A subway network modeling method and a subway network model

Abstract

This invention relates to the field of subway operation network technology, and in particular to a subway network modeling method and a subway network model. The subway network modeling method of this invention utilizes complex network theory to extract the core features of the basic components of the subway operation system, establishing a fully directed network model of the subway operation system. Directed nodes and directed arcs represent stations and track segments, respectively. Each node and arc is assigned a symbol, with positive and negative numbers representing upward and downward traffic, respectively, thus describing the spatial directionality of stations and passenger flow. Furthermore, it can accurately describe the subway service performance in both interference-free and interference-affected scenarios. For example, in an interference scenario where one-way stations are closed, the impact of interference occurring at directed stations on system service performance can be analyzed.

Description

Technical Field

[0001] This invention relates to the field of subway operation network technology, and in particular to a subway network modeling method and a subway network model. Background Technology

[0002] Due to the network characteristics of subway systems, using network science and graph theory to describe subway operation systems is a common method for studying subway service performance, such as identifying vulnerable stations, optimizing train timetables, redundancy of network routes, and network connectivity. Most subway networks established in traditional studies are undirected and focus solely on the geographical attributes of the subway system. These networks use nodes and arcs to represent undirected stations and segments, respectively, to study subway service capacity. While this helps apply topology theory to subway networks, it neglects the directional characteristics of the network. With continuous advancements in science and technology, traditional subway network description methods are increasingly unable to reveal the dynamic directional characteristics of subway supply and passenger demand. Some researchers have recognized the significance of directed arcs and developed partially directed models to describe subway networks. Both models utilize undirected nodes to represent stations.

[0003] However, a typical subway station has two or more directional stations, the number of which depends on the number of train directions running through the station. Passenger demand at different stations within a station varies at the same time, and the spatiotemporal passenger flow at opposite stations within a station often changes accordingly. Existing undirected and partially directed subway network models cannot adequately explain the precise direction and location of passengers. Furthermore, when subway lines experience faults, especially when only one unidirectional station experiences a fault, existing undirected and partially directed subway network models cannot accurately describe the fault situation. Summary of the Invention

[0004] Therefore, the technical problem to be solved by the present invention is to overcome the fact that the traditional subway network model in the prior art still cannot describe the spatial directionality of platform trains and passenger flow, nor can it be used to describe the impact of interference occurring at directed stations on the system service performance.

[0005] To address the aforementioned technical problems, this invention provides a subway network modeling method, comprising:

[0006] Using directed node N ±ij Represents a directed site, where N +ij N represents the j-th station in the up direction of line i. -ij This represents the j-th station in the downward direction of line i;

[0007] Using directed arc A ±ij Indicates a directed road segment, where A +ij A represents the j-th segment in the up direction of line i.-ij This represents the j-th road segment in the down direction of line i;

[0008] Construct a subway network G = {N} based on the directed stations and the directed road segments. ±ij A ±ij}

[0009] Preferably, the directed node N ±ij =N +ij ∪N -ij Among them, the uplink node N +ij ={N +ij |i∈L,j∈P i}, Downlink node N -ij ={N -ij |i∈L,j∈P i}, L={1,2,3,…,n l} represents the set of subway line codes, n l This indicates the total number of subway lines. Represents a set of site codes. This represents the total number of stations on line i.

[0010] Preferably, the directed arc A ±ij =A +ij ∪A -ij Among them, the upward arc A +ij ={A +ij |i∈L,j∈E i}, downward arc A -ij ={A -ij |i∈L,j∈E i}, This represents a set of road segment codes.

[0011] Preferably, constructing the subway network based on the directed stations and the directed road segments includes:

[0012] Uplink node and upstream node via the ascending arc connect,

[0013] Downlink node and downlink nodes via the downward arc connect,

[0014] Uplink node N i1 and downlink node N -i1 Merge into a single directed node;

[0015] Uplink node and downlink nodes Merge into a single directed node;

[0016] The above steps yield the topology of the subway network.

[0017] Preferably, the station type is set according to the topology, specifically including:

[0018] When a station consists of a single directed node, the station is designated as a terminal station (TN) without transfer.

[0019] When a station consists of 2x1 (x1 = 2, 3, 4...) directed nodes, the station is set as a transfer station (NT) that is not the first or last station.

[0020] When a station consists of 2 directed nodes, the station is set as NN, which is neither the first / last station nor a transfer station.

