nd Edition). Edward Elgar. England
56 Meng Qiang. Bilevel transportation modeling and optimization. PhD Thesis, Department of Civil Engineering. Hong Kong University of Science and Technology. 2000: 57~71
57 Dafermos, D. and Sparrow, F. T. The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards. 1969, 73B: 91~118
58 Fisk C. Some developments in equilibrium traffic assignment. Transportation Research Part B. 1980, 14(3): 243~255
59 Sheffi Y, Powell W B. An algorithm for the equilibrium assignment problem with random link times. Networks. 1982, 12: 191~207
60沈颖,朱翀,徐英俊.道路饱和度计算方法研究.交通与安全. 2007, (1): 125~129
2 Bruno De Borger, Kurt Van Dender.Transport tax reform, commuting, and endogenous values of time. Journal of Urban Economics. 2003, 53(3): 510~530
3胡欣,江小群.城市经济学.上海:立信会计出版社. 2005: 18~36
4 Small K. A. Special issue:congestion pricing. Transportation. 1992, 19:287~291
5 Pigou A.C. the economics of welfare. Macmillan. 1920: 5~10
6 Knight F. H. Some fallacies in the interpretation of social cost. Quarterly Journal of Economics. 1924, 38(August): 582~606
7 Button K. J, Verhoef E. Road Pricing, Traffic Congestion and the Environment: Issues of Efficiency and Social Feasibility. Edward Elgar, Aldershot. 1998: 156~194
8 Gibbons E. O'Mahony M. External cost internalisation of urban transport: a case study of Dublin. Journal of Environmental Management. 2002, 64(4): 401~410
9 Werner Rothengatter. How good is first best? Marginal cost and other pricing principles for user charging in transport. Transport Policy. 2003, 10:121~130
10 John R. Meyer, JoséA. Gómez-Ibá?ez, William B. Tye, Clifford Winston. Essays in transportation economics and policy. Brookings institution press. Washington, D.C. 1999: 99~102
11 Richard H. M. Emmerink. Information and pricing in road transportation. Springer. 1998: 35~57
12 Vickrey W. S. Congestion theory and transport investment. American Economic Review. 1969, 59: 251~261
13 Arnott R., de Palma A., Lindsey R. Economics of bottleneck. Journal of Urban Economics. 1990, 27: 11~30
14 Arnott R., de Palma A., Lindsey R. Departure time and route choice for the morning commute. Transportation Research Part B. 1990, 24: 209~228
15 Laih C. H. Queuing at a bottleneck with single- and multi-step tolls. Transportation Research Part A. 1994, 28: 197~208
16 Liu,N.L., McDonald, J.E. Economics efficiency of second-best congestionpricing schemes in urban highway systems. Transportation Research Part B. 1999, 33: 157~188
17 Liu, N.L, McDonald, J.E. Efficient congestion tolls in the presence of unPriced congestion:A peak and off-peak simulation model. Journal of Urban Economics. 1998, 44: 352~366
18 Liu, N.L, Boyce, D.E. Variational inequality formulation of the system-optimal travel choice problem and efficient congestion tolls for a general transportation network with multiple time periods. Regional Science and Urban Economics. 2002, 32: 627~650
19 S. Proost, K.Van Dender, et al. How large is the gap between present and efficient transport prices in Europe? Transport Policy. 2002, 9: 41~57
20 Andréde Palma, Robin Lindsey, Emile Quinet. Time-varying road pricing and choice of toll locations. Research in Transportation Economics. 2004, 9: 107~131
21 David A. Hensher, Sean M. Puckett. Road user charging: The global relevance of recent developments in the United Kingdom. Transport Policy. 2005, 12: 377~383
22 Stef Proost, Ahksaya Sen. Urban transport pricing reform with two levels of government: A case study of Brussels. Transport Policy. 2006, 13:127~139
23 Stef Proost, Kurt Van Dender. Optimal urban transport pricing in the presence of congestion, economies of density and costly public funds. Transportation Research Part A. 2008, 42: 1220~1230
