Rail transit congestion propagation evaluation and control method considering mass passenger flow early warning information

Abstract

The application discloses a rail transit congestion propagation evaluation and control method considering large passenger flow early warning information, comprising: two levels of macro and micro scales, the macro scale method faces common congestion scenes, comprising constructing a macro urban rail transit topological network, dividing different states of stations, defining state transition paths of stations, constructing a macro scale congestion propagation quantitative model and designing a congestion propagation control strategy simulation method; the micro scale method faces occasional congestion scenes, comprising constructing a micro urban rail transit topological network, defining a cell state set, setting a simulation time step, constructing a micro scale congestion propagation quantitative model and designing a congestion propagation control strategy simulation method. The application adds an early warning state when describing the state of the station to describe the process of the station receiving congestion early warning information and taking relevant measures, thereby improving the existing method.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit technology, and more specifically to a method for assessing and controlling the spread of congestion in rail transit that takes into account early warning information for large passenger flows. Background Technology

[0002] As a primary mode of passenger transport, urban rail transit systems are increasingly plagued by congestion, a problem affecting the normal operation of the network. Large passenger flows in rail transit networks refer to situations where a large number of passengers gather at a station within a short period due to factors such as morning and evening rush hours, emergencies, or large-scale events. This causes existing facilities and passenger flow management to exceed the station's maximum capacity, resulting in congestion. Furthermore, the network-based operation of rail transit allows this congestion to spread throughout the network, posing a threat to its safe operation. Passenger congestion can be categorized into two types: recurring and sporadic. Recurring congestion refers to the periodic and regular characteristics of passenger flow in sections or on platforms within a certain timeframe, such as commuter traffic during morning and evening rush hours. Sporadic congestion refers to congestion caused by weather, emergencies, or large-scale events.

[0003] To address passenger congestion, various congestion control strategies can be implemented at congested stations, transfer stations, and intermediate stations in rail transit systems to disperse overcrowded passenger flows. These strategies primarily include two aspects: capacity supply management and passenger demand management. Capacity supply management mainly focuses on optimizing train operations by adjusting schedules and increasing train frequency to enhance capacity and meet passenger transport demands during periods of high congestion. Passenger demand management, on the other hand, focuses on controlling or reducing passenger flow entering congested stations through flow restriction measures, thereby alleviating the pressure on passenger evacuation within the station. This, combined with capacity supply management, improves congestion evacuation efficiency.

[0004] Currently, the main approach is to employ complex network propagation dynamics theory (such as the classic SIS and SIR propagation models) to construct a quantitative evaluation model for congestion propagation and congestion strategies. This is combined with computer simulation technology to simulate the propagation process of congestion in rail transit networks, quantifying the scale of congestion propagation, such as the scope and duration of its impact. The effectiveness of congestion strategies is then evaluated by adjusting simulation parameters. Zhang Qi et al. proposed a simulation method for urban rail transit congestion propagation based on cellular automata, primarily analyzing the congestion propagation process at stations and between sections in commuting scenarios. Geng Danyang et al. proposed an evaluation method and system for flow control measures under sudden events in urban rail transit. This method analyzes the propagation mechanism of congested passenger flow by constructing a passenger travel choice behavior model under sudden events and building a simulation environment for such events, and conducts simulation analysis on flow control measures of different intensities. Li Lingyan constructed a large-scale passenger flow congestion propagation model based on the classic SIRS propagation model, calibrating the model parameters based on passenger transport capacity, and analyzing the changing trend of the number of congested stations in the network over time through simulation. Su Huailang, based on complex network theory and cellular automata methods, constructed a congestion propagation simulation network for peak-hour large passenger flows to simulate the congestion propagation process. Gao Liran, utilizing propagation models and cellular automata theory, constructed a congestion propagation simulation network for sudden large passenger flow scenarios, quantifying indicators such as the impact time and scope of congestion propagation. Xiong Zhihua et al., based on the SIR model, quantitatively analyzed various parameters in the rail transit congestion propagation model, constructed a quantitative model of congestion propagation rate, and analyzed the characteristics of congestion propagation.

[0005] In actual operation, when a large-scale passenger congestion event occurs in the rail transit network, the operation management department will take immediate control measures. Furthermore, stations that are not experiencing congestion can take advance passenger flow control measures after receiving congestion warnings from neighboring stations to reduce the impact of large-scale congestion on network operation. However, current methods based on classical propagation models mainly classify rail transit stations into three categories: "normal (no congestion)," "congested," and "resumed normal operation." This classification method cannot characterize the impact of stations taking relevant control measures in advance after receiving large-scale congestion warnings on congestion propagation. Therefore, it cannot accurately describe the actual propagation process of congestion, leading to an inability to accurately quantify the scale of congestion propagation. Consequently, it is impossible to effectively simulate and evaluate the congestion propagation process and evacuation effects before and after the implementation of congestion control strategies, resulting in poor implementation effects of congestion control strategies and making it difficult to provide effective support for the formulation of passenger transport organization strategies in actual operation.