[0021] When a station consists of 2x2+1 (x2 = 1, 2, 3...) directed nodes, the station is set as both the terminal station and the transfer station TT.

[0022] Preferably, the formula for calculating the efficiency of the topology network is:

[0023] Where N is the total number of nodes in the network, when node N o With N p When they are connected, d op =10, otherwise d op =0, if node N o With N p If they belong to the same transfer station, then d op =1.

[0024] Preferably, the formula for calculating the connectivity of the topology network is as follows: Where n op Let N be the connectivity coefficient, if node N o With N p If they are connected, then n op =1, otherwise n op =0, where N is the total number of nodes in the network.

[0025] The present invention also provides a subway network model, which is constructed using the subway network modeling method described above, and is used to describe a unidirectional station interference scenario.

[0026] Preferably, the subway network model is also used to describe the distribution characteristics of passenger flow in both directions.

[0027] Preferably, the metro network model is also used to describe the dynamic service capabilities of each directed metro station.

[0028] The technical solution of the present invention has the following advantages compared with the prior art:

[0029] The subway network modeling method described in this invention utilizes complex network theory to extract the core features of the basic components of the subway operation system, establishes a fully directed network model for the subway operation system, and uses directed nodes and directed arcs to represent stations and road segments, respectively. Each node and arc is assigned a symbol, with positive and negative numbers representing up and down traffic, respectively, to describe the spatial directionality of stations and passenger flow. In addition, it can accurately describe the subway service performance in both interference-free and interference-affected scenarios. For example, in the interference scenario where one-way stations are closed, the impact of interference occurring at directed stations on the system service performance can be analyzed. Attached Figure Description

[0030] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0031] Figure 1 This is a flowchart illustrating the implementation of a subway network modeling method according to the present invention.

[0032] Figure 2 This is a schematic diagram of a fully directed subway network constructed based on a subway network modeling method of the present invention;

[0033] Figure 3 This is a schematic diagram of a line in a fully directed metro network constructed based on a metro network modeling method of the present invention.

[0034] Figure 4 This is a schematic diagram of a topological structure where the terminal station is not a transfer station;

[0035] Figure 5 This is a schematic diagram of the topology of a transfer station that is not the first or last station;

[0036] Figure 6 This is a schematic diagram of a topology that is neither the first nor the last station nor a transfer station;

[0037] Figure 7 This is a schematic diagram of a topological structure where a station is both the first and last stop and a transfer station.

[0038] Figure 8 This is a schematic diagram of the undirected Suzhou Metro network topology;

[0039] Figure 9 This is a schematic diagram of the topology of a partially directed Suzhou Metro network.

[0040] Figure 10 This is a schematic diagram of the fully directed Suzhou Metro network topology.

[0041] Figure 11This is a map showing the Shenzhen Metro lines and their components;

[0042] Figure 12 This is a schematic diagram of the passenger flow distribution results at the originating station based on partially directed networks and fully directed networks;

[0043] Figure 13 This is a schematic diagram of the arrival station passenger flow distribution results based on partially directed networks and fully directed networks;

[0044] Figure 14 This is a diagram showing the waiting times for passengers at various directional stations in a typical transfer station (Shenzhen Metro Window of the World Station). Detailed Implementation

[0045] The core of this invention is to provide a subway network modeling method and a subway network model, which can accurately describe the spatial directionality of stations and passenger flow, as well as the impact of interference occurring at directed stations on system service performance.

[0046] To enable those skilled in the art to better understand the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely 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.

[0047] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the implementation of a subway network modeling method according to the present invention. The specific steps are as follows:

[0048] S101: Utilizing directed node N ±ij Represents a directed site, where N +ij N represents the j-th station in the up direction of line i. -ij This represents the j-th station in the downward direction of line i;

[0049] The directed node N ±ij =N +ij ∪N -ij Among them, the uplink node N +ij ={N +ij |i∈L,j∈P i}, Downlink node N -ij ={N -ij |i∈L,j∈P i}, L={1,2,3,…,n l} represents the set of subway line codes, n l This indicates the total number of subway lines. Represents a set of site codes. This represents the total number of stations on line i.

