Subway network collaborative passenger flow control method, device and equipment

By constructing a subway network passenger flow control model and using a non-optimal value acceptance optimization algorithm for network-wide coordinated control, the problem of network-level congestion caused by local control was solved, and the efficient and stable operation of the subway system was achieved.

CN121998455APending Publication Date: 2026-05-08SHIJIAZHUANG TIEDAO UNIV
View PDF 0 Cites 0 Cited by

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
SHIJIAZHUANG TIEDAO UNIV
Filing Date
2026-02-10
Publication Date
2026-05-08

AI Technical Summary

Technical Problem

Existing subway passenger flow control methods are mostly limited to the station or line level, lacking network-wide coordination. This leads to chain reactions and network-wide congestion caused by localized flow control measures, affecting the overall operational efficiency and safety of the system.

Method used

By acquiring train operation plans and passenger travel information of the metro network, a passenger spatiotemporal coordinate system is constructed, a network passenger flow control model is established, and a non-optimal value acceptance optimization algorithm is adopted to generate a collaborative solution covering multiple stations, time periods, and control volumes, thereby achieving overall passenger flow control from a network-wide perspective.

Benefits of technology

It effectively avoids the spatial and temporal transfer of passenger flow pressure and secondary congestion caused by localized flow control, improves the operational balance, stability and transportation efficiency of the subway network, and provides scientific and predictive passenger flow control measures.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN121998455A_ABST
    Figure CN121998455A_ABST
Patent Text Reader

Abstract

The invention provides a subway line network collaborative passenger flow control method, device and equipment, and relates to the technical field of rail transit. According to the method, the train operation plan and the passenger travel information of the whole network are obtained, and the passenger space-time coordinates are accurately constructed, so that the dynamic distribution and evolution process of the passenger flow in the whole network is completely described in the space-time dimension; and constructing a line-network-level passenger flow management and control model on the basis, taking the passenger flow of each entry point as a collaborative decision variable, and solving by using an intelligent optimization algorithm combined with non-optimal value acceptance to generate a collaborative scheme covering a plurality of stations, time periods and management and control quantities. The method breaks through the limitation that traditional local management and control only aims at a single station or a single line, systematic overall planning and active regulation and control are carried out on passenger flow sources, paths and bottlenecks from the perspective of the whole network, passenger flow pressure space-time transfer and secondary congestion are avoided, the scientificity of passenger flow management and control measures is improved, and the management and control efficiency is improved. And the balance, the stability and the transportation efficiency of the overall operation of the metro line network are enhanced.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] This invention relates to the field of rail transit technology, and in particular to a method, device and equipment for coordinated passenger flow management of a subway network. Background Technology

[0002] As the backbone of public transportation in large cities, urban rail transit plays a crucial role in ensuring citizens' travel and the city's operation through safe and efficient operation. With the expansion of urban scale and the development of networked operations, large passenger flows during peak hours have become a common challenge, easily leading to platform congestion, train delays, and even safety hazards.

[0003] Currently, in response to high passenger flow pressure, most passenger flow control methods used in subway operations are still limited to a local perspective at the station or line level. Station-level control is usually activated when platform or passageway congestion exceeds a safe threshold, controlling the number of people entering the platform by closing some entrance gates or using flow control barriers. Line-level control attempts to coordinate the passenger flow entering multiple stations on a line to balance the load of stations within the line and prevent excessive pressure from being concentrated on a particular transfer station or station with high passenger flow. These methods are effective to some extent in dealing with localized, isolated congestion problems.

[0004] However, the subway network is a highly coupled, dynamically interconnected, and complex system, with passenger flow exhibiting continuity and correlation in both time and space. Control strategies limited to localized areas have significant drawbacks: when strong flow control measures are implemented at a bottleneck (such as a congested station or section), the intercepted or delayed passenger flow does not disappear but may trigger a chain reaction, causing congestion to shift spatially and temporally. For example, limiting flow at an upstream station to alleviate high load on a section of Line A may cause passengers to flock to the parallel Line B or choose earlier travel times, thus transferring pressure to other nodes in the network or at other times. The effectiveness of localized control is greatly reduced, and it may even unintentionally create new bottlenecks.

[0005] More seriously, in complex networks where multiple lines intersect, this congestion transfer effect can be amplified dramatically, rapidly propagating between different lines through transfer nodes. Seemingly reasonable decisions in certain areas, without network-wide coordination, can trigger unpredictable surges in passenger flow, exacerbating the imbalance in capacity matching between lines. Ultimately, this can lead to congestion spreading across the network, transforming localized problems into widespread network inefficiencies and even the risk of system paralysis, impacting the overall reliability and security of the system. Summary of the Invention

[0006] This invention provides a method, device, and equipment for coordinated passenger flow management across a metro network, which solves the problem of low operational efficiency caused by localized management strategies.

[0007] In a first aspect, the present invention provides a method for coordinated passenger flow management in a metro network. This method includes: acquiring train operation plans for the metro network, as well as passenger origin-destination and route selection information; determining the spatiotemporal coordinates of passengers in the metro network based on the train operation plans, origin-destination and route selection information, where the spatiotemporal coordinates include the spatial location of the passenger at any given time; constructing a network passenger flow management model based on the passenger's spatiotemporal coordinates in the metro network, with time as the vertical axis, metro lines as the horizontal axis, and lines connecting stations representing the passenger's travel trajectory; and, based on the network passenger flow management model, using the passenger flow at each entrance station as the decision variable, and aiming to reduce passenger flow pressure in bottleneck sections within the metro network, employing a non-optimal value acceptance optimization algorithm to obtain a coordinated passenger flow management scheme; the coordinated passenger flow management scheme includes multiple management stations, management time periods, and managed passenger flow.