[0006] Therefore, how to provide a method for assessing and controlling congestion propagation in rail transit that takes into account early warning information of large passenger flows is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a method for assessing and controlling the spread of congestion in rail transit that takes into account early warning information of large passenger flow. Compared with the current method based on the classical propagation model, the present invention adds an early warning status when describing the station status to describe the process of the station receiving congestion early warning information and taking relevant measures. This can accurately quantify the scale of congestion propagation and is more in line with the actual operation scenario.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] Methods for assessing and controlling congestion propagation in rail transit that consider large passenger flow early warning information include:

[0010] Determine the type of passenger congestion, including frequent and occasional occurrences;

[0011] For frequently occurring congestion scenarios, a macro-scale congestion propagation quantification model is constructed, and a simulation method for congestion propagation control strategies is designed; specifically including:

[0012] Based on the scale-free characteristics of complex urban rail transit networks, a macroscopic urban rail transit topology network is constructed.

[0013] The different states of stations in the macro-urban rail transit topology network are divided into normal operation state S, warning state A, and congestion state I;

[0014] Define the state transition path of a site based on its different states;

[0015] A macro-scale congestion propagation quantification model is constructed based on the state transition paths of the macro-urban rail transit topology network and stations.

[0016] For sporadic congestion scenarios, a micro-scale congestion propagation quantification model is constructed, and a simulation method for congestion propagation control strategies is designed, specifically including:

[0017] Based on complex network theory and cellular automata principles, a microscopic urban rail transit topology network is constructed.

[0018] Define the set of cell states in a microscopic urban rail transit topology network, including normal operation state S, warning state A, and congestion state I;

[0019] Define the state transition path of a site cell based on its state.

[0020] Set the simulation time step;

[0021] Based on the principle of cellular automata, and according to the state transition path of station cells and the simulation time step, the congestion propagation process of the microscopic urban rail transit topology network is discretized, and a microscopic-scale congestion propagation quantitative model is constructed.

[0022] Preferably, based on the scale-free characteristics of the complex network inherent in rail transit networks, a macroscopic urban rail transit topology network is constructed, specifically as follows:

[0023] The macroscopic urban rail transit topology network is defined as G=(V,E);

[0024] Where G represents the macroscopic urban rail transit topology network; V is the set of stations in the network, i.e., V = {v s |s=1,2,...,N}, where N is the total number of stations, and E is the set of edges in the network, defined as E={e sl |s,l=1,2,...,N;s≠l}, where each edge represents the connection between stations, i.e., the interval in the rail transit network.

[0025] Preferably, the state transition path of a site is defined based on different site states, wherein the state transition path includes the following cases:

[0026] Normal operation state S → Warning state A → Congestion state I → Normal operation state S;

[0027] Normal operating state S → Warning state A → Normal operating state S;

[0028] Normal operating state S → Congested state I → Normal operating state S.

[0029] Preferably, the mean-field evolution equation of the macroscale crowding propagation quantization model is:

[0030]

[0031]

[0032]

[0033] Among them, S k (t), I k (t) and A k (t) represents the relative densities of stations with degree k at time t in normal, warning, and congested states, respectively, satisfying S k (t)+A k (t)+I k (t) = 1, β0 is the crowding propagation rate, δ is the crowding recovery rate, β α (ρ,k) represents the probability that a station transitions from a warning state to a congested state, and Θ(t)∈[0,1] represents the average probability at time t that any edge in the macroscopic urban rail transit topology is connected to a congested station, defined as:

[0034]

[0035] in, Let p(k) be the average degree of all stations in the macroscopic urban rail transit topology network, and let p(k) be the degree distribution of the nodes. The probability of a normal station changing to an alert state is:

[0036]

[0037] Where ρ∈(0,1); k inf This represents the number of congested stations among the stations connected to the normal station with degree k.

[0038] Preferably, the stations in the microscopic urban rail transit topology network are defined as station cells, and the microscopic urban rail transit topology network is defined as G. M =(H,I R ,M); where G M Represent the microscopic urban rail transit topology network; define the set of stations in the network as H = {1,2,...,N}. m}, N m Let I be the number of stations in the network. When considering the different lines corresponding to a station, define the set of station cells I. R ={i r |i∈H,r∈R};Let R={1,2,...,r,...,N r} represents the set of routes, N r Let i be the number of lines in set R; therefore, element i r Let M represent the station cell of line r corresponding to station i. ij |i,j=1,2,...,N m ;i≠j} is defined as the set of directed edges connecting stations in the network, representing the direction of train operation and passenger congestion propagation in operation.

[0039] Preferably, the formula for calculating the simulation time step ΔT is:

[0040]

[0041] in, The departure time interval for each section.

[0042] Preferably, the microscale crowding propagation quantification model is as follows:

[0043] 1) Define the state evolution rules for site cells:

[0044]

[0045] In the formula, x(j r ,t+1) represents station cell j rThe state of (j∈H, r∈R) at time t+1, x(i1,t),…, For site cell j r The states of all neighboring cells at time t. For a station cell j within a simulation time step r All N d Neighboring station cells i1, i2, ... For site cell j r The rate of transmission, For site cell j r Recovery rate of congestion propagation at time t;

[0046] 2) Based on the state evolution rules and state transition paths of the station cell, define the state of the station cell at the next time step t+1:

[0047] i) When site cell j r When the state at time t is the normal operating state S, the state transition function f a (t) is represented as:

[0048]

[0049] Where, j r f represents the station cell of line r corresponding to station or node j. α This represents the state evolution of a site cell after one time step under normal operating conditions. θ1, θ2, and θ3 are parameters that can be set according to actual operating conditions; propagation rate. Affected by train occupancy rate and transfer passenger flow:

[0050]

