城市轨道交通客流分配模型与算法的研究
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摘要
随着城市轨道交通基础建设的不断发展,城市轨道交通已经成为特大、大型城市分担城市地面公共交通的重要组成部分。由于轨道交通网络规模的扩展,乘客到达目的地会存在多条路径,研究多路径情况下的乘客出行路径选择行为以及在此基础上的客流分配,具有重要的理论价值和现实意义。
围绕轨道交通网络客流分配问题,本文主要进行了如下的研究工作：
1、对北京市轨道交通乘客出行意愿调查数据进行整理、统计和分析,得到了不同类型的乘客在不同出行条件下对于路径选择的一般性规律和影响乘客路径选择的主要因素,并为模型的相关参数估计提供了数据依据。
2、综合考虑影响乘客路径选择的定量因素,包括出行时间、换乘时间以及换乘次数,构造了路径广义费用模型。提出基于Logit关系的乘客路径选择概率模型。考虑北京市轨道交通网络拓扑的特点,采用改进Dijkstra算法和基于深度优先的图的遍历算法应用于有效路径搜索。通过对实例分析,验证本文所提出的模型及算法的有效性。
3、考虑到乘客出行的舒适度问题,提出更加符合现实的路径广义费用模型。将Fisk随机用户均衡配流模型应用在城市轨道交通网络的配流问题中,利用MSA和MSWA(相继加权平均算法)两种算法进行求解。通过算例分析,比较了两种算法的收敛效果。
As the Urban continuous development of rail transit infrastructure, urban rail transit has shared an important part of the city ground public transportation. The research of the passenger route choice behavior under multiple paths during traveling as well as the passenger flow distribution, has important theoretical value and practical significance.
Around the problem of rail transit passenger flow assignment, the paper study as following:
Firstly, statistic and analysis the survey data of Beijing rail transit. Obtain the main factors that impact on passenger route choice, and general rule for path selection of different types of passengers travel in different conditions
Secondly, considering the quantitative factors that influence the route choice behavior, improved the cost model by adding transfer time. Then, get the passenger route choice probability based on Logit model. Meanwhile, a modified Dijkstra algorithm and the depth first traversal algorithm for the model was given while searching effective routes in this paper. At last, an example is given to validate effectiveness of the model and algorithm.
Finally, taking the issue of passenger comfort, the path cost should add the qualitative factor (congestion costs). Then, based on Fisk's stochastic user equilibrium assignment model, use the MSA and the MSWA (successively weighted average algorithm) to solve the model. Examples are shown to compare the effect of two algorithms on convergence.
围绕轨道交通网络客流分配问题,本文主要进行了如下的研究工作：
1、对北京市轨道交通乘客出行意愿调查数据进行整理、统计和分析,得到了不同类型的乘客在不同出行条件下对于路径选择的一般性规律和影响乘客路径选择的主要因素,并为模型的相关参数估计提供了数据依据。
2、综合考虑影响乘客路径选择的定量因素,包括出行时间、换乘时间以及换乘次数,构造了路径广义费用模型。提出基于Logit关系的乘客路径选择概率模型。考虑北京市轨道交通网络拓扑的特点,采用改进Dijkstra算法和基于深度优先的图的遍历算法应用于有效路径搜索。通过对实例分析,验证本文所提出的模型及算法的有效性。
3、考虑到乘客出行的舒适度问题,提出更加符合现实的路径广义费用模型。将Fisk随机用户均衡配流模型应用在城市轨道交通网络的配流问题中,利用MSA和MSWA(相继加权平均算法)两种算法进行求解。通过算例分析,比较了两种算法的收敛效果。
As the Urban continuous development of rail transit infrastructure, urban rail transit has shared an important part of the city ground public transportation. The research of the passenger route choice behavior under multiple paths during traveling as well as the passenger flow distribution, has important theoretical value and practical significance.
Around the problem of rail transit passenger flow assignment, the paper study as following:
Firstly, statistic and analysis the survey data of Beijing rail transit. Obtain the main factors that impact on passenger route choice, and general rule for path selection of different types of passengers travel in different conditions
Secondly, considering the quantitative factors that influence the route choice behavior, improved the cost model by adding transfer time. Then, get the passenger route choice probability based on Logit model. Meanwhile, a modified Dijkstra algorithm and the depth first traversal algorithm for the model was given while searching effective routes in this paper. At last, an example is given to validate effectiveness of the model and algorithm.
