A method for dispatching shuttle buses during rail transit flow-limited operation

Abstract

The present invention discloses a method for scheduling shuttle buses during rail transit flow-limited operation, comprising: constructing a shuttle bus candidate route generation model, obtaining a set of shuttle bus candidate routes based on the shuttle bus candidate route generation model; constructing a joint decision-making model for shuttle bus route plans and departure frequencies, linearizing the joint decision-making model for shuttle bus route plans and departure frequencies; and solving the linearized model to obtain a shuttle bus route layout plan and the departure frequencies of each route. The present invention discloses a shuttle bus configuration and scheduling method that considers passenger travel preferences, station service capabilities, and the balance of interests between passengers and enterprises during rail transit flow-limited operation, providing decision-making support for bus companies in planning and operating shuttle bus routes.

Description

Technical Field

[0001] The present invention belongs to the technical field of public transportation, and in particular relates to a shuttle bus dispatching method during rail transit current-limited operation. Background Art

[0002] With the rapid development and network operation of urban rail transit systems, rail transit passenger volume continues to grow, and the network's operating load is increasing. Some lines are already operating in an oversaturated state during peak passenger flow periods. To alleviate platform and carriage congestion and ensure line safety, cities such as Beijing, Shanghai, and Shenzhen have implemented regular passenger flow control strategies at some high-traffic rail transit stations. However, flow control measures cannot fundamentally resolve the mismatch between supply and demand in the rail transit system and may significantly increase travel time for some passengers, reducing the service quality and attractiveness of public transportation. Therefore, to effectively alleviate the supply-demand imbalance of rail transit during peak passenger flow periods and prevent rail transit passengers from switching to individual transportation modes, it is necessary to study the coordinated operation of rail transit and shuttle buses. Using shuttle buses, passengers at restricted stations can be transported to nearby unrestricted stations. This can balance passenger flow distribution within the rail transit network, fully leverage the shuttle bus's function in alleviating rail transit passenger flow, and enhance the overall transportation capacity of the public transportation system.

[0003] Given the rail transit network and the temporal and spatial distribution of passenger flow, how to configure feeder bus services to quickly relieve the accumulation of stranded passengers at rail transit flow-restricted stations is a complex planning decision-making problem that requires comprehensive consideration of factors such as line layout, departure frequency, and fleet size. Existing studies have mostly discussed emergency bus scheduling methods around the evacuation of stranded passengers in the context of rail transit accidents. However, the research results related to emergency bus scheduling cannot be directly applied to the problem of feeder bus scheduling during rail transit flow-restricted operation. This is mainly because: (1) When rail transit service is interrupted, stranded passengers must first use other modes of transportation to leave, while rail transit flow-restricted operation requires consideration of passengers' acceptance of the "feeder bus + rail transit" combination travel mode and their travel choice preferences; (2) When dispatching emergency buses, the goal is to evacuate stranded passengers as quickly as possible, and the impact on the service level of surrounding stations is rarely considered; (3) Flow-restricted strategies are often long-term management measures for rail transit systems to cope with normalized large passenger flows, requiring precise vehicle configuration to reduce the number of vehicles used and vehicle-kilometers, and save operating costs. Rail transit accidents are sporadic and short-lived, so scholars are more concerned about how to quickly dispatch vehicles to transport stranded passengers. Therefore, the present invention proposes a method for dispatching shuttle buses when rail transit is running with limited current. Summary of the Invention

[0004] The present invention proposes a shuttle bus scheduling method when rail transit is running with limited flow, so as to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above objectives, the present invention provides a method for dispatching shuttle buses during rail transit current-limited operation, comprising:

[0006] Constructing a feeder bus candidate route generation model, and obtaining a feeder bus candidate route set based on the feeder bus candidate route generation model;

[0007] Constructing a joint decision-making model for feeder bus route plans and departure frequencies, and linearizing the joint decision-making model for feeder bus route plans and departure frequencies;

[0008] The linearized model is solved to obtain the layout plan of the connecting bus routes and the departure frequency of each route.

[0009] Optionally, based on a given rail transit network layout and flow-limited stations, the feeder bus candidate route generation model is solved to obtain a feeder bus candidate route set.

[0010] Optionally, the objective function of the feeder bus candidate route generation model is to maximize the number of feeder bus candidate routes, and the constraints include: directed arcs with flow-limited stations at both ends cannot be used as feeder bus candidate routes, the one-way travel time of the feeder bus candidate route does not exceed the maximum one-way travel time of the feeder bus that passengers can accept, and the selected stations meet the given rail transit network layout and flow-limited stations; wherein, the objective function is as follows:

[0011]

[0012] Where N is the set of rail transit stations and their corresponding feeder bus stations, S is the set of rail transit stations with limited flow, and when the directed arc connecting stations i and j is a candidate feeder bus route, then a i,j =1, otherwise it is 0, where i,j∈N.