[0008] Secondly, embodiments of the present invention provide a metro network collaborative passenger flow control device. This device includes a communication module and a processing module. The communication module is used to acquire the train operation plan of the metro network, as well as the origin-destination information and route selection information of passengers. The processing module is used to determine the spatiotemporal coordinates of passengers in the metro network based on the train operation plan, origin-destination information, and route selection information. The spatiotemporal coordinates include the spatial location of passengers at any given time. Based on the spatiotemporal coordinates of passengers in the metro network, a network passenger flow control model is constructed, with time as the vertical axis, the metro line as the horizontal axis, and the lines connecting each station representing the passenger's travel trajectory. Based on the network passenger flow control model, with the passenger flow at each entrance station as the decision variable and the goal of reducing passenger flow pressure in bottleneck sections within the metro network, an optimization algorithm based on non-optimal value acceptance is used to solve the problem, resulting in a network collaborative passenger flow control scheme. The network collaborative passenger flow control scheme includes multiple control stations, control periods, and control passenger flow.

[0009] Thirdly, embodiments of the present invention provide an electronic device including a memory and a processor. The memory stores a computer program, and the processor is configured to call and run the computer program stored in the memory to perform the steps of the method as described in the first aspect and any possible implementation thereof.

[0010] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the method as described in the first aspect and any possible implementation thereof.

[0011] This invention provides a method, device, and equipment for coordinated passenger flow management across a metro network. By acquiring train operation plans and passenger travel information from the entire network, this invention accurately constructs passenger spatiotemporal coordinates, thus comprehensively depicting the dynamic distribution and evolution of passenger flow across the entire network in a spatiotemporal dimension. Based on this, a network-level passenger flow management model is constructed, using passenger flow at each entry station as a coordinated decision variable. An intelligent optimization algorithm incorporating non-optimal value acceptance is used to solve the problem, generating a coordinated solution covering multiple stations, time periods, and control volumes. This invention overcomes the limitations of traditional localized management that only targets a single station or line, achieving systematic coordination and proactive control of passenger flow sources, paths, and bottlenecks from a network-wide perspective. It avoids the spatiotemporal transfer of passenger flow pressure and secondary congestion caused by improper localized flow control, effectively improving the scientific nature and predictability of passenger flow management measures, thereby significantly enhancing the overall balance, stability, and transportation efficiency of the metro network. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention, 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating a subway network coordinated passenger flow control method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a passenger flow control process provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of a network passenger flow control model provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of a subway network collaborative passenger flow control device provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0014] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0015] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner to facilitate understanding.

[0016] Furthermore, the terms "comprising" and "having," and any variations thereof, used in the description of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or modules is not limited to the steps or modules listed, but may optionally include other steps or modules not listed, or may optionally include other steps or modules inherent to such process, method, product, or device.

[0017] To make the objectives, technical solutions, and advantages of the present invention clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0018] As mentioned in the background section, passenger flow management and traffic flow control are conceptually similar, but the latter, due to its longer development in the road traffic field, has gradually evolved into a more mature technology. On highways, ramp signals control the flow of vehicles entering the highway, thereby alleviating congestion on the highway network. On urban roads, various signal control strategies can be used to optimize traffic distribution and alleviate congestion on urban road networks. With the development of modern technology, in addition to traditional operations research methods, deep learning is being increasingly widely applied to the field of traffic flow management. Given the closed and highly planned characteristics of subway systems, their passenger flow management mechanisms and methods differ significantly from those of general road traffic flow control. Therefore, this issue has gradually become one of the key research directions in the field of transportation.

[0019] At the station level, micro-simulation models of the boarding and alighting process can be established, providing theoretical support and decision-making basis for the formulation of station passenger organization plans. Furthermore, optimization models can be built around station flow control strategies, supporting improvements in station throughput efficiency. At the line level, the focus is on determining the number of passengers managed at each station on the line, thereby achieving coordinated organization of passenger flow within a single line. At the line level, the balance of flow control strategies is typically a major concern during the modeling process. In addition, some related studies have considered passenger waiting time factors. Besides traditional simulation and optimization modeling methods, some research has also begun to explore the application of machine learning in passenger flow management.

[0020] However, most of the above methods focus on passenger flow management at a single station, a few stations, or a single line, with few studies conducted systematically at the metro network level. This lack of comprehensive consideration of the overall network structure and passenger flow distribution characteristics often results in control strategies that are ill-suited to the complex and ever-changing actual operating environment, making it difficult to guarantee their effectiveness.

[0021] As the scale of subway systems continues to expand, passenger flow management has gradually extended from individual stations or lines to the entire rail transit network. Network-level passenger flow management solutions primarily aim to maximize the match between passenger demand and transport capacity, minimize delayed passenger flow, and minimize passenger waiting time. These solutions output coordinated passenger flow management across different time periods and stations to address the mismatch between passenger volume and its temporal and spatial distribution. However, existing network-level passenger flow management studies have largely failed to fully consider the dynamic distribution characteristics of passenger flow in the spatiotemporal dimensions, as well as the time lag effect between station congestion and interval congestion. Therefore, before formulating passenger flow management strategies, it is necessary to conduct in-depth analysis of the originating stations and times of passenger flow within intervals to improve the scientific rigor and relevance of the strategies.

[0022] Many large cities face the challenge of subway transport capacity failing to meet actual passenger demand. During morning and evening rush hours, large-scale passenger gatherings reduce subway service levels and passenger satisfaction, easily leading to train delays and, in severe cases, train malfunctions, disrupting normal operations. Furthermore, large crowds on platforms increase the risk of stampedes, posing a significant threat to passenger safety and seriously jeopardizing the subway's image of safety, reliability, and punctuality. To address these issues, current subway systems commonly employ methods such as increasing capacity and controlling passenger flow. However, upgrading and modifying fixed facilities within the subway system is difficult, and train intervals during peak hours are already near their minimum, leaving little room for adjustment. In addition, the existing subway system's operating... Figure 1 These are typically manually compiled periodic operation schedules, which are difficult to adjust and costly to increase transport capacity. Therefore, passenger flow management has become the mainstream means of resolving the contradiction between transport capacity and passenger demand.

