Abstract
Traffic assignment has been recognized as one of the key technologies in supporting transportation planning and operations. To better address the perfectly rational issue of the expected utility theory (EUT) and the overlapping path issue of the multinomial logit (MNL) model that are involved in the traffic assignment process, this paper proposes a cumulative prospect value (CPV)-based generalized nested logit (GNL) stochastic user equilibrium (SUE) model. The proposed model uses CPV to replace the utility value as the path performance within the GNL model framework. An equivalent mathematical model is provided for the proposed CPV-based GNL SUE model, which is solved by the method of successive averages (MSA). The existence and equivalence of the solution are also proved for the equivalent model. To demonstrate the performance of the proposed CPV-based GNL SUE model, three road networks are selected in the empirical test. The results show that the proposed model can jointly deal with the perfectly rational issue and the overlapping path issue, and additionally, the proposed model is shown to be applicable for large road networks.
摘要
交通分配是交通规划和运营的关键技术之一。为了更好地解决交通分配过程中涉及的期望效用 理论(EUT)的完全理性问题和多项式logit(MNL)模型的路径重叠问题, 本文提出了基于累积前景值 (CPV)的广义巢式logit(GNL)随机用户平衡(SUE)模型, 即基于CPV 的GNL SUE 模型。该模型在GNL 模型框架内使用CPV 代替效用值作为路径性能。对于该模型, 给出等价的数学模型, 并使用相继平 均法(MSA)对该数学模型进行求解, 同时模型解的存在性和等价性也被证明。为了展示基于CPV 的 GNL SUE 模型的性能, 选择三个道路网络作为测试实例, 结果表明, 提出的模型可以同时处理完全理 性问题和路径重叠问题, 并且适用于大型道路网络。
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
DAGANZO C F, SHEFFI Y. On stochastic models of traffic assignment [J]. Transportation Science, 1977, 11: 253–274. DOI: https://doi.org/10.1287/trsc.11.3.253.
SHEFFI Y. Urban transportation networks [M]. New Jersey: Prentice-Hall, 1985.
BEKHOR S, PRASHKER J N. Stochastic user equilibrium formulation for generalized nested logit model [J]. Transportation Research Record Journal of the Transportation Research Board, 2001, 1752: 84–90. DOI: https://doi.org/10.3141/1752-12.
BEKHOR S, REZNIKOVA L, TOLEDO T. Application of cross-nested logit route choice model in stochastic user equilibrium traffic assignment [J]. Transportation Research Record: Journal of the Transportation Research Board, 2007, 2003: 41–49. DOI: https://doi.org/10.3141/2003-06.
BEKHOR S, TOLEDO T, REZNIKOVA L. A path-based algorithm for the cross-nested logit stochastic user equilibrium traffic assignment [J]. Computer-Aided Civil and Infrastructure Engineering, 2010, 24(1): 15–25. DOI: https://doi.org/10.1111/j.1467-8667.2008.00563.x.
CHEN A, PRAVINVONGVUTH S, XU Xiang-dong, RYU S, CHOOTINAN P. Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models [J]. Transportation Research Part A: Policy and Practice, 2012, 46: 1343–1358. DOI: https://doi.org/10.1016/j.tra.2012.04.003.
AVINERI E, PRASHKER J N. Violations of expected utility theory in route-choice stated preferences [J]. Transportation Research Record: Journal of the Transportation Research Board, 2004, 1894: 222–229. DOI: https://doi.org/10.3141/1894-23.
WANG Qian, XU Wei. A user equilibrium model based on cumulative prospect theory for degradable transport network [C]// 4th International Joint Conference on Computational Sciences and Optimization (CSO). IEEE. 2011: 1078–1082. DOI: https://doi.org/10.1109/CSO.2011.62.
XU Hong-li, LOU Ying-yan, YIN Ya-feng, ZHOU Jing. A prospect-based user equilibrium model with endogenous reference points and its application in congestion pricing [J]. Transportation Research Part B: Methodological, 2011, 45(2): 311–328. DOI: https://doi.org/10.1016/j.trb.2010.09.003.
JOU Rong-chang, CHEN Ke-hong. An application of cumulative prospect theory to freeway drivers’ route choice behaviours [J]. Transportation Research Part A: Policy and Practice, 2013, 49: 123–131. DOI: https://doi.org/10.1016/j.tra.2013.01.011.
