大眾捷運系統是城市發展與民眾日常通勤重要的一環，隨著城市人口成長與區域發展的擴大，不僅捷運路網與路線越來越複雜，同時吸引了更多的乘客使用，尖峰時刻在某些交會站或主要路線上造成擁擠的現象，甚至可能發生旅客推擠等意外事故。針對上述問題，本研究使用時空路網模型推估捷運乘客的路徑選擇行為，進行捷運乘客的均衡流量指派，以分散尖峰時段的旅客流量，減少特定時間和空間區域的擁擠現象，進而降低因擁擠可能產生意外事故的風險。模式中將列車的擁擠程度、轉乘步行時間、列車運行時間，以及轉乘次數納入隨機使用者均衡指派模型中的一般化成本函數，作為捷運乘客流量分派的主要憑藉因素。在實證研究方面，本研究以臺北捷運系統為例，針對尖峰時刻乘客運量資料進行瓶頸分析，以及對應的流量指派，據以評估相關因素對於分散捷運路網尖峰時段乘客流量的影響，研究發現若旅客考量路徑的一般化成本可使流量轉移至一般化成本較小之路徑，達到尖峰流量分散之效果。相關研究成果，可以提供臺北捷運公司進行尖峰流量分散運用於需求管理策略之參考，同時可以降低尖峰時刻人員與車輛的調度成本。

A Mass Rapid Transit (MRT) system is an important component of urban development and residents’ daily commuting. With the expansion of urban development, not only the MRT network is more and more complex but also they attract more passengers, resulting in overcrowded passenger flows concentrating at some interchange stations and/or main lines. The highly concentrated phenomena have caused serious crowdedness problem in peak periods and potential traffic accidents. To resolve this problem, this study applies the time-space network model to investigate the temporal and spatial distributions of passenger flows and potential traffic bottlenecks, which can achieve the goals of peak spreading on passenger flows and reducing the number of accidents due to overcrowded. Thereby, the purpose of this study is to conduct an equilibrium traffic assignment model for over-concentrated demands and/or MRT passenger flows, and accordingly reducing severe crowdedness problems in specific temporal periods and spatial locations so as to increase the level of service of an MRT system. For the research target, potential passengers’ route switching behaviors are analyzed by a time-space network model, in which penalties for the degree of crowdedness in train, transfer walking time, train running time, and the number of transfer times are incorporated into the generalized cost function of a SUE-based MRT passenger flow assignment model. In the empirical study, a stochastic equilibrium assignment model by using the Taipei MRT’s information and O-D data to examine the effect of passengers’ peak spreading. The results of study can provide a reference for the Taipei Rapid Transit Corporation in preparing variable pricing and transportation demand management strategies of spreading overcrowded passenger flows, while reducing the crew, vehicle and costs at peak time period.

1. Ministry of Transportation and Communication (MOTC) (2017), website:
http://stat.motc.gov.tw/mocdb/stmain.jsp?sys=100
2. Taipei Rapid Transit Corporation Wikipedia (2017), Retrieved March 15, 2017, website: http://zh.wikipedia.org/wiki/Taipei metro
3. Taipei Rapid Transit Corporation official website (2017), Retrieved March 16, 2017, website: https://www.metro.taipei/cp.aspx?n=91974F2B13D997F1
4. Taipei City Government Data Open platform “Data Taipei” (2018), website: http://data.taipei/opendata/datalist/datasetMeta?oid=63f31c7e-7fc3-418b-bd82-b95158755b4d
5. Tokyo Metro Co., Ltd. (2017), Traffic Performance by Station. Retrieved October, 2017, website: http://www.tokyometro.jp/en/corporate/enterprise/transportation/ranking/index.html
6. Transport for London (TfL), (2017), Peak and off-peak times. Retrieved November 4, 2017, website: https://tfl.gov.uk/fares-and-payments/fares/peak-and-off-peak-times
7. Washington Metropolitan Area Transit Authority (WMATA), (2017), Fare of Washington Metro. Retrieved October 31, 2017, website: https://www.wmata.com/fares/index.cfm
8. Wikipedia, (2017), Transportation demand management. Retrieved October 26, 2017, website: https://en.wikipedia.org/wiki/Transportation_demand_management
9. Chinatimes, (2013), Taipei MRT Crowdedness phenomenon in at rush hours. website: http://www.chinatimes.com/newspapers/20130419000486-260107
10. Bekhor, S., Albert, G. (2014). Accounting for sensation seeking in route choice behavior with travel time information. Transportation Research Part F, 22, 39-49.