[0023] Based on strategic considerations, subway passenger flow management is generally divided into station-level, line-level, and network-level passenger flow management. When platform passenger flow exceeds warning thresholds and may endanger safety, single-station-level passenger flow management should be implemented. Station-level passenger flow management plans need to determine the passenger flow control measures to be taken at individual stations, such as closing turnstiles and escalators, to control passenger flow within the station. If station-level management cannot alleviate passenger flow pressure, passenger flow management can be implemented at multiple stations on the same line. Therefore, line-level passenger flow management coordinates the number of personnel managed at multiple stations on the line to alleviate passenger flow pressure at transfer stations or stations with high passenger volume, balances passenger flow entering each station, and effectively allocates line transport capacity. When the occupancy rate of multiple sections of the network exceeds warning thresholds, network-level passenger flow management can be implemented. Network-level passenger flow management takes a network-wide perspective, coordinating the number of personnel managed at each station to alleviate passenger flow pressure at the line, section, and station levels. Although several cities have conducted preliminary explorations of subway passenger flow management, current measures are mostly based on human experience and are fixed, lacking quantitative analysis. Furthermore, most measures only target individual stations, lacking coordination. Developing a reasonable passenger flow management plan is a crucial aspect of subway operation in the face of large passenger flows.

[0024] like Figure 1 As shown, the present invention provides a method for coordinated passenger flow management in a subway network. The method includes steps S101-S104.

[0025] S101. Obtain train operation plans for the metro network, as well as passenger origin, destination, and route selection information.

[0026] S102. Based on train operation plans, origin and destination information, and route selection information, determine the spatiotemporal coordinates of passengers in the subway network.

[0027] In this embodiment of the application, the spatiotemporal coordinates include the spatial location of the passenger at any given time.

[0028] As one possible implementation, step S102 can be specifically implemented as steps S1021-S1024.

[0029] S1021. Based on the passenger's origin and destination information and route selection information, determine the travel route and transfer nodes for each passenger.

[0030] S1022. Based on the train operation plan, calculate the passenger's travel time in each section, as well as the boarding and alighting times at the station.

[0031] In some embodiments, the train operation plan includes the arrival and departure times of each train, the travel time between sections, and the stop time at each station.

[0032] S1023. Based on each passenger's travel route and transfer nodes, as well as the passenger's travel time within each section and the time of boarding and alighting at the station, calculate the location of each passenger at each time step by time slice. In some embodiments, location includes a station, section, or transfer passage; S1024. Based on the location of each passenger at each time, the spatiotemporal trajectory is summarized to obtain the spatiotemporal coordinates of the passenger in the subway network.

[0033] In some embodiments, the present invention can determine a passenger's location at different times based on passenger origin-destination (OD) information, passenger route information, and train timetables. During train operation, passengers can board the train when it arrives at a station. The arrival and departure times of the train can determine the time when passengers can board. After arriving at their destination, passengers can disembark. Since the train's travel time is fixed, the passenger's location at different times can be determined based on the train's travel time within a section. If the passenger is transferring, the transfer time should also be included. The passenger's location can be determined based on the passenger's arrival time, the train's arrival and departure times, and the train's travel time within each section, thereby determining the passenger's spatiotemporal coordinates. ,in Indicates location, It indicates time. By accumulating the passenger flow of a certain interval at a certain moment, the complete passenger flow situation of that interval can be obtained.

[0034] S103. Based on the spatiotemporal coordinates of passengers in the metro network, with time as the vertical axis, metro lines as the horizontal axis, and the lines connecting each station representing the passenger's travel trajectory, a network passenger flow control model is constructed.

[0035] As one possible implementation, step S103 can be specifically implemented as steps S1031-S1034.

[0036] S1031. Establish a two-dimensional spatiotemporal network by discretizing the operation of the subway network into multiple continuous time layers with time as the vertical axis and the space where the subway line is located as the horizontal axis.

[0037] S1032. In each time layer of the two-dimensional spatiotemporal network, the stations in the metro network are divided to obtain entry stations and section nodes. Entry stations correspond to the passenger flow entering the station, and section nodes correspond to the passenger flow running in the section.

[0038] S1033. Based on the spatiotemporal coordinates of passengers in the subway network, solid lines are used to connect the nodes in each time layer in a two-dimensional spatiotemporal network to draw the travel trajectory of each passenger.

[0039] S1034. In the two-dimensional spatiotemporal network after drawing the travel trajectory, the direction of passenger flow control adjustment is represented by dashed lines, and a network passenger flow control model representing the passenger travel trajectory, dynamic evolution of passenger flow, and control intervention process is drawn.

[0040] In some embodiments, the present invention can construct a network spatiotemporal model for passenger flow control based on the spatiotemporal evolution of passengers in the subway system, and divide it into station entry nodes and section nodes, while establishing the linkage relationship between the two, such as... Figure 2 As shown. Figure 3 As shown, with time as the vertical axis, the operation process of the rail network is discretized into multiple time layers. Each time layer depicts the spatial distribution of passenger flow within the corresponding time period and is further subdivided into station entry node areas and interval node areas. The lines connecting the areas represent the actual travel trajectory of passengers in time sequence, that is, after a passenger enters a station, he enters the corresponding interval at a later time as the train runs. The dashed lines are used to represent the adjustment direction in the passenger flow control process.

[0041] For example, in the passenger flow management process, the present invention can input inbound passenger flow data, OD data, path data, and expected interval passenger flow data, process them region by region through inbound node areas and interval node areas, and obtain relevant passenger flow data. If the expected output value is not obtained, an adjustment process is performed by calculating the gradient of the objective function with respect to inbound passenger flow and interval passenger flow, adding perturbation to update variable values, thereby continuously optimizing model performance.

[0042] S104. Based on the network passenger flow control model, with the passenger flow at each station as the decision variable and the goal of reducing passenger flow pressure in bottleneck sections within the metro network, an optimization algorithm based on non-optimal value acceptance is used to solve the problem and obtain a network-coordinated passenger flow control scheme.