YANG Ju-fen, JIANG Gui-yan. Development of an enhanced route choice based on cumulative prospect theory [J]. Transportation Research Part C: Emerging Technologies, 2014, 47: 168–178. DOI: https://doi.org/10.1016/j.trc.2014.06.009.
HOROWITZ J. Reconsidering the multinomial probit model [J]. Transportation Research Part B: Methodological, 1991, 25(6): 433–438. DOI: https://doi.org/10.1016/0191-2615(91)90036-I.
MCFADDEN D. A method of simulated moments for estimation of discrete response models without numerical integration [J]. Econometrica, 1989, 57(5): 995–1026. DOI: 0012-9682(198909)57:5<995:AMOSMF>2.0.CO;2-Z.
PRASHKER J N, BEKHOR S. Route choice models used in the stochastic user equilibrium problem: A review [J]. Transport Reviews, 2004, 24(4): 437–463. DOI: https://doi.org/10.1080/0144164042000181707.
FREJINGER E, BIERLAIRE M. Capturing correlation with subnetworks in route choice models [J]. Transportation Research Part B: Methodological, 2007, 41(3): 363–378. DOI: https://doi.org/10.1016/j.trb.2006.06.003.
LAI Xin-jun, LI Jun. Modelling stochastic route choice behaviours with a closed-form mixed logit model [J]. Mathematical Problems in Engineering, 2015, 1–9. DOI: https://doi.org/10.1155/2015/729089.
ZHOU Zhong, CHEN A, BEKHOR S. C-logit stochastic user equilibrium model: Formulations and solution algorithm [J]. Transportmetrica, 2012, 8(1): 17–41. DOI: https://doi.org/10.1080/18128600903489629.
LIU B Q, ZHANG Y H, DU W. A simplified C-logit stochastic user equilibrium model on bimodal transportation network [J]. Mathematical Problems in Engineering, 2020, 2020: 1–8. DOI: https://doi.org/10.1155/2020/3702965.
YONG Gui, HUANG Hai-jun, LIU Tian-liang, XU Yan. Bounding the inefficiency of the C-Logit stochastic user equilibrium assignment [J]. Journal of Systems Science and Complexity, 2016, 29(6): 1629–1649. DOI: https://doi.org/10.1007/s11424-016-4320-4.
DUNCAN L C, WATLING D P, CONNORS R D, RASMUSSEN T K, NIELSEN O A. Path size logit route choice models: Issues with current models, a new internally consistent approach, and parameter estimation on a large-scale network with GPS data [J]. Transportation Research Part B: Methodological, 2020, 135: 1–40. DOI: https://doi.org/10.1016/j.trb.2020.02.006.
QIU Song-Lin, CHENG Lin, XU Xiang-dong. Path-size logit-based stochastic user equilibrium assignment model [J]. Journal of Southeast University(Science and Technology), 2012, 42(1): 173–176. DOI: https://doi.org/10.3969/j.issn.1001-0505.2012.01.032. (in Chinese)
PRASHKER J N, BEKHOR S. Investigation of stochastic network loading procedures [J]. Transportation Research Record Journal of the Transportation Research Board, 1998, 1645: 94–102. DOI: https://doi.org/10.3141/1645-12.
PAPOLA A, MARZANO V. A network generalized extreme value model for route choice allowing implicit route enumeration [J]. Computer-Aided Civil and Infrastructure Engineering, 2013, 28(8): 560–580. DOI: https://doi.org/10.1111/mice.12007.
MCFADDEN D. Modelling the choice of residential location [J]. Transportation Research Record Journal of the Transportation Research Board, 1978, 673(672): 72–77.
LU Xiao-shan, LIU Tian-liang, HUANG Hai-jun. Pricing and mode choice based on nested logit model with trip-chain costs [J]. Transport Policy, 2015, 44: 76–88. DOI: https://doi.org/10.1016/j.tranpol.2015.06.014.
KAROONSOONTAWONG A, LIN Dung-ying. Combined gravity model trip distribution and paired combinatorial logit stochastic user equilibrium problem [J]. Networks and Spatial Economics, 2015, 15(4): 1011–1048. DOI: https://doi.org/10.1007/s11067-014-9279-x.
RYU S, CHEN A, XU Xiang-dong, CHOI K. Modeling demand elasticity and route overlapping in stochastic user equilibrium through paired combinatorial logit model [J]. Transportation Research Record: Journal of the Transportation Research Board, 2014, 2429: 8–19. DOI: https://doi.org/10.3141/2429-02.