24 Xuegang (Jeff) Ban, Henry X. Liu. A Link-Node Discrete-Time Dynamic Second Best Toll Pricing Model with a Relaxation Solution Algorithm. Networks and Spatial Economics. 2009, 9(2): 243~267
25 JoséHolguín-Veras, Mecit Cetin. Optimal tolls for multi-class traffic: Analytical formulations and policy implications. Transportation Research Part A. 2009, 43: 445~467
26 Kwang Sik Kim, Keeyeon Hwang. An Application of Road Pricing Schemes to Urban Expressways in Seoul.Cities. 2005, 22(1): 43~53
27 Jan Rouwendal, Erik T.Verhoef. Basic Economic Principles of Road Pricing: from Theory to Applications. Transport Policy. 2006, 13(2):106~114
28 Se-il Mun, Ko-ji Konishi, Kazuhiro Yoshikawa. Optimal cordon pricing in a non-monocentric city. Transportation Research Part A. 2005, 39: 723~736
29 David Levinson. Micro-Foundations of Congestion and Pricing: A Game Theory Perspective. Transportation Research Part A. 2005, 39: 691~704
30 Byung-Wook Wie. Dynamic Stackelberg Equilibrium Congestion Pricing. Transportation Research Part C. 2007, 15: 154~174
31 Christelle Viauroux. Structural estimation of congestion costs. European Economic Review. 2007, 51: 1~25
32 Yang H., Lam W. H. K.. Optimal road tolls under conditions of queuing and congestion. Transportation Research Part A. 1996, 30: 319~332
33 Yang H., Michael G. H. Bell. Traffic restraint, road pricing and network equilibrium. Transportation Research Part B. 1997, 31: 303~314
34 Yang H., Huang H-J. Principle of marginal cost pricing: How does it work in a general road work. Transportation Research Part A. 1998, 32 (1): 45~54
35 Yang H., Xu W., He B. S., Meng Q. Road pricing for congestion control with unknown demand and cost functions. Transportation Research Part C. 2010, 18 (2): 157~175
36黄海军, Michael G. H. Bell,杨海.公共与个体竞争交通系统的定价研究.管理科学学报. 1998, 1(2): 17~23
37晏克非,张国强,覃煜.基与车辆动态导航的拥挤定价.交通运输工程学报. 2001, 1(3): 74~76
38王健.道路拥挤定价下的公共交通收费问题研究.哈尔滨工业大学博士学位论文. 2003: 1~19
39王健,安实,赵泽斌.基于财政补贴的拥挤定价下公交收费策略研究.管理工程学报. 2006, 20(2): 84~88
40王健,田禹,安实.基于环境保护的拥挤定价下公交收费策略研究.系统工程学报. 2006, 21(2): 211~215
41唐毓敏,冯苏苇.政策博弈下的道路交通拥挤定价.管理科学学报. 2008, 11(4): 67~82
42张中安,冯苏苇.公务车与私家车博弈下的交通拥挤收费效果研究.交通运输系统工程与信息. 2008, 8(2): 85~90
43朱广芹,佟光霁,代磊磊.城市道路交通拥挤收费的博弈分析.系统工程理论与实践. 2009, 29(7): 147~152
44刘南,陈达强.多时段城市路网拥挤定价收费的效率分析.系统管理学报. 2007, 16(5): 477~482
45钟绍鹏,邓卫.动态多用户类型和多模式拥挤收费模型.东南大学学报(自然科学版). 2008, 38(5): 866~872
46姚红云,张小宁,孙立军.弹性需求下多类型用户拥挤收费模型.中国公路学报. 2008, 21(6): 102~108
47李志纯,谷强,史峰.弹性需求下拥挤道路收费的模型与算法研究.交通运输工程学报. 2001, 9: 81~85
48史峰,李志纯.网络扩容和拥挤道路使用收费的组合模型及求解算法.中国公路学报. 2003, 2: 90~94
49张华歆,周溪召.多模式交通网络的拥挤道路收费双层规划模型.系统工程理论方法应用. 2005, 6: 546~551
50陈来荣,张岚.基于双层规划的拥挤定价模型及算法.北京工业大学学报. 2006, 6: 526~529
51 Walters , A. A. The theory and measurement of private and social cost of highway congestion. Econometrica. 1961, 29: 676~699
52 Dafermos , S. C. , Sparrow , F. T. Optimal resource allocation and toll patterns in ues-optimized transportation network. Journal of Transportation Economics and Policy. 1971, 5: 198~200
53 Dafermos , S. C. Toll patterns for multiclass-user transportation networks. Transportation Sciences. 1973, 7: 211~223
54 Smith , M. J. The marginal cost taxation of a transportation network. Transportation Research. 1979, 13B: 237~242
55 Button , K. J. Transport Economics (2nd Edition). Edward Elgar. England
56 Meng Qiang. Bilevel transportation modeling and optimization. PhD Thesis, Department of Civil Engineering. Hong Kong University of Science and Technology. 2000: 57~71
57 Dafermos, D. and Sparrow, F. T. The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards. 1969, 73B: 91~118
58 Fisk C. Some developments in equilibrium traffic assignment. Transportation Research Part B. 1980, 14(3): 243~255
59 Sheffi Y, Powell W B. An algorithm for the equilibrium assignment problem with random link times. Networks. 1982, 12: 191~207
60沈颖,朱翀,徐英俊.道路饱和度计算方法研究.交通与安全. 2007, (1): 125~129