[0051] Where station j is a transfer station, for station cell j r , Cell j represents the transfer from other lines at station j to the corresponding line r at station j. r The number of passengers; This represents the cell j corresponding to line r in station j. r Passenger flow transferring to other lines at station j; V j,r This indicates that for line r, the train arrives at platform j. r Previous cross-sectional passenger flow; O j,r This indicates that node j corresponds to cell j of line r. r Passenger flow exiting the station; I j,r This indicates that node j corresponds to cell j of line r. r Passenger flow entering the station; C j,rThis represents the maximum passenger capacity of a train for line r, which can be considered as the passenger transport capacity in that direction of operation; ω1 is a binary variable of 0 and 1. When ω1 = 1, it represents the station cell j. r For a transfer station, when ω1=0, station cell j r Indicates the stations on a single line;

[0052] ii) When site cell j r When in warning state A, the state transition function f β (t) is defined as:

[0053]

[0054] in, To enhance recovery capabilities after taking relevant measures in advance; For each time step, the station cell j reaches the destination. r The number of passengers alighting; For a time step intrinsic site cell j r The number of passengers waiting to board; This indicates the passenger transport capacity within a given time step.

[0055] iii) When site cell j r When in a crowded state I, its state transition function f r (x) is defined as:

[0056]

[0057] The above equation describes the state evolution of a crowded site cell after one time step; let That is, in a congested state, the site cells use To ensure a probability of returning to normal operation, To maintain the existing congestion status with a certain probability.

[0058] Preferably, after constructing the microscale crowding propagation quantification model, the method further includes:

[0059] Based on a microscale congestion propagation quantification model, this paper simulates and analyzes the congestion propagation evolution process under different passenger flow congestion control measures from the perspectives of train operation optimization and passenger flow organization optimization, and obtains the degree of mitigation of congestion propagation in rail transit networks by different control measures.

[0060] Preferably, after constructing the macro-scale crowding propagation quantification model, the method further includes:

[0061] Based on the macro-scale congestion propagation quantification model, the impact of train operation optimization on the scale of congestion propagation is simulated by changing the control parameters in the macro-scale congestion propagation quantification model. The impact of transportation organization optimization strategies on the scale of congestion propagation is evaluated, and the control effects of different transportation organization optimization strategies on congestion propagation are compared through multiple simulations.

[0062] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for assessing and controlling the spread of congestion in rail transit that considers early warning information of large passenger flows, which has the following advantages:

[0063] 1) Compared with traditional methods, this invention adds "early warning status" when describing the station status, which fully considers the role of stations in rail transit in suppressing the spread of congestion by receiving early warning information in advance and taking corresponding control strategies in a timely manner, and is more in line with actual operation scenarios.

[0064] 2) Construct a quantitative model of congestion propagation from both macro and micro levels, and design a simulation method for congestion propagation control strategy, which can be applied to different application scenarios in actual operation. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0066] Figure 1 The flowchart of the rail transit congestion propagation assessment and control method considering large passenger flow early warning information provided by the present invention is shown below.

[0067] Figure 2 This is a schematic diagram of the site state transition path provided by the present invention;

[0068] Figure 3 A diagram showing neighboring nodes;

[0069] Figure 4 This is a schematic diagram comparing the evolution trend of average density at congested sites using the present invention and classical methods.

[0070] Figure 5 A schematic diagram illustrating the evolution trend of average density at congested stations under train operation optimization. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] This invention discloses a method for assessing and controlling congestion propagation in rail transit that considers early warning information for large passenger flows, such as... Figure 1 As shown, it includes:

[0073] Determine the type of passenger congestion, including frequent and occasional occurrences;

[0074] For frequently occurring congestion scenarios, a macro-scale congestion propagation quantification model is constructed and a simulation method for congestion propagation control strategies is designed;

[0075] For sporadic congestion scenarios, a microscale congestion propagation quantification model is constructed and a simulation method for congestion propagation control strategies is designed.

[0076] Specifically, the macro-scale congestion propagation quantitative assessment and control method mainly utilizes the mean-field method to construct a quantitative assessment model that can be used to simulate the congestion propagation process, analyze the propagation trend and characteristics of congestion propagation in the global rail transit network, and evaluate the effectiveness of the congestion control method by changing the model control parameters during the simulation process from the perspective of train operation organization optimization. The specific process is as follows:

[0077] S101: Based on the scale-free characteristics of the complex network of rail transit network, construct a macroscopic urban rail transit topology network.

[0078] The macroscopic urban rail transit topology network includes nodes and edges, defined as G = (V, E); where G represents the macroscopic urban rail transit topology network; V is the set of stations (nodes) in the network, i.e., V = {v s |s=1,2,...,N}, where N is the total number of stations (nodes). E is the set of edges (intervals) in the network, defined as E={e sl |s,l=1,2,...,N;s≠l}, each edge represents the connection between stations (intervals in the rail transit network), and the length of the edge connecting adjacent stations in the network represents the distance between stations.

[0079] S102: Divide the different states of stations in the macro-urban rail transit topology network.

[0080] Based on the changes in the operational status of rail transit stations under the influence of large passenger flows, this invention classifies stations into three categories:

[0081] The first category is stations that are operating normally without being impacted by large passenger flows (represented by S). Since in actual operation, stations that have recovered from congestion to normal operation have a certain probability of becoming congested again, this invention also considers stations that have recovered from congestion to normal operation as state S.