11. Ben-Akiva, M.E., DePalma, A., and Kaysi, I. (1991). Dynamic network models and driver information system. Transportation Research Part A, 25(5), 34-46
12. Bolland, J., Ashmore, D. (2002). Traffic peak spreading in congested urban environments. In 25th Australasian Transport Research Forum.
13. Bovy, P. H.L., Uges, R., and Hoogendoorn, S. (2003). Modeling route choice behavior in multimodal transport networks. 10th International Conference on Travel Behaviour Research, Luzern.
14. Bianchi, R., Jara-Dı́az, S. R., and Ortúzar, J. D. D. (1998). Modelling new pricing strategies for the Santiago Metro. Transport Policy, 5(4), 223-232. SCIENCE CHINA: Technological Sciences, 45(12), 1269-1278.
15. Ceapa, I., Smith, C., and Capra, L. (2012). Avoiding the Crowds: Understanding Tube Station Congestion Patterns from Trip Data. In Proceedings of the ACM SIGKDD International Workshop on Urban Computing, 134-141.
16. Chen, B. Y., Si, B. F., Jiang, M. Q., and Yang, X. B. (2015). Schedule-based Equilibrium Assignment Model and Algorithm for Urban Subway Network. SCIENTIA SINICA Technologica, 45(12), 1269.
17. Chen, H. K., and Hsueh, C. F. (1998). A model and an algorithm for the dynamic user-optimal route choice problem. Transportation Research Part B: Methodological, 32(3), 219-234.
18. Cheu, R. L., Kreinovich, V., and Manduva, S. R. (2007). Traffic assignment for risk averse drivers in a stochastic network. Published in the Proceedings of the Annual Meeting of the Transportation Research Board of the National Academies TRB'07, Washington, DC, January 13-17, 2008.
19. Daamen, W, Hoogendoorn, SP (2004). Level difference impacts in passenger route choice modelling. In TRAIL conference proceedings 2004, A world of transport, infrastructure and logistics, 103-127, Delft: DUP Science.
20. Daganzo, C. F., Sheffi, Y. (1977). On stochastic models of traffic assignment. Transportation Science, 11(3), 253–274.
21. Fielding, G. J. (1995), Congestion pricing and the future of transit. Journal of Transport Geography, 3(4), 239-246.
22. Frejinger, E., Bierlaire, M., and Ben-Akiva, M. (2009). Sampling of alternatives for route choice modeling. Transportation Research B, 43(10), 984-994.
23. Frumin. M., Zhao. J. (2012). Analyzing passenger incidence behavior in heterogeneous transit services using smartcard data and schedule-based assignment. Transportation Research Record, No. 2274, 52-60.
24. Golledge, R. G. (1995). Path selection and route preference in human navigation: a progress report. Presented at the Conference on Spatial Information Theory (COSIT), Australiac
25. Grange, L., Raveaub, S., and González F. (2012). A fixed point route choice model for transit networks that addresses route correlation. Presented at 15th Edition of the Euro Working Group on Transportation, Paris
26. Grison, E., Gyselinck, V., and Burkhardt, J. M. (2014). Exploring factors related to users’ experience of public transport: users profiles and route choice. In Transport Research Arena (TRA) 5th Conference: Transport Solutions from Research to Deployment.
