Journal of Shandong University(Engineering Science) ›› 2023, Vol. 53 ›› Issue (4): 18-29.doi: 10.6040/j.issn.1672-3961.0.2023.063

• Transportation Engineering—Special Issue for Intelligent Transportation • Previous Articles     Next Articles

Research review of highway differentiated toll collection

Jianqing WU(),Yanqiang HUO,Jianzhu WANG*(),Hongyu GUO   

  1. School of Qilu Transportation, Shandong University, Jinan 250002, Shandong, China
  • Received:2023-04-02 Online:2023-08-20 Published:2023-08-18
  • Contact: Jianzhu WANG E-mail:jianqingwusdu@sdu.edu.cn;jzwang@sdu.edu.cn

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Abstract:

In order to formulate a scientific and reasonable scheme for highway differentiated toll collection, the background, realization manners, related theories and key technologies are systematically described, and the cases upgraded in Guangxi, Tianjin and Hebei are briefly introduced with design essentials and application effects, and outlooks on the research trend of highway differentiated toll collection are given.

Key words: highway, differentiated toll collection, travel behavior selection, congestion-based charging, vehicle classification-based charging

CLC Number: 

  • U491

Fig.1

Schematic diagram of marginal cost principle"

1 人民日报. 截至2022年底综合交通运输网络总里程超600万公里[EB/OL]. (2023-02-27)[2023-06-05]. https://www.gov.cn/xinwen/2023-02/27/content_5743414.htm
2 中华人民共和国交通运输部. 关于推进供给侧结构性改革促进物流业"降本增效"的若干意见[EB/OL]. (2016-08-01)[2023-06-05]. https://xxgk.mot.gov.cn/2020/jigou/zhghs/202006/t20200630_3319708.html.
3 中共中央, 国务院. 交通强国建设纲要[EB/OL]. (2019-09-19)[2023-06-05]. https://www.gov.cn/zhengce/2019-09/19/content_5431432.htm.
4 中华人民共和国交通运输部, 国家发展改革委, 财政部. 全面推广高速公路差异化收费实施方案[EB/OL]. (2021-06-02)[2023-06-05]. https://www.gov.cn/zhengce/zhengceku/2021-06/15/content_5617919.htm.
5 吴建清, 宋修广. 智慧公路关键技术发展综述[J]. 山东大学学报(工学版), 2020, 50 (4): 52- 69.
WU Jianqing , SONG Xiuguang . Review on smart highways critical technology[J]. Journal of Shandong University(Engineering Science), 2020, 50 (4): 52- 69.
6 刘丹琦. 高速公路货车差异化收费机制研究[D]. 北京: 北京交通大学, 2020.
LIU Danqi. Research on differential tolling mechanism of expressway trucks[D]. Beijing: Beijing Jiaotong University, 2020.
7 黎俊廷. 基于预约的高速公路差异化定价模型研究[D]. 广州: 华南理工大学, 2020.
LI Junting. Research on differential pricing model of freeway based on trip reservation[D]. Guangzhou: South China University of Technology, 2020.
8 HAURIE A , MARCOTTE P . On the relationship between Nash-Cournot and Wardrop equilibria[J]. Networks, 1985, 15 (3): 295- 308.
doi: 10.1002/net.3230150303
9 BRACKEN J , MCGILL J T . Mathematical programs with optimization problems in the constraints[J]. Operations Research, 1973, 21 (1): 37- 44.
doi: 10.1287/opre.21.1.37
10 POZO D , SAUMA E , CONTRERAS J . Basic theoretical foundations and insights on bilevel models and their applications to power systems[J]. Annals of Operations Research, 2017, 254 (1): 303- 334.
11 TURVEY R . Marginal cost[J]. The Economic Journal, 1969, 79 (314): 282- 299.
doi: 10.2307/2230169
12 WALTERS A A . The theory and measurement of private and social cost of highway congestion[J]. Econometrica: Journal of the Econometric Society, 1961, 29 (4): 676- 699.