[0082] The second category is stations in an early warning state (denoted by A). For normally operating stations, if information about large passenger flows at upstream congested stations can be obtained in real time, relevant measures or control strategies can be taken in advance to improve the station's passenger transport organization capacity, reduce the impact of large passenger flows in the network, and control the scale of congestion propagation in the network. This invention introduces "early warning state" stations (A) in the congestion propagation simulation process, that is, normally operating stations will become early warning stations with a probability of α after receiving congestion early warning information in the network.

[0083] The third category is stations that experience congestion due to large passenger flows (represented by I).

[0084] S103: Define the state transition path of a site based on its different states.

[0085] In actual operation, both normal operation and warning status sites are at risk of becoming congested sites. When a normal operation site is connected to a congested site, the normal operation site will become congested with a probability of propagation rate or propagation intensity β0; or when a normal operation site receives congestion warning information from a neighboring site, the site will become a warning site with a certain probability α.

[0086] The probability that a warning site becomes a congested site is β. α In actual operation, because stations in the early warning state will take congestion control strategies (such as transportation organization optimization, flow restriction measures, etc.) in advance to avoid congestion, therefore, 0 < β α <β0. The recovery rate or dissipation rate of a congested station turning into a normal station as the station adopts control strategies to disperse the congested passenger flow is δ.

[0087] Based on the definitions of the parameters above, the state transition paths of stations in the congestion propagation model include the following cases, as illustrated in the state transition diagram below. Figure 2 As shown:

[0088] ① Normal operation state S → Warning state A → Congestion state I → Normal operation state S;

[0089] ② Normal operation state S → Warning state A → Normal operation state S;

[0090] ③ Normal operating state S → Congested state I → Normal operating state S.

[0091] S104: Construct a macro-scale crowding propagation quantification model.

[0092] Let S k (t), I k (t) and A k (t) represents the relative density of a station with degree k at time t in normal operation, warning, and congestion states, respectively, satisfying the following normalization condition:

[0093] S k (t)+A k (t)+I k (t)=1

[0094] Let S(t), A(t), and I(t) be the average densities of all stations in the rail transit network at time t under normal operation, warning, and congestion conditions, respectively. This density is defined by the relative density of nodes of degree k.

[0095]

[0096]

[0097]

[0098] Where p(k) represents the degree distribution of the nodes. The degree of a node represents the number of edges connected to a single node.

[0099] Based on the above definitions, the mean-field evolution equation of the macro-scale congestion propagation quantification model considering large passenger flow early warning information, using the mean-field method, is defined as follows:

[0100]

[0101]

[0102]

[0103] Among them, S k (t), I k (t) and A k (t) represents the relative densities of stations with degree k at time t in normal, warning, and congested states, respectively, satisfying S k (t)+A k (t)+I k (t) = 1, β0 is the crowding propagation rate, δ is the crowding recovery rate, β α (ρ,k) represents the probability that a station transitions from an alert state to a congested state, and Θ(t)∈[0,1] represents the average probability that any edge in the network is connected to a congested station at time t, defined as:

[0104]

[0105] in, This is the average degree of all nodes in the network.

[0106] Currently, some cities' rail transit operations employ a tiered system for assessing high passenger flow risks. Stations with high designed passenger volumes, such as transfer hubs (i.e., stations with significant scale), are designated as key monitoring and control points. Therefore, to align with actual rail transit operation scenarios, the probability of a normal station transitioning to an alert status is defined as follows:

[0107]

[0108] Where, ρ∈(0,1); k inf Let k be the number of congested stations connected to a normally operating station of degree k. The formula indicates that the higher the degree of a node, the higher the warning rate, showing a direct proportional relationship. This formula describes how a normally operating station of degree k, upon receiving a warning message, can choose to take relevant control measures in advance to reduce the risk of becoming a congested station.

[0109] Therefore, the above congestion propagation quantification model can be used to simulate the changing trend of the number of congested stations in a rail transit network under the influence of large passenger flows, and to simulate the congestion propagation process.

[0110] S105: Simulation method for congestion propagation control strategy.

[0111] Based on a macro-scale congestion propagation quantification model, this study simulates the impact of train operation optimization (such as changes in transport capacity) on the scale of congestion propagation by changing control parameters in the model. Model parameters are calibrated using rail transit operation indicators such as transport demand under congested conditions, train throughput capacity, and actual passenger transport capacity after implementing relevant control measures. The impact of transport organization optimization strategies on the scale of congestion propagation (such as changes in the number of stations under congested conditions) is evaluated, and the control effects of different transport organization optimization strategies (i.e., different parameter combinations) on congestion propagation are compared through multiple simulations. The main parameters are as follows.

[0112] ① Crowding transmission rate β0

[0113] Under the influence of large passenger flows, the spread of congestion is mainly related to the inability of train capacity to fully meet transportation demand, such as the increased time intervals between trains due to longer station stops. Therefore, the congestion spread rate can be defined by the supply-demand imbalance:

[0114]

[0115] Wherein, N1 represents the train throughput capacity required under congested conditions; N2 represents the actual transport capacity under congested conditions; and N3 represents the designed throughput capacity. In actual operation, N2 is a quantity that varies with the operating cycle; for example, when congestion occurs, the increased train delay time at stations leads to a decrease in passenger transport capacity, thus the transport capacity under congestion is a variable quantity; this invention takes N2 as the average throughput capacity after events such as delays occur.

