Subway dynamic pricing method and device and computer readable storage medium

Abstract

The invention belongs to the technical field of rail transit, and relates to a subway dynamic pricing method and device and a computer readable storage medium. Obtaining a time scheduling strategy based on a first ticket price reward mechanism that the passenger accepts the riding in advance, a second ticket price reward mechanism that the passenger accepts the riding delay, and a first ticket price punishment mechanism that the passenger does not accept the riding in advance or the riding delay; constructing a supply-demand ratio variance of the station in a preset time period under the time scheduling strategy, and constructing a pricing objective function by minimizing the supply-demand ratio variance of the station in the preset time period; constructing a first pricing constraint function according to the first ticket price reward proportion, the second ticket price reward proportion and the first ticket price penalty proportion; constructing a second pricing constraint function by taking the condition that the total income of the station in the preset time period is greater than the total income when the time scheduling strategy is not adopted as a constraint; and solving the pricing target function, the first pricing constraint function and the second pricing constraint function to obtain a first ticket price reward proportion, a second ticket price reward proportion and a first ticket price penalty proportion.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit, and particularly to a subway dynamic pricing method, device and computer-readable storage medium. Background Art

[0002] With the expansion of the urban rail transit network, the passenger volume of many subway systems has increased significantly, especially during the morning and evening rush hours. On the contrary, the low passenger volume during off-peak hours has led to serious waste of resources and inefficient utilization of operating costs. The periodic surge in passenger flow and the uneven distribution of passenger flow between platforms have led to an imbalance between supply and demand based on platforms. In addition, the low transportation fare has caused many subway operators to be in a loss state for a long time. Therefore, it is urgent to take urgent and effective measures to adjust and optimize the subway operation system.

[0003] The prior art solves the vehicle scheduling problem by introducing a dynamic pricing strategy into the intelligent transportation system. Specifically, the initial pricing of the intelligent transportation system is static, and its main pricing goal is to cover the operating costs of the operator and generate profits within the acceptable range of passengers. Since the 1970s, with the increase in demand, the intelligent transportation system has begun to introduce a dynamic pricing strategy to solve the vehicle scheduling problem, maximizing the operator's profit while improving passenger satisfaction.

[0004] However, the prior art research on dynamic pricing strategies has basically focused on railway, vehicle or shared bicycle systems. In railway operations, a large number of studies have tried to use dynamic pricing to balance the supply and demand of railway seats. For example: 1. Using a mixed integer linear programming model to develop a railway timetable, which minimizes the overall travel cost of passengers while ensuring the revenue of the train company; 2. Using a non-concave non-linear mixed integer optimization model to solve the fare and seat allocation problems, aiming to maximize the railway ticket revenue; 3. By optimizing the existing fare mechanism and combining intertemporal pricing and demand-based pricing strategies, a new railway dynamic pricing system is proposed. In taxi operations, Qian et al. formulated the daily time pricing scheme for the taxi industry as a discrete-time stochastic dynamic programming and used approximate dynamic programming to identify the optimal sequence of price multipliers; Liu et al. constructed a taxi network service model including taxis and ride-hailing services to study the impact of pricing strategies and other factors on equilibrium and market performance. However, the number of railway seats is fixed, the distance between stations is much greater than the distance between adjacent subway platforms, and the departure time interval is also longer. The focus of its pricing and scheduling strategy is to consider the allocation of seat resources, while subway operation scheduling needs to focus on the overall passenger flow distribution. Therefore, the railway price adjustment strategy cannot be directly applied to the subway system; and the pick-up and drop-off points of taxis are relatively flexible, which is completely different from the operation characteristics of the subway system. Therefore, the dynamic pricing strategy for taxis cannot be applied to the subway system either.

[0005] In summary, in the prior art, there is no subway dynamic pricing method that takes into account the supply-demand balance of subway platforms and optimizes the revenue of operators to effectively relieve subway congestion and improve the platform service level. Summary of the Invention

[0006] For this reason, the technical problem to be solved by the present invention is to overcome the problem that there is no subway dynamic pricing method in the prior art that takes into account the supply-demand balance of subway platforms and optimizes the revenue of operators to effectively relieve subway congestion and improve the platform service level.

[0007] To solve the above technical problems, the present invention provides a subway dynamic pricing method, including: Obtaining a time scheduling strategy based on a first fare reward mechanism for passengers to accept early boarding on the same platform, a second fare reward mechanism for passengers to accept delayed boarding on the same platform, and a first fare penalty mechanism for passengers not accepting early boarding or delayed boarding on the same platform; Based on the number of passengers at each moment of the platform within a preset period under the time scheduling strategy, constructing a supply-demand ratio equation for each moment of the platform within the preset period and a supply-demand ratio variance of the platform within the preset period; taking the minimization of the supply-demand ratio variance of the platform within the preset period as the goal, constructing a pricing objective function of the time scheduling strategy; Taking the values of the first fare reward ratio under the first fare reward mechanism, the second fare reward ratio under the second fare reward mechanism, and the first fare penalty ratio under the first fare penalty mechanism as constraints, constructing a first pricing constraint function of the time scheduling strategy; Taking the total revenue of the platform within a preset period under the time scheduling strategy being greater than the total revenue when no time scheduling strategy is adopted as a constraint, constructing a second pricing constraint function of the time scheduling strategy; Solving the pricing objective function, the first pricing constraint function, and the second pricing constraint function of the time scheduling strategy to obtain the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio.

[0008] Preferably, constructing a supply-demand ratio equation for each moment of the platform within a preset period and a supply-demand ratio variance of the platform within the preset period based on the number of passengers at each moment of the platform within the preset period under the time scheduling strategy includes: Based on the number of passengers at each moment of the platform within a preset period when no time scheduling strategy is adopted, the proportion of passengers who take early boarding on the same platform due to the first fare reward mechanism, the proportion of passengers who take delayed boarding on the same platform due to the second fare reward mechanism, the proportion of passengers who take early boarding due to the first fare penalty mechanism, and the proportion of passengers who take delayed boarding due to the first fare penalty mechanism, obtaining the number of passengers at each moment of the platform under the time scheduling strategy; Based on the ratio of the number of passengers on the platform at each moment to the number of platforms in the subway station, obtain the supply-demand ratio equation of the platform at each moment; Based on the supply-demand ratio of the platform at each moment within a preset time period, the average supply-demand ratio of the platform within the preset time period, and the duration of the preset time period, construct the supply-demand variance of the platform within the preset time period.

[0009] Preferably, the number of passengers on the platform at each moment under the time scheduling strategy is expressed as: , where, represents the number of passengers on the platform at moment under the time scheduling strategy; represents the number of passengers on the platform at moment without adopting the time scheduling strategy; represents the proportion of passengers who board the train in advance on the same platform due to the first fare reward mechanism; represents the first fare reward ratio; represents the proportion of passengers who delay boarding on the same platform due to the second fare reward mechanism; represents the second fare reward ratio; represents the proportion of passengers who board the train in advance due to the first fare penalty mechanism; represents the proportion of passengers who delay boarding due to the first fare penalty mechanism; represents the first fare penalty ratio; The supply-demand ratio equation of the platform at each moment is expressed as: , where, represents the supply-demand ratio equation of the platform at moment; represents the number of platforms; The supply-demand variance of the platform within the preset time period is expressed as: , where, represents the supply-demand variance of the platform within the preset time period; represents the duration of the preset time period.

[0010] Preferably, the pricing objective function of the time scheduling strategy is expressed as: , where, represents the pricing objective function of the time scheduling strategy; represents the supply-demand variance of the platform within the preset time period; represents the duration of the preset time period; represents the platform Supply-demand ratio equation at moment; The first pricing constraint function of the time scheduling strategy is expressed as: , , , wherein, represents the first fare reward ratio; represents the second fare reward ratio; represents the first fare penalty ratio; The second pricing constraint function of the time scheduling strategy is expressed as: , wherein, represents the total income of the platform within the preset time period under the time scheduling strategy; represents the total income without adopting the time scheduling strategy; , wherein, represents the total price of passenger p taking the train from platform at moment without adopting the time scheduling strategy; , wherein, represents the number of passengers on the platform at moment under the time scheduling strategy; represents the total price of passenger p taking the train from platform at moment without adopting the time scheduling strategy; The number of passengers on the platform at moment under the time scheduling strategy; represents the total price of passenger p taking the train from platform at moment without adopting the time scheduling strategy; represents the number of passengers on the platform at moment under the time scheduling strategy; represents the total price of passenger p taking the train from platform at moment without adopting the time scheduling strategy.

[0011] Preferably, it further includes: Based on the second fare penalty mechanism that passengers do not accept changing platforms to take the train at the current moment within the preset platform, a space scheduling strategy is obtained; Based on the number of passengers at each platform within the preset platform at the current moment under the spatial scheduling strategy, construct the supply-demand ratio equation for each platform within the preset platform at the current moment and the variance of the supply-demand ratio of the preset platform at the current moment; taking the minimization of the variance of the supply-demand ratio of the preset platform at the current moment as the goal, construct the pricing objective function of the spatial scheduling strategy; Taking the value of the second fare penalty ratio under the second fare penalty mechanism as a constraint, construct the pricing constraint function of the spatial scheduling strategy; Solve the pricing objective function and the constraint function of the spatial scheduling strategy to obtain the second fare penalty ratio.

