The Journal of The Korea Institute of Intelligent Transport Systems (한국ITS학회 논문지)

The Korea Institute of Intelligent Transport Systems (한국ITS학회)
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Generalized K Path Searching in Seoul Metropolitan Railway Network Considering Entry-Exit Toll

진입-진출 요금을 반영한 수도권 도시철도망의 일반화 K-경로탐색

  • Received : 2022.08.09
  • Accepted : 2022.11.25
  • Published : 2022.12.31
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Abstract

The basic way to charge vehicles for using road and public transport networks is the entry-exit toll system. This system works by reading Hi-Pass and public transportation cards of the vehicles using card readers. However, the problems of navigating a route in consideration of entry-exit toll systems include the non-additive costs of enumerating routes. This problem is known as an NP-complete task that enumerates all paths and derives the optimal path. So far, the solution to the entry-exit toll system charging has been proposed in the form of transforming the road network. However, unlike in the public transport network where the cards are generalized, this solution has not been found in situations where network expansion is required with a transfer, multi-modes and multiple card readers. Hence, this study introduced the Link Label for a public transportation network composed of card readers in which network expansion is bypassed in selecting the optimal path by enumerating the paths through a one-to-one k-path search. Since the method proposed in this study constructs a relatively small set of paths, finding the optimal path is not burdensome in terms of computing power. In addition, the ease of comparison of sensitivity between paths indicates the possibility of using this method as a generalized means of deriving an optimal path.

도로교통망과 대중교통망에서 요금을 부과하는 기본방식은 진입-진출요금체계이다. 진입-진출요금체계는 HI-PASS 및 대중교통카드를 이용하는 단말기를 통과하는 방식으로 적용된다. 한편 진입-진출요금을 고려해서 경로를 탐색하는 문제는 경로의 열거를 포함하는 비가산성문제를 포함하고 있다. 이는 모든 경로를 열거해서 최적해를 도출하는 NP-완전문제로 알려져 있다. 지금까지 진입-진출요금에 대한 해법은 도로망을 대상으로 네트워크를 변형하는 기법이 제안되었으며 교통카드가 일반화된 대중교통망과 같이 환승, 다수단, 복수단말기와 같이 네트워크확장이 요구되는 상황에서는 검토되지 않았다. 본 연구는 교통카드단말기로 구성된 대중교통망에 대하여 링크표지를 도입해서 네트워크확장을 우회하면서 One-to-One K-경로탐색을 통해 경로를 열거함으로서 최적해를 선정하는 방안을 마련하였다. 본 연구에서 제안하는 방법은 비교적 적은 경로집합을 구성하기 때문에 컴퓨팅 파워의 부담없이 최적해를 도출하는 것이 가능하며, 경로간 민감도를 비교하기 용이한 측면에서 보다 일반화된 최적경로해법으로 활용이 가능하다.

Keywords

Acknowledgement

본 연구는 한국 ITS학회 2022년 춘계 국제학술대회에서 발표된 논문을 수정하여 제출한 것입니다.