doi: 10.2307/1911814
13 YANG H , HUANG H J . Principle of marginal-cost pricing: how does it work in a general road network?[J]. Transportation Research Part A: Policy and Practice, 1998, 32 (1): 45- 54.
doi: 10.1016/S0965-8564(97)00018-9
14 YAN H , LAM W H . Optimal road tolls under conditions of queueing and congestion[J]. Transportation Research Part A: Policy and Practice, 1996, 30 (5): 319- 332.
doi: 10.1016/0965-8564(96)00003-1
15 YANG H , MENG Q . Departure time, route choice and congestion toll in a queuing network with elastic demand[J]. Transportation Research Part B: Methodological, 1998, 32 (4): 247- 260.
doi: 10.1016/S0191-2615(97)00041-6
16 MTOI E T , MOSES R . Calibration and evaluation of link congestion functions: applying intrinsic sensitivity of link speed as a practical consideration to heterogeneous facility types within urban network[J]. Journal of Transportation Technologies, 2014, 4 (2): 141- 149.
doi: 10.4236/jtts.2014.42014
17 WANG J Y T , EHRGOTT M , CHEN A . A bi-objective user equilibrium model of travel time reliability in a road network[J]. Transportation Research Part B: Methodological, 2014, 66, 4- 15.
doi: 10.1016/j.trb.2013.10.007
18 ÇOLAK S , LIMA A , GONZáLEZ M C . Understanding congested travel in urban areas[J]. Nature Communications, 2016, 7 (1): 1- 8.
19 SMITH B L , DEMETSKY M J . Traffic flow forecasting: comparison of modeling approaches[J]. Journal of Transportation Engineering, 1997, 123 (4): 261- 266.
doi: 10.1061/(ASCE)0733-947X(1997)123:4(261)
20 WILLIAMS B M , HOEL L A . Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: theoretical basis and empirical results[J]. Journal of Transportation Engineering, 2003, 129 (6): 664- 672.
doi: 10.1061/(ASCE)0733-947X(2003)129:6(664)
21 ZIVOT E , WANG J . Vector autoregressive models for multivariate time series[J]. Modeling Financial Time Series with S-PLUS, 2006, 385- 429.
22 HOCHREITER S , SCHMIDHUBER J . Long short-term memory[J]. Neural Computation, 1997, 9 (8): 1735- 1780.
doi: 10.1162/neco.1997.9.8.1735
23 CHUNG J, GULCEHRE C, CHO K H, et al. Empirical evaluation of gated recurrent neural networks on sequence modeling[DB/OL]. (2014-12-11)[2023-06-05]. https://arxiv.org/abs/1412.3555.
24 GUO S, LIN Y, FENG N, et al. Attention based spatial-temporal graph convolutional networks for traffic flow forecasting[C]// Proceedings of the AAAI Conference on Artificial Intelligence. [S.l.]: [s.n.], 2019: 922-929.
25 LI C, CUI Z, ZHENG W, et al. Spatio-temporal graph convolution for skeleton based action recognition[C]// Proceedings of the AAAI Conference on Artificial Intelligence. [S.l.]: [s.n.], 2018: 3482-3489.
26 LIANG Y, KE S, ZHANG J, et al. GeoMAN multi-level attention networks for geo-sensory time series prediction[C]// Proceedings of the 27th International Joint Conference on Artificial Intelligence. [S.l.]: [s.n.], 2018: 3428-3434.
27 LI Y, YU R, SHAHABI C, et al. Diffusion convolutional recurrent neural network: data-driven traffic forecasting[DB/OL]. (2017-07-06)[2023-06-05]. https://arxiv.org/abs/1707.01926.