[0043] In this embodiment of the application, the network-coordinated passenger flow control scheme includes multiple control stations, control periods, and control passenger flow.

[0044] As one possible implementation, step S104 can be specifically implemented as steps one through five.

[0045] Step 1: Initialize the optimization algorithm parameters for non-optimal value acceptance. The optimization algorithm parameters include initial temperature, temperature decay coefficient, maximum number of iterations, and minimum target change threshold. Then, randomly generate an initial passenger flow control plan that meets the basic constraints.

[0046] Step 2: In each iteration, a random perturbation is applied to the current passenger flow control scheme in the network passenger flow control model to generate a new candidate control scheme; the candidate control scheme includes the passenger flow of each station in the metro network at each time period.

[0047] Step 3: Substitute the candidate control schemes into the network passenger flow control model to deduce the new interval passenger flow distribution and calculate the objective function value.

[0048] In some embodiments, the objective function value is used to measure the degree of relief of passenger flow pressure in the bottleneck section.

[0049] For example, step three can be specifically implemented as steps A1-A5.

[0050] A1. Based on the candidate control plan and the network passenger flow control model, adjust the passenger flow of each station at each time period to obtain the adjusted passenger flow data. A2. The adjusted passenger flow data is combined with the passengers' origin and destination information and route selection information to re-deductively apply the data to the online passenger flow control model, resulting in a new distribution of passenger flow across the entire network. A3. Check whether the new passenger flow distribution in each section meets the capacity safety constraints of each section; the capacity safety constraint is that the passenger flow in any section is less than or equal to the set capacity threshold. A4. If any threshold does not meet the capacity safety constraint, delete the candidate control scheme, change the random perturbation, and regenerate a new candidate control scheme. A5. If each section meets the capacity safety constraint, calculate the passenger flow pressure index of the bottleneck section under the new passenger flow distribution and use it as the objective function value of the candidate control scheme.

[0051] Step 4: Based on the optimization algorithm for non-optimal value acceptance, and the objective function value of the current temperature and the candidate control scheme, calculate the non-optimal value acceptance probability, and use the non-optimal value acceptance probability to determine whether to accept the candidate control scheme as the current passenger flow control scheme. Step 5: Reduce the current temperature according to the temperature decay coefficient, and repeat steps 2 to 5 until the preset iteration termination condition is met, and output the network-coordinated passenger flow management plan.

[0052] In some embodiments, this invention can utilize a pre-constructed spatiotemporal network for passenger flow management in a metro network, using inbound passenger flow, OD data, path data, and interval passenger flow data as inputs to output a passenger flow management strategy. To efficiently optimize the passenger flow management scheme, this method proposes an algorithm that considers the acceptance of non-optimal values ​​within the spatiotemporal network of passenger flow management. The algorithm uses the current inbound passenger flow control scheme as the initial solution and calculates the corresponding interval passenger flow distribution state through the mapping relationship in the spatiotemporal network. Subsequently, during the neighborhood search process, the station inbound control quantity within a certain time period is randomly selected for disturbance adjustment, and based on passenger OD and path information, the changes in inbound passenger flow are transmitted to the interval passenger flow in subsequent time periods, thereby updating the passenger flow distribution in the entire spatiotemporal network. For each new scheme generated by the disturbance, the algorithm evaluates its merits based on the objective function: if the interval passenger flow operation state is improved and does not violate interval capacity and operational safety constraints, the scheme is accepted; if the objective function value deteriorates, the inferior solution is accepted with a certain probability according to the non-optimal value acceptance criterion, thereby avoiding the algorithm from falling into local optima. As the iteration process progresses, the annealing temperature is gradually reduced to decrease the probability of accepting inferior solutions, allowing the search process to gradually transition from global exploration to local fine-grained optimization. After the algorithm's termination condition is met, the corresponding passenger flow control scheme and its implementation results in each time period are output. This scheme can achieve coordinated allocation of passenger flow in time and space within the network while satisfying interval capacity constraints, providing an operable decision-making basis for time-segmented and station-specific entry control in actual operation.

[0053] For example, the variables of the number of people entering the station and the number of passengers in the interval after initialization control. Maximum number of iterations Minimum difference value Minimum temperature ,temperature Temperature change rate Step length The subway network passenger flow control system is initialized based on passenger flow entering stations, OD distribution, route selection, and interval passenger flow. The objective function for passenger flow control at the current temperature is calculated. If the number of iterations and temperature do not meet the requirements, a perturbation is added to the variables based on the gradient of the objective function with respect to the variables. If this perturbation is the current optimal value, the variables are updated; otherwise, the variables are updated based on the acceptance of non-optimal values. If the number of iterations and temperature meet the requirements, it is determined whether the stopping condition has been met. If so, the passenger flow control scheme is output; otherwise, the optimization of passenger flow control is repeated. The specific steps are as follows: Step 1: Initialize minimum temperature ,temperature Maximum number of iterations Minimum iterative change value Temperature change rate objective function value Randomly generate a passenger flow control plan, specifically a passenger flow control plan for time 1 and temperature 1. Then, check the feasibility of the control plan based on the relationship between the controlled entry rate and the controlled entry volume and the controlled entry volume. If feasible, proceed to Step 2; otherwise, repeat Step 1. Step 2: Iteratively optimize the passenger flow control plan by combining the spatiotemporal network of passenger flow control.

[0054] While do; While do; Step 2.1: Calculate the gradient between the number of passengers entering the station and the passenger flow in the interval using the adjustment process network, and regenerate a new passenger flow control plan.

[0055] Step 2.2: Check the feasibility of the passenger flow control plan by comparing the controlled entry rate with the controlled entry volume and the controlled entry volume. If it is feasible, proceed to Step 3.3; otherwise, proceed to Step 3.1.

[0056] Step 2.3: Based on the passenger flow control situation and in conjunction with the passenger flow control network, regenerate the passenger flow for each section and calculate the target value for the current plan. Step 2.4: Determine the optimization results If the current objective function value is less than the optimal value, that is... then Passenger flow control plan updated Continue End if Calculate the acceptance of non-optimal values Generate random numbers .

