Control station identification of rail transport network based on loading coefficient
【Abstract】Urban rail transit passenger flow is critical to the efficiency and safety of rail transit operations. This paper proposes to measure the network load with load coefficients which are taken as the edge weights of rail transit network, based on passenger flow, creating the rail transit network model. The controllability theory of complex network is used to analyze the controllability of the rail transit network, and the identification method for identifying the control nodes of rail transit network is given to realize the control of finite-flow stations of urban rail transit network. With the Beijing subway network taken as an example, the network model with load coefficients is established, and the selection of its control nodes is analyzed. The results show that the current normalized control nodes cannot make the network fully controllable. Meanwhile, it also faces a large number of selected finite-flow stations as well as high cost. Applying load coefficients to the selection of finite-flow stations cannot only make the network fully controllable, but also obtain fewer control nodes at lower cost and the control nodes are distributed mainly on the overloaded line. The proposed method can effectively find the control nodes and provide an effective reference for the selection of the actual finite-flow stations.
【Keywords】 complex network; rail transport network; driver nodes; finite-flow station; load coefficient;
 Xu X Y. Passenger flow control with multi-station coordination in subway networks: Algorithm development and real-world case study [J]. Transport Metrica B, 2019, 7 (1): 446–472.
Zhao P, Yao X M, Yu D D. Cooperative passenger inflow control of urban mass transist in peak hours [J]. Journal of Tongji University: Natural Science, 2013, 42 (9): 1340–1346 (in Chinese).
 Liu Y Y, Slotine J J, Barabási A L. Controllability of complex networks [J]. Nature, 2011, 473 (7346): 167–173.
 Yuan Z Z, Zhao C, Di Z R, et al. Exact controllability of complex networks [J]. Nature Communications, 2013, 4 (1): 2447–2485.
 Chin S P, Cohen J, Albin A, et al. A mathematical analysis of network controllability through driver nodes [J]. IEEE Transactions on Computational Social Systems, 2017, 4 (2): 40–51.
 Zhao C, Zeng A, Jiang R, et al. Controllability of flow-conservation networks [J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2017, 96 (1): 012314.
 Song K, Li G, Chen X, et al. Target controllability of two-layer multiplex networks based on network flow theory [J]. IEEE Transactions on Cybernetics, 2019, DOI: 10.1109/TCYB.2019.2906700.
 Menara T, Bassett D S, Pasqualetti F. Structural controllability of symmetric networks [J]. IEEE Transactions on Automatic Control, 2019, 64 (9): 3740–3747.
 Latora V, Marchiori M. Is the Boston subway a small-world network? [J]. Physica A: Statistical Mechanics and its Applications, 2002, 314 (1): 109–113.
 Seaton K A, Hackett L M. Stations,trains and small-world networks [J]. Physica A: Statistical Mechanics and its Applications, 2003, 339 (3): 635–644.
 Feng J, Xu Q, Li X M, et al. Complex network study on urban rail transit systems [J]. Journal of Transportation Systems Engineering and Information Technology, 2017, 17 (6): 242–247 (in Chinese).
 Lee K, Jung W S, Park J S, et al. Statistical analysis of the metropolitan seoul subway system: Network structure and passenger flows [J]. Physica A: Statistical Mechanics and its Applications, 2008, 387 (24): 6231–6234.
 Meng X L, Xiang W L, Wang L. Controllability of train service network [J]. Mathematical Problems in Engineering, 2015, 2015 (4): 1–8.
 Zeng L, Liu J, Qin Y, et al. A passenger flow control method for subway network based on network controllability [J]. Discrete Dynamics in Nature and Society, 2018, 2018: 1–12.
 Yang X H, Chen G, Chen S Y, et al. Study on some bus transport networks in China with considering spatial characteristics [J]. Transportation Research Part A: Policy and Practice, 2014, 69: 1–10.
 Chang M X, Zhao A Q, Lv L M. Research on structural characteristics of urban rail transit network based on complex network theory [J]. Computer Systems & Applications, 2017, 26 (2): 254–259 (in Chinese).
 Zhang J, Zhao M, Liu H, et al. Networked characteristics of the urban rail transit networks [J]. Physica A: Statistical Mechanics and its Applications, 2013, 392 (6): 1538–1546.
 Kalman R E. Mathematical description of linear dynamical systems [J]. Society for Industrial and Applied Mathematics, 1963, 1 (2): 152–192.
 Wang L F, Zhao Y K, Duan L, et al. Effect of cut vertexes-removal on controllability of complex networks [J]. Control and Decision, 2019, 34 (11): 2310–2316 (in Chinese).
 Lin C T. Structural controllability [J]. IEEE Transactions on Automatic Control, 1974, 19 (3): 201–208.
 Commault C, Woude J V D. A Classification of nodes for structural controllability [J]. IEEE Transactions on Automatic Control, 2019, 64 (9): 3877–3882.
 Liu R, Li S, Yang L. Collaborative optimization for metro train scheduling and train connections combined with passenger flow control strategy [J]. Omega, 2019, DOI: 10.1016/j.omega.2018.10.020.
 Chen F, Wu Q B, Zhang H H, et al. Relationship analysis on station capacity and passenger flow: A case of Beijing subway line 1 [J]. Journal of Transportation on Systems Engineering and Information Technology, 2009, 9 (2): 93–98 (in Chinese).
 Kuhn H W. The Hungarian method for the assignment problem [J]. Naval Research Logistics, 1955, 2 (1/2): 83–97.
 Munkres James. Algorithms for the assignment and transportation problems [J]. Journal of the Society for Industrial and Applied Mathematics, 1957, 5 (1): 32–38.
 Beijing Subway. Passenger flow information on official website [EB/OL]. (2019-04-11) [2019-07-15]. https://www.bjsubway.com/support/cxyd/klxx (in Chinese).
 Weibo of Beijing MTR Corporation Limited. Passenger flow information on the official website [EB/OL]. (2019-03-12) [2019-07-15]. https://weibo.com/bjmtr (in Chinese).