28 YU B, YIN H, ZHU Z. Spatio-temporal graph convolutional networks: a deep learning framework for traffic forecasting[DB/OL]. (2017-09-14)[2023-06-05]. https://arxiv.org/abs/1709.04875.
29 王燕. 基于期望效用理论与前景理论的出行决策模型对比研究[D]. 成都: 西南交通大学, 2011.
WANG Yan. Research on model comparison for travel decision based on expected utility theory and prospect theory[D]. Chengdu: Southwest Jiaotong University, 2011.
30 刘瑞霞, 邬冬华, 凌和良. 不确定条件下判断和决策的新领域—前景理论[J]. 运筹与管理, 2005, 14 (2): 14- 18.
doi: 10.3969/j.issn.1007-3221.2005.02.004
LIU Ruixia , WU Donghua , LING Heliang . New research into judgment and decision-making under uncertainty-prospect theory[J]. Operations Research and Management Science, 2005, 14 (2): 14- 18.
doi: 10.3969/j.issn.1007-3221.2005.02.004
31 周国梅, 傅小兰. 决策的期望效用理论的发展[J]. 心理科学, 2001, 24 (2): 219- 220.
doi: 10.3969/j.issn.1671-6981.2001.02.032
ZHOU Guomei , FU Xiaolan . The development of expected utility theory of decision-making[J]. Journalof Psychological Science, 2001, 24 (2): 219- 220.
doi: 10.3969/j.issn.1671-6981.2001.02.032
32 闫乃帅. 出行者的路径选择行为建模及模拟方法分析[D]. 淄博: 山东理工大学, 2010.
YAN Naishuai. Traveler's route choice behavior model and simulation analysis[D]. Zibo: Shandong University of Technology, 2010.
33 CASCETTA E . Random utility theory[J]. Transportation Systems Analysis: Models and Applications, 2009, 89- 167.
34 丁丽. 基于随机效用理论的常规公交线网可达性研究[D]. 成都: 西南交通大学, 2017.
DING Li. Study of bus transportation network accessibility based on random utility[D]. Chengdu: Southwest Jiaotong University, 2017.
35 邵昀泓, 王炜, 程琳. 出行方式决策的随机效用模型研究[J]. 公路交通科技, 2006, (8): 110- 115.
doi: 10.3969/j.issn.1002-0268.2006.08.026
SHAO Yunhong , WANG Wei , CHENG Lin . Study on the individual travel mode choice based on the discrete choice theory[J]. Journal of Highway and Transportation Research and Development, 2006, (8): 110- 115.
doi: 10.3969/j.issn.1002-0268.2006.08.026
36 殷焕焕, 关宏志, 秦焕美, 等. 基于非集计模型的居民出行方式选择行为研究[J]. 武汉理工大学学报(交通科学与工程版), 2010, 34 (5): 1000- 1003.
YIN Huanhuan , GUAN Hongzhi , QIN Huanmei , et al. Study of travel mode choice behavior based on disaggregate model[J]. Journal of Wuhan University of Technology(Transportation Science & Engineering), 2010, 34 (5): 1000- 1003.
37 LUCE R D . Individual choice behavior: a theoretical analysis[M]. [S.l.]: Courier Corporation, 2012.
38 MCFADDEN D . Conditional logit analysis of qualitative choice behavior[J]. Frontiers in Econometrics, 1974, (4): 105- 142.
39 BHAT C R . Analysis of travel mode and departure time choice for urban shopping trips[J]. Transportation Research Part B: Methodological, 1998, 32 (6): 361- 371.
doi: 10.1016/S0191-2615(98)00004-6
40 SMALL K A . Approximate generalized extreme value models of discrete choice[J]. Journal of Econometrics, 1994, 62 (2): 351- 382.
doi: 10.1016/0304-4076(94)90028-0
41 SWAIT J . Choice set generation within the generalized extreme value family of discrete choice models[J]. Transportation Research Part B: Methodological, 2001, 35 (7): 643- 666.
doi: 10.1016/S0191-2615(00)00029-1
42 周嘉男, 何丹恒, 罗霞. 基于Logit模型的路径选择及交通流分配[J]. 大连交通大学学报, 2013, 34 (1): 31- 34.
doi: 10.3969/j.issn.1673-9590.2013.01.007
