基于随机路径选择的城市轨道交通客流分配悖论
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摘要
在城市轨道交通网络中,当改善1条已有的轨道线路(包括提高发车频率和降低服务票价等)或者新增1条轨道线路之后,将会发生客流分配悖论。为了分析该交通悖论的特征,基于传统的和改进的Logit模型的随机网络加载结果,采用公式解析和数值计算的方法,研究了悖论的形成条件,推导了悖论边界曲线和悖论区域大小,讨论了不同的Logit模型在预测随机交通悖论方面的差异性,并最终得到了轨道线路的服务质量(包括运行时间和服务票价等)差异、乘客的随机路径选择行为、乘客的出行时间价值和随机感知误差的大小等因素对客流分配悖论产生的作用机理,为避免悖论的发生提供了理论指导。
A paradox of passenger flow distribution happens after an existing rail transit line is improved(i.e., departure frequency increases or transit fare decreases) or a new line is provided in an urban rail transit network. In order to analyze characteristics of the paradox, its occurrence conditions are derived by the methods of analytic formula and numerical computation. According to loading results of random networks based on traditional and improved Logit models, respectively, boundary curve and area size of the paradox are obtained, and the differences of the two Logit models in forecasting a stochastic traffic paradox is discussed. The mechanism of differences of service quality(i.e., traveling time or transit fare) among rail transit lines, passengers′ stochastic behaviors of route choice, values of time, and stochastic perceived error magnitudes effect on the paradox are proposed, which provides a theoretical guidance for avoiding it.
A paradox of passenger flow distribution happens after an existing rail transit line is improved(i.e., departure frequency increases or transit fare decreases) or a new line is provided in an urban rail transit network. In order to analyze characteristics of the paradox, its occurrence conditions are derived by the methods of analytic formula and numerical computation. According to loading results of random networks based on traditional and improved Logit models, respectively, boundary curve and area size of the paradox are obtained, and the differences of the two Logit models in forecasting a stochastic traffic paradox is discussed. The mechanism of differences of service quality(i.e., traveling time or transit fare) among rail transit lines, passengers′ stochastic behaviors of route choice, values of time, and stochastic perceived error magnitudes effect on the paradox are proposed, which provides a theoretical guidance for avoiding it.
引文
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[4] 赵春雪,傅白白,王天明.拥挤交通网络的Braess悖论现象[J].交通运输系统工程与信息,2012,12(4):155-160. ZHAO Chunxue, FU Baibai, WANG Tianming. Braess′ paradox phenomenon of congest traffic networks [J]. Journal of Transportation Systems Engineering and Information Technology, 2012,12(4):155-160.(in Chinese)
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[17] 戴婧彤.考虑拥挤效应的随机交通悖论分析[D].哈尔滨:哈尔滨工业大学,2016. DAI Jingtong. An analysis of stochastic assignment paradox considering congestion effect [D]. Harbin: Harbin Institute of Technology, 2016. (in Chinese)
[18] ZHANG F N, YANG H, LIU W. The downs-thomson paradox with responsive transit service [J]. Transportation Research Part A, 2014,70:244-263.
[19] ZHANG F N, LINDSEY R, YANG H. The downs-thomson paradox with imperfect mode substitutes and alternative transit administration regimes [J]. Transportation Research Part B, 2016,86:104-127.
[20] WANG W, WANG D Z W, ZHANG F N, et al. Overcoming the downs-thomson paradox by transit subsidy policies [J]. Transportation Research Part A, 2017,95:126-147.
[21] SZETO W Y, JIANG Y. Transit assignment: approach-based formulation, extragradient method, and paradox [J]. Transportation Research Part B, 2014,62:51-76.
[22] WANG Y, SZETO W Y. Excessive Noise Paradoxes in urban transportation networks [J]. Transportmetrica A: Transportation Science, 2017,13(3):195-221.
[23] 刘剑锋.基于换乘的城市轨道交通网络流量分配建模及其实证研究[D].北京:北京交通大学,2012. LIU Jianfeng. Transfer-based MODELING FLOW ASSIGNMENT WITH EMPIRICAL ANALYSIS FOR URBAN RAIL TRANSIT NETWORK [D]. Beijing: Beijing Jiaotong University, 2012. (in Chinese)
[24] 张帆.城市轨道交通网络客流分配模型及方法研究[D].北京:北京交通大学,2016. ZHANG Fan. Research on passenger flow assignment model and method of urban rail transit network [D]. Beijing: Beijing Jiaotong University, 2016. (in Chinese)
[25] 于晓桦,晏克非,牟振华,等.基于多级网络的多模式交通配流研究[J].交通信息与安全,2018,36(1):103-110. YU Xiaohua, YAN Kefei, MOU Zhenhua, ZHANG Hui. A study of multimodal traffic assignment based on multi-level network [J]. Journal of Transportation Information and Safety, 2018,36(1):103-110. (in Chinese)
[2] ZHANG X N, LAM W H K, HUANG H J. Braess′ s paradoxes in dynamic traffic assignment with simultaneous departure times and route choices [J]. Transportmetrica, 2008a,4(3):209-225.