Finally, taking the issue of passenger comfort, the path cost should add the qualitative factor (congestion costs). Then, based on Fisk's stochastic user equilibrium assignment model, use the MSA and the MSWA (successively weighted average algorithm) to solve the model. Examples are shown to compare the effect of two algorithms on convergence.
引文
[1]http://zh.wikipedia.org/zh-cn/%E5%8C%97%E4%BA%AC%E5%9C%B0%E9%93%81 [Z].维基百科：2010.
[2]Naohiko H., hyodo T., Uchiyama H. A study on characteristics of non ⅡA route choice mels on high density railway network[J]. Journal of Infrastructer Planning and Management, 2004(765):131-142.
[3]吴祥云,刘灿齐.轨道交通客流量均衡分配模型与算法[J].同济大学学报(自然科学版),2004,32(9)：1 158-1162.
[4]四兵锋,毛保华,刘智丽.无缝换乘条件下城市轨道交通网络客流分配模型及算法[J].铁道学报,2007,29(6)：12-1 8.
[5]孔繁钰,陈小峰.轨道交通随机均衡配流模型和算法[J].重庆工学院学报(自然科学版),2007,21(11)：26-30.
[6]孔繁钰,李献忠.弹性需求下的轨道交通客流分配模型和算法[J].西安工程大学学报,2008,22(1)：104-108.
[7]牛新奇,潘荫荣.轨道交通系统中清分算法的研究[J].计算机时代,2005(2)：17-21.
[8]顾磊.城市轨道交通统一票务收入结算分配算法与方案[J].计算机工程,2006,32(15)：239-244.
[9]杨甲,罗钦,徐瑞华.城市轨道交通网络清分方法研究[J].城市轨道交通研究,2009(5)：22-25.
[10]赖树坤,毛保华.城市轨道交通系统票务清分算法的研究[J].城市交通(铁道运输与经济),2007,29(6)：42-45.
[11]赵峰,张星臣,刘智丽.城市轨道交通系统运费清分方法研究[J].交通运输系统工程与信息,2007,7(6)：85-90.
[12]叶晋,史有群,杨学斌,等.遗传算法在轨道交通换乘路径求解问题上的应用[J].电脑与信息技术,2009,17(4)：24-27.
[13]Guan J. F., Yang Hai, Wirasinghe S. C. Simultaneous optimization of transit line configuration and passenger line assignment[J]. Transportation Research Part B,2006,40:885-902.
[14]徐瑞华,罗钦,高鹏.基于多路径的城市轨道交通网络客流分布模型及算法研究[J].铁道学报,2009,31(2)：110-114.
[15]刘剑锋,孙福亮,柏贇,等.城市轨道交通乘客路径选择模型及算法[J].交通运输系统工程与信息,2009,9(2)：81-86.
[16]四兵锋,张好智,高自友.求解logit随机网络配流问题的改进Dial算法[J].中国公路学报, 2009,22(1).
[17]Finney D. Probit Analysis[M]. England:Cambridge Univ.Press,1964.
[18]Daganzo C. F., Sheffi Y. On stochastic models of traffic assignmen[J]. Transportation Science, 1977,11:253-274.
[19]Lerman S. R., Manski C. F. An estimator for the generalized multinomial probit choice model: 56th Anual TRB Meeting, Washington,D.C.,1978[C].
[20]Clark C. E. The greatest of a finite set of random variables[J]. Operations Research, 1961,9:145-162.
[21]Horowitz J. L., Sparmann J. M., Daganzo C. F. An investigation of the accuracy of the Clark approximation for the multinomial probit model[J]. Transport Science,1982,16:382-401.
[22]Nielsen A. A stochastic transit assignment model considering differences in passengers utility functions[J]. Transportation Research B,2000,34:377-402.
[23]Garrido R. A., Mahmassani H. S. Forecasting freight transportation demand with the space-time multinomial probit model[J]. Transportation Research B,2000,34:403-418.
[24]Williams H. C. W. L. On the formulation of travel demand models and economic evaluation measures of user benefit[J]. Envrionment and planning,1977,9A:285-344.
[25]Fisk C. Some development in equilibrium traffic assigment[J]. Transport Research, 1980,14B:243-255.
[26]黄海军.城市交通网络平衡分析——理论与实践[M]//北京：人民交通出版社,1994：153-167.
[27]Sheffi Y., Powell W. B. An algorithm for equilibrium assignment problem with randon link times[J]. Networks,1982,12:191-207.