[0057] If then The passenger flow control plan has been updated.

[0058] End if End while Update temperature

[0059] End while Step 3: Check the changes in the iteration values ​​to determine whether the algorithm has ended.

[0060] If then Algorithm complete, proceed to Step 5. Else Proceed to Step 2 End if Step 4: The algorithm ends and outputs the passenger flow control plan.

[0061] This invention provides a method for coordinated passenger flow management across a metro network. By acquiring train operation plans and passenger travel information for the entire network, it accurately constructs passenger spatiotemporal coordinates, thereby comprehensively depicting the dynamic distribution and evolution of passenger flow across the entire network in a spatiotemporal dimension. Based on this, a network-level passenger flow management model is constructed, using passenger flow at each entry station as a coordinated decision variable. An intelligent optimization algorithm incorporating non-optimal value acceptance is used to solve the problem, generating a coordinated solution covering multiple stations, time periods, and control volumes. This invention overcomes the limitations of traditional localized management that only targets a single station or line, achieving systematic coordination and proactive control of passenger flow sources, paths, and bottlenecks from a network-wide perspective. It avoids the spatiotemporal transfer of passenger flow pressure and secondary congestion caused by improper localized flow restrictions, effectively improving the scientific nature and predictability of passenger flow management measures, thereby significantly enhancing the overall balance, stability, and transportation efficiency of the metro network.

[0062] Furthermore, to reduce large-scale passenger gatherings, meet congestion control requirements, and alleviate the contradiction between transport capacity and passenger demand, this method takes subway network passenger flow management as its starting point, and formulates a reasonable and effective passenger flow management strategy that includes three elements: passenger flow management stations, passenger flow management time, and passenger flow management personnel. When formulating subway passenger flow management plans on the demand side, the focus is on the overall network synergy, taking into account multiple perspectives at the station and section levels. The aim is to provide subway operation managers with an executable and quantifiable basis for formulating passenger flow management plans, thereby improving the overall network operation efficiency and service level.

[0063] Optionally, the metro network coordinated passenger flow control method provided in this embodiment of the invention further includes steps S201-S204 before step S103.

[0064] S201. Based on the spatiotemporal coordinates of passengers in the metro network, calculate the actual passenger flow of each operating section in the metro network in different time slots.

[0065] S202. Based on the actual passenger flow of each operating section in the metro network in different time slots and the design capacity threshold of each operating section, calculate the section congestion of each operating section in each time slot.

[0066] For example, in embodiments of the present invention, the actual passenger flow obtained by statistics can be divided by the design or safety capacity threshold of the interval to obtain a standardized ratio (such as a percentage), which is a quantified congestion index.

[0067] S203. Based on the congestion level of each operating section in each time slot and the preset congestion warning threshold, the operating sections and time slots in the peak passenger flow state are identified.

[0068] In some embodiments, the preset congestion warning threshold is a configurable system parameter, typically set based on operational safety procedures and historical experience (e.g., set to 85% of the capacity threshold).

[0069] For example, embodiments of the present invention can identify interval-time combinations in which congestion exceeds a warning threshold in multiple consecutive time slices to determine persistent congestion.

[0070] For example, embodiments of the present invention can identify intervals where congestion rises sharply in a short period of time and exceeds a higher threshold (such as an emergency threshold) in order to cope with sudden large passenger flows.

[0071] S204. Based on the operating sections and time slots during peak passenger flow, determine the bottleneck sections and bottleneck time periods that need to be controlled.

[0072] In some embodiments, the present invention can calculate passenger flow and congestion at different times in each interval based on the spatiotemporal coordinates of passengers. First, the passenger set... The passengers are sorted according to their arrival time. Then, the boarding and alighting process is analyzed, and the spatiotemporal coordinates of each passenger are marked based on this process, i.e., time and location. Finally, based on the passengers' spatiotemporal coordinates, the number of passengers at the source points and the number of people in each section at each time are calculated. According to the threshold requirements of the bottleneck section, the passenger flow in the bottleneck section and the station are updated.

[0073] Thus, this invention, through quantitative statistics and dynamic identification, transforms traditional experience-based bottleneck judgment into precise detection based on real-time data and preset thresholds. This invention can not only locate the current congested area but also predict the spatiotemporal distribution of peak passenger flow, thereby elevating control decisions from passive response to proactive early warning. This ensures the precise allocation and timing optimization of control resources, providing a clear and objective target orientation for subsequent coordinated regulation.

[0074] Accordingly, based on steps S201-S204, step S103 can also be specifically implemented as steps B1-B6.

[0075] B1. For each bottleneck interval and bottleneck time period, identify the spatiotemporal coordinates of each target passenger located in the bottleneck interval during the bottleneck time period.

[0076] For example, the identification process relies on a refined dataset that has been built and contains all passenger IDs and their complete spatiotemporal trajectories (time slices, locations). By querying and matching in this dataset, all passenger records whose spatial location attributes fall within the bottleneck interval during a specified bottleneck period can be efficiently filtered out.

[0077] B2. Based on the spatiotemporal coordinates of each target passenger, trace each passenger individually to determine the entry station and entry time of each target passenger.

[0078] For example, embodiments of the present invention can utilize the inherent temporal relationship of passenger spatiotemporal trajectory data. Starting from the passenger's record point within the bottleneck section, the trajectory is traced in reverse (time order) until the first entry or entry into the toll area type location event in the passenger's travel record is found. The location and time of this event are the entry point and entry time.

[0079] B3. Statistically analyze the entry stations and entry times of all target passengers corresponding to each bottleneck section and bottleneck time period to determine the set of passenger flow source points, which includes multiple entry stations that contribute to the congestion of the subway line.

[0080] B4. Based on the entry stations and entry times of all target passengers corresponding to each bottleneck interval and bottleneck time period, as well as the set of passenger flow origin points, determine the contribution of each entry station in the set of passenger flow origin points.