[3] LIN W H, LO H K. Investigating braes′s paradox with time-dependent queues [J]. Transportation Science, 2009,43(1):117-126.
[4] 赵春雪,傅白白,王天明.拥挤交通网络的Braess悖论现象[J].交通运输系统工程与信息,2012,12(4):155-160. ZHAO Chunxue, FU Baibai, WANG Tianming. Braess′ paradox phenomenon of congest traffic networks [J]. Journal of Transportation Systems Engineering and Information Technology, 2012,12(4):155-160.(in Chinese)
[5] DI X, HE X Z, GUO X L, LIU H X. Braess paradox under the boundedly rational user equilibria [J]. Transportation Research Part B, 2014,67:86-108.
[6] HWANG M C, CHO H J. The classical braess paradox problem revisited: a generalized inverse method on non-unique path flow cases [J]. Networks and Spatial Economics, 2016,16(2):605-622.
[7] WANG W, WANG D Z W, SUN H J, et al. Braes′s paradox of traffic networks with mixed equilibrium behaviors [J]. Transportation Research Part E, 2016,93:95-114.
[8] TIRATANAPAKHOM T, KIM H, NAM D, LIM Y. Braes′s paradox in the uncertain demand and congestion assumed stochastic transportation network design problem [J]. KSCE Journal of Civil Engineering, 2016,20(7):2928-2937.
[9] FISK C. More paradoxes in the equilibrium assignment problem [J]. Transportation Research Part B, 1979,13(4):3035-309.
[10] YANG C, CHEN A. Sensitivity analysis of the combined travel demand model with applications [J]. European Journal of Operational Research, 2009,198(3):909-921.
[11] NAGURNEY A. Congested urban transportation networks and emission paradoxes [J]. Transportation Research Part D, 20005(2):145-151.
[12] YANG H, BELL M G H. A Capacity paradox in network design and how to avoid it [J]. Transportation Research Part A, 1998,32(7):539-545.
[13] YIN Y, IEDA H. Optimal improvement scheme for network reliability [J]. Transportation Research Record, 2002,1783:1-6.
[14] SZETO W Y. Cooperative game approaches to measuring network reliability considering paradoxes [J]. Transportation Research Part C, 2011,19(2):229-241.
[15] SHEFFI Y, DAGANZO C. Another paradox of traffic flow [J]. Transportation Research 1978,12(1):43-46.
[16] YAO J, CHEN A. An analysis of logit and weibit route choices in stochastic assignment paradox [J]. Transportation Research Part B, 2014,69:31-49.
[17] 戴婧彤.考虑拥挤效应的随机交通悖论分析[D].哈尔滨:哈尔滨工业大学,2016. DAI Jingtong. An analysis of stochastic assignment paradox considering congestion effect [D]. Harbin: Harbin Institute of Technology, 2016. (in Chinese)
[18] ZHANG F N, YANG H, LIU W. The downs-thomson paradox with responsive transit service [J]. Transportation Research Part A, 2014,70:244-263.
[19] ZHANG F N, LINDSEY R, YANG H. The downs-thomson paradox with imperfect mode substitutes and alternative transit administration regimes [J]. Transportation Research Part B, 2016,86:104-127.
[20] WANG W, WANG D Z W, ZHANG F N, et al. Overcoming the downs-thomson paradox by transit subsidy policies [J]. Transportation Research Part A, 2017,95:126-147.
[21] SZETO W Y, JIANG Y. Transit assignment: approach-based formulation, extragradient method, and paradox [J]. Transportation Research Part B, 2014,62:51-76.
[22] WANG Y, SZETO W Y. Excessive Noise Paradoxes in urban transportation networks [J]. Transportmetrica A: Transportation Science, 2017,13(3):195-221.
[23] 刘剑锋.基于换乘的城市轨道交通网络流量分配建模及其实证研究[D].北京:北京交通大学,2012. LIU Jianfeng. Transfer-based MODELING FLOW ASSIGNMENT WITH EMPIRICAL ANALYSIS FOR URBAN RAIL TRANSIT NETWORK [D]. Beijing: Beijing Jiaotong University, 2012. (in Chinese)
[24] 张帆.城市轨道交通网络客流分配模型及方法研究[D].北京:北京交通大学,2016. ZHANG Fan. Research on passenger flow assignment model and method of urban rail transit network [D]. Beijing: Beijing Jiaotong University, 2016. (in Chinese)
[25] 于晓桦,晏克非,牟振华,等.基于多级网络的多模式交通配流研究[J].交通信息与安全,2018,36(1):103-110. YU Xiaohua, YAN Kefei, MOU Zhenhua, ZHANG Hui. A study of multimodal traffic assignment based on multi-level network [J]. Journal of Transportation Information and Safety, 2018,36(1):103-110. (in Chinese)