[0012] Preferably, based on the number of passengers at each platform within the preset platform at the current moment under the spatial scheduling strategy, constructing the supply-demand ratio equation for each platform within the preset platform at the current moment and the variance of the supply-demand ratio of the preset platform at the current moment includes: Based on the number of passengers at each platform within the preset platform at the current moment when the spatial scheduling strategy is not adopted and the proportion of passengers who change platforms to take the train due to the second fare penalty mechanism at the current moment after the spatial scheduling strategy is adopted, obtain the number of passengers at each platform within the preset platform at the current moment under the spatial scheduling strategy; Based on the ratio of the number of passengers at each platform within the preset platform at the current moment to the number of platforms in the subway station, obtain the supply-demand ratio equation for each platform within the preset platform at the current moment; Based on the supply-demand ratio of each platform within the preset platform at the current moment, the average value of the supply-demand ratio of the preset platform at the current moment, and the number of preset platforms, construct the variance of the supply-demand ratio of the preset platform at the current moment.

[0013] Preferably, the number of passengers at each platform within the preset platform at the current moment under the spatial scheduling strategy is expressed as: , , where, represents the number of passengers at platform at moment under the spatial scheduling strategy; represents the number of passengers at platform at moment when the spatial scheduling strategy is not adopted; represents the proportion of passengers who change platforms to take the train due to the second fare penalty mechanism; represents the second fare penalty ratio; represents the number of passengers at platform adjacent to platform at moment under the spatial scheduling strategy; represents the number of passengers at platform at moment when the spatial scheduling strategy is not adopted; The supply-demand ratio equation of each platform within the preset platform at the current moment is expressed as: , wherein, represents the supply-demand ratio equation of platform at moment represents the number of platforms; The supply-demand variance of the preset platform at the current moment is expressed as: , wherein, represents the supply-demand variance of the preset platform at moment represents the number of preset platforms.

[0014] Preferably, the pricing objective function of the spatial scheduling strategy is expressed as: , wherein, represents the pricing objective function of the spatial scheduling strategy; represents the supply-demand variance of the preset platform at moment represents the number of preset platforms; represents the supply-demand ratio equation of platform at moment The pricing constraint function of the spatial scheduling strategy is expressed as: , wherein, represents the second fare penalty ratio.

[0015] The present invention also provides a subway dynamic pricing device, including: a time scheduling strategy construction module, configured to obtain a time scheduling strategy based on a first fare reward mechanism for passengers to accept early boarding at the same platform, a second fare reward mechanism for passengers to accept delayed boarding at the same platform, and a first fare penalty mechanism for passengers not to accept early boarding or delayed boarding at the same platform; a time scheduling pricing objective function construction module, configured to construct a supply-demand ratio equation of each moment within a preset time period of the platform and a supply-demand variance of the platform within the preset time period based on the number of passengers at each moment of the platform within the preset time period under the time scheduling strategy; and construct a pricing objective function of the time scheduling strategy with the goal of minimizing the supply-demand variance of the platform within the preset time period; A time scheduling first pricing constraint function construction module is used to construct a first pricing constraint function of the time scheduling strategy with the first fare reward ratio under the first fare reward mechanism, the second fare reward ratio under the second fare reward mechanism, and the first fare penalty ratio under the first fare penalty mechanism as constraints; A time scheduling second pricing constraint function construction module is used to construct a second pricing constraint function of the time scheduling strategy with the total income of the platform within a preset time period under the time scheduling strategy being greater than the total income when the time scheduling strategy is not adopted as a constraint; A time scheduling pricing acquisition module is used to solve the pricing objective function, the first pricing constraint function, and the second pricing constraint function of the time scheduling strategy to obtain the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio.

[0016] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned subway dynamic pricing method are implemented.

[0017] The subway dynamic pricing method provided by this application has the following beneficial effects: 1. During the peak period of subway operation, passengers' acceptance of boarding in advance or delaying boarding can both alleviate the problem of insufficient supply-demand ratio at the platform during the peak period, and can also increase the income of the operator during the off-peak period. Therefore, this application obtains a time scheduling strategy based on the first fare reward mechanism for passengers to accept boarding in advance at the same platform, the second fare reward mechanism for passengers to accept delaying boarding at the same platform, and the first fare penalty mechanism for passengers not to accept boarding in advance or delaying boarding at the same platform, and uses fare rewards and penalties to encourage and restrain passengers to travel at off-peak times; in order to make the supply-demand ratio of each platform under this time scheduling strategy be in a balanced state within the scheduling period, thereby improving the service level of the platform during the scheduling time, therefore, with the goal of minimizing the variance of the supply-demand ratio of each platform under the time scheduling strategy within a preset time period, a pricing objective function of the time scheduling strategy is constructed; at the same time, in order to make the fare reward ratio and penalty ratio based on time scheduling be within a reasonable range, thereby maximizing the acceptance degree of passengers for this time scheduling strategy, this application constructs a first pricing constraint function of the time scheduling strategy with the values of the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio as constraints; in addition, in order to optimize the income of the operator, a second pricing constraint function of the time scheduling strategy is constructed with the total income of each platform under the time scheduling strategy within the scheduling period being greater than the total income without scheduling as a constraint; finally, by solving the objective function and the constraint function, pricing is carried out with the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio, so as to encourage passengers to travel at off-peak times, not only effectively balance the supply-demand ratio of the platform in terms of time, but also increase the income of the operator.

[0018] 2. The present application also finds that if passengers accept changing platforms during peak hours, it can also effectively relieve the pressure on the supply-demand ratio of some platforms during peak hours. Therefore, based on the second fare penalty mechanism where passengers do not accept changing platforms within the preset platform at the current moment, the present application obtains a space scheduling strategy. To balance the supply-demand ratio of multiple preset platforms at each moment under this space scheduling strategy and improve the service level of multiple platforms at each moment, the present application constructs a pricing objective function for the space scheduling strategy with the goal of minimizing the variance of the supply-demand ratio of the preset platform at the current moment. At the same time, with the value of the second fare penalty ratio under the second fare penalty mechanism as a constraint, a pricing constraint function for the space scheduling strategy is constructed. By solving the objective function and the constraint function, pricing is carried out with the second fare penalty ratio, thereby motivating passengers to travel at off-peak times spatially through the way of fare penalty, so as to effectively balance the supply-demand ratio of platforms spatially. At the same time, this penalty mechanism will inevitably increase the income of the operator.