ZHOU Jianan , HE Danheng , LUO Xia . Research on route selection survey methodology and traffic assignment based on logit model[J]. Journal of Dalian Jiaotong University, 2013, 34 (1): 31- 34.
doi: 10.3969/j.issn.1673-9590.2013.01.007
43 VEGA A , REYNOLDS-FEIGHAN A . A methodological framework for the study of residential location and travel-to-work mode choice under central and suburban employment destination patterns[J]. Transportation Research Part A: Policy and Practice, 2009, 43 (4): 401- 419.
doi: 10.1016/j.tra.2008.11.011
44 FISK C . Some developments in equilibrium traffic assignment[J]. Transportation Research Part B: Methodological, 1980, 14 (3): 243- 255.
doi: 10.1016/0191-2615(80)90004-1
45 TRAIN K E . Discrete choice methods with simulation[M]. [S.l.]: Cambridge University Press,2009.
46 DAGANZO C F , SHEFFI Y . On stochastic models of traffic assignment[J]. Transportation Science, 1977, 11 (3): 253- 274.
doi: 10.1287/trsc.11.3.253
47 KAHNEMAN D , TVERSKY A . Prospect theory: an analysis of decision under risk[J]. Econometrica, 1979, 47 (2): 363- 391.
48 VICKREY W S . Congestion theory and transport investment[J]. The American Economic Review, 1969, 59 (2): 251- 260.
49 雷志敏. 城市道路拥挤收费定价研究[D]. 武汉: 武汉理工大学, 2010.
LEI Zhimin. Research on urban road congestion[D]. Wuhan: Wuhan University of Technology, 2010.
50 靳雪振. 基于地感线圈数据的高速公路交通拥堵状态预测研究[D]. 广州: 华南理工大学, 2021.
JIN Xuezhen. Research on prediction of freeway traffic congestion based on ground induction coil data[D]. Guangzhou: South China University of Technology, 2021.
51 石译雄. 基于环形线圈的车型识别研究[D]. 长沙: 长沙理工大学, 2009.
SHI Yixiong. Research of automobile classifying method based on inductive loop[D]. Changsha: Changsha University of Science and Technology, 2009.
52 王荣旭. 基于压电传感器的车辆动态称重系统开发[D]. 济南: 山东大学, 2021.
WANG Rongxu. Development of vehicle dynamic weighing system based on piezoelectric sensor[D]. Jinan: Shandong University, 2021.
53 孙文本. 基于压电薄膜的车型分类研究[D]. 天津: 天津大学, 2014.
SUN Wenben. Vehicle classification research based on piezoelectricity sensor[D]. Tianjin: Tianjin Univer-sity, 2014.
54 CHEN J , XU H , WU J , et al. Deer crossing road detection with roadside LiDAR sensor[J]. IEEE Access, 2019, (7): 65944- 65954.
55 于洋洋. 机载激光雷达点云滤波与分类算法研究[D]. 合肥: 中国科学技术大学, 2020.
YU Yangyang. Research on filtering and classification algorithms of LIDAR data[D]. Hefei: University of Sciennce and Technology of China, 2020.
56 Lü B , XU H , WU J , et al. Revolution and rotation-based method for roadside LiDAR data integration[J]. Optics & Laser Technology, 2019, 119, 105571- 105577.
57 WU J , XU H , LIU W . Points registration for roadside LiDAR sensors[J]. Transportation Research Record, 2019, 2673 (9): 627- 639.
doi: 10.1177/0361198119843855
58 Lü B , XU H , WU J , et al. Raster-based background filtering for roadside LiDAR data[J]. IEEE Access, 2019, 7, 76779- 76788.
doi: 10.1109/ACCESS.2019.2919624
59 WU J , TIAN Y , XU H , et al. Automatic ground points filtering of roadside LiDAR data using a channel-based filtering algorithm[J]. Optics & Laser Technology, 2019, 115, 374- 383.
60 ZHAO J , XU H , LIU H , et al. Detection and tracking of pedestrians and vehicles using roadside LiDAR sensors[J]. Transportation Research Part C: Emerging Technologies, 2019, 100, 68- 87.