[0116] ② Crowding recovery rate δ

[0117] In actual operation, the value of δ is related to factors such as the degree of congestion, train throughput capacity, platform passenger capacity, and evacuation strategies, and can be defined as:

[0118]

[0119] N4 represents the train's transport capacity after the station adopts a control strategy, and N4 is usually greater than N3.

[0120] ③ Warning rate parameter ρ

[0121] According to the warning rate formula, the value of α is related to the spatial location of the station (degree value), where the key parameter ρ can be defined by the rate of change of throughput capacity:

[0122]

[0123] Specifically, the micro-scale congestion propagation quantitative assessment and control method mainly targets the impact of a sudden surge in passenger flow on a specific station. Unlike macro-scale scenarios, which primarily quantify the average trend of congestion propagation across the global network, micro-scale scenarios need to consider the interactions between stations during congestion propagation. Therefore, this invention combines cellular automata theory with macro-scale quantitative models to construct a micro-scale congestion propagation quantitative assessment model. Furthermore, from the perspective of train operation and passenger flow organization optimization, the implementation effects of different congestion control methods and operational organization strategies are evaluated during simulation by changing the model's control parameters. The specific steps include:

[0124] S201: Construct a microscopic urban rail transit topology network based on complex network theory and cellular automata principles.

[0125] This network includes all rail transit stations, platforms, and train operating sections. Stations in the network are defined as station cells. Using a macroscopic model, the elements of a cellular automaton are defined, including cell space, neighboring nodes, states, and evolution rules. To distinguish the up and down directions of each line, each station cell includes up-line platform cells and down-line platform cells. If a station is a transfer station, then all platforms of all adjacent lines included in that station are defined as a single station cell. Furthermore, according to the principles of cellular automata, the platforms at transfer stations will influence each other. Therefore, stations within the network are divided into transfer stations and non-transfer stations, based on the number of lines N passing through each station. c Each site cell contains 2N c Each station has a single cell; and the direction of passenger flow propagation on the cells is unidirectional. In practical processing, for ease of calculation, modeling and analysis are based on station cells.

[0126] The above topological network is defined using cellular space and used as a microscale simulation network for passenger congestion propagation in urban rail transit. This microscale urban rail transit topological network can be described as a directed network, namely G. M =(H,I R ,M); where G M Represent the microscopic urban rail transit topology network; define the set of stations in the network as H = {1,2,...,N}. m}, that is, the set of site cells, N m The number of nodes or stations in the network, i.e., the station cells are numbered; when considering the different lines corresponding to a station, the set of station cells I is defined. R ={i r |i∈H,r∈R};Let R={1,2,...,r,...,N r} represents the set of routes, N r Let i be the number of lines in set R; therefore, element i r Let M represent the station cell of line r corresponding to station i. ij |i,j=1,2,...,N m ; i≠j} is defined as the set of directed edges connecting stations in the network, which can be represented as the direction of train operation and passenger congestion propagation. Further, neighboring nodes or neighboring cells are defined, such as Figure 3 As shown; node v1 is a neighbor node of nodes v2, v3, v4, and v5, and v1 is a transfer station (passed by 2 lines). By definition, v1 includes 2 up-line platform cells and 2 down-line platform cells.

[0127] S202: Define the set of cell states.

[0128] In practical applications, the set of cell states can be described by a discrete set of multiple integers. Based on the macroscopic scale model, this invention classifies the station states into normal operation state, warning state, and congestion state. The station cell i in line r is defined as follows: r The state vector at time t is x(i) r ,t)∈U, where the elements in the set U={1,2,3} represent the three states {normal, warning, congestion} respectively. The state transition path of the cellular station or platform is the same as that of the macro-scale model.

[0129] S203: Set the simulation time step.

[0130] In a rail transit network, passenger flow changes at each platform are affected by the exchange of passengers during train arrivals, and the propagation of congestion along the line from train operation to congestion also takes time. Therefore, updating the state of station cells also takes time; for example, at least one train will arrive and depart within a time interval.

[0131] A simulation time step ΔT is set as the congestion propagation time; within one time step, a station cell remains in only one state. The maximum average train departure interval for each section in the network is selected as the simulation time step ΔT for cell state updates, and calculated using the following formula:

[0132]

[0133] in This defines the departure time interval for each interval. Furthermore, based on the principles of cellular automata, the states of all cells in the network are updated simultaneously.

[0134] S204: Construct a quantitative model of crowding propagation at the microscale.

[0135] 1) Discretize the congestion propagation process of the rail transit network. For a single line r, let station cell j r For neighboring site cells i r The downstream platform, i.e., the direction of passenger flow or congestion propagation, is determined by the station cell i. r To site cell j r The time interval between time t+1 and time t is one time step ΔT. Station cell j r The state x(j) at time t+1 r ,t+1) is determined by its state x(j) at time t. r ,t), neighboring cell i r The state x(i) at time t r ,t) jointly decide; in addition, according to the site cell j r At time t, with different states and different state transition paths, station cell j rThe state at time t+1 is affected by different parameters. If the station cell j r If the corresponding station is a transfer station, then station cell j r The status is affected not only by passenger flow at upstream neighboring stations on line r, but also by passenger flow transferring from other lines r' via transfer stations. The parameters considered in this invention include: station cell j within a time step. r All neighboring site cells i1, i2, ... For site cell j r The rate of transmission (or the intensity of transmission). Site cell j r Recovery rate of congestion propagation at time t

[0136] In summary, site cell j r The state evolution rules can be represented by implicit equations:

[0137]

[0138] In the formula, x(i1,t),…, For site cell j r The states of all neighboring cells at time t. The evolution rule refers to the state of each station cell j. r The current state and the states of its neighbors determine the dynamic function of the cell state of the station at the next moment.