[0019] 3. The present application conducts dynamic pricing in two dimensions of time and space, and uses this dynamic pricing to schedule the travel time and location of passengers, thereby achieving the balance of the supply-demand ratio of platforms in time and space. It not only effectively alleviates the subway congestion problem, improves the service level of platforms, but also increases the income of the operator. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein: Figure 1 is a flowchart of the subway dynamic pricing method provided by the present application; Figure 2 is a schematic diagram of several adjacent stations of the subway station provided by the present application; among them, Figure 2 in (a) is the first schematic diagram of adjacent stations of the subway station, Figure 2 in (b) is the second schematic diagram of adjacent stations of the subway station, Figure 2 in (c) is the third schematic diagram of adjacent stations of the subway station, Figure 2 in (d) is the fourth schematic diagram of adjacent stations of the subway station, Figure 2 in (e) is the fifth schematic diagram of adjacent stations of the subway station, Figure 2 in (f) is the sixth schematic diagram of adjacent stations of the subway station, Figure 2 in (g) is the seventh schematic diagram of adjacent stations of the subway station, Figure 2 in (h) is the eighth schematic diagram of adjacent stations of the subway station; Figure 3 is a schematic diagram of the principle of the time-space scheduling strategy provided by the present application; among them, Figure 3 in (a) is a schematic diagram of the dimensions of the time-space scheduling strategy, Figure 3In (b) is a schematic diagram comparing before and after the time scheduling strategy, Figure 3 In (c) is a schematic diagram comparing before and after the space scheduling strategy; Figure 4 This is a schematic diagram of passengers' boarding behavior with and without the time scheduling strategy provided by this application; among them, Figure 4 In (a) is a schematic diagram of passengers' boarding behavior when the time scheduling strategy is not adopted, Figure 4 In (b) is a schematic diagram of passengers' boarding behavior when the time scheduling strategy is adopted; Figure 5 This is a schematic diagram of passengers' boarding behavior with and without the time scheduling strategy provided by this application; among them, Figure 5 In (a) is a schematic diagram of passengers' boarding behavior when the time scheduling strategy is not adopted, Figure 5 In (b) is a schematic diagram of passengers' boarding behavior when the time scheduling strategy is adopted; Figure 6 This is a schematic diagram of passengers' boarding behavior with and without the space scheduling strategy provided by this application; among them, Figure 6 In (a) is a schematic diagram of passengers' boarding behavior when the space scheduling strategy is not adopted, Figure 6 In (b) is a schematic diagram of passengers' boarding behavior when the space scheduling strategy is adopted; Figure 7 This is the attitude of passengers towards different scheduling strategies provided by this application; among them, Figure 7 In (a) is a schematic diagram of the proportion of passengers willing to board in advance due to the first fare penalty ratio in the time scheduling strategy, Figure 7 In (b) is a schematic diagram of the proportion of passengers willing to board in advance due to the first fare reward ratio in the time scheduling strategy, Figure 7 In (c) is Figure 7 In (a) and Figure 7 In (b) is the data fitting curve, Figure 7 In (d) is a schematic diagram of the proportion of passengers willing to board late due to the first fare penalty ratio in the time scheduling strategy, Figure 7 In (e) is a schematic diagram of the proportion of passengers willing to board late due to the second fare reward ratio in the time scheduling strategy, Figure 7 In (f) is Figure 7 In (d) and Figure 7 In (e) is the data fitting curve, Figure 7 In (g) is a schematic diagram of the proportion of passengers willing to change platforms to board due to the second fare penalty ratio in the space scheduling strategy, Figure 7 In (h) is a schematic diagram of the proportion of passengers willing to change platforms to board due to the fare reward ratio in the space scheduling strategy,Figure 7 in (i) is Figure 7 in (g) and Figure 7 the data fitting curve of (h) in Figure 8 is the subway line schematic diagram provided by the embodiment of the present application; wherein, Figure 8 in (a) is the subway line schematic diagram after numbering the platforms according to the subway line and location, Figure 8 in (b) is the subway line schematic diagram based on the fully oriented network; Figure 9 is Figure 8 the supply-demand ratio schematic diagram of each platform in the subway line shown in Figure 10 is the passenger flow situation of Platform 104 before and after adopting Strategies 1, 2, and 3 during the morning peak period at 8:00 and the evening peak period at 18:20 provided by the embodiment of the present application; wherein, Figure 10 in (a) is the passenger flow situation of Platform 104 before and after adopting Strategy 1 during the morning peak period at 8:00, Figure 10 in (b) is the passenger flow situation of Platform 104 before and after adopting Strategy 2 during the morning peak period at 8:00, Figure 10 in (c) is the passenger flow situation of Platform 104 before and after adopting Strategy 3 during the morning peak period at 8:00, Figure 10 in (d) is the passenger flow situation of Platform 104 before and after adopting Strategy 1 during the evening peak period at 18:20, Figure 10 in (e) is the passenger flow situation of Platform 104 before and after adopting Strategy 2 during the evening peak period at 18:20, Figure 10 in (f) is the passenger flow situation of Platform 104 before and after adopting Strategy 3 during the evening peak period at 18:20; Figure 11 is the passenger flow situation of Platform -115 before and after adopting Strategies 1, 2, and 3 during the morning peak period at 8:00 and the evening peak period at 18:20 provided by the embodiment of the present application; wherein, Figure 11 in (a) is the passenger flow situation of Platform -115 before and after adopting Strategy 1 during the morning peak period at 8:00, Figure 11 in (b) is the passenger flow situation of Platform -115 before and after adopting Strategy 2 during the morning peak period at 8:00, Figure 11 in (c) is the passenger flow situation of Platform -115 before and after adopting Strategy 3 during the morning peak period at 8:00, Figure 11 in (d) is the passenger flow situation of Platform -115 before and after adopting Strategy 1 during the evening peak period at 18:20, Figure 11 in (e) is the passenger flow situation of Platform -115 before and after adopting Strategy 2 during the evening peak period at 18:20, Figure 11In (f), it shows the passenger flow situation of Platform -115 before and after adopting Strategy 3 at 18:20 during the evening rush hour; Figure 12 This is the platform supply - demand ratio situation of Platform -257 and Platform -263 before and after adopting Strategies 1, 2, and 3 at 8:00 during the morning rush hour provided by the embodiments of the present application; among them, Figure 12 In (a), it is the platform supply - demand ratio situation of Platform -257 before and after adopting Strategy 1 at 8:00 during the morning rush hour, Figure 12 In (b), it is the platform supply - demand ratio situation of Platform -257 before and after adopting Strategy 2 at 8:00 during the morning rush hour, Figure 12 In (c), it is the platform supply - demand ratio situation of Platform -257 before and after adopting Strategy 3 at 8:00 during the morning rush hour, Figure 12 In (d), it is the platform supply - demand ratio situation of Platform -263 before and after adopting Strategy 1 at 8:00 during the morning rush hour, Figure 12 In (e), it is the platform supply - demand ratio situation of Platform -263 before and after adopting Strategy 2 at 8:00 during the morning rush hour, Figure 12 In (f), it is the platform supply - demand ratio situation of Platform -263 before and after adopting Strategy 3 at 8:00 during the morning rush hour; Figure 13 This is the platform supply - demand ratio situation of Platform 476 and Platform 477 before and after adopting Strategies 1, 2, and 3 at 18:20 during the evening rush hour provided by the embodiments of the present application; among them, Figure 13 In (a), it is the platform supply - demand ratio situation of Platform 476 before and after adopting Strategy 1 at 18:20 during the evening rush hour, Figure 13 In (b), it is the platform supply - demand ratio situation of Platform 476 before and after adopting Strategy 2 at 18:20 during the evening rush hour, Figure 13 In (c), it is the platform supply - demand ratio situation of Platform 476 before and after adopting Strategy 3 at 18:20 during the evening rush hour, Figure 13 In (d), it is the platform supply - demand ratio situation of Platform 477 before and after adopting Strategy 1 at 18:20 during the evening rush hour, Figure 13 In (e), it is the platform supply - demand ratio situation of Platform 477 before and after adopting Strategy 2 at 18:20 during the evening rush hour, Figure 13 In (f), it is the platform supply - demand ratio situation of Platform 477 before and after adopting Strategy 3 at 18:20 during the evening rush hour; Figure 14 This is the passenger flow situation of each platform before and after adopting Strategy 4 during the morning rush hour and the evening rush hour provided by the embodiments of the present application; among them, Figure 14 In (a), it is the passenger flow situation of Platform 104 before and after adopting Strategy 4 at 8:00 during the morning rush hour, Figure 14 In (b), it is the passenger flow situation of Platform 104 before and after adopting Strategy 4 at 18:20 during the evening rush hour,Figure 14 Among them, (c) shows the passenger flow situation of Platform - 257 before and after adopting Strategy Four at 8:00 during the morning peak period. Figure 14 Among them, (d) shows the passenger flow situation of Platform - 263 before and after adopting Strategy Four at 8:00 during the morning peak period. Figure 14 Among them, (e) shows the passenger flow situation of Platform - 115 before and after adopting Strategy Four at 8:00 during the morning peak period. Figure 14 Among them, (f) shows the passenger flow situation of Platform - 115 before and after adopting Strategy Four at 17:20 during the evening peak period. Figure 14 Among them, (g) shows the passenger flow situation of Platform - 476 before and after adopting Strategy Four at 17:40 during the evening peak period. Figure 14 Among them, (h) shows the passenger flow situation of Platform - 477 before and after adopting Strategy Four at 17:40 during the evening peak period. Detailed implementation manners

[0021] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited do not limit the present invention.

[0022] The periodic interference of large passenger flows in the subway station usually occurs during the commuting time. The commuting time refers to the time period when people move back and forth between their residences and destinations for daily activities such as work or study, and it is also one of the periods with the highest urban traffic flow. Therefore, it is a key consideration factor in urban traffic planning and management. Different from other transportation networks, the capacity of the subway platform is much larger than the number of train tickets. It is necessary to consider not only the operator's income but also the congestion degree of the platform.

[0023] Please refer to Figure 1 , Figure 1 as shown in the flow chart of the subway dynamic pricing method provided by this application. This method specifically includes: S10: Obtain a time scheduling strategy based on the first fare reward mechanism for passengers to accept early boarding on the same platform, the second fare reward mechanism for passengers to accept late boarding on the same platform, and the first fare penalty mechanism for passengers not to accept early boarding or late boarding on the same platform.

[0024] S20: Based on the number of passengers at each moment of the platform within the preset time period under the time scheduling strategy, construct the supply - demand ratio equation at each moment of the platform within the preset time period and the supply - demand ratio variance of the platform within the preset time period; with the goal of minimizing the supply - demand ratio variance of the platform within the preset time period, construct the pricing objective function of the time scheduling strategy.

[0025] S30: With the first fare reward ratio under the first fare reward mechanism, the second fare reward ratio under the second fare reward mechanism, and the first fare penalty ratio under the first fare penalty mechanism as constraints, construct the first pricing constraint function of the time scheduling strategy.

[0026] S40: With the total income of the platform within the preset time period under the time scheduling strategy being greater than the total income when the time scheduling strategy is not adopted as the constraint, construct the second pricing constraint function of the time scheduling strategy.