[0013] Optionally, the objective function of the joint decision-making model for the feeder bus route plan and departure frequency is to minimize the total system cost, which includes passenger travel costs and bus operating costs. The objective function is as follows:

[0014]

[0015] In the formula, the set of OD pairs of travel demand in the rail transit network is K = {1, 2, ..., k, ..., |K|}, where k represents a specific OD pair and They represent the starting station and the terminal station of OD pair k respectively, The set of candidate feeder bus routes R = {1, 2, ..., r, ..., |R|}, where r represents a specific candidate feeder bus route, and its starting station and terminal station are represented by and express, α w is the unit economic value of passenger waiting time, α m is the unit economic value of the passenger's travel time, α p is the penalty cost for failing to serve passengers, α o is the bus operating cost, is the number of passengers who successfully boarded the connecting bus candidate route r between OD pairs k during the study period, is the number of passengers who failed to take the connecting bus line between OD pairs k during the study period, f r is the departure frequency of the candidate bus route r, W r The time required for passengers to walk to the corresponding rail transit station after getting off the connecting bus candidate line r terminal. is the time required for k passengers to take a train from the corresponding rail transit station of the connecting bus candidate line r terminal to their destination, E k is the time required for k passengers to complete their trip by rail transit, v r Represents the number of vehicles configured for the connecting bus candidate route r.

[0016] Optionally, the constraints of the joint decision-making model for the feeder bus route plan and departure frequency include:

[0017] The total number of vehicles allocated to each feeder bus route shall not exceed the number of vehicles available to the enterprise;

[0018] Vehicles can be allocated to candidate routes only if they are included in the final feeder bus network plan, and the candidate route's departure frequency is no less than the acceptable minimum departure frequency of the feeder bus route and no more than the acceptable maximum departure frequency of the feeder bus route;

[0019] If and only if the candidate route is included in the final connecting bus network plan and the starting station of the candidate route is consistent with the starting station of the OD pair, the candidate route can serve the corresponding passengers between the OD pairs;

[0020] The total number of passengers assigned to a single candidate route during the study period does not exceed the passenger capacity of the candidate route during that period;

[0021] The number of additional passengers at the corresponding rail transit station at the terminal of the candidate bus route during the study period shall not exceed the upper limit;

[0022] If the detour time between an OD pair and a connecting bus candidate route and rail transit exceeds the upper limit of the detour time acceptable to passengers, the passengers of the corresponding OD pair will give up choosing the corresponding candidate route.

[0023] Optionally, the joint decision-making model of the feeder bus route plan and departure frequency further includes calculating the number of passengers who fail to successfully board the feeder bus between all OD pairs.

[0024] Optionally, by introducing auxiliary variables, the constraints in the joint decision-making model of the feeder bus route plan and the departure frequency, which include the absolute value function and the product of the binary variable and the integer variable, are linearized to adjust the Perform linearization.

[0025] The present invention also discloses 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 shuttle bus scheduling method when the rail transit is running with limited current are realized.

[0026] The present invention also discloses a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned shuttle bus scheduling method when the rail transit is running with limited current.

[0027] Compared with the prior art, the present invention has the following advantages and technical effects:

[0028] The present invention provides a method for configuring and dispatching a shuttle bus, which takes into account passenger travel preferences, station service capabilities, and the interest game between passengers and enterprises during rail transit flow-limited operation. First, a shuttle bus candidate line generation model is constructed. Then, a shuttle bus candidate line set is obtained based on the shuttle bus candidate line generation model. Then, a shuttle bus line plan and departure frequency joint decision-making model is constructed. The shuttle bus line plan and departure frequency joint decision-making model is linearized. The model constructed by the present invention is a mixed integer nonlinear programming model, which is equivalently converted into a mixed integer linear programming model and can be solved by a commercial solver. Finally, the linearized model is solved to obtain a shuttle bus line layout plan and the departure frequency of each line, thereby providing decision support for bus companies to plan and operate shuttle bus lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0030] Figure 1 A schematic diagram of a directed network of rail transit network layout and flow-limited stations according to an embodiment of the present invention;

[0031] Figure 2 Flowchart of a method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0033] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0034] Example 1

[0035] The scheduling problem of feeder buses during rail transit flow-limited operation requires comprehensive decision-making on feeder bus route plans, departure frequency, fleet size, etc. Therefore, a two-stage method for feeder bus scheduling is proposed, such as Figure 1-Figure 2 In the first stage, the generation principle of candidate feeder bus routes is determined, and a set of candidate routes is generated through modeling. In the second stage, given the candidate routes, station service capacity, and number of available vehicles, a model is built to determine the layout plan of the feeder bus routes, the departure frequency of each route, and the minimum fleet size.