[0081] The contribution of a certain entry station is used to characterize the number of passengers that originate from that entry station and merge into the bottleneck section during the bottleneck period.

[0082] For example, in embodiments of the present invention, after tracing all target passengers, grouping and statistically analyzing them according to the entry station and the time period to which the entry time belongs. The number of target passengers included in each group represents the contribution of that entry station to the target bottleneck interval during the corresponding time period. This process transforms qualitative source analysis into a quantitative contribution matrix.

[0083] B5. Based on the bottleneck interval, bottleneck time period, set of passenger flow origin points, and contribution of each entry station, determine the coordinated control target.

[0084] For example, embodiments of the present invention can reduce the predicted passenger flow (composed of the contributions from each source point) of the target bottleneck section during the bottleneck period to the desired level by coordinating the adjustment of the passenger flow (i.e., the source of the contribution) of each entry point in the set of passenger flow source points during the relevant entry period. This objective can be directly reflected in the objective function of the optimization model (such as minimizing the difference between the bottleneck passenger flow and the expected value) or key constraints.

[0085] B6. Add the coordinated control target to the network passenger flow management model.

[0086] For example, embodiments of the present invention can integrate variables and equations reflecting the relationship between the source point, contribution, and bottleneck interval, so that when the model optimizes the scheme, it can understand how and to what extent the control of a certain entry point will affect the specific bottleneck interval downstream, thereby laying a mathematical model foundation for achieving precise and coordinated source control.

[0087] Thus, based on identifying bottlenecks, this invention further traces the source of passenger flow and quantifies the contribution of each entry point, establishing a complete causal chain of bottleneck-source-contribution. This enables differentiated and refined control strategies from the source, avoiding one-size-fits-all flow restrictions and truly achieving the synergistic goal of alleviating congestion and alleviating congestion, significantly improving the systematicness and effectiveness of control measures.

[0088] Optionally, the metro network coordinated passenger flow control method provided in this embodiment of the invention further includes steps S301-S304 after step S104.

[0089] During the implementation of the S301 online-network collaborative passenger flow control scheme, real-time data on actual passenger flow from the metro automatic fare collection system and train operation data from the train operation control system will be collected.

[0090] In some embodiments, train operation data includes actual train arrival and departure times and section operation status data.

[0091] For example, embodiments of the present invention can collect real-time records of the number of people passing through the entrance gates of each station, and store them in a structured manner according to the station number and the timestamp of passage, forming a real-time passenger flow time series.

[0092] S302. Based on actual passenger flow data and driving data, update the network passenger flow control model to obtain the updated passenger spatiotemporal coordinates and interval passenger flow status.

[0093] For example, in embodiments of the present invention, the actual passenger flow data collected can replace the predicted passenger flow input for the corresponding station and time period in the original model; and the actual arrival and departure times provided by the train operation control system can be used to dynamically correct the train spatiotemporal trajectory and interval running time parameters in the model.

[0094] S303. Based on the updated passenger spatiotemporal coordinates and interval passenger flow status, compare them with the expected interval passenger flow distribution status corresponding to the network-coordinated passenger flow control scheme to determine the passenger flow status deviation value of the key bottleneck interval during the key period.

[0095] For example, in an embodiment of the present invention, the real-time predicted passenger flow of the interval generated by the model during this period can be subtracted from the expected passenger flow target value in the original control plan, and the absolute value can be taken to obtain the absolute deviation of passenger flow; further, the absolute deviation can be divided by the expected passenger flow target value to obtain the standardized relative deviation percentage.

[0096] S304. If the passenger flow status deviation exceeds the preset deviation, the non-optimal value acceptance optimization algorithm is activated. Taking the current actual passenger flow distribution status as the initial condition and the updated model parameters as the basis, a new round of optimization calculation is performed to generate a corrected network-coordinated passenger flow control scheme.

[0097] In some embodiments, the preset deviation can be the absolute deviation of passenger flow in the key bottleneck section exceeding an absolute threshold (e.g., 100 people), or the standardized relative deviation percentage exceeding a relative threshold (e.g., 15%).

[0098] For example, embodiments of the present invention can use the optimal or near-optimal solution obtained from the previous round of optimization calculation as the initial solution for the current optimization iteration; significantly reduce the maximum number of iterations or convergence accuracy requirements of the optimization algorithm, with the primary goal of obtaining a feasible correction scheme within a limited time; and during the optimization process, prioritize adjusting the control variables of stations and time periods that deviate significantly from the original scheme.

[0099] Thus, based on the static optimization scheme, this invention introduces a dynamic feedback and adjustment mechanism based on real-time data, constructing a closed-loop control system of perception-evaluation-decision-execution. This invention enables passenger flow management strategies to adapt to fluctuations and uncertainties in actual operating conditions, effectively overcoming the problem of scheme failure caused by passenger flow prediction deviations or sudden events, and significantly improving the robustness, real-time performance, and overall execution reliability of the management system.

[0100] This invention primarily addresses the mismatch between subway supply and demand by designing a subway network-coordinated passenger flow management method, providing a feasible solution for subway passenger flow control. For the first time, it starts with the evolutionary analysis of passenger flow within the subway network to determine the spatiotemporal coordinates of passengers. A spatiotemporal network structure for passenger flow management is established, and a passenger flow management optimization algorithm based on non-optimal value acceptance is designed. This solves the problem of pre-set passenger flow management schemes and lack of flexible adjustment space in reality, achieving precise control across the entire network. The innovations of this invention include: analyzing the spatiotemporal coordinates of passenger flow based on actual operational conditions to determine bottleneck intervals and passenger flow origin points; establishing a spatiotemporal network for passenger flow management, which represents passenger spatial location on a plane, time on a vertical axis, passenger trajectories on solid lines, and adjustment directions on dashed lines; and designing an optimization algorithm with non-optimal value acceptance as its core based on the input spatiotemporal coordinates of passenger flow and the passenger flow management spatiotemporal network.