WANG Jian, PEETA S, HE Xiao-zheng, ZHAO Jin-bao. Combined multinomial logit modal split and paired combinatorial logit traffic assignment model [J]. Transportmetrica A: Transport Science, 2018, 14(9): 737–760. DOI: https://doi.org/10.1080/23249935.2018.1431701.
ZHANG R, YAO E J, PAN L. Optimizing EV-based P&R subsidy policies for commuting corridor based on cross-nested logit model [J]. International Journal of Sustainable Transportation, 2019, 13(7): 461–478. DOI: https://doi.org/10.1080/15568318.2018.1482032.
LI Xue-fei, LANG Mao-xiang. Multi-class and multi-criteria stochastic user equilibrium model based on generalized nested logit model [J]. Journal of Transportation Systems Engineering and Information Technology, 2014, 14(4): 139–145. DOI: https://doi.org/10.16097/j.cnki.1009-6744.2014.04.024.
KAHNEMAN D, TVERSKY A. A prospect theory: An analysis of decisions under risk [J]. Econometrics, 1979, 47: 313–327. DOI: https://doi.org/10.2307/1914185.
TVERSKY A, KAHNEMAN D. Advances in prospect theory: Cumulative representation of uncertainty [J]. Journal of Risk and Uncertainty, 1992, 5(4): 297–323. DOI: https://doi.org/10.1007/978-3-319-20451-2_24.
CONNORS R D, SUMALEE A. A Network equilibrium model with travelers’ perception of stochastic travel times [J]. Transportation Research Part B: Methodological, 2009, 43(6): 614–624. DOI: https://doi.org/10.1016/j.trb.2008.12.002.
WANG Wei, SUN Hui-jun. Cumulative prospect theory-based user equilibrium model with stochastic perception errors [J]. Journal of Central South University, 2016, 23(9): 2465–2474. DOI: https://doi.org/10.1007/s11771-016-3305-8.
Bureau of Public Roads. Traffic assignment manual [M]. Washington DC: US Department of Commerce, Urban Planning Division, 1964.
LO H K, LUO X W, SIU B W Y. Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion [J]. Transportation Research Part B: Methodological, 2006, 40(9): 792–806. DOI: https://doi.org/10.1016/j.trb.2005.10.003.
SHASHKIN A. A functional central limit theorem for the level measure of a Gaussian random field [J]. Statistics & Probability Letters, 2013, 83(2): 637–643. DOI: https://doi.org/10.1016/j.spl.2012.11.007.
PRELEC D. The probability weighting function [J]. Econometrica, 1998, 66(3): 497–527. DOI: https://doi.org/10.2307/2998573.
POWELL W B, SHEFFI Y. The convergence of equilibrium algorithms with predetermined step sizes [J]. Transportation Science, 1982, 16(1): 45–55. DOI: https://doi.org/10.1287/trsc.16.1.45.
JIANG Nan, XIE Chi. Computing and analyzing mixed equilibrium network flows with gasoline and electric vehicles [J]. Computer-Aided Civil and Infrastructure Engineering, 2014, 29(8): 626–641. DOI: https://doi.org/10.1111/mice.12082.
LEBLANC L J. An algorithm for the discrete network design problem [J]. Transportation Science, 1975, 9(3): 183–199. DOI: https://doi.org/10.1287/trsc.9.3.183.
WANG Tong-gen, XIE Chi, XIE Jun, WALLER T. Path-constrained traffic assignment: A trip chain analysis under range anxiety [J]. Transportation Research Part C: Emerging Technologies, 2016, 68: 447–461. DOI: https://doi.org/10.1016/j.trc.2016.05.003.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item
Project(KYLX16_0271) supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China
Contributors
YAN Dong-mei edited the draft of manuscript. GUO Jian-hua provided the concept and design. Both authors reviewed the results and approved the final version of the manuscript.
Conflict of interest
YAN Dong-mei and GUO Jian-hua declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Yan, Dm., Guo, Jh. A stochastic user equilibrium model solving overlapping path and perfectly rational issues. J. Cent. South Univ. 28, 1584–1600 (2021). https://doi.org/10.1007/s11771-021-4718-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-021-4718-6
Key words
- stochastic user equilibrium
- cumulative prospect theory
- generalized nested logit
- method of successive averages