[0050] S102: Utilizing directed arc A ±ij Indicates a directed road segment, where A +ij A represents the j-th segment in the up direction of line i. -ij This represents the j-th road segment in the down direction of line i;

[0051] The directed arc A ±ij =A +ij ∪A -ij Among them, the upward arc A +ij ={A +ij |i∈L,j∈E i}, downward arc A -ij ={A -ij |i∈L,j∈E i}, This represents a set of road segment codes.

[0052] S103: Construct a subway network G = {N} based on the directed stations and the directed road segments. ±ij A ±ij}

[0053] Uplink node and upstream node via the ascending arc connect,

[0054] Downlink node and downlink nodes via the downward arc connect,

[0055] Uplink node N i1 and downlink node N -i1 Merge into a single directed node;

[0056] Uplink node and downlink nodes Merge into a single directed node;

[0057] The above steps yield the topology of the subway network.

[0058] Let directed node N and directed arc A represent directed stations and directed road segments, respectively, such as Figure 2 As shown, they are represented by circles with arrows and line segments with arrows, respectively. Figure 3 As shown, the identifiers and symbols in the nodes and arc subscripts represent the station number and direction of movement, respectively, and positive and negative numbers represent up and down, respectively.

[0059] Based on the above embodiments, this embodiment sets the station type according to the topology, specifically as follows:

[0060] When a station consists of a single directed node, that station is designated as a terminal station (TN) without transfers. Figure 4 As shown, N i01 This indicates that the station on line i is the first or last station, not a transfer station;

[0061] When a station consists of 2x1 (x1 = 2, 3, 4...) directed nodes, the station is designated as a transfer station (NT) that is not the terminal station. Figure 5 As shown, N of line i ij N -ij N of line i' i ' j '、N -i ' j The fact that the stations converge here indicates that this station is a transfer station rather than the first or last station;

[0062] When a station consists of two directed nodes, the station is set as NN, which is neither the first nor the last station nor a transfer station. Figure 6 As shown, N ij N -ij This indicates that the station is neither the first nor the last stop, nor a transfer station;

[0063] When a station consists of 2x2+1 (x2 = 1, 2, 3...) directed nodes, the station is designated as both the terminal station and a transfer station TT, such as... Figure 7 As shown, N of line i i01 N of line i' i'j' N -i'j' The fact that they converge at this station indicates that it is both the first and last stop and a transfer station.

[0064] Based on the above embodiments, the present invention also provides a subway network model constructed based on the above subway network modeling method, which can be used to describe unidirectional station interference scenarios:

[0065] As of October 2022, the fully directed network modeling method of this invention has been applied to 5 lines and 154 stations (including 14 transfer stations) of the Suzhou Metro. Figures 8 to 10 The diagrams show undirected networks using traditional methods, partially directed networks, and Suzhou Metro under a fully directed network as presented in this invention.

[0066] We solve for the number of nodes, arcs, network topology characteristics, efficiency, and connectivity of the Suzhou Metro model under both undirected, partially directed, and fully directed conditions, with and without interference:

[0067] The efficiency between nodes refers to the distance d between two nodes.ij The reciprocal of the distances between nodes, the network efficiency of the entire urban rail transit network is the average of the sum of the reciprocals of the distances between effective nodes in the network, and its specific formula is: When node N o With N p When they are connected, d op =10, otherwise d op =0, if node N o With N p If they belong to the same transfer station, then d op =1. Furthermore, the formula for calculating the connectivity rate of urban rail transit networks is: Where n op Let N be the connectivity coefficient, if node N o With N p If they are connected, then n op =1, otherwise n op =0, where N is the total number of nodes in the network.

[0068] The characteristics of the three networks of Suzhou Metro under normal circumstances are shown in Table 1:

[0069] Table 1. Characteristics of the three networks of Suzhou Metro under normal circumstances

[0070] Undirected networks Partial Directed Networks Fully Directed Networks Number of nodes N 154 154 326 Arc number A 163 326 382 Efficiency E <![CDATA[8.488×10 -6 ]]> <![CDATA[8.488×10 -6 ]]> <![CDATA[2.175×10 -6 ]]> Connectivity C 1.058 2.117 1.172