27. Guo, Z., Wilson, N. H. (2011). Assessing the cost of transfer inconvenience in public transport systems: A case study of the London Underground. Transportation Research Part A: Policy and Practice, 45(2), 91-104.
28. Gwee, E., Currie, G. (2013). Review of time-based public transport fare pricing. JOURNEYS.
29. Hochmair, H. H., Frank, A. U. (2002). Influence of estimation errors on way finding-decisions in unknown street networks - analyzing the least-angle strategy, Spatial Cognition and Computation, 2, 283–313.
30. Hong, L., Li, W., and Zhu, W. (2017). Assignment passenger flows on a metro network based on automatic collection data and timetable. Discrete Dynamics in Nature and Society, article ID 4373871,10 pages
31. Jhonston, R., Bates, J. J., and Roberts, M. (1989). A survey of peak spreading in London: methodology and initial results. In Proceedings 17th PTRC Annual Meeting, University of Sussex, UK.
32. Jong, J.C., Lin. J., Lin, J. W., and Lin, C. M. (2012). A time-space network model for MRT system passenger flows simulation. Conference on Computer Application in Civil and Hydraulic Engineering (CCACHE 2011), Taiwan.
33. Jong, J.C., Lin. J., Lin, J. W., and Lin, C. M. (2012). Calculation of MRT service performance indicators of passenger flow with a simulation model. Transportation Planning Journal, 41(3), 279-310
34. Jong, J.C., Chang, E.F. (2010). The simulation of passengers’ time-space characteristics using ticket sales records with insufficient data. Computers in Railways, XII, pp.419-430, WIT Press.
35. Jong, J.C., Huang, S.H., Lee, C.K., Lai, Y.C., Lin, K.S., and Liou, J.R. (2012). Rail capacity analysis for urban rapid transit system-A case study for the Banqiao-Nangang line of taipei MRT system, Journal of the Chinese Institute of Transportation, 24(1), 113-134.
36. Kang, K., Han, K., and Kim, J. (2010). A study on passenger level change mode choice in a public transport transfer system - Gwangmyeong station case. Journal of the Eastern Asia Society for Transportation Studies, 8, 1370-1379.
37. Kittelson and Associates, Inc. (2013). Transit Capacity and Quality of Service Manual, 3rd Edition, TCRP Report 165, Transportation Research Board, National Research Council, U.S.A.
38. Lam, S. H., Xie, F. (2002). Transit path-choice models that use revealed preference and stated preference data. Transportation Research Record: Journal of the Transportation Research Board, 1799, 58-65.
39. Lan, L. W., Lee, H. Y., and Wen, C. H. (2010). Effects of temporally differential fares on Taipei metro riders ‘mode and time-of-day choices. International Journal of Transport Economics, 97-118.
40. Liu, Y., Charles, P. (2013). Spreading peak demand for urban rail transit through differential fare policy: A review of empirical evidence. In Australasian Transport Research Forum 2013 Proceedings.
41. Lin, H.P. (2015). Exploring Passengers’ Path Choice Behavior at Peak Time for Mass Rapid Transit Systems. Master thesis, Department of Transportation and Communication Management Science, National Cheng Kung University (NCKU), Taiwan.
42. McFadden, D. (1986). The choice theory approach to market research. Marketing Science, 5(4), 275-297.
43. McFadden, D., Train, K. (2000). Mixed MNL models for discrete response. Journal of Applied Econometrics, 447-470.
44. Myojo, S. (2006a). Daily estimation of passenger flow in large and complicated urban railway network. Presented at the 7th World Congress on Railway Research, WCRR, Montreal, Canada.
45. Nagasaki, Y., Asuka, M., and Koyama, K. (2006). A fast method for estimating railway passenger flow. Computers in Railways, X, 179-187, WIT Press.