[0139] 2) Based on the state evolution rules and state transition paths of the station cell, define the state of the station cell at the next time step t+1:

[0140] ① When station cell j r When the state at time t is the normal state S (i.e., x(j) r When t) = 1), its state is defined by the propagation intensity, and the state transition function is expressed as:

[0141]

[0142] Among them, f α This represents the state evolution result of a normal-state site cell after one time step; the propagation intensity value in the formula... Affected by train occupancy rate and transfer passenger flow:

[0143]

[0144] If station j is a transfer station, for station cell j r , Cell j represents the transfer from other lines at station j to the corresponding line r at station j. r The number of passengers;

[0145] For site j, This represents the cell j corresponding to line r in station j. r Passenger flow transferring to other lines at station j;

[0146] V j,r For line r, the train arrives at platform j. r Previous cross-sectional passenger flow;

[0147] O j,r Node j corresponds to cell j of line r. r Passenger flow exiting the station;

[0148] I j,r Node j corresponds to cell j of line r. r Passenger flow entering the station;

[0149] C j,r For line r, the maximum passenger capacity of the train can be regarded as the passenger flow transport capacity in that direction of operation.

[0150] Furthermore, θ1, θ2, and θ2 are parameters that can be set according to actual operating conditions; in the formula... Describes the transfer passenger flow for station cell j r The influence of state; The impact of congested passenger flow propagation on this line r is described. ω1 is a binary variable of 0-1; when ω1=1, it represents the station cell j. r It is a transfer station.

[0151] When ω1=0, station cell j r This represents a station within a single line r. At this point, the station cell j... r The state is only affected by passenger flow at the upstream neighboring station on line r, meaning that the above propagation intensity formula does not include transfer passenger flow factors; in this scenario, the propagation intensity is defined as follows:

[0152]

[0153] Train arrives at station cell j r Previous cross-sectional passenger flow;

[0154] Node j corresponds to cell j of line r. r Passenger flow exiting the station;

[0155] Node j corresponds to cell j of line r. r Passenger flow entering the station;

[0156] For line r, the maximum passenger capacity of a train can be considered as the passenger transport capacity in that direction of operation.

[0157] ②When station cell j r When in warning state A (i.e., x(j) r Since t) = 2), the subway operation department will take relevant measures in advance. Therefore, the state of the crowded passenger flow at time t+1 is determined by the station cell j. r The propagation effect of all upstream neighbors and site cell j r Recovery capacity after taking relevant measures This is jointly determined, where recovery capacity or recovery rate can be defined as:

[0158]

[0159] in, For each time step, the station cell j reaches the destination. r The number of passengers alighting; For a time step intrinsic site cell j r The number of passengers waiting to board. This represents the passenger flow capacity within a time step. The above formula can be described as the recovery rate of a station after passenger flow management measures reduce the number of passengers on the platform, improving the recovery from a warning or congestion state to a normal state. This value changes over time and is generally non-negative; the higher the recovery rate, the more effective the passenger flow management measures. In this scenario, for station cell j... r The intensity of the crowding propagation effect can be defined as:

[0160]

[0161] Therefore, when site cell j r When in a warning state, its state transition function f β (t) is defined as:

[0162]

[0163] ③ When station cell j r When in a crowded state I (x(j) r The state transition function is defined as follows: (t) = 3)

[0164]

[0165] The above equation describes the state evolution of a crowded site cell after one time step; let That is, in a congested state, the site cells use To restore the probability to the normal state, with To maintain the existing congestion status with a certain probability.

[0166] S205: Simulation method for congestion propagation control strategy.

[0167] Furthermore, based on a micro-scale congestion propagation quantification model, from the perspectives of train operation optimization (such as increasing capacity) and passenger flow organization optimization (such as implementing flow control measures to improve recovery rate), simulation analysis is conducted on the congestion propagation evolution process under different passenger flow congestion control measures (simulations are performed with different parameter combinations). This yields the degree to which different control measures alleviate congestion propagation in the rail transit network. In actual operation, two main types of indicators are considered:

[0168] The range of influence of congestion transmission R p This metric represents the maximum number of nodes in a congested state within the simulation time.

[0169] Duration of Crowded Propagation T p This indicator represents the time from the onset of congestion in an urban rail transit network due to a surge in passenger flow until the congestion dissipates (returns to normal).

[0170] Specifically, based on the micro-scale congestion propagation quantification model, the simulation analysis steps for optimizing train operation and passenger flow organization are as follows:

[0171] The first step involves using a microscale congestion propagation quantification model, combined with rail transit passenger flow card swiping data, to calculate passenger flow entering and exiting stations, cross-sectional passenger flow, and transfer passenger flow. This quantifies parameters such as congestion propagation intensity and recovery rate within the microscale congestion propagation quantification model. Since the recovery rate requires calibration of the number of passengers boarding and alighting within a specific time step, which necessitates data acquisition through surveys or video recordings, it can be estimated from cross-sectional and transfer passenger flow data for ease of calculation in practice.