[28]陆化普,黄海军.交通规划理论研究前沿[M].北京：清华大学出版社,2007.
[29]Cascetta E., Nuzzolo A., Russo F.,等. A new route choice logit model overcoming ⅡA problems specification and some calibration result for interurban networks[J]. Transpotation and traffic theory,1996:691-711.
[30]Bell M. G. H., Lam W. H. K., Ploss G.,等. Stochastic user equilibrium assigment and iterative balancing[J]. Transportation and Traffic Theory,1993:427-439.
[31]Huang H. J. A combined algorithm for solving and calibrating the stochastic traffic assigment model[J]. Journal of the Operational Research Society,1995,46:977-987.
[32]Dial R. B. A probabilisitc multi-path traffic assigment model which obviates the need for path enumeration[J]. Transportation Research,1971,5:83-111.
[33]陆化普.交通规划理论与方法(第2版)[M].北京：清华大学出版社,1997.
[34]贺振欢,杨肇夏,蒋熙.Dial算法的几点改进[J].北方交通大学学报,2002,26(5)：89-91.
[35]邓军生,孔繁钰.MSA算法求解轨道交通SUE模型问题研究[J].重庆科技学院学报(自然科学版),2008,10(1)：129-131.
[36]Ren hualing, Gao Ziyou, Lam William H. k.,等. Assessing the benefits of integrated en-route transit information systems and time-varying transit pricing system in a congested transit network[J]. Transportation Planning and Technology,2009,32(3):215-237.
[37]宋一凡,高自友.拥挤条件下的公交平衡配流[J].中国公路学报,1999,12(4)：88-95.
[38]Roads Bureau of Public. Traffic Assignment Manual. U.S. Dept. of Commerce[M]. Washington D.C.:Urban Planning Division,1964.
[39]北京京港地铁有限公司.北京地铁4号线清分清算项目研究报告[R].北京：北京交通大学,2007.
[40]Robbins H., Monro S. A stochastic approximation method[J], Ann Math Stat, 1951,22(3):400-407.
[41]Henry X. Liu, Xiaozheng He, Bingsheng He. Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem[J]. Networks and Spatial Economics,2009,9(4):485-503.
[42]Polyak BT. New method of stochastic approximation type[J]. Autom Remote Control, 1990,51(7):937-946.
[43]Nagurney A., Zhang D. Projected dynamical systems and variational inequalities with applications[M]. Kluwer,Boston, Massachusetts,1996.
[2]Naohiko H., hyodo T., Uchiyama H. A study on characteristics of non ⅡA route choice mels on high density railway network[J]. Journal of Infrastructer Planning and Management, 2004(765):131-142.
[3]吴祥云,刘灿齐.轨道交通客流量均衡分配模型与算法[J].同济大学学报(自然科学版),2004,32(9)：1 158-1162.
[4]四兵锋,毛保华,刘智丽.无缝换乘条件下城市轨道交通网络客流分配模型及算法[J].铁道学报,2007,29(6)：12-1 8.
[5]孔繁钰,陈小峰.轨道交通随机均衡配流模型和算法[J].重庆工学院学报(自然科学版),2007,21(11)：26-30.
[6]孔繁钰,李献忠.弹性需求下的轨道交通客流分配模型和算法[J].西安工程大学学报,2008,22(1)：104-108.
[7]牛新奇,潘荫荣.轨道交通系统中清分算法的研究[J].计算机时代,2005(2)：17-21.
[8]顾磊.城市轨道交通统一票务收入结算分配算法与方案[J].计算机工程,2006,32(15)：239-244.
[9]杨甲,罗钦,徐瑞华.城市轨道交通网络清分方法研究[J].城市轨道交通研究,2009(5)：22-25.
[10]赖树坤,毛保华.城市轨道交通系统票务清分算法的研究[J].城市交通(铁道运输与经济),2007,29(6)：42-45.
[11]赵峰,张星臣,刘智丽.城市轨道交通系统运费清分方法研究[J].交通运输系统工程与信息,2007,7(6)：85-90.
[12]叶晋,史有群,杨学斌,等.遗传算法在轨道交通换乘路径求解问题上的应用[J].电脑与信息技术,2009,17(4)：24-27.
[13]Guan J. F., Yang Hai, Wirasinghe S. C. Simultaneous optimization of transit line configuration and passenger line assignment[J]. Transportation Research Part B,2006,40:885-902.