[0101] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0102] Figure 4 A schematic diagram of a subway network collaborative passenger flow control device according to an embodiment of the present invention is shown. The passenger flow control device 400 includes a communication module 401 and a processing module 402.

[0103] The communication module 401 is used to obtain the train operation plan of the subway network, as well as the origin and destination information and route selection information of passengers.

[0104] Processing module 402 is used to determine the spatiotemporal coordinates of passengers in the metro network based on train operation plans, origin and destination information, and route selection information. The spatiotemporal coordinates include the spatial location of passengers at any given time. Based on the spatiotemporal coordinates of passengers in the metro network, a network passenger flow control model is constructed with time as the vertical axis, metro lines as the horizontal axis, and lines connecting each station representing the passenger's travel trajectory. Based on the network passenger flow control model, the entry passenger flow at each station is used as the decision variable, and the goal is to reduce passenger flow pressure in bottleneck sections within the metro network. An optimization algorithm based on non-optimal value acceptance is used to solve the problem, resulting in a network-coordinated passenger flow control scheme. The network-coordinated passenger flow control scheme includes multiple control stations, control periods, and control passenger flow.

[0105] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. The electronic device 500 includes: a processor 501, a memory 502, and a computer program 503 stored in the memory 502 and executable on the processor 501. When the processor 501 executes the computer program 503, it implements the steps in the above-described method embodiments. Alternatively, when the processor 501 executes the computer program 503, it implements the functions of each module / unit in the above-described device embodiments.

[0106] For example, the computer program 503 may be divided into one or more modules / units, which are stored in the memory 502 and executed by the processor 501 to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program 503 in the electronic device 500.

[0107] The processor 501 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0108] The memory 502 can be an internal storage unit of the electronic device 500, such as a hard disk or memory of the electronic device 500. The memory 502 can also be an external storage device of the electronic device 500, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device 500. Furthermore, the memory 502 can include both internal and external storage units of the electronic device 500. The memory 502 is used to store the computer program and other programs and data required by the terminal. The memory 502 can also be used to temporarily store data that has been output or will be output.

[0109] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for coordinated passenger flow management across a subway network, characterized in that, include: Obtain train operation plans for the subway network, as well as passenger origin, destination, and route selection information; Based on the train operation plan, origin and destination information and route selection information, the spatiotemporal coordinates of passengers in the subway network are determined, and the spatiotemporal coordinates include the spatial location of passengers at any time. Based on the spatiotemporal coordinates of the passengers in the metro network, a network passenger flow control model is constructed with time as the vertical axis, metro lines as the horizontal axis, and the lines connecting each station representing the passenger's travel trajectory. Based on the aforementioned network passenger flow control model, with the passenger flow at each entrance station as the decision variable and the goal of reducing passenger flow pressure in bottleneck sections within the metro network, an optimization algorithm based on non-optimal value acceptance is used to solve the problem, resulting in a network-coordinated passenger flow control scheme. The network-coordinated passenger flow control scheme includes multiple control stations, control periods, and control passenger flow.

2. The subway network coordinated passenger flow control method according to claim 1, characterized in that, The process of determining the spatiotemporal coordinates of passengers within the subway network based on the train operation plan, origin and destination information, and route selection information includes: Based on passengers' origin and destination information and route selection information, determine each passenger's travel route and transfer nodes; Based on the train operation plan, the passenger's travel time within each section and the boarding and alighting times at stations are calculated; the train operation plan includes the arrival and departure times of each train, the travel time within each section, and the stop time at each station. Based on each passenger's travel route and transfer nodes, as well as the passenger's travel time within each section and the time of boarding and alighting at the station, the location of each passenger at each time point is estimated on a time-by-time basis. The location includes the station, section, or transfer passage. Based on the location of each passenger at each time, the spatiotemporal trajectory is summarized to obtain the spatiotemporal coordinates of the passenger in the subway network.

3. The metro network coordinated passenger flow control method according to claim 1, characterized in that, The model for managing passenger flow within the metro network is constructed based on the passenger's spatiotemporal coordinates within the metro network. The model uses time as the vertical axis, metro lines as the horizontal axis, and lines connecting stations to represent passenger travel trajectories. This includes: By establishing a two-dimensional spatiotemporal network with time as the vertical axis and the space where the subway lines are located as the horizontal axis, the operation process of the subway network is discretized into multiple continuous time layers. In each time layer of the two-dimensional spatiotemporal network, each station in the metro network is divided to obtain entry stations and section nodes. The entry stations correspond to the passenger flow entering the station, and the section nodes correspond to the passenger flow running in the section. Based on the spatiotemporal coordinates of the passengers in the subway network, the travel trajectories of each passenger are drawn by connecting the nodes in each time layer with solid lines in a two-dimensional spatiotemporal network. In the two-dimensional spatiotemporal network after drawing travel trajectories, dashed lines are used to represent the adjustment direction of passenger flow control, and a network passenger flow control model representing passenger travel trajectories, dynamic evolution of passenger flow, and control intervention process is drawn.

4. The subway network coordinated passenger flow control method according to claim 1, characterized in that, Before constructing the network passenger flow control model based on the passenger's spatiotemporal coordinates in the subway network, with time as the vertical axis, subway lines as the horizontal axis, and lines connecting stations representing passenger travel trajectories, the following steps are also included: Based on the spatiotemporal coordinates of the passengers in the metro network, the actual passenger flow of each operating section in the metro network in different time slots is statistically analyzed. Based on the actual passenger flow of each operating section in the metro network during different time slots, and the design capacity threshold of each operating section, the congestion of each operating section in each time slot is calculated. Based on the congestion level of each operating section in each time slot and the preset congestion warning threshold, the operating sections and time slots in the peak passenger flow state are identified. Based on the operating sections and time slots during peak passenger flow, identify the bottleneck sections and bottleneck periods that require control.