References

  1. Azevedo, J. A., Costa, M. E. O. S., Madeira, J. J. E. R. S. and Martins, E. Q. V.(1993), "An Algorithm from the Ranking of Shortest Paths", European Journal of Operational Research, vol. 69, pp.97-106. https://doi.org/10.1016/0377-2217(93)90095-5
  2. Bernstein, D. and Gabriel, G.(1997), "Solving the Nonadditive Traffic Equilibrium Problem", In Pardalos, P. M., Wl Hearn, D. L. and Hager, W. W. eds. Network Optimization, Springer, New York, pp.72-102.
  3. Dijkstra, E. W.(1959), "A Note on Two Problems in Connexion with Graphs", Numerishe Matematilk, vol. 1, pp.269-271. https://doi.org/10.1007/BF01386390
  4. Gabriel, S. and Bernstein, D.(1997), "The Traffic Equilibrium Problem With Nonadditive Path Costs", Transportation Science, vol. 20, no. 5, pp.337-348. https://doi.org/10.1287/trsc.31.4.337
  5. Gabriel, S. and Bernstein, D.(2000), "Nonadditive Shortest Paths: Sub-problem in Multi-agent Competitive Network Models", Computational and Mathematical Organization Theory, vol. 6, no. 1, pp.29-45. https://doi.org/10.1023/A:1009621108971
  6. Larsson, T., Lindberg, P., Patriksson, M. and Rydergren, C.(2002), "On Traffic Equilibrium Models with A Nonliner Time/Money Relation", In Patricsson M. and Labbe, M. eds. Transportation Planning-State of the Art, Publisher: Kluwer, pp.19-31.
  7. Lee, M,, Kim, H., Park, D. and Shin, S.(2008), "A Link-Based Label Correcting Multi-Objective Shortest Paths Algorithm in Multi-Modal Transit Networks", Journal of Korean Society of Transportation, vol. 26, no. 1, pp.127-135.
  8. Lee, M. and Lee, C.(2020), "An Application of a Link-Based Optimal Pathfinding Algorithm with the Integrated Transit Network from Smart Card Systems", KSCE(Korean Society of Civil Engineers) Journal of Civil Engineering, vol. 24, pp.3474-3487. https://doi.org/10.1007/s12205-020-0274-0
  9. Lee, M. and Nam, D.(2019), "A Link-Label Based Node-to-Link Optimal Path Algorithm Considering Non Additive Path Cost", The Journal of the Korea Institute of Intelligent Transport Systems, vol. 18, no. 3, pp.91-99.
  10. Lee, M.(2004), Transportation Network Models and Algorithms Considering Directional Delay and Prohibitions for Intersection Movement, Doctoral Dissertation, University of Wisconsin at Madison.
  11. Lee, M.(2017), "Transportation Card Based Optimal M-Similar Paths Searching for Estimating Passengers' Route Choice in Seoul Metropolitan Railway Network", The Journal of The Korea Institute of Intelligent Transport Systems, vol. 16, no. 2, pp.1-12. https://doi.org/10.12815/kits.2017.16.2.01
  12. Lee, M.(2018), "Link Label Based Optimal Path Algorithm Considering Station Transfer Penalty-Focusing on A Smart Card Based Railway Network", Journal of the Korean Society of Civil Engineers, vol. 38, no. 6, pp.941-947.
  13. Lee, M., Baek N., Nam, D. and Shin, S.(2004), "Finding a Minimum Fare Route in the Distance-Based Fare System", Journal of Korean Society of Transportation, vol. 22, no. 6, pp.101-108.
  14. Lee, M., Baek, N., Moon, B. and Kang, W.(2005), "Finding the K Least Fare Routes In the Distance-Based Fare Policy", Journal of Korean Society of Transportation, vol. 23, no. 1, pp.103-114.
  15. Lee, M., Park, J., Jeong, J. and Park, D.(2008), "A Multi-Objective Shortest Paths Finding Considering Multi-Class in A Multi-Modal Transit Network for Providing User-Customized Route Information", The Journal of the Korea Institute of Intelligent Transport Systems, vol. 7, no. 3, pp.1-14.
  16. Lo, K. and Chen, A.(2000), "Traffic Equilibrium Problem with Route-specific Costs: Formulation and Algorithms", Transportation Research Part B, vol. 34, no. 6, pp.493-513. https://doi.org/10.1016/S0191-2615(99)00035-1
  17. Martins, E. Q. V.(1984), "An Algorithm for Ranking Paths That May Contain Cycles", European Journal of Operational Research, vol. 18, pp.123-130. https://doi.org/10.1016/0377-2217(84)90269-8
  18. Meng, Q., Lee, D. H., Cheu, R. L. and Yang, H.(2004), "Logit-Based Stochastic User Equilibrium Problem for Entry-Exit Toll Schemes", Journal of Transportation Engineering, vol. 130, no. 6, pp.805-813. https://doi.org/10.1061/(ASCE)0733-947X(2004)130:6(805)
  19. Moore, E. F.(1957), The Shortest Path through A Maze, Harvard University Press, Cambridge.
  20. Scott, K. and Bernstein, D.(1997), Solving a Best Path Problem when the Value of Time Function is Nonlinear, preprint 980976 of the Transportation Research Board.
  21. Shin, H.(2022), Estimating Revenues of Integrated Fare System for Seoul Metropolitan Public Transportation Using Smartcard Data, Doctoral Dissertation, Seoul National University.
  22. Shin, S. and Baek, N.(2016), "A Logit Type of Public Transit Trip Assignment Model Considering Stepwise Transfer Coefficients", Journal of Korean Society of Transportation, vol. 34, no. 6, pp.570-579. https://doi.org/10.7470/jkst.2016.34.6.570
  23. Shin, S.(2004), "Finding the First K Loopless Paths in A Transportation Network", Journal of Korean Society of Transportation, vol. 22, no. 6, pp.121-131.
  24. Shin, S., Baek, N. and Nam, D.(2016), "A Heuristic Optimal Path Search Considering Cumulative Transfer Functions", Journal of Korean Society of Transportation, vol. 15, no. 3, pp.60-67.
  25. Yang, H., Zhang, X. and Meng, Q.(2004), "Modeling Private Highways in Networks With Entry-Exit Based Toll Charges", Transportation Research B, vol. 38, pp.191-213. https://doi.org/10.1016/S0191-2615(03)00050-X