A rapid flow distribution calculation method for railway throat areas

Abstract

The present invention discloses a method for calculating the rapid distribution of traffic in the throat area of ​​railways, and belongs to the field of railway transportation technology. A solution is provided for the problem that traditional methods rely on manual experience and the existing model calculation is complex. The steps are as follows: input relevant data; construct a traffic distribution optimization model, balance the goals such as the difference between the plan and the actual train, and set constraints; discretize and segment the passenger train ratio parameters, and use the "big M method" to convert the nonlinear equation into a linear constraint; construct a capacity simulation model based on queuing theory, pre-calculate the capacity value to generate a capacity table; combine the linearized model and the capacity table, solve with the CPLEX solver, and obtain the optimized distribution result. The method provided by the present invention realizes rapid and accurate distribution of traffic, balances the difference between the plan and the actual, can quickly respond to dynamic demands, and provides a scientific basis for the management of traffic in the throat area.

Description

Technical Field

[0001] The present invention relates to the technical field of railway transportation, and in particular to a method for calculating rapid flow distribution in a railway throat area. Background Art

[0002] Railway choke points, as core nodes of railway hubs, are key passages connecting trunk lines, branch lines, and stations. They undertake important functions such as train dispatching, passing, and overtaking. The rationality of their traffic distribution directly determines the overall capacity and operational efficiency of the railway network. With the continuous growth of railway transportation demand, especially the rapid expansion of the high-speed rail network and the popularization of mixed passenger and freight operation, the transportation organization challenges faced by choke points are becoming increasingly severe, mainly reflected in the following aspects:

[0003] 1) Traditional chokepoint traffic allocation relies heavily on manual experience and simple rules. These methods lack dynamic adaptability to complex operating environments and struggle to address issues such as multi-path conflicts, differentiated train types, and real-time demand fluctuations. Furthermore, traditional methods are unable to quantitatively assess the impact of different allocation schemes on overall efficiency and lack a scientific basis for optimization, making them unable to meet the requirements of efficient, safe, and flexible modern railway operations. Furthermore, they struggle to cope with complex operating environments and diverse train demands.

[0004] 2) Existing optimization models often contain nonlinear terms, resulting in high computational complexity and low solution efficiency, making it difficult to quickly respond to dynamically changing needs in practical applications.

[0005] This shows that traditional methods and existing models face significant technical bottlenecks when dealing with complex and dynamic bottleneck flow distribution problems. Developing an optimization method that combines computational efficiency and accuracy has important theoretical significance and engineering application value. With the advancement of intelligent and digital transformation of railways, real-time and accurate flow distribution has become the key to improving transportation efficiency. Therefore, there is an urgent need for an efficient computational method that can quickly handle dynamic demand, balance multi-objective optimization, and adapt to infrastructure constraints to achieve scientific distribution of flow in bottleneck areas and improve the overall efficiency of the railway network. Summary of the Invention

[0006] The purpose of this invention is to provide a method for rapidly allocating traffic flow within railway bottlenecks. This method can rapidly allocate traffic flow across routes within a railway bottleneck, given the required traffic flow for each route, the proportion of passenger trains to total trains in operation, and the proportion of passenger trains operating on trunk and branch lines. This method provides a theoretical basis and technical support for improving the throughput capacity of bottlenecks.

[0007] To achieve the above object, the present invention provides a method for calculating rapid flow distribution in a railway throat area, comprising the following steps:

[0008] Input the route data of the throat area, the demand flow of each route in the throat area, the demand ratio of passenger trains to the total trains, and the demand ratio of passenger trains on trunk lines and branch lines;

[0009] Based on the data, a method for rapid flow distribution calculation in railway throat areas is developed.

[0010] Preferably, the method for calculating rapid flow distribution in a railway throat area based on the data specifically includes:

[0011] Establish a flow distribution optimization model in the throat area.

[0012] Preferably, the method for establishing the throat area flow distribution model specifically includes:

[0013] An objective function was established to minimize the following two components: 1. The difference between the planned and actual number of trains provided on bottleneck routes; 2. The proportion of planned passenger trains to total trains in operation, as well as the square of the difference between the planned and actual passenger train proportions on trunk and branch lines. By introducing weighting coefficients, these two optimization objectives were balanced.