[14]徐瑞华,罗钦,高鹏.基于多路径的城市轨道交通网络客流分布模型及算法研究[J].铁道学报,2009,31(2)：110-114.
[15]刘剑锋,孙福亮,柏贇,等.城市轨道交通乘客路径选择模型及算法[J].交通运输系统工程与信息,2009,9(2)：81-86.
[16]四兵锋,张好智,高自友.求解logit随机网络配流问题的改进Dial算法[J].中国公路学报, 2009,22(1).
[17]Finney D. Probit Analysis[M]. England:Cambridge Univ.Press,1964.
[18]Daganzo C. F., Sheffi Y. On stochastic models of traffic assignmen[J]. Transportation Science, 1977,11:253-274.
[19]Lerman S. R., Manski C. F. An estimator for the generalized multinomial probit choice model: 56th Anual TRB Meeting, Washington,D.C.,1978[C].
[20]Clark C. E. The greatest of a finite set of random variables[J]. Operations Research, 1961,9:145-162.
[21]Horowitz J. L., Sparmann J. M., Daganzo C. F. An investigation of the accuracy of the Clark approximation for the multinomial probit model[J]. Transport Science,1982,16:382-401.
[22]Nielsen A. A stochastic transit assignment model considering differences in passengers utility functions[J]. Transportation Research B,2000,34:377-402.
[23]Garrido R. A., Mahmassani H. S. Forecasting freight transportation demand with the space-time multinomial probit model[J]. Transportation Research B,2000,34:403-418.
[24]Williams H. C. W. L. On the formulation of travel demand models and economic evaluation measures of user benefit[J]. Envrionment and planning,1977,9A:285-344.
[25]Fisk C. Some development in equilibrium traffic assigment[J]. Transport Research, 1980,14B:243-255.
[26]黄海军.城市交通网络平衡分析——理论与实践[M]//北京：人民交通出版社,1994：153-167.
[27]Sheffi Y., Powell W. B. An algorithm for equilibrium assignment problem with randon link times[J]. Networks,1982,12:191-207.
[28]陆化普,黄海军.交通规划理论研究前沿[M].北京：清华大学出版社,2007.
[29]Cascetta E., Nuzzolo A., Russo F.,等. A new route choice logit model overcoming ⅡA problems specification and some calibration result for interurban networks[J]. Transpotation and traffic theory,1996:691-711.
[30]Bell M. G. H., Lam W. H. K., Ploss G.,等. Stochastic user equilibrium assigment and iterative balancing[J]. Transportation and Traffic Theory,1993:427-439.
[31]Huang H. J. A combined algorithm for solving and calibrating the stochastic traffic assigment model[J]. Journal of the Operational Research Society,1995,46:977-987.
[32]Dial R. B. A probabilisitc multi-path traffic assigment model which obviates the need for path enumeration[J]. Transportation Research,1971,5:83-111.
[33]陆化普.交通规划理论与方法(第2版)[M].北京：清华大学出版社,1997.
[34]贺振欢,杨肇夏,蒋熙.Dial算法的几点改进[J].北方交通大学学报,2002,26(5)：89-91.
[35]邓军生,孔繁钰.MSA算法求解轨道交通SUE模型问题研究[J].重庆科技学院学报(自然科学版),2008,10(1)：129-131.
[36]Ren hualing, Gao Ziyou, Lam William H. k.,等. Assessing the benefits of integrated en-route transit information systems and time-varying transit pricing system in a congested transit network[J]. Transportation Planning and Technology,2009,32(3):215-237.
[37]宋一凡,高自友.拥挤条件下的公交平衡配流[J].中国公路学报,1999,12(4)：88-95.
[38]Roads Bureau of Public. Traffic Assignment Manual. U.S. Dept. of Commerce[M]. Washington D.C.:Urban Planning Division,1964.
[39]北京京港地铁有限公司.北京地铁4号线清分清算项目研究报告[R].北京：北京交通大学,2007.
[40]Robbins H., Monro S. A stochastic approximation method[J], Ann Math Stat, 1951,22(3):400-407.
[41]Henry X. Liu, Xiaozheng He, Bingsheng He. Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem[J]. Networks and Spatial Economics,2009,9(4):485-503.
[42]Polyak BT. New method of stochastic approximation type[J]. Autom Remote Control, 1990,51(7):937-946.
[43]Nagurney A., Zhang D. Projected dynamical systems and variational inequalities with applications[M]. Kluwer,Boston, Massachusetts,1996.