[0071] Interference Scenario 1: Under extreme conditions such as earthquakes, fires, and torrential rains, the transportation network will be disrupted. That is, if one or more nodes are interrupted, the topological characteristics of the transportation network will be affected. Taking Typhoon Muifa as an example, according to meteorological forecasts, to ensure safety, Suzhou Rail Transit successively suspended operations at Qihe Station, Fuxiang Station, Suzhou North Railway Station, Dawan Station, Fuyuan Road Station, Likou Station, Xutugang Station, and Yangchenghu Middle Road Station on Line 2, and Yangchenghu South Station on Line 5, starting at 22:00 on September 14, 2022. Calculate the topological characteristics of the Suzhou Metro network under this interference scenario and define the rate of change of network efficiency. Network connectivity rate of change As shown in Table 2:

[0072] Table 2 Characteristics of three Suzhou Metro networks under bidirectional platform interruption conditions

[0073] Undirected networks Partial Directed Networks Fully Directed Networks Number of nodes N' 145 145 310 Arc number A' 154 308 364 Efficiency E' <![CDATA[9.579×10 -6 ]]> <![CDATA[9.579×10 -6 ]]> <![CDATA[2.423×10 -6 ]]> Connectivity C' 1.062 2.124 1.174 Efficiency change rate ΔE -0.128 -0.128 -0.114 rate of change of connectivity ΔC <![CDATA[-3.427×10 -3 ]]> <![CDATA[-3.427×10 -3 ]]> <![CDATA[-2.060×10 -3 ]]>

[0074] Interference Scenario 2: Based on Interference Scenario 1, assume that only the same stations on the upline are interrupted, namely Qihe Station, Fuxiang Station, Suzhou North Railway Station, Dawan Station, Fuyuan Road Station, Likou Station, Xutugang Station, and Yangchenghu Middle Road Station on Line 2, and Yangchenghu South Station on Line 5 is suspended. Calculate the topological characteristics of the Suzhou Metro network under this interference scenario, and the rate of change of network efficiency. Network connectivity rate of change As shown in Table 3:

[0075] Table 3 Characteristics of three Suzhou Metro networks under one-way platform interruption conditions

[0076] Undirected networks Partial Directed Networks Fully Directed Networks Number of nodes N” 145 145 319 Arc number A” 154 317 373 Efficiency E” <![CDATA[9.579×10 -6 ]]> <![CDATA[9.579×10 -6 ]]> <![CDATA[2.280×10 -6 ]]> Connectivity C” 1.062 2.186 1.169 Efficiency change rate ΔE' -0.128 -0.128 -0.048 rate of change of connectivity ΔC' <![CDATA[-3.427×10 -3 ]]> <![CDATA[-3.275×10 -2 ]]> <![CDATA[2.134×10 -3 ]]>

[0077] As can be seen, the subway operation network model constructed based on the modeling method shown in this invention has the following advantages:

[0078] (1) The proposed network model takes into account the spatial orientation and temporal dynamics of the basic components of the subway operation system, and can more accurately reflect the core characteristics of the subway operation system.

[0079] (2) Under interference conditions, both the proposed network model and existing models can be used to describe changes in network performance when bidirectional stations are temporarily closed. However, undirected and partially directed network models cannot describe scenarios where unidirectional stations are closed. For example, the subway operation network will be disrupted in the event of emergencies such as earthquakes, fires, rainstorms, and epidemics. When unidirectional stations are interrupted, traditional network models cannot describe the scenarios where unidirectional stations are disrupted; only the invented fully directed network model can simulate the supply and demand changes at unidirectional stations. Subsequently, unidirectional passenger flow data and train operation data based on the fully directed network can be used to rationally allocate emergency resources, reduce economic losses, and improve the operational safety of the subway network. Therefore, compared to traditional network models, which cannot describe scenarios where unidirectional stations are disrupted, the proposed network can describe more specific and broader interference scenarios.

[0080] (3) Under interference conditions, the network impact index calculated using the proposed fully directed network model is more accurate than that of traditional undirected networks and partially directed networks.

[0081] Based on the above embodiments, this embodiment uses transaction records from October 13 to November 30, 2013 (excluding November 12 due to a super typhoon hitting Shenzhen) for a period of 7 weeks to identify the Shenzhen Metro network (e.g., Figure 11 The dynamic nodes and arcs are shown in the figure. The research data contains 139,897,144 valid transaction records. Each transaction record includes the card-swipe entry time and card-swipe exit time associated with each smart card ID. Subway passenger flow distribution statistics are performed based on both partially directed and fully directed networks, and the results are as follows: Figure 12 , Figure 13 As shown, O_neg and O_pos represent the passenger flow (number of people) originating from a certain directional station in the up and down directions, respectively; D_neg and D_pos represent the passenger flow (number of people) arriving at a certain directional station in the up and down directions, respectively; and O_non and D_non represent the number of OD pairs of passengers originating from and arriving at a certain station, respectively, based on the statistics of undirected stations.