[0027] S50: Solve the pricing objective function, the first pricing constraint function, and the second pricing constraint function of the time scheduling strategy to obtain the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio.

[0028] Specifically, when passenger p is expected to take the subway, some intelligent devices will calculate the nearest subway station for the passenger . Usually, passengers will take the train at the nearest platform according to their own needs. If passengers take the train during the peak period, through the time scheduling strategy, the mechanism of fare rewards and penalties can be used to guide passengers to take the train earlier or later. For example, for passengers who are expected to take the train at platform s at time t, if the passenger accepts to take the train earlier at platform s, their train fare will be rewarded at the first fare reward ratio. Similarly, if the passenger accepts to take the train later at platform s, their train fare will be rewarded at the second fare reward ratio. If the passenger insists on taking the train at platform s at time t, their train fare will be penalized at the first fare penalty ratio. Therefore, the time scheduling strategy provided by this application is based on the different attitudes of passengers towards fare rewards and penalties, thereby guiding passengers to adjust their train-taking time and balancing the supply-demand ratio of platform s in terms of time.

[0029] Furthermore, in step S20, constructing the supply-demand ratio equation for each moment within the preset time period of the platform and the supply-demand ratio variance of the platform within the preset time period based on the number of passengers at each moment of the platform under the time scheduling strategy includes: S200: Based on the number of passengers at each moment of the platform when the time scheduling strategy is not adopted, the proportion of passengers who take the train earlier at the same platform due to the first fare reward mechanism, the proportion of passengers who take the train later at the same platform due to the second fare reward mechanism, the proportion of passengers who take the train earlier due to the first fare penalty mechanism, and the proportion of passengers who take the train later due to the first fare penalty mechanism, obtain the number of passengers at each moment of the platform under the time scheduling strategy.

[0030] Specifically, the number of passengers at each moment of the platform under the time scheduling strategy is expressed as: , where represents the platform under the time scheduling strategy The number of passengers at time; Indicates the number of passengers on the platform when no time scheduling strategy is adopted at time; Indicates the proportion of passengers who board the train in advance on the same platform due to the first fare reward mechanism; Indicates the first fare reward ratio; Indicates the proportion of passengers who board the train late on the same platform due to the second fare reward mechanism; Indicates the second fare reward ratio; Indicates the proportion of passengers who board the train in advance due to the first fare penalty mechanism; Indicates the proportion of passengers who board the train late due to the first fare penalty mechanism; Indicates the first fare penalty ratio.

[0031] S201: Based on the ratio of the number of passengers on the platform at each moment to the number of platforms in the subway station, obtain the supply-demand ratio equation of the platform at each moment.

[0032] Specifically, the supply-demand ratio equation of the platform at each moment is expressed as: , where Indicates the supply-demand ratio equation of the platform at time; Indicates the number of platforms.

[0033] S202: Based on the supply-demand ratio of the platform at each moment within the preset time period, the average supply-demand ratio of the platform within the preset time period, and the duration of the preset time period, construct the supply-demand ratio variance of the platform within the preset time period.

[0034] Specifically, the supply-demand ratio variance of the platform within the preset time period is expressed as: , where Indicates the supply-demand ratio variance of the platform within the preset time period; Indicates the duration of the preset time period.

[0035] Furthermore, this application constructs an objective function with the goal of minimizing the supply-demand ratio variance of the platform within the preset time period, which means that the supply-demand ratio curve of the platform within the preset time period is more stable, thereby improving the service level of the platform in the time dimension; at the same time, with the discount value ranges of the first fare reward mechanism, the second fare reward mechanism, and the first fare penalty mechanism and the better revenue of the operator as constraints, a constraint function is constructed.

[0036] Specifically, the pricing objective function of the time scheduling strategy is expressed as: , Among them, represents the pricing objective function of the time scheduling strategy; represents the variance of the supply-demand ratio of the platform within the preset time period; represents the duration of the preset time period; represents the platform at the supply-demand ratio equation at the moment.

[0037] The first pricing constraint function of the time scheduling strategy is expressed as: , , , Among them, represents the first fare reward ratio; represents the second fare reward ratio; represents the first fare penalty ratio.

[0038] The second pricing constraint function of the time scheduling strategy is expressed as: , Among them, represents the total income of the platform within the preset time period under the time scheduling strategy; represents the total income without adopting the time scheduling strategy; , Among them, represents the total price that passenger p takes the vehicle from platform at time t without adopting the time scheduling strategy; represents the set of passengers; , Among them, represents the number of passengers on the platform at the moment under the time scheduling strategy; represents the total price that passenger p takes the vehicle from platform at time without adopting the time scheduling strategy; the number of passengers on the platform at the moment under the time scheduling strategy; represents the total price that passenger p takes the vehicle from platform at time without adopting the time scheduling strategy; represents the number of passengers on the platform at the moment under the time scheduling strategy; Indicates the total price for passenger p to take the train at the platform at the moment without adopting the time scheduling strategy.

[0039] As Figure 2 shown are several schematic diagrams of adjacent stations of a subway station provided by an embodiment of the present application; among them, Figure 2 (a) in is the first schematic diagram of adjacent stations of a subway station, Figure 2 (b) in is the second schematic diagram of adjacent stations of a subway station, Figure 2 (c) in is the third schematic diagram of adjacent stations of a subway station, Figure 2 (d) in is the fourth schematic diagram of adjacent stations of a subway station, Figure 2 (e) in is the fifth schematic diagram of adjacent stations of a subway station, Figure 2 (f) in is the sixth schematic diagram of adjacent stations of a subway station, Figure 2 (g) in is the seventh schematic diagram of adjacent stations of a subway station, Figure 2 (h) in is the eighth schematic diagram of adjacent stations of a subway station.

[0040] As Figure 3 shown is a schematic diagram of the principle of the time-space scheduling strategy provided by an embodiment of the present application; among them, Figure 3 (a) in is a schematic diagram of the dimensions of the time-space scheduling strategy, Figure 3 (b) in is a schematic diagram of the comparison before and after the time scheduling strategy, Figure 3 (c) in is a schematic diagram of the comparison before and after the space scheduling strategy. It can be seen from Figure 3 (a) in that for the number of passengers at platform s at time t, if a time dimension scheduling strategy is adopted for platform s, the number of passengers at platform s at t - 1 and t + 1 moments will be most affected. Therefore, in constructing the time scheduling strategy of the present application, three adjacent time slots of platform s are selected, and by calculating the number of passengers at the platform in the three adjacent time slots, the total income of platform s in the three adjacent time slots under the time scheduling strategy is calculated. In other embodiments of the present application, the preset time period can also be extended to four, five or other multiple adjacent time slots, and the present application does not make any limitation thereto.

[0041] As Figure 4 shown is a schematic diagram of the boarding behavior of passengers whether to board the train in advance with or without the time scheduling strategy provided by the present application; among them, Figure 4 (a) in is a schematic diagram of the boarding behavior of passengers whether to board the train in advance without adopting the time scheduling strategy, Figure 4Figure (b) in [the figure] is a schematic diagram of the boarding behavior of passengers regarding whether they board the vehicle in advance under the time scheduling strategy. It can be seen from the figure that the first fare reward mechanism and the first fare penalty mechanism under the time scheduling strategy can affect the boarding behavior of passengers, making them willing to depart in advance to avoid the peak period and depart at another time period, such as t - 1, t - 2 or other times, thus reducing the number of passengers boarding the vehicle at time t.

[0042] As Figure 5 shown is a schematic diagram of the boarding behavior of passengers regarding whether they board the vehicle late with or without the time scheduling strategy provided by this application; among them, Figure 5 Figure (a) in [the figure] is a schematic diagram of the boarding behavior of passengers regarding whether they board the vehicle late without adopting the time scheduling strategy, Figure 5 Figure (b) in [the figure] is a schematic diagram of the boarding behavior of passengers regarding whether they board the vehicle late under the time scheduling strategy. It can be seen from the figure that the second fare reward mechanism and the first fare penalty mechanism under the time scheduling strategy can make passengers willing to wait until the peak period ends to board the vehicle, such as departing at t + 1, t + 2 moments, and can also reduce the number of passengers boarding the vehicle at time t.

[0043] Specifically, the embodiments of this application also provide a calculation formula for the number of passengers who choose to board the vehicle in advance or late under the time scheduling strategy: , , where, represents the number of passengers who choose to board the vehicle in advance at platform s under the time scheduling strategy; if passenger p accepts boarding the vehicle in advance under the time scheduling strategy, then , otherwise, ; represents the time when passenger p accepts boarding the vehicle in advance under the time scheduling strategy; represents the start time of the morning peak at platform s; , , where, represents the number of passengers who choose to board the vehicle late at platform s under the time scheduling strategy; if passenger p accepts boarding the vehicle late under the time scheduling strategy, then , otherwise, ; represents the time when passenger p accepts boarding the vehicle late under the time scheduling strategy; represents the end time of the morning peak at platform s.