46. Nielsen, O. A. (2000). A stochastic transit assignment model considering differences in passenger utility functions. Transportation Research Part B, 34, 377-402.
47. Nielsen, O. A., Frederiksen, R. D. (2006) Optimization of timetable-based, stochastic transit assignment models based on MSA. Annals of Operations Research, 144, 263–285.
48. Prato, C. G., Bekhor, S., and Pronello, C. (2012). Latent variables and route choice behavior. Transportation, 39(2), 299-319.
49. Prud'homme, R., Koning, M., Lenormand, L., and Fehr, A. (2012). Public transport congestion costs: The case of the Paris subway. Transport Policy, 21, 101-109
50. Powell, W. B., Sheffi, Y. (1982) The convergence of equilibrium algorithms with predetermined step sizes, Transportation Science, 16, 45–55.
51. Raveau, S., Guo, Z., Muñoz, J. C., and Wilson, N. H. (2014). A behavioural comparison of route choice on metro networks: Time, transfers, crowding, topology and socio-demographics. Transportation Research Part A: Policy and Practice, 66, 185-195.
52. Raveau, S., Guo, Z., Munoz, J. C., and Wilson, N. H. M. (2012). Route choice analysis for metro networks - A comparison between Santiago and London, Presented at the 15th Euro Working Group on Transportation, Descartes.
53. Sheffi, Y. (1985). Urban Transportation Networks. Prentice-Hall, INC.
54. Si, B. F., Zhong, M., Liu, J. F., Gao, Z. Y. and Wu, J. J. (2013). Development of a transfer-cost-based logit assignment model for the Beijing rail transit network using automated fare collection data. Journal of Advanced Transportation; 47, 297–318
55. Tong, C. O., Wong S. C. (1999). A stochastic transit assignment model using a dynamic schedule-based network. Transportation Research Part B, 33(2), 107-121.
56. Taipei Rapid Transit Corporation (2007). 2007 TRTC Annual report.
57. Taipei Rapid Transit Corporation (2008). 2008 TRTC Annual report.
58. Taipei Rapid Transit Corporation (2009). 2009 TRTC Annual report.
59. Taipei Rapid Transit Corporation (2010). 2010 TRTC Annual report.
60. Taipei Rapid Transit Corporation (2011). 2011 TRTC Annual report.
61. Taipei Rapid Transit Corporation (2012). 2012 TRTC Annual report.
62. Taipei Rapid Transit Corporation (2013). 2013 TRTC Annual report.
63. Taipei Rapid Transit Corporation (2014). 2014 TRTC Annual report.
64. Taipei Rapid Transit Corporation (2015). 2015 TRTC Annual report.
65. Taipei Rapid Transit Corporation (2016). 2016 TRTC Annual report.
66. U.S. Federal Transit Administration (FTA), (1996). Passenger Transfer System Review: A Synthesis of Transit Practice. TCRP Synthesis 19, Transportation Research Board National Research Council, Washington, D.C.
67. Wardrop, J. G. (1952). Some theoretical aspects of road traffic research. Institution of Civil Engineers—Proceedings, 1(2), 325–362
68. Xu, J., Ning, Y., Wei, H., Xie, W., Guo, J., Jia, L., and Qin, Y. (2015). Route choice in subway station during morning peak hours: A case of Guangzhou subway. Discrete Dynamics in Nature and Society, Article ID 151434, 8 pages.
69. Yan, S. Y. and Lin, C. G. (1997). Airline scheduling for the temporary closure of 69 Airports. Transportation Science, 31(1), 77-82
70. Yeh, I.S. (2017). Analysis and Application of Dynamic Behavior of Taipei MRT Passengers, Journal of the Chinese Statistical Association Vol. 55, (2017) 69-95.
71. Zhang, Y. S., Yao, E. J., and Yang, Y. (2013). A route-planning algorithm based on subway passenger routes choice behavior analysis. In Proceedings of the Second International Conference on Transportation Information and Safety.