5. The subway network coordinated passenger flow control method according to claim 4, characterized in that, The method of constructing a network passenger flow control model based on the passenger's spatiotemporal coordinates in the subway network, with time as the vertical axis, subway lines as the horizontal axis, and lines connecting stations to represent passenger travel trajectories, further includes: For each bottleneck interval and bottleneck time period, the spatiotemporal coordinates of each target passenger located in the bottleneck interval during the bottleneck time period are identified. Based on the spatiotemporal coordinates of each target passenger, passenger-by-passenger tracing is performed to determine the entry station and entry time of each target passenger; The entry stations and entry times of all target passengers corresponding to each bottleneck section and bottleneck time period are statistically analyzed to determine the set of passenger flow source points, which includes multiple entry stations that contribute to the congestion of the subway line. Based on the entry stations and entry times of all target passengers corresponding to each bottleneck interval and bottleneck period, and the set of passenger flow source points, the contribution of each entry station in the set of passenger flow source points is determined. The contribution of a certain entry station is used to characterize the number of passengers who take that entry station as their starting point and merge into the bottleneck interval during the bottleneck period. Based on the bottleneck interval, bottleneck period, set of passenger flow source points, and contribution of each entry point, the coordinated control target is determined. Add the coordinated control target to the network passenger flow management model.

6. The metro network coordinated passenger flow control method according to claim 1, characterized in that, The network passenger flow management model, using the passenger flow at each entrance station as the decision variable and aiming to reduce passenger flow pressure in bottleneck sections within the metro network, employs a non-optimal value acceptance optimization algorithm to obtain a network-coordinated passenger flow management scheme, including: Step 1: Initialize the optimization algorithm parameters for non-optimal value acceptance. The optimization algorithm parameters include initial temperature, temperature decay coefficient, maximum number of iterations, and minimum target change threshold. Then, randomly generate an initial passenger flow control scheme that meets the basic constraints. Step 2: In each iteration, a random perturbation is applied to the current passenger flow control scheme in the network passenger flow control model to generate a new candidate control scheme; the candidate control scheme includes the passenger flow of each station in the metro network at each time period; Step 3: Substitute the candidate control scheme into the network passenger flow control model to deduce the new interval passenger flow distribution and calculate the objective function value. The objective function value is used to measure the degree of relief of passenger flow pressure in the bottleneck interval. Step 4: Based on the optimization algorithm for non-optimal value acceptance, and based on the current temperature and the objective function value of the candidate control scheme, calculate the non-optimal value acceptance probability, and use the non-optimal value acceptance probability to determine whether to accept the candidate control scheme as the current passenger flow control scheme. Step 5: Reduce the current temperature according to the temperature decay coefficient, and repeat steps 2 to 5 until the preset iteration termination condition is met, and output the network-coordinated passenger flow management scheme.

7. The metro network coordinated passenger flow control method according to claim 6, characterized in that, The step of substituting the candidate control scheme into the network passenger flow control model to deduce the new interval passenger flow distribution and calculate the objective function value includes: Based on the candidate control scheme and the network passenger flow control model, the passenger flow of each station in each time period is adjusted to obtain the adjusted passenger flow data. The adjusted passenger flow data, combined with passengers' origin and destination information and route selection information, is re-analyzed in the network passenger flow control model to obtain a new distribution of passenger flow across the entire network. Check whether the new passenger flow distribution in each interval meets the capacity safety constraints of each interval; the capacity safety constraint is that the passenger flow in any interval is less than or equal to a set capacity threshold. If any threshold fails to meet the capacity safety constraint, the candidate control scheme is deleted, the random perturbation is changed, and a new candidate control scheme is generated. If each interval meets the capacity safety constraint, then the passenger flow pressure index of the bottleneck interval under the new interval passenger flow distribution is calculated as the objective function value of the candidate control scheme.

8. The subway network coordinated passenger flow control method according to claim 1, characterized in that, The process based on the network passenger flow control model, using the passenger flow at each entrance station as the decision variable and aiming to reduce passenger flow pressure in bottleneck sections within the metro network, employs a non-optimal value acceptance optimization algorithm to obtain the network-coordinated passenger flow control scheme. This process further includes: During the implementation of the online-network collaborative passenger flow control scheme, real-time data on actual passenger flow from the subway automatic fare collection system and train operation data from the train operation control system are collected; the train operation data includes actual train arrival and departure times and section operation status data. Based on the actual passenger flow data and driving data, the network passenger flow control model is updated to obtain the updated passenger spatiotemporal coordinates and interval passenger flow status. Based on the updated passenger spatiotemporal coordinates and interval passenger flow status, a comparison is made with the expected interval passenger flow distribution status corresponding to the network-coordinated passenger flow control scheme to determine the passenger flow status deviation value of the key bottleneck interval during the key period. If the passenger flow status deviation exceeds the preset deviation, the optimization algorithm for the non-optimal value acceptance is activated. Using the current actual passenger flow distribution status as the initial condition and the updated model parameters as the basis, a new round of optimization calculation is quickly executed to generate a corrected network-coordinated passenger flow control scheme.

9. A subway network collaborative passenger flow control device, characterized in that, include: The communication module is used to obtain the train operation plan of the subway network, as well as the origin and destination information and route selection information of passengers; The processing module is used to determine the spatiotemporal coordinates of passengers in the metro network based on the train operation plan, origin and destination information, and route selection information. The spatiotemporal coordinates include the spatial location of passengers at any given time. Based on the spatiotemporal coordinates of passengers in the metro network, a network passenger flow control model is constructed with time as the vertical axis, metro lines as the horizontal axis, and lines connecting stations representing passenger travel trajectories. Based on the network passenger flow control model, the module uses the passenger flow at each entrance station as the decision variable, aims to reduce passenger flow pressure in bottleneck sections within the metro network, and employs a non-optimal value acceptance optimization algorithm to obtain a network-coordinated passenger flow control scheme. The network-coordinated passenger flow control scheme includes multiple control stations, control periods, and control passenger flow.

10. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor being configured to invoke and run the computer program stored in the memory to perform the method as described in any one of claims 1 to 8.