[0172] The second step involves simulating the congestion propagation process under different train densities and flow control measures from the perspective of train operation and passenger flow organization optimization. For train operation optimization, when stations in the network are under warning or congestion conditions, capacity is increased by increasing train density without changing scheduling strategies such as train formation and stopping plans. This includes adding spare trains, adjusting departure intervals, recalculating passenger flow capacity, and updating relevant parameters in the model.

[0173] For passenger flow organization (such as flow control measures), for stations in a state of early warning or congestion, the flow control process is simulated by increasing the recovery rate of nodes. According to the recovery rate formula, for a station cell j... rWhen the inbound passenger flow exceeds the outbound passenger flow, the recovery rate becomes negative. Therefore, to improve the recovery rate, it is necessary to control the inbound passenger flow over a certain time step to avoid the impact of large-scale passenger flow aggregation on network operation. In the micro-scale model, the congestion propagation intensity parameter under different flow restriction measures is calculated based on the changes in inbound passenger flow.

[0174] The third step involves calculating the evolution of rail transit congestion propagation under different congestion control strategies (i.e., different combinations of congestion propagation and recovery rate parameters) based on a microscale model. This quantifies two key indicators: the scope of congestion propagation's impact and its duration. Through multiple simulation experiments, the results of these indicators under different parameter combinations are compared to quantitatively evaluate the effectiveness of train operation and passenger flow organization optimization.

[0175] To verify the effectiveness of this invention, a simulation was conducted using the rail transit network of City A as a case study. Based on the 2015 metro network topology of City A, the network had 267 nodes with an average degree of 2.283 and a maximum degree of 5. Assuming that stations become congested due to high passenger flow, the initial model conditions S(t) and I(t) were set to S(0) = 0.99 and I(0) = 0.01, respectively, to calculate the scale of congestion propagation. The impact of changes in control parameters on the scale of congestion propagation under the two scenarios is compared below, with each parameter calibrated by the average transport capacity during the operation and evacuation cycles.

[0176] 1) This scenario compares the method provided by the present invention with a method based on the classical propagation model. Figure 4 The graph shows the evolution of the average density of congested stations over time in both methods. The parameters for this scenario are set as follows: congestion propagation rate β0 = 0.5, recovery rate δ = 0.3; the unit time in the model is defined as: t = L / V; where L is the distance between adjacent stations; and V is the train speed. Figure 4 As shown, under the same initial conditions, the average density of congested sites in the congestion propagation quantification model considering early warning information is lower than that in the classical propagation model. This means that the method provided by this invention can effectively control the scale of congestion propagation. Therefore, when the model considers congestion early warning information and takes corresponding control strategies in advance, it can effectively reduce the impact of congestion in the network, which is more consistent with actual operational conditions.

[0177] 2) This scenario considers a situation where, with a constant congestion propagation rate (β0 = 0.3), when congestion occurs at a station and adjacent stations receive congestion warnings, the station implements a control strategy. From a train operation optimization perspective, this involves increasing the value of N4 to alter transport capacity, thereby controlling congestion propagation and improving evacuation efficiency. The parameter values ​​for this scenario are: ρ = 0.2, δ = 0.3; ρ = 0.3, δ = 0.35; ρ = 0.4, δ = 0.4. Figure 5As shown, since the congestion propagation rate is a fixed value, increasing transport capacity does not delay the occurrence of congestion during peak hours. However, as the passenger transport capacity of stations and sections increases, the scale of congestion propagation is effectively controlled; on the other hand, as the congestion recovery rate increases, the rate of recovery to normal stations is accelerated, effectively reducing the impact of congestion propagation. The simulation results also illustrate the necessity of considering early warning information and taking effective control measures during station operation.

[0178] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0179] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for assessing and controlling congestion propagation in rail transit considering early warning information for large passenger flows, characterized in that, include: Determine the type of passenger congestion, including frequent and occasional occurrences; For frequently occurring congestion scenarios, a macro-scale congestion propagation quantification model is constructed and a simulation method for congestion propagation control strategies is designed; Specifically, it includes: Based on the scale-free characteristics of complex urban rail transit networks, a macroscopic urban rail transit topology network is constructed. The different states of stations in the macro-urban rail transit topology network are divided into normal operation state S, warning state A, and congestion state I; Define the state transition path of a site based on its different states; A macro-scale congestion propagation quantification model is constructed based on the state transition paths of the macro-urban rail transit topology network and stations. For sporadic congestion scenarios, a micro-scale congestion propagation quantification model is constructed, and a simulation method for congestion propagation control strategies is designed, specifically including: Based on complex network theory and cellular automata principles, a microscopic urban rail transit topology network is constructed. Define the set of cell states in a microscopic urban rail transit topology network, including normal operation state S, warning state A, and congestion state I; Define the state transition path of a site cell based on its state. Set the simulation time step; Based on the principle of cellular automata, and according to the state transition path of station cells and the simulation time step, the congestion propagation process of the micro-scale urban rail transit topology network is discretized, and a micro-scale congestion propagation quantitative model is constructed. The mean-field evolution equation of the macroscale crowding propagation quantization model is: ； ； ； in, , and Let be the relative densities of stations with degree k at time t in normal, warning, and congested states, respectively, satisfying the following conditions: , For the rate of transmission in crowded areas, For congestion recovery rate, The probability of a site transitioning from a warning state to a congested state. Let be the average probability that any edge in the macroscopic urban rail transit topology network is connected to a congested station at time t; the probability that a normal station changes to a warning state is: ； in ; This represents the number of congested stations among those connected to a normal station with degree k. The microscale crowding propagation quantification model is as follows: 1) Define the state evolution rules for station cells; 2) Based on the state evolution rules and state transition paths of the station cell, define the state of the station cell at the next time step t+1: i) When the site cell When the state at time t is the normal operating state S, the state transition function is... Represented as: ； in, This represents the station cell of line r corresponding to station or node j. This represents the state evolution result of a site cell after one time step under normal operating conditions. , and These are parameters that can be set according to actual operating conditions. For a station cell within a simulation time step All N d Neighboring station cells i1, i 2， …, site cells The rate of transmission; ii) When site cells When in warning state A, the state transition function Defined as: ； in, ; ; To enhance recovery capabilities after taking relevant measures in advance; A cell that arrives at a station within a time step The number of passengers alighting; For a time step intrinsic site cell The number of passengers waiting to board; This indicates the passenger transport capacity within a given time step. iii) When the site cell When in crowded state I, its state transition function Defined as: ； The above equation describes the state evolution of a crowded site cell after one time step; let That is, in a crowded state, the site cells are... To ensure a probability of returning to normal operation, To maintain the existing congestion status with a certain probability.