[0044] In addition, the embodiments of this application also provide a calculation formula for the number of passengers at platform s at t - 1 moment and t + 1 moment under the time scheduling strategy when only considering three adjacent time slots: , , Among them, represents the number of passengers at platform s at the (t - 1)th moment under the time scheduling strategy; represents the number of passengers at platform s at the (t + 1)th moment under the time scheduling strategy.

[0045] Furthermore, specifically, when passenger p expects to take the subway at Some intelligent devices will calculate the nearest subway station for the passenger , and usually the passenger will take the train at the nearest platform according to their own needs. represents the distance between the position of passenger p and the nearest platform. If the platform is in the peak period, the space scheduling strategy can guide passengers to change platforms to take the train through the fare penalty mechanism. Considering the income of the operator, the reward mechanism is not implemented in the space scheduling strategy. For example, for a passenger who expects to take the train at platform s at time t, if the passenger does not accept changing platforms to take the train at time t, the passenger's fare will be penalized at the second fare penalty ratio. The passenger can choose to accept the penalty and take the train as originally planned, or choose to take the train from the next platform to avoid the penalty. Therefore, the space scheduling strategy provided in this application guides passengers to change platforms to take the train based on the passenger's attitude towards the fare penalty, and balances the supply - demand ratio of the platform spatially.

[0046] Specifically, in addition to dynamic pricing in the time dimension, it also includes: S100: Obtain the space scheduling strategy based on the second fare penalty mechanism that passengers do not accept changing platforms within the preset platform at the current moment.

[0047] S200: Based on the number of passengers at each platform within the preset platform at the current moment under the space scheduling strategy, construct the supply - demand ratio equation for each platform within the preset platform at the current moment and the supply - demand ratio variance of the preset platform at the current moment; with the goal of minimizing the supply - demand ratio variance of the preset platform at the current moment, construct the pricing objective function of the space scheduling strategy.

[0048] S300: With the value of the second fare penalty ratio under the second fare penalty mechanism as the constraint, construct the pricing constraint function of the space scheduling strategy.

[0049] S400: Solve the pricing objective function and the constraint function of the space scheduling strategy to obtain the second fare penalty ratio.

[0050] Furthermore, in step S200, based on the number of passengers at each platform within the preset platform at the current moment under the space scheduling strategy, constructing the supply - demand ratio equation for each platform within the preset platform at the current moment and the supply - demand ratio variance of the preset platform at the current moment includes: S201: Obtain the number of passengers at each platform within the preset platform at the current moment under the spatial scheduling strategy based on the number of passengers at each platform within the preset platform at the current moment without adopting the spatial scheduling strategy and the proportion of passengers who change platforms to take the train due to the second fare penalty mechanism after adopting the spatial scheduling strategy.

[0051] Specifically, the number of passengers at each platform within the preset platform at the current moment under the spatial scheduling strategy is expressed as: , , where, represents the number of passengers at platform at moment under the spatial scheduling strategy; represents the number of passengers at platform at moment without adopting the spatial scheduling strategy; represents the proportion of passengers who change platforms to take the train due to the second fare penalty mechanism; represents the second fare penalty ratio; represents the number of passengers at the adjacent platform to platform at moment under the spatial scheduling strategy; represents the number of passengers at platform at moment without adopting the spatial scheduling strategy.

[0052] S202: Obtain the supply-demand ratio equation for each platform within the preset platform at the current moment based on the ratio of the number of passengers at each platform within the preset platform at the current moment to the number of platforms in the subway station.

[0053] Specifically, the supply-demand ratio equation for each platform within the preset platform at the current moment is expressed as: , where, represents the supply-demand ratio equation for platform at moment represents the number of platforms.

[0054] S203: Construct the supply-demand variance of the preset platform at the current moment based on the supply-demand ratio of each platform within the preset platform at the current moment, the average supply-demand ratio of the preset platform at the current moment, and the number of preset platforms.

[0055] Specifically, the supply-demand variance of the preset platform at the current moment is expressed as: , where, represents The variance of the supply-demand ratio of the preset platform at a moment; Indicates the number of preset platforms.

[0056] Furthermore, similar to the time dimension, the present application constructs an objective function with the goal of minimizing the variance of the supply-demand ratio of the preset platform at time t, which means that the supply-demand ratio curves of multiple platforms at time t are more stable, thereby improving the service level of the platforms in the spatial dimension; at the same time, a constraint function is constructed with the discount value range of the second fare penalty mechanism as the constraint.

[0057] Specifically, the pricing objective function of the spatial scheduling strategy is expressed as: , Among them, Indicates the pricing objective function of the spatial scheduling strategy; Indicates The variance of the supply-demand ratio of the preset platform at time t; Indicates the number of preset platforms; Indicates The supply-demand ratio equation of platform at time t; The pricing constraint function of the spatial scheduling strategy is expressed as: , Among them, Indicates the second fare penalty ratio.

[0058] It can be seen from (c) in Figure 3 that for the number of passengers boarding at platform s at time t, if a spatial dimension scheduling strategy is adopted for platform s, the number of passengers at platforms s-1 and s+1 at time t will be most affected. Therefore, in constructing the spatial scheduling strategy, the present application selects three adjacent platforms, calculates the number of passengers of the three adjacent platforms, and thus calculates the total revenue of the three adjacent platforms at time t under the spatial scheduling strategy. In other embodiments of the present application, the preset platforms can also be set to four, five or other multiple adjacent platforms, and the present application does not limit this.

[0059] As Figure 6 shows, it is a schematic diagram of the boarding behavior of passengers whether to change platforms when there is or without a spatial scheduling strategy provided by the present application; among them, Figure 6 in (a) is a schematic diagram of the boarding behavior of passengers whether to change platforms when no spatial scheduling strategy is adopted, Figure 6 in (b) is a schematic diagram of the boarding behavior of passengers whether to change platforms under the spatial scheduling strategy. It can be seen from the figure that the second fare penalty mechanism under the spatial scheduling strategy can make passengers willing to change platforms to board, for example, departing from platform s-1 or platform s+1, so that the number of passengers boarding at platform s at time t can be reduced.

[0060] Specifically, the embodiment of the present application further provides a calculation formula for the number of passengers choosing to transfer platforms under the spatial scheduling strategy: , , wherein, represents the number of passengers choosing to transfer platforms under the spatial scheduling strategy; if passenger p accepts to transfer platforms for boarding under the spatial scheduling strategy, then , otherwise, ; represents the distance between passenger p and the recommended platform ; represents the maximum distance that passenger p is willing to walk under the spatial scheduling strategy.

[0061] In addition, the embodiment of the present application further provides the total income of the preset platform under the spatial scheduling strategy and the total income of the preset platform without adopting the spatial scheduling strategy when only considering three adjacent platforms: , , wherein, represents the total income of the preset platform under the spatial scheduling strategy; represents the number of passengers on platform s - 1 at time t under the spatial scheduling strategy; represents the total price for passenger p to board from platform at time without adopting the spatial scheduling strategy; represents the number of passengers on platform s at time t under the spatial scheduling strategy; represents the proportion of passengers who transfer platforms for boarding due to the second fare penalty mechanism; represents the total price for passenger p to board from platform at time without adopting the spatial scheduling strategy; represents the number of passengers on platform s + 1 at time t under the spatial scheduling strategy; represents the total price for passenger p to board from platform s + 1 at time t without adopting the spatial scheduling strategy; represents the total income of the preset platform without adopting the spatial scheduling strategy.

[0062] The embodiments of this application also conducted a research on passengers' preferences for different scheduling strategies to evaluate whether passengers have different attitudes towards different scheduling strategies. This questionnaire survey was released on a certain platform (www.wjx.cn). The time range of the questionnaire survey was from November 4, 2024, to December 23, 2024, and a total of 546 responses were received. Among them, responses completed within 20 seconds were discarded. In addition, respondents who had never taken the subway were excluded because they might not understand the subway itinerary arrangement method. Finally, 519 valid samples were retained. Table 1 shows the questions of the questionnaire survey and the response data for each question in the valid samples: Table 1

[0063] From the data in Table 1, it can be seen that men accounted for 49.71% of the samples, 52.6% of the passengers lived in cities with a passenger flow intensity greater than 0.7, and 91.71% of the passengers had experienced crowded platforms. In addition, whether it is a reward or a punishment, passengers tend to prefer the early boarding strategy. More than 35% of the passengers also accept all strategies. And the advance or delay time is generally within 20 minutes, and the distance from the terminal platform willing to adjust is within 2000 meters.