[0014] Set constraints to ensure that the provided train schedule is less than or equal to the required train schedule.

[0015] Constraints are set to ensure that the actual train schedules provided are within the range defined by the minimum train demand limit and the maximum train supply capacity.

[0016] Constraints are set to ensure that total traffic volumes remain below the capacity of the rail infrastructure in the throat area.

[0017] Equations are established for the ratio of the number of passenger trains actually provided to the total number of trains provided, as well as the ratio of the number of trains running on the trunk and branch lines.

[0018] The nonlinear equations in the throat flow distribution optimization model are transformed into linear constraints through the linearization method.

[0019] Preferably, the method for linearizing the throat flow distribution model specifically includes:

[0020] The proportion of parameter passenger trains in the total number of trains running, as well as the proportion of passenger trains running on trunk lines and branch lines are divided into equally spaced sections with a step size of 0.05.

[0021] Binary variables are introduced and the “Big M method” is used to perform piecewise linearization on the nonlinear equations of the three parameters and transform them into linear constraints.

[0022] The constraints of total traffic volume and infrastructure capacity are modified by introducing two sets of binary variables that linearly constrain the three parameters to ensure that in each segment, the total traffic volume of the model always remains below the infrastructure capacity of the throat area.

[0023] A railway infrastructure capacity simulation calculation model based on queuing theory is established. The segmented points in the discrete three-dimensional parameter definition domain space are input into the model to pre-calculate the infrastructure capacity table of the throat area.

[0024] Preferably, the method for establishing a railway infrastructure capacity simulation calculation model based on queuing theory specifically includes:

[0025] A proportional calculation equation is established to calculate the ratio of the number of passenger trains in the simulation calculation model to the total number of trains provided, as well as the ratio of the number of trains running on the main line and branch line.

[0026] Establish a threshold calculation equation to calculate the maximum queue length of the line.

[0027] Establish a queuing theory model for the throat area path.

[0028] Preferably, the method for establishing the queuing theory model of the throat area path specifically includes:

[0029] Establish the train arrival rate equation in the throat area and calculate the train arrival rate.

[0030] Establish the throat area line service rate equation and calculate the line service rate.

[0031] Combining the above-constructed proportional calculation equation, queuing theory model, and threshold calculation equation, the Python interface (Stormy) of the Storm simulation software was used to perform simulation calculations to obtain the railway infrastructure capacity.

[0032] Based on the establishment of the simulation calculation method, each segment point in the discrete three-dimensional parameter definition domain space is input into the model, and the corresponding capacity value is calculated. All calculated capacity values ​​constitute the throat area infrastructure capacity table.

[0033] The MIP problem is solved using the CPLEX solver. During the solution process, the capacity parameters in the optimization model are obtained by looking up the throat area infrastructure capacity table.

[0034] Through this calculation process, the optimized path flow in the throat area is obtained.

[0035] Therefore, the present invention adopts a method for calculating the rapid flow distribution in a railway throat area with the above structure, which has the following beneficial effects:

[0036] (1) The invention establishes a linearized throat area flow distribution optimization model to quickly distribute and calculate the flow of each path in the throat area. Based on this, the throat area flow distribution optimization model is first constructed. The distribution optimization model takes the throat area line data, the demand flow of each path in the throat area, the demand ratio of passenger trains to running trains and the demand ratio of passenger trains on the main line and branch line as input. The objective function comprehensively considers the difference between the planned and actual trains and the minimization of the passenger train ratio error, and balances the two optimization objectives through the weight coefficient. By establishing an equation, the proportion of passenger trains to running trains on the line and the proportion of passenger trains on the main line and branch line are calculated. At the same time, constraints are set to ensure that the total number of trains actually provided is less than the total number of trains required and is between the minimum train demand limit and the maximum train supply capacity, so that the total traffic volume is always kept below the throat area infrastructure capacity, thereby ensuring the rationality and feasibility of flow distribution. Secondly, the proportion calculation equation in the optimization model is linearized. By dividing the definition domain of the proportion of passenger trains to running trains and the proportion of passenger trains on the main line and branch line into independent and equally spaced segments, the parameters are discretized. The "Big M method" was also used to transform nonlinear equations into linear constraints piecewise by introducing binary variables to facilitate solution. A railway infrastructure capacity simulation model based on queuing theory was then constructed. Capacity values ​​within the discretized space of proportional parameters were precalculated, and a capacity table for choke points was constructed. Finally, the linearized choke point flow distribution optimization model was solved using the CPLEX solver. During the solution process, the capacity values ​​in the optimization model were obtained by querying the choke point infrastructure capacity table.

