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A Passenger Flow Control Method for Subway Network Based on Network Controllability

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A Passenger Flow Control Method for Subway Network Based on Network Controllability Hindawi Discrete Dynamics in Nature and Society Volume 2018, Article ID 5961090, 12 pages https://doi.org/10.1155/2018/5961090 Research Article A Passenger Flow Control Method for Subway Network Based on Network Controllability Lu Zeng,1,2 Jun Liu ,2 Yong Qin,3 Li Wang ,2 and Jie Yang4 1 College of Applied Science, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi Province, China 2School of Trafc and Transportation, Beijing Jiaotong University, Beijing 100044, China 3State Key Laboratory of Rail Trafc Control and Safety, Beijing Jiaotong University, Beijing 100044, China 4School of Electrical Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi Province, China Correspondence should be addressed to Li Wang; [email protected] Received 1 March 2018; Revised 14 June 2018; Accepted 5 August 2018; Published 4 September 2018 AcademicEditor:JuanL.G.Guirao Copyright © 2018 Lu Zeng et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te volume of passenger fow in urban rail transit network operation continues to increase. Efective measures of passenger fow control can greatly alleviate the pressure of transportation and ensure the safe operation of urban rail transit systems. Te controllability of an urban rail transit passenger fow network determines the equilibrium state of passenger fow density in time and space. First, a passenger fow network model of urban rail transit and an evaluation index of the alternative set of fow control stations are proposed. Ten, the controllable determination model of the urban rail transit passenger fow network is formed by converting the passenger fow distribution into a system state equation based on system control theory. Te optimization method of passenger fow control stations is established via driver node matching to realize the optimized control of network stations. Finally, a real-world case study of the Beijing subway network is presented to demonstrate that the passenger fow network is controllable when driver nodes compose 25.3% of the entire network. Te optimization of the fow control station, set during the morning peak, proves the efciency and validity of the proposed model and algorithm. 1. Introduction relationship between station capacity and demand based on queuing network theory. Cortes´ [2, 3] developed a strategy to Due to their large size, fast speed, and safety, urban rail transit control public transport lines using stop-station waiting and systems have become the backbone of city transportation. interchange station operation by minimizing the waiting time In recent years, the volume of passenger fow has increased rapidly. Congestion of passenger fow is very high, especially and uniform time interval. D. Felipe et al. [4] proposed a new during the morning and evening rush hours, which is a severe mathematical programming model by minimizing the time challenge for the operational safety of urban rail transit. delay of a bus. Te model controls the number of passengers With network integration of urban rail transit, traditional boarding the bus to minimize the delay time. In conclusion, passenger fow control methods cannot accommodate the current passenger fow control methods focus on a single increasingly large-volume, line-intensive, complex organiza- station, line, or local network. Few works have considered tional conditions in modern transit systems. Te strategy of the use of optimization fow control methods to control fow control optimization for urban rail transit network con- the overall stability of the network. In addition, existing trollability provides a new perspective for network control. passenger fow control is mainly based on static relationships Along with the increasing in urban rail transit passenger between stations and does not consider the timing sequence. volume, research on subway passenger fow control and Tis paper optimizes the current fow control method via related topics has attracted the interest of many scholars. Xu network controllability according to the characteristics of et al. [1] proposed a fow control method and analyzed the urban rail transit network and distribution. 2 Discrete Dynamics in Nature and Society Te study of network controllability began relatively network and defned the driver nodes based on immune recently, and we can divide the main research methods into transmission and cascade failures. An improved theoretical three categories: fock control, traction control, and structural model for the control of complex network and a dual graph control. Te early theory of complex network control was of train service network were constructed. Ravindran [25] initiated by the study of large-scale system focking control. identifed driver nodes with a maximum matching algorithm Flocking control is the analysis of emerging behavior based and classifed the nodes. Te key regulatory genes in the on simulations of biological groups in nature. Most focking cancer signal network were identifed by controllable analysis. control studies are based on the Boids model [5], in which an Te topology and controllability of the U.S. power grid were individual is defned as a node in a cluster system, and the analyzed by Li [26], and a new method was proposed to connections between individual are defned as edges. Tanner quantify the probability of the intermittent node becoming and Olfai et al. [6, 7] introduced a discontinuous control the driver node. method based on this model and an algorithm to control the Previous research on network controllability has mainly state of change. been based on the general characteristics of complex net- Pinning control is representative of complex network works. In recent years, a few studies have examined con- control. Wang et al. [8, 9] combined pinning control and trollable analysis of real networks. However, these studies focking control and applied pinning control to a scale-free have mainly focused on the analysis of complex topological dynamic network. Te results showed that pinning control properties. Tere is no specifc strategy for the optimization with a high degree of nodes requires fewer controllers than of network controllability. Most studies have ignored the the conventional pinning control. Chen et al. [10] studied function attributes of the nodes and edge weights in the actual the pinning control of complex dynamic networks and the network, making it impossible to propose efective control controllability of directed networks and proposed the theory methods and coping strategies for specifc issues. of “network of networks”. Fu [11] demonstrated that the Tis paper analyzes the topological characteristics of an preferential pinning strategy of stochastic pinning is superior urban rail transit passenger fow network. Ten, a control- to the preferential pinning strategy of clustered complex lability model of the passenger fow network is constructed networks. A new pinning strategy based on the cluster degree based on traditional control theory. An improved control- was proposed, and the results indicated that the new cluster lability determination method for uncontrollable networks pinning strategy was superior to the RP strategy when there is proposed, and the minimum number of driver nodes in were fewer pinning nodes. the controllability passenger fow network is calculated. Te Liu [12] studied the controllability of directed networks method of fow control optimization is built based on driver in 2011 and applied the judgment of the state-space equation node matching, and the specifc fow control station set for of control theory to network controllability for the frst time. controllability of the passenger fow network is presented. In addition, the directed network was transformed into a Te method is validated based on actual passenger fow data binary graph, and the maximum matching was calculated. for the Beijing subway network. In the actual fow control Liu’s research represented a new starting point for network process, the passenger fow will change. Te set of fow controllability and laid the foundation for subsequent studies control stations is obtained at diferent time periods. When by others. A great deal of subsequent work has begun to the passenger fow is relatively stable, the fow control stations focus on the impact of network topology on the controllable tend to be fxed. performance of network structure [13–18]. Based on Liu’s research, the relationship between the controllability and 2. Controllability Model of the Urban Rail energy consumption of diferent types of networks was Transit Passenger Flow Network analyzed from the perspective of energy consumption [19]. Nepusz [20] converted the network to an edge-based model 2.1. Basic Indicators of the Passenger Flow Network. Te by considering the dynamics of the edges of the network. model of the passenger fow network must be built based Lombardi [21] applied a controllable matrix to the network. on the rail infrastructure line. We defne the station as a Te value of the matrix element was the path gain from node and the rail connecting two adjacent stations as an the input signal to the node. Chen et al. [22] evaluated edge. Te nodes and edges constitute a physical network of changes and control costs of network controllability under urbanrailtransit.Wethensuperimposepassengerfowon cascade failure conditions. Te number
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