[0064] As Figure 7 shown is the attitude of passengers towards different scheduling strategies. Among them, Figure 7 in (a) is a schematic diagram of the proportion of passengers willing to accept early boarding due to the first fare penalty ratio in the time scheduling strategy, Figure 7 in (b) is a schematic diagram of the proportion of passengers willing to accept early boarding due to the first fare reward ratio in the time scheduling strategy, Figure 7 in (c) is Figure 7 the data fitting curve of (a) in Figure 7 and (b) in Figure 7 in (d) is a schematic diagram of the proportion of passengers willing to accept delayed boarding due to the first fare penalty ratio in the time scheduling strategy, Figure 7 in (e) is a schematic diagram of the proportion of passengers willing to accept delayed boarding due to the second fare reward ratio in the time scheduling strategy, Figure 7 in (f) is Figure 7 the data fitting curve of (d) in Figure 7 and (e) in Figure 7 in (g) is a schematic diagram of the proportion of passengers willing to accept changing platforms to board due to the second fare penalty ratio in the space scheduling strategy, Figure 7 in (h) is a schematic diagram of the proportion of passengers willing to accept changing platforms to board due to the fare reward ratio in the space scheduling strategy, Figure 7 in (i) is Figure 7 the data fitting curve of (g) in Figure 7The data fitting curve of (h) in; wherein, when the ratio of the scheduled price to the original price is less than 1, it indicates that there is a reward mechanism; when the ratio of the current price to the original price is greater than 1, it indicates that there is a penalty mechanism.

[0065] Combined with Table 1 and Figure 7 From the data in, it can be seen that different levels of rewards or penalties lead to different proportions of passengers accepting the discounts; however, for the highest rewards and the lowest penalties, there may be some irrational choices. In the questionnaire about the three strategy preferences under the reward mechanism, 43.2% of the respondents chose two or more of the highest rewards; similarly, in the questionnaire about the preferences under the penalty mechanism, 42.2% of the participants chose two or more of the lowest penalties; therefore, the data of price advantages can be excluded or it can be considered that these passengers will not change their travel schedules due to price changes. In addition, passengers are often less sensitive to low-level rewards. Considering the operating income and expenses of the subway operating company, the present application believes that a penalty mechanism can be implemented for the subway system.

[0066] Since the results of the questionnaire survey are data points of different prices, only the general trends and changes between the data points can be obtained; in addition, due to the randomness of the samples, after trying and comparing various curve fitting methods, the present application finally adopted the curve with the best fitting effect, aiming to weaken the random fluctuations in the data and more clearly highlight the trends behind the data.

[0067] The following verifies the effectiveness of the subway dynamic pricing method provided by the present application through specific examples: The data collected from a certain subway (HZM) system in 2019 in this embodiment is used as a case study to verify the proposed scheduling method. The data set is collected using the 24-hour timekeeping method based on Beijing time and describes the passenger flow during the subway operation from 6:00 am to 11:00 pm on January 2nd.

[0068] This embodiment found according to the results of the questionnaire survey that: 10 minutes is the most common preferred time for trip adjustment. Therefore, in order to facilitate passenger flow scheduling within a specific time period, this embodiment uses ten-minute time periods for discretization. In addition, shorter time intervals are considered more beneficial during peak hours. It is worth noting that HZM trains usually consist of 6 carriages, and passengers queue near the doors, so they gather within an area of about 60 square meters from the platform. Further, usually four to five passengers can be accommodated per square meter, and seven to ten passengers can be accommodated per square meter in crowded situations; therefore, The maximum value of is 600.

[0069] As Figure 8 shown is the subway line schematic diagram in this embodiment; wherein, Figure 8Among them, (a) is a subway line schematic diagram after numbering the platforms according to the subway line and location. Figure 8 Among them, (b) is a subway line schematic diagram based on a fully oriented network, where both the platforms and the tracks are oriented.

[0070] According to the statistics of the platforms with the highest inbound passenger flow in 102 time periods every day, the frequencies of platforms 104 and -115 on Line 1, -257 and -263 on Line 2, and 476 and 477 on Line 4 are the highest. Therefore, in this embodiment, these six platforms during two peak time periods are selected for analysis. Specifically, the supply-demand ratio based on the platform is as Figure 9 shown. In addition, it can be seen from Figure 9 that platforms -257 and -263 on Line 2 are only congested during the morning peak period, while platforms 466 and 467 on Line 4 are only congested during the evening peak period. Therefore, in this embodiment, the specific congestion periods of these platforms are analyzed. The corresponding time represents the total passenger flow within the next 10 minutes. For example, the supply-demand ratio based on the platform at 8:00 represents the ratio from 8:00 to 8:10. In order to explore the scheduling strategies applicable to each platform, different observation indicators are adopted for specific time slots of the platform, including the service level (platform supply-demand ratio) and the total operator revenue. For the convenience of subsequent explanation, the scheduling strategies in this embodiment are marked as the following several types: Strategy 1: The combination of the early boarding strategy and the delayed boarding strategy based on the time scheduling strategy; Strategy 2: The early boarding strategy based on the time scheduling strategy; Strategy 3: The delayed boarding strategy based on the time scheduling strategy; Strategy 4: The strategy of changing the boarding platform based on the space scheduling strategy.

[0071] In addition, the number of passengers accepting this strategy is random among the total number of passengers, which means that the price change is random. Under the penalty mechanism, the revenue is definitely greater than the original revenue.

[0072] The time dimension strategy and the space dimension strategy aim to find the optimal price and the corresponding proportion of passengers accepting the offer. By traversing the fitted passenger preference curve and aiming to maximize the service level, the optimal price will be obtained, and then the total passenger revenue of all platforms and time periods involved in this strategy will be calculated.

[0073] As shown in Table 2 is the time dimension strategy selection algorithm provided in this embodiment: Table 2

[0074] As shown in Table 3 is the space dimension strategy selection algorithm provided in this embodiment: Table 3

[0075] Specifically, in the time dimension, Strategies One, Two, and Three are adopted during the peak hours at the research platform, and the corresponding metrics are compared with those before the implementation of the strategies. In the space dimension, Strategy Four will be implemented at the research platform, and the corresponding metrics will be compared with those before the implementation of the strategy. At the same time, the same platform is selected in both the time and space dimensions, and the high passenger flow period during the peak hours is selected for the research. For the convenience of recording, in the following charts, the platform will be represented by the letter P and the platform number. For example, P104 represents Platform 104.

[0076] As Figure 10 shown are the passenger flow situations at Platform 104 before and after adopting Strategies One, Two, and Three at 8:00 during the morning peak hours and 18:20 during the evening peak hours; among them, Figure 10 in (a) is the passenger flow situation at Platform 104 before and after adopting Strategy One at 8:00 during the morning peak hours, Figure 10 in (b) is the passenger flow situation at Platform 104 before and after adopting Strategy Two at 8:00 during the morning peak hours, Figure 10 in (c) is the passenger flow situation at Platform 104 before and after adopting Strategy Three at 8:00 during the morning peak hours, Figure 10 in (d) is the passenger flow situation at Platform 104 before and after adopting Strategy One at 18:20 during the evening peak hours, Figure 10 in (e) is the passenger flow situation at Platform 104 before and after adopting Strategy Two at 18:20 during the evening peak hours, Figure 10 in (f) is the passenger flow situation at Platform 104 before and after adopting Strategy Three at 18:20 during the evening peak hours.

[0077] As Figure 11 shown are the passenger flow situations at Platform -115 before and after adopting Strategies One, Two, and Three at 8:00 during the morning peak hours and 18:20 during the evening peak hours; among them, Figure 11 in (a) is the passenger flow situation at Platform -115 before and after adopting Strategy One at 8:00 during the morning peak hours, Figure 11 in (b) is the passenger flow situation at Platform -115 before and after adopting Strategy Two at 8:00 during the morning peak hours, Figure 11 in (c) is the passenger flow situation at Platform -115 before and after adopting Strategy Three at 8:00 during the morning peak hours, Figure 11 in (d) is the passenger flow situation at Platform -115 before and after adopting Strategy One at 18:20 during the evening peak hours, Figure 11 in (e) is the passenger flow situation at Platform -115 before and after adopting Strategy Two at 18:20 during the evening peak hours, Figure 11 in (f) is the passenger flow situation at Platform -115 before and after adopting Strategy Three at 18:20 during the evening peak hours.

[0078] Table 4 shows the service level and total revenue data before and after adopting Strategies One, Two, and Three at Platforms 104 and -115: Table 4

[0079] From the data in Table 4, it can be seen that implementing Strategy Two at 8:00 on Platform 104 can significantly improve the service level and overall revenue. Specifically, the service level has increased by 12.5% compared to the original, and the total revenue for three adjacent time slots has increased from 2,885 yuan to 6,468 yuan. However, the results during the evening peak period show that the original service level is the highest. Combining Figure 10 it can be seen that although the passenger flow during the evening peak period is quite high, it is relatively stable, indicating that when there are significant differences in passenger flow between adjacent time slots, the scheduling strategy based on the time dimension is the most effective. Additionally, combining Figure 11 with Table 3, it can be seen that the experimental results of the three strategies implemented at Platform -115 show a similar pattern to that of Platform 104: during the morning peak period, Strategy Two is still the most effective, with the service level increasing from 16.37 to 217.39, and the total revenue for three adjacent time slots increasing from 3,522 yuan to 9,902 yuan; however, during the evening peak period, the service level is still the best under the original conditions. From Figure 11 it can be seen that the passenger flow during the evening peak period remains relatively stable, further confirming the previous hypothesis. Therefore, the following conclusion can be drawn from this embodiment: in order to improve the service level during these periods, the duration of the front and back time slots can be extended.