[0037] (2) The present invention achieves rapid and accurate allocation of traffic flow in railway bottleneck areas, effectively balancing the discrepancy between planned and actual train operations. This method can quickly and effectively respond to dynamically changing demand and provides a scientific basis for traffic flow management in bottleneck areas.

[0038] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flow chart of a method for calculating rapid distribution of flow in a railway throat area provided by the present invention;

[0040] Figure 2 A schematic diagram of a scenario for a method for rapid flow distribution calculation in a railway throat area provided by the present invention;

[0041] Figure 3 This is a flow chart of the railway infrastructure capacity simulation calculation based on queuing theory provided by the present invention. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0043] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0044] Example

[0045] like Figure 1-3 As shown, the present invention provides a method for calculating rapid flow distribution in a railway throat area, comprising the following steps:

[0046] S1. Input the route data of the throat area, the demand flow of each route in the throat area, the proportion of passenger trains in the total train demand, and the proportion of passenger trains in the demand for trains running on trunk lines and branch lines.

[0047] S11. Establish a throat area flow distribution optimization model. The specific model is as follows:

[0048] (1);

[0049] (2);

[0050] (3);

[0051] (4);

[0052] (5);

[0053] (6);

[0054] (7);

[0055] (8);

[0056] Figure 2 This is a specific scenario studied by this model. In this scenario, the path 、 Constituting trunk lines, paths 、 The branch line is a branch line. In this scenario, stations A to D are arranged in sequence, forming four key stations. At the same time, the figure marks each railway section with numbers 1 to 14. Assume that the two lines of the main line (path ,path ) traffic flow is equal, the two lines of the branch line (path ,path ) traffic flow is equal. Based on this premise, for this research scenario, it can be simplified to focus on the path 、 The objective function (1) consists of two parts, which aims to minimize the number of trains planned to be provided on the throat area path. The actual number of trains provided While ensuring the difference, try to meet the traffic distribution requirements of the line as much as possible. , that is, minimize ,in 、 、 To balance the weight coefficients of multiple objectives, 、 Respectively, the trunk line (path ,path ) The ratio of the number of trains planned to be provided to the number of trains actually provided to the total number of trains, 、 are the ratios of the planned and actual passenger trains provided on the trunk lines to the total number of trains on the trunk lines, 、 Branch lines (paths ,path ) The ratio of the number of passenger trains planned and actually provided to the total number of trains on the branch line. Constraint (2) ensures that after optimization, the number of trains available is Train frequency less than or equal to demand Constraint (3) sets upper and lower limits for each line, representing the minimum demand limits for trains. and the maximum supply capacity of the train Constraint (4) ensures that the total traffic volume Maintaining rail infrastructure capacity at the junction Equation (5-7) is used to calculate the number of passenger trains actually provided as a proportion of the total number of trains provided and the number of trains running on trunk and branch lines, where: , Indicates the train type, where Indicates a passenger train, Indicates a freight train, For the line Provided on Equation (8) is used to calculate the capacity of railway infrastructure. Calculate capacity It can be expressed as the traffic flow distribution Related functions.

[0057] S2. Since the traffic flow optimization model (1-8) contains nonlinear terms (5-7), it is necessary to linearize the model and formulate the NP-Hard problem as a MIP problem. First, the parameters Discretize.

[0058] Will The domain of is divided into 9 equally spaced segments independently, with the segmentation points being . Introducing the collection 、 、 Respectively A set of segmentation points, where the value of each set is The specific value at the segmentation point can be calculated by equation (9-11).

[0059] (9);

[0060] (10);

[0061] (11);

[0062] In addition, the definition (Similarly, and as well as , respectively (as well as and ) has lower and upper bounds on its value.