doi: 10.1016/j.trc.2019.01.007
61 WU J , XU H , ZHENG Y , et al. Automatic vehicle classification using roadside LiDAR data[J]. Transportation Research Record, 2019, 2673 (6): 153- 164.
doi: 10.1177/0361198119843857
62 CHEN Z, PEARS N H, FREEMAN M, et al. Road vehicle classification using support vector machines[C]// Proceedings of the International Conference on Intelligent Computing and Intelligent Systems. Shanghai, China, 2009: 214-218.
63 MISHRA P , BANERJEE B . Multiple kernel based KNN classifiers for vehicle classification[J]. International Journal of Computer Applications, 2013, 71 (6): 1- 7.
doi: 10.5120/12359-8673
64 陈雷兴. 深度学习的车型视频识别算法及系统实现[D]. 南京: 南京大学, 2018.
CHEN Leixing. Algorithm and system implementation of vehicle recognition on video sequence based on deep learning[D]. Nanjing: Nanjing University, 2018.
65 GIRSHICK R, DONAHUE J, DARRELL T, et al. Rich feature hierarchies for accurate object detection and semantic segmentation[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Columbus, OH, USA, 2014: 580-587.
66 HE K , ZHANG X , REN S , et al. Spatial pyramid pooling in deep convolutional networks for visual recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37 (9): 1904- 1916.
doi: 10.1109/TPAMI.2015.2389824
67 GIRSHICK R. Fast R-CNN[C]//Proceedings of the IEEE International Conference on Computer Vision. [S.l.]: [s.n.], 2015: 1440-1448.
68 REN S, HE K, GIRSHICK R, et al. Faster R-CNN: towards real-time object detection with region proposal networks[C]//Proceedings of the Advances in Neural Information Processing Systems. [S.l.]: [s.n.], 2015.
69 REDMON J, DIVVALA S, GIRSHICK R, et al. You only look once: unified, real-time object detection[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. [S.l.]: [s.n.], 2016: 779-788.
70 REDMON J, FARHADI A. Yolov3: an incremental improvement[EB/OL]. (2018-04-08)[2023-06-05]. https://arxiv.org/abs/1804.02767.
71 REDMON J, FARHADI A. YOLO9000: better, faster, stronger[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. [S.l.]: [s.n.], 2017: 7263-7271.
72 BOCHKOVSKIY A, WANG C Y, LIAO H Y M. Yolov4: optimal speed and accuracy of object detection[EB/OL]. (2020-04-23)[2023-06-05]. https://arxiv.org/abs/2004.10934.
73 LIU W, ANGUELOV D, ERHAN D, et al. Ssd: single shot multibox detector[C]// Proceedings of the Computer Vision-ECCV 2016: 14th European Conference. Amsterdam, the Netherlands: Springer International Publishing, 2016: 21-37.
74 刘贵宁. 高速公路收费系统差异化收费改造方案研究[J]. 西部交通科技, 2019, (6): 179- 181.
LIU Guining . Research on differential charging reconstruction plan of expressway toll system[J]. Western China Communications Science & Technology, 2019, (6): 179- 181.
75 谢锦男, 史美罗. 集装箱车辆高速公路差异化收费系统设计与实现[J]. 集装箱化, 2020, 31 (9): 21- 24.
XIE Jinnan , SHI Meiluo . Design and implementation of container vehicle expressway differential toll system[J]. Containerization, 2020, 31 (9): 21- 24.
76 高军. 高速公路差异化收费实践探讨[J]. 价值工程, 2022, 41 (19): 19- 21.
GAO Jun . Discussion on the practice of differentiated toll collection on expressways[J]. Value Engineering, 2022, 41 (19): 19- 21.
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