[0080] As Figure 12 shown, the platform supply-demand ratio before and after adopting Strategies One, Two, and Three at 8:00 during the morning peak period for Platforms -257 and -263; among them, Figure 12 in (a) is the platform supply-demand ratio of Platform -257 before and after adopting Strategy One at 8:00 during the morning peak period, Figure 12 in (b) is the platform supply-demand ratio of Platform -257 before and after adopting Strategy Two at 8:00 during the morning peak period, Figure 12 in (c) is the platform supply-demand ratio of Platform -257 before and after adopting Strategy Three at 8:00 during the morning peak period, Figure 12 in (d) is the platform supply-demand ratio of Platform -263 before and after adopting Strategy One at 8:00 during the morning peak period, Figure 12 in (e) is the platform supply-demand ratio of Platform -263 before and after adopting Strategy Two at 8:00 during the morning peak period, Figure 12 in (f) is the platform supply-demand ratio of Platform -263 before and after adopting Strategy Three at 8:00 during the morning peak period.

[0081] Table 5 shows the service levels and total revenue data before and after adopting Strategies 1, 2, and 3 at Platforms -257 and -263: Table 5

[0082] Combined with Figure 12 the data in Table 5, it can be seen that the optimal scheduling strategy for Platform -257 is Strategy 2, which only selects the premium ride strategy. The service level of Platform -257 is 434.78, and the total revenue within three time slots reaches 14,094 yuan. However, Platform -263 is not suitable for any time - dimension strategy, which may be due to the high sensitivity of passengers to the penalty mechanism, and a small increase in price may cause many people to change their travel plans.

[0083] As Figure 13 shown, the following are the platform supply - demand ratios of Platforms 476 and 477 before and after adopting Strategies 1, 2, and 3 at 18:20 during the evening peak period; among them, Figure 13 in (a) is the platform supply - demand ratio of Platform 476 before and after adopting Strategy 1 at 18:20 during the evening peak period, Figure 13 in (b) is the platform supply - demand ratio of Platform 476 before and after adopting Strategy 2 at 18:20 during the evening peak period, Figure 13 in (c) is the platform supply - demand ratio of Platform 476 before and after adopting Strategy 3 at 18:20 during the evening peak period, Figure 13 in (d) is the platform supply - demand ratio of Platform 477 before and after adopting Strategy 1 at 18:20 during the evening peak period, Figure 13 in (e) is the platform supply - demand ratio of Platform 477 before and after adopting Strategy 2 at 18:20 during the evening peak period, Figure 13 in (f) is the platform supply - demand ratio of Platform 477 before and after adopting Strategy 3 at 18:20 during the evening peak period.

[0084] Table 6 shows the service levels and total revenue data of Platforms 476 and 477 before and after adopting Strategies 1, 2, and 3: Table 6

[0085] Combined with Figure 13 the data in Table 6, it can be seen that the best case for Platforms 476 and 477 is to adopt Strategy 2, that is, the early - ride strategy; under this strategy, the service levels θ of Platforms 476 and 477 are 4.05×10^6 and 2.2×10^4 respectively, and the total revenues within three time slots are 10,145 yuan and 8,325 yuan respectively.

[0086] As Figure 14Shown are the passenger flow conditions at each platform before and after adopting Strategy Four during the morning peak and evening peak hours; among them, Figure 14 in (a) is the passenger flow condition at Platform 104 before and after adopting Strategy Four at 8:00 during the morning peak hour, Figure 14 in (b) is the passenger flow condition at Platform 104 before and after adopting Strategy Four at 18:20 during the evening peak hour, Figure 14 in (c) is the passenger flow condition at Platform -257 before and after adopting Strategy Four at 8:00 during the morning peak hour, Figure 14 in (d) is the passenger flow condition at Platform -263 before and after adopting Strategy Four at 8:00 during the morning peak hour, Figure 14 in (e) is the passenger flow condition at Platform -115 before and after adopting Strategy Four at 8:00 during the morning peak hour, Figure 14 in (f) is the passenger flow condition at Platform -115 before and after adopting Strategy Four at 17:20 during the evening peak hour, Figure 14 in (g) is the passenger flow condition at Platform 476 before and after adopting Strategy Four at 17:40 during the evening peak hour, Figure 14 in (h) is the passenger flow condition at Platform 477 before and after adopting Strategy Four at 17:40 during the evening peak hour.

[0087] As shown in Table 7 are the service level and total revenue data of Platforms 104 and -115 before and after adopting Strategy Four: Table 7

[0088] As shown in Table 8 are the service level and total revenue data of Platforms -257 and -263 before and after adopting Strategy Four: Table 8

[0089] As shown in Table 9 are the service level and total revenue data of Platforms 476 and 477 before and after adopting Strategy Four: Table 9

[0090] Through Figure 14It can be seen from the data in Tables 7 to 9 that after adopting Strategy Four, the service level and revenue of Platform 1 (Platform 104 and Platform -115) are higher than before. Among them, the service level of Platform -115 during the morning peak period after adopting Strategy Four is 178.57, and the revenue of Platform -114, Platform -115, and Platform -116 reaches 7,618 yuan. It can be seen that the application of the space scheduling strategy is more common; among the two platforms on Line 2 (Platform -257 and Platform -263) and the two platforms on Line 4 (Platform 476 and Platform 477), Platform -263 and Platform 476 are not suitable for the space dimension scheduling strategy, and the effect has not improved after adopting this strategy. Specifically, from Figure 14 it can be seen that passengers are too sensitive to the penalty mechanism, resulting in many passengers changing their trips after the implementation of this strategy. At the same time, it can be seen that due to the significant supply-demand ratio between adjacent platforms, the space scheduling strategy improves the performance of Platform -257 and Platform 477. The service level of Platform -257 is 2,500, and the total revenue of Platform -256, Platform -257, and Platform -258 is 9,441 yuan, while the service level of Platform 477 is 66.67, and the revenue of Platform 476, Platform 477, and Platform 478 is 6,686 yuan.

[0091] The embodiment of the present application also provides a subway dynamic pricing device, which includes: A time scheduling strategy construction module 10, configured to obtain a time scheduling strategy based on a first fare reward mechanism for passengers to accept early boarding on the same platform, a second fare reward mechanism for passengers to accept delayed boarding on the same platform, and a first fare penalty mechanism for passengers not to accept early boarding or delayed boarding on the same platform.

[0092] A time scheduling pricing objective function construction module 20, configured to construct a supply-demand ratio equation for each moment of the platform within a preset period and a supply-demand ratio variance of the platform within a preset period based on the number of passengers at each moment of the platform within a preset period under the time scheduling strategy; and construct a pricing objective function of the time scheduling strategy with the goal of minimizing the supply-demand ratio variance of the platform within a preset period.

[0093] A time scheduling first pricing constraint function construction module 30, configured to construct a first pricing constraint function of the time scheduling strategy with the value ranges of the first fare reward ratio under the first fare reward mechanism, the second fare reward ratio under the second fare reward mechanism, and the first fare penalty ratio under the first fare penalty mechanism as constraints.

[0094] A time scheduling second pricing constraint function construction module 40, configured to construct a second pricing constraint function of the time scheduling strategy with the constraint that the total revenue of the platform within a preset period under the time scheduling strategy is greater than the total revenue when the time scheduling strategy is not adopted.

[0095] A time scheduling pricing acquisition module 50 is configured to solve a pricing objective function, a first pricing constraint function, and a second pricing constraint function of a time scheduling policy, so as to obtain a first fare reward ratio, a second fare reward ratio, and a first fare penalty ratio.

[0096] An embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned subway dynamic pricing method are implemented.

[0097] In summary, the present application firstly introduces a dynamic pricing mechanism considering time and space into the subway operation system, analyzes the passenger flow changes in adjacent time slots of the platform from the time perspective, and analyzes the passenger flow changes between adjacent platforms from the space perspective. It not only balances the supply-demand ratio of the subway platform in time and space, improves the platform service level, but also increases the operator's revenue, thereby improving the overall resource efficiency of the subway on a wider scale.

[0098] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0099] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowcharts and / or block diagrams, and the combination of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0100] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0101] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable apparatus to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one process or multiple processes and / or blocks Figure 1 one process or multiple processes and / or blocks Figure 1 or steps for implementing the functions specified in one block or multiple blocks.

[0102] Obviously, the above-described embodiments are merely examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. And the obvious changes or modifications derived therefrom still fall within the protection scope of the present invention.