[0063] S21. Based on the discretization of parameters and the establishment of the original model, a linearized model is constructed. The specific model is as follows:

[0064] , (12);

[0065] , (13);

[0066] , (14);

[0067] , (15);

[0068] , (16);

[0069] , (17);

[0070] , , (18);

[0071] , (19);

[0072] , (20);

[0073] , (twenty one);

[0074] , (twenty two);

[0075] , (twenty three);

[0076] (twenty four);

[0077] The model uses the "Big M method" to linearize nonlinear terms by introducing binary variables. Definition is a binary variable, if ,but ,otherwise .definition is a binary variable, if ,but ,otherwise Among them, constraints (12-15) are used to linearize equation (5), constraints (16-19) are used to linearize equation (6), constraints (20-23) are used to linearize equation (7), and constraint (24) is used to ensure that the total traffic volume of the model remains within the capacity of the railway infrastructure at the intersection after linearization. The following are the parameters used in constraints (12, 13, 16, 17, 20, 21, 24) is set to a large positive number.

[0078] S3. On the basis of the linear model, a railway infrastructure capacity simulation calculation model based on queuing theory is established to simulate the railway infrastructure capacity of the research scenario. The specific model is as follows:

[0079] (25);

[0080] (26);

[0081] (27);

[0082] (28);

[0083] (29);

[0084] (30);

[0085] Where: Indicates a specific line of the studied scenario, Indicates the train type, where Indicates a passenger train, Indicates a freight train. is the total number of trains, The line in the queuing theory model superior Equations (25-27) are used to calculate the train ratio on the line, where is the trunk (path) in the queuing theory model ,path The ratio of the number of trains running on is the ratio of the number of passenger trains running on the trunk line to the total number of trains running on the trunk line in the queuing theory model, For the branch line (path) in the queuing theory model ,path The proportion of passenger trains running on the branch line to the total number of trains running on the branch line.

[0086] Equation (28) is obtained by dividing the number of trains on the line by the time span under consideration. To calculate the route Train arrival rate Equation (29) is solved by substituting the minimum train departure time Multiply by the corresponding train group The proportion on the line and the weighted sum to get the line Service rate Equations (28-29) together form the circuit Train queuing theory model on . Equation (30) is used to calculate the maximum queue length of trains on the trunk line and branch line respectively.

[0087] S31. Perform loop termination determination based on the solution generation situation, as follows:

[0088] S32. Initialize the total number of trains , where The step size by which the number of trains is increased.

[0089] S33, calculated 、 、 .

[0090] S34, calculated 、 The maximum queue length of trunk and branch line trains under this train flow distribution is calculated by equation (30): 、 .

[0091] S35, 、 、 、 As input, a train queuing theory model is established.

[0092] S36. Using the Python interface (Stormy) of the Storm simulation software, the expected queue lengths of trunk and branch line trains based on the train queuing theory model under the train flow distribution are calculated. 、 Perform calculations.

[0093] S37. Determine whether the expected train queue length is less than or equal to the maximum train queue length. If so, update the total number of trains. , repeat steps S3.5 to S3.7. If not satisfied, , ,by As the output, the loop is terminated. Then the schedule capacity under the current traffic distribution is .

[0094] S4. Based on the established railway infrastructure capacity simulation calculation model based on queuing theory, each segment point in the discrete three-dimensional domain space is Input into the model and calculate the corresponding capacity value , all calculated capacity values ​​constitute the infrastructure capacity table ,in Corresponding to the variable segmentation point.

[0095] S41. The line flow optimization problem can be expressed as optimizing the objective function (1) under the constraints (2-7, 12-24). , according to the flow value In the capacity table Obtained by looking up the table.

[0096] S42. The mixed integer programming (MIP) problem is solved using the CPLEX solver.

[0097] Therefore, the present invention adopts the aforementioned method for rapid flow distribution calculation in railway bottleneck areas. By establishing a linearized bottleneck flow distribution optimization model, it rapidly calculates the flow distribution of each path in the bottleneck area. This method achieves rapid and accurate flow distribution in railway bottleneck areas, effectively balancing the discrepancy between planned and actual train operations. This method can quickly and effectively respond to dynamically changing demand, providing a scientific basis for flow management in the bottleneck area.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for rapid flow distribution calculation in railway throat areas, characterized by: The following steps are involved: S1. Input the route data of the throat area, the demand flow of each route within the throat area, the proportion of passenger trains in the total train operation, and the proportion of passenger trains in operation on the trunk and branch lines. S2. Build a flow distribution optimization model for the throat area and quickly calculate the flow distribution of each path in the throat area; S3. The three parameters in the model, namely the proportion of passenger trains to total trains, the proportion of mainline trains, and the proportion of branch line trains, were discretized into equally spaced segments with a step size of 0.