[0082] It can be seen that, compared with undirected nodes, the network model constructed based on the method of this invention can not only count the number of passengers originating from or arriving at a certain station, but also reveal the distribution characteristics of passenger flow in both directions.

[0083] Shenzhen Metro's Window of the World Station is a typical transfer station, and passenger waiting time is one of the commonly used indicators to describe the metro's service capacity. Figure 14 The network model is based on the statistical data of passenger waiting time at the four directed stations within the Window of the World station. Obviously, the network model constructed based on the method of this invention can also reveal the dynamic service capabilities of each directed station of the subway.

[0084] The subway network modeling method described in this invention utilizes complex network theory to extract the core features of the basic components of the subway operation system, establishing a fully directed network model for the system. Directed nodes and directed arcs represent stations and segments, respectively, with each node and arc assigned a symbol: positive and negative numbers represent upward and downward travel, respectively. Since the operation of a subway station involves many stations and segments, the fully directed representation of station points and arcs effectively explains the accurate travel direction and location of passengers, revealing the dynamic directed characteristics of subway supply and passenger demand. This solves the problem that undirected or partially directed models are not ideal for capturing the spatial characteristics of subway networks. Furthermore, it can accurately describe subway service performance in both interference-free and interference-affected scenarios. For example, in interference scenarios where one-way stations are closed, the impact of interference occurring at directed stations on system service performance can be analyzed. This fully directed subway network model description method further identifies key subway stations and segments, enabling better allocation of limited investment, personnel, and other resources, reducing economic losses, and ultimately improving subway safety and passenger satisfaction.

[0085] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A subway network modeling method, characterized in that, include: Using directed nodes Indicates a directed site, where, This represents the j-th station in the up direction of line i. This represents the j-th station in the downward direction of line i; Using directed arcs Indicates a directed road segment, where, This represents the j-th segment in the up direction of line i. This represents the j-th road segment in the down direction of line i; Construct a subway network based on the directed stations and the directed road segments. ; The directed node Among them, the uplink node Downlink node , This represents the set of subway line codes. This indicates the total number of subway lines. Represents a set of site codes. This represents the total number of stations on line i. The directed arc Among them, the ascending arc Downward arc , Represents the set of road segment codes; The construction of the subway network based on the directed stations and the directed road segments includes: Uplink node and upstream node via the ascending arc connect, ; Downlink node and downlink nodes via the downward arc connect, ; Uplink node and downlink nodes Merge into a single directed node; Uplink node and downlink nodes Merge into a single directed node; The above steps yield the topology of the subway network.

2. The subway network modeling method according to claim 1, characterized in that, Based on the aforementioned topology, the site type is set, specifically including: When a station consists of a single directed node, the station is designated as a terminal station (TN) without transfers. When a station consists of 2x1 directed nodes, x1=2,3,4..., the station is set as a transfer station (NT) that is not the first or last station. When a station consists of 2 directed nodes, the station is set as NN, which is neither the first / last station nor a transfer station. When a station consists of 2x2+1 directed nodes, where x2=1,2,3..., the station is set as both the first and last stop and a transfer station TT.

3. The subway network modeling method according to claim 2, characterized in that, The formula for calculating the efficiency of the aforementioned topology network is: ; Where N is the total number of nodes in the network, when the node and When they are connected, ,otherwise If node and If they belong to the same transfer station, then 1.

4. The subway network modeling method according to claim 1, characterized in that, The formula for calculating the connectivity of the topological network is as follows: ,in Let be the connectivity coefficient, if node and If they are connected, then ,otherwise N is the total number of nodes in the network.

5. A subway network model, characterized in that, It is constructed using the subway network modeling method as described in any one of claims 1-4, and is used to describe the interference scenario of one-way stations.

6. The subway network model according to claim 5, characterized in that, Used to describe the distribution characteristics of passenger flow in both directions.

7. The subway network model according to claim 5, characterized in that, Used to describe the dynamic service capabilities of each directional station in a subway system.

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