Claims

1. A subway dynamic pricing method, characterized in that, Including: Obtaining a time scheduling strategy based on a first fare reward mechanism for passengers accepting early boarding at the same platform, a second fare reward mechanism for passengers accepting delayed boarding at the same platform, and a first fare penalty mechanism for passengers not accepting early or delayed boarding at the same platform; Based on the number of passengers at each moment within a preset time period under the time scheduling strategy, constructing a supply-demand ratio equation for each moment within the preset time period at the platform and a variance of the supply-demand ratio at the platform within the preset time period; Taking the minimization of the variance of the supply-demand ratio at the platform within the preset time period as the objective, constructing a pricing objective function for the time scheduling strategy; Taking the values of the first fare reward ratio under the first fare reward mechanism, the second fare reward ratio under the second fare reward mechanism, and the first fare penalty ratio under the first fare penalty mechanism as constraints, constructing a first pricing constraint function for the time scheduling strategy; Taking the total revenue at the platform within the preset time period under the time scheduling strategy being greater than the total revenue without adopting the time scheduling strategy as a constraint, constructing a second pricing constraint function for the time scheduling strategy; Solving the pricing objective function, the first pricing constraint function, and the second pricing constraint function of the time scheduling strategy to obtain the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio.

2. The subway dynamic pricing method according to claim 1, wherein Based on the number of passengers at each moment within a preset time period under the time scheduling strategy, constructing a supply-demand ratio equation for each moment within the preset time period at the platform and a variance of the supply-demand ratio at the platform within the preset time period includes: Based on the number of passengers at each moment within the preset time period at the platform without adopting the time scheduling strategy, the proportion of passengers boarding early at the same platform due to the first fare reward mechanism after adopting the time scheduling strategy, the proportion of passengers boarding late at the same platform due to the second fare reward mechanism, the proportion of passengers boarding early due to the first fare penalty mechanism, and the proportion of passengers boarding late due to the first fare penalty mechanism, obtaining the number of passengers at the platform at each moment under the time scheduling strategy; Based on the ratio of the number of passengers at each moment at the platform to the number of platforms at the platform within the subway station, obtaining the supply-demand ratio equation for each moment at the platform; Based on the supply-demand ratio at each moment within the preset time period at the platform, the average value of the supply-demand ratio at the platform within the preset time period, and the duration of the preset time period, constructing the variance of the supply-demand ratio at the platform within the preset time period.

3. The subway dynamic pricing method according to claim 2, wherein The number of passengers at the platform at each moment under the time scheduling strategy is expressed as: ， Among them, represents the number of passengers on the platform under the time scheduling strategy at moment; represents the number of passengers on the platform when the time scheduling strategy is not adopted at moment; represents the proportion of passengers who board the train in advance on the same platform due to the first fare reward mechanism; represents the first fare reward ratio; represents the proportion of passengers who board the train later on the same platform due to the second fare reward mechanism; represents the second fare reward ratio; represents the proportion of passengers who board the train in advance due to the first fare penalty mechanism; represents the proportion of passengers who board the train later due to the first fare penalty mechanism; represents the first fare penalty ratio; The supply-demand ratio equation for each moment at the platform is expressed as: ， Among them, represents the platform at the supply-demand ratio equation at the moment; represents the number of platforms; The variance of the supply-demand ratio at the platform within the preset time period is expressed as: ， Among them, represents the variance of the supply-demand ratio of the platform within a preset time period; represents the duration of the preset time period.

4. The subway dynamic pricing method according to claim 1, wherein The pricing objective function of the time scheduling strategy is expressed as: ， Among them, represents the pricing objective function of the time scheduling strategy; represents the variance of the supply-demand ratio of the platform within the preset time period; represents the duration of the preset time period; represents the platform at the supply-demand ratio equation at the moment; The first pricing constraint function of the time scheduling strategy is expressed as: ， ， ， Among them, represents the first fare reward ratio; represents the second fare reward ratio; represents the first fare penalty ratio; The second pricing constraint function of the time scheduling strategy is expressed as: ， Among them, represents the total income of the platform within a preset time period under the time scheduling strategy; represents the total income when the time scheduling strategy is not adopted; ， Among them, represents the total price of passenger p taking the train at time t from the platform without adopting a time scheduling strategy; the total price of taking the train; represents the set of passengers; ， Among them, represents the number of passengers on the platform under the time scheduling strategy at moment; represents the total price for passenger p to take the train from the platform at moment when the time scheduling strategy is not adopted; the number of passengers on the platform under the time scheduling strategy at moment; represents the total price for passenger p to take the train from the platform at moment when the time scheduling strategy is not adopted; the number of passengers on the platform under the time scheduling strategy at moment; represents the total price for passenger p to take the train.

5. The subway dynamic pricing method according to claim 1, wherein Also including: Obtaining a space scheduling strategy based on a second fare penalty mechanism for passengers not accepting platform transfer within the preset platform at the current moment; Based on the number of passengers at each platform within the preset platform at the current moment under the space scheduling strategy, constructing a supply-demand ratio equation for each platform within the preset platform at the current moment and a variance of the supply-demand ratio of the preset platform at the current moment; Taking the minimization of the variance of the supply-demand ratio of the preset platform at the current moment as the objective, constructing a pricing objective function for the space scheduling strategy; Taking the value of the second fare penalty ratio under the second fare penalty mechanism as a constraint, constructing a pricing constraint function for the space scheduling strategy; Solve the pricing objective function and constraint function of the space scheduling strategy to obtain the second fare penalty ratio.

6. The subway dynamic pricing method according to claim 5, characterized in that, Based on the number of passengers at each platform within the preset platform at the current moment under the space scheduling strategy, construct the supply-demand ratio equation for each platform within the preset platform at the current moment and the variance of the supply-demand ratio of the preset platform at the current moment, including: Based on the number of passengers at each platform within the preset platform at the current moment without the space scheduling strategy and the proportion of passengers who change platforms to take the train due to the second fare penalty mechanism at the current moment after the space scheduling strategy is adopted, obtain the number of passengers at each platform within the preset platform at the current moment under the space scheduling strategy; Based on the ratio of the number of passengers at each platform within the preset platform at the current moment to the number of platforms in the subway station, obtain the supply-demand ratio equation for each platform within the preset platform at the current moment; Based on the supply-demand ratio of each platform within the preset platform at the current moment, the average value of the supply-demand ratio of the preset platform at the current moment, and the number of preset platforms, construct the variance of the supply-demand ratio of the preset platform at the current moment.

7. The subway dynamic pricing method according to claim 6, wherein, The number of passengers at each platform within the preset platform at the current moment under the space scheduling strategy is expressed as: ， ， Among them, represents the number of passengers on the platform at a certain moment under the space scheduling strategy; The number of passengers; represents the number of passengers on the platform at a certain moment when the space scheduling strategy is not adopted; The number of passengers; represents the proportion of passengers who change platforms to take the train due to the second fare penalty mechanism; represents the second fare penalty ratio; represents the number of passengers on the platform adjacent to the platform at a certain moment under the space scheduling strategy; The number of passengers; represents the number of passengers on the platform at a certain moment when the space scheduling strategy is not adopted; The number of passengers; The supply-demand ratio equation for each platform within the preset platform at the current moment is expressed as: ， Among them, represents the supply-demand ratio equation of the platform at a certain moment ; represents the number of platforms; The variance of the supply-demand ratio of the preset platform at the current moment is expressed as: ， Among them, represents the variance of the supply-demand ratio of the preset platform at a certain moment; represents the number of preset platforms.

8. The subway dynamic pricing method according to claim 5, characterized in that, The pricing objective function of the space scheduling strategy is expressed as: ， Among them, represents the pricing objective function of the space scheduling strategy; represents the variance of the supply-demand ratio of the preset platform at time represents the number of preset platforms; represents the supply-demand ratio equation of platform at time The pricing constraint function of the space scheduling strategy is expressed as: ， Among them, represents the second ticket price penalty ratio.

9. A subway dynamic pricing device, characterized in that, Including: A time scheduling strategy construction module for obtaining the time scheduling strategy based on the first fare reward mechanism for passengers to accept early boarding at the same platform, the second fare reward mechanism for passengers to accept delayed boarding at the same platform, and the first fare penalty mechanism for passengers not to accept early boarding or delayed boarding at the same platform; A time scheduling pricing objective function construction module for constructing the supply-demand ratio equation for each moment within the preset time period of the platform and the variance of the supply-demand ratio of the platform within the preset time period based on the number of passengers at each moment within the preset time period of the platform under the time scheduling strategy; Construct the pricing objective function of the time scheduling strategy with the goal of minimizing the variance of the supply-demand ratio of the platform within the preset time period; A time scheduling first pricing constraint function construction module for constructing the first pricing constraint function of the time scheduling strategy with the values of the first fare reward ratio under the first fare reward mechanism, the second fare reward ratio under the second fare reward mechanism, and the first fare penalty ratio under the first fare penalty mechanism as constraints; A time scheduling second pricing constraint function construction module for constructing the second pricing constraint function of the time scheduling strategy with the constraint that the total income of the platform within the preset time period under the time scheduling strategy is greater than the total income without the time scheduling strategy; A time scheduling pricing acquisition module for solving the pricing objective function, the first pricing constraint function, and the second pricing constraint function of the time scheduling strategy to obtain the first fare reward ratio, the second fare reward ratio, and the first fare penalty ratio.

10. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the subway dynamic pricing method according to any one of claims 1 to 8 are implemented.

Images