05. The "big M method" was used to introduce binary variables and transform the nonlinear equations into linear constraints. S4. Construct a railway infrastructure capacity simulation model based on queuing theory, pre-calculate the capacity values ​​corresponding to the segment parameters, and generate a throat area infrastructure capacity table; S5. Combining the throat area flow distribution optimization model and the capacity table converted into linear constraints in step S3, use the CPLEX solver to solve the mixed integer programming problem to obtain the optimized path flow distribution result.

2. The method for rapid flow distribution calculation in a railway throat area according to claim 1 is characterized by: In step S2, the method for establishing the throat area flow distribution optimization model specifically includes: S21. Establish an objective function to minimize the following two parts: The difference between the planned number of trains provided and the actual number of trains provided on the throat area routes; The proportion of planned passenger trains to the total number of trains in operation, and the square of the difference between the planned proportion of passenger trains on trunk and branch lines and the actual proportion provided; By introducing the weight coefficient, a balanced consideration of the two optimization objectives is achieved; S22. Establish constraints, including: The actual train schedule provided is less than or equal to the required train schedule; The actual number of trains provided is within the range defined by the minimum train demand being limited by the maximum train supply capacity; Total traffic volumes remain below the capacity of the rail infrastructure in the choke point; S23. Establish equations to calculate the ratio of the actual number of passenger trains provided to the total number of trains provided, as well as the ratio of the number of trains running on trunk lines and branch lines.

3. The method for rapid flow distribution calculation in railway throat areas according to claim 1 is characterized by: In step S3, the parameter discretization specifically includes the following steps: S31. Introduce binary variables and use the "Big M method" to perform piecewise linearization on the nonlinear equations of the three parameters and convert them into linear constraints; S32. Modify the constraints of total traffic volume and infrastructure capacity by introducing two sets of binary variables to linearly constrain the three parameters, ensuring that in each segment, the total traffic volume of the flow distribution optimization model always remains below the infrastructure capacity of the throat area.

4. The method for rapid flow distribution calculation in a railway throat area according to claim 1 is characterized by: In step S4, the method for establishing a railway infrastructure capacity simulation calculation model based on queuing theory includes: S41. Establish a proportion calculation equation to calculate the ratio of the number of passenger trains in the simulation calculation model to the total number of provided trains, as well as the ratio of the number of trains running on the trunk line and branch line; S42. Establish a threshold calculation equation to calculate the maximum queue length of the line; S43. Establish a queuing theory model for the throat area path.

5. The method for rapid flow distribution calculation in railway throat areas according to claim 4 is characterized by: In step S43, the method for establishing the queuing theory model of the throat area path includes: Establish the train arrival rate equation in the throat area and calculate the train arrival rate; Establish the throat area line service rate equation and calculate the line service rate; Combining the above-constructed proportional calculation equation, queuing theory model, and threshold calculation equation, the Python interface Stormy of the Storm simulation software is used to perform simulation calculations to obtain the railway infrastructure capacity.

6. The method for rapid flow distribution calculation in railway throat areas according to claim 1 is characterized by: In step S5, the steps for obtaining the optimized path flow distribution result are as follows: S51. Based on the established simulation calculation method, each segment point in the discrete three-dimensional parameter definition domain space is input into the throat area flow distribution optimization model converted into a linear constraint in step S3, and the corresponding capacity value is calculated. All calculated capacity values ​​constitute the throat area infrastructure capacity table; S52. Solve the mixed integer programming (MIP) problem using a CPLEX solver, wherein the capacity parameters of the throat area flow distribution optimization model converted into linear constraints in step S3 are obtained by looking up the throat area infrastructure capacity table; S53. Through this calculation process, the optimized path flow in the throat area is obtained.

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