2. The method for assessing and controlling congestion propagation in rail transit considering large passenger flow early warning information as described in claim 1, characterized in that, Based on the scale-free characteristics of complex urban rail transit networks, a macroscopic urban rail transit topology network is constructed, specifically as follows: The macro-level urban rail transit topology network is defined as follows: ; Where G represents the macroscopic urban rail transit topology network; V is the set of stations in the network, i.e. N is the total number of stations, and E is the set of edges in the network, defined as follows: Each edge represents the connection between stations, that is, the section in the rail transit network.

3. The method for assessing and controlling congestion propagation in rail transit considering early warning information for large passenger flows, as described in claim 1, is characterized in that... The state transition path of a site is defined based on its different states. The state transition path includes the following cases: Normal operation state S → Warning state A → Congestion state I → Normal operation state S; Normal operating state S → Warning state A → Normal operating state S; Normal operating state S → Congested state I → Normal operating state S.

4. The method for assessing and controlling congestion propagation in rail transit considering early warning information for large passenger flows, as described in claim 2 or 3, is characterized in that... Defined as: ； in, This represents the average degree of all stations in the macroscopic urban rail transit topology network. Let represent the degree distribution of the nodes.

5. The method for assessing and controlling congestion propagation in rail transit considering early warning information for large passenger flows, as described in claim 1, is characterized in that... In a microscopic urban rail transit topology network, a station is defined as a station cell. The microscopic urban rail transit topology network is defined as... ;in, Represent the microscopic urban rail transit topology network; define the set of stations in the network. N m To represent the number of stations in the network, and considering the different lines corresponding to each station, we define a set of station cells. ;make For the set of routes, N r Let R be the number of lines in set R; therefore, the element This represents the station cell of line r corresponding to station i. , is defined as the set of directed edges connecting stations in the network, representing the direction of train operation and passenger congestion propagation in operation.

6. The method for assessing and controlling congestion propagation in rail transit considering large passenger flow early warning information as described in claim 5, characterized in that, Simulation time step The calculation formula is: ； in, The departure time interval for each section.

7. The method for assessing and controlling congestion propagation in rail transit considering early warning information for large passenger flows, as described in claim 5, is characterized in that... The state evolution rule for a site cell is: ； In the formula, For site cells The state at time t+1 , , ,…, For site cells The states of all neighboring cells at time t. For a station cell within a simulation time step All N d Neighboring station cells i1, i 2， …, site cells The rate of transmission, For site cells Recovery rate of congestion propagation at time t; Transmission rate Affected by train occupancy rate and transfer passenger flow: ； Where station j is a transfer station, for station cells , This represents a cell representing a transfer from other lines at station j to the corresponding line r within station j. The number of passengers; This represents the cell corresponding to line r in station j. Passenger flow transferring to other lines within the station; This indicates that for line r, the train arrives at platform r. Previous cross-sectional passenger flow; This indicates that station j corresponds to the cell of line r. The number of passengers exiting the station; This indicates that station j corresponds to the cell of line r. Passenger flow entering the station; This represents the maximum passenger capacity of a train for line r, which can be considered as the passenger transport capacity in the direction of operation. For a binary variable of 0-1, when At that time, it represents a site cell. As a transfer station, when At that time, site cells This refers to the stations on a single line.

8. The method for assessing and controlling congestion propagation in rail transit considering large passenger flow early warning information as described in claim 1, characterized in that, After constructing the microscale crowding propagation quantification model, it also includes: Based on a microscale congestion propagation quantification model, this paper simulates and analyzes the congestion propagation evolution process under different passenger flow congestion control measures from the perspectives of train operation optimization and passenger flow organization optimization, and obtains the degree of mitigation of congestion propagation in rail transit networks by different control measures.

9. The method for assessing and controlling congestion propagation in rail transit considering large passenger flow early warning information as described in claim 1, characterized in that, After constructing the macro-scale crowding propagation quantification model, it also includes: Based on the macro-scale congestion propagation quantification model, the impact of train operation optimization on the scale of congestion propagation is simulated by changing the control parameters in the macro-scale congestion propagation quantification model. The impact of transportation organization optimization strategies on the scale of congestion propagation is evaluated, and the control effects of different transportation organization optimization strategies on congestion propagation are compared through multiple simulations.

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