[0036] exist Figure 1 In the directed network G(N,A) shown, N is a set of nodes, and A is an arc connecting any two different nodes. For ease of expression, the rail transit and its adjacent connecting bus terminal in the network G(N,A) are represented as the same node; in addition to the arcs connecting adjacent nodes, only some arcs between non-adjacent nodes that can serve as candidate connecting bus routes are shown. The OD (Origin Destination) travel demand between any rail transit stations in the network can be estimated based on historical automatic ticket vending system data, and the shortest path of each OD pair in the rail transit network can be determined by calculation. The time required for passengers between the kth OD pair to complete the trip using the shortest path in the rail transit network is recorded as T k The probability that passengers between each OD pair in the rail transit network choose a combined travel mode consisting of a feeder bus and rail transit to reach their destination can be estimated based on the questionnaire survey results. Therefore, it is assumed that the travel demand for the feeder bus between each OD pair in G(N,A) is given and fixed. In summary, the core problem of the studied feeder bus scheduling during the limited-flow operation of rail transit is: given the bus travel demand, candidate routes, available vehicles, and the service capacity of rail transit stations, the model determines the final feeder bus route and its departure frequency, so that the weighted sum of passenger travel cost and enterprise operating cost is minimized.

[0037] When there are multiple connecting bus routes connecting flow-restricted stations with non-flow-restricted stations, passengers may choose different routes to complete their trips between the same starting and ending points. Figure 1 Consider a passenger queuing outside Metro Station 3 who originally planned to take a train to Metro Station 11. If multiple connecting bus routes are available outside the restricted station, this passenger can choose to take connecting bus route 1 to Metro Station 2 and then directly enter the station to take the train to Metro Station 11 (the order of stations they pass through is 2-3-4-5-10-11); or take connecting bus route 2 to Metro Station 10 and then directly enter the station to take the train to their destination (the order of stations they pass through is 10-11); or take connecting bus route 3 to Metro Station 9 and then directly enter the station to take the train (the order of stations they pass through is 9-5-10-11). Therefore, when multiple travel paths exist in a network, it is necessary to consider how to allocate travel demand across these different paths. In practice, passengers may forgo some travel mode combinations with excessively long detours and instead choose to queue outside the restricted station to enter. Therefore, when modeling and allocating passenger flow demand, it is also important to consider the maximum detour time that passengers can tolerate.

[0038] The symbolic meanings of the sets, parameters, and variables involved in the model are shown in Table 1.

[0039] Table 1

[0040]

[0041]

[0042]

[0043] Feeder bus candidate route generation model

[0044] Given the rail transit network layout and flow-limited stations, the following mathematical model is constructed to generate all candidate feeder bus routes.

[0045]

[0046] Objective function (1) aims to maximize the number of candidate feeder bus routes to ensure that all directed arcs that meet the requirements in the network G(N,A) are included in the set of candidate feeder bus routes. Constraint (2) indicates that directed arcs with both ends being flow-limited stations cannot be used as candidate feeder bus routes. Constraint (3) ensures that the one-way travel time of the candidate feeder bus route does not exceed B max . Constraints (4) define the range of decision variables.

[0047] Joint decision-making model for feeder bus route plan and departure frequency

[0048] Given passenger travel demand and a set of candidate feeder bus routes, the following mathematical model is constructed to determine the optimal feeder bus route layout plan and the departure frequency of each route.

[0049]

[0050] The objective function (5) aims to minimize the total system cost (the weighted sum of passenger travel costs and bus operating costs), where the first and second parts are the waiting time cost and detour time (i.e., the increased travel time due to the combination of travel modes) of passengers who successfully board the connecting bus line; the third part is the penalty cost that the bus company needs to pay when there are passengers who fail to board the connecting bus, which is proportional to the number of passengers not served; the fourth part is the operating cost of the connecting bus, which is determined by the required number of buses (i.e., the minimum required fleet size).

[0051] Constraints (6) and (7) ensure that the total number of vehicles allocated to each feeder bus route does not exceed the number of vehicles available to the enterprise. Constraints (8) and (9) indicate that vehicles can be allocated to the candidate route r only if it is included in the final feeder bus network plan, and the departure frequency of route r must be no less than F min and not greater than F max . Constraints (10)-(13) indicate that candidate route r can serve passengers between OD pair k if and only if candidate route r is included in the final connecting bus network plan and the starting station of candidate route r is consistent with the starting station of OD pair k. Constraint (14) is used to calculate the number of passengers between OD pair k who failed to take the connecting bus smoothly. Constraint (15) ensures that the total number of passengers assigned to candidate route r during the study period does not exceed the passenger capacity of route r during the period. In order to avoid the introduction of connecting bus services causing excessive passenger flow at non-flow-restricted stations, constraints (16) and (17) are set to ensure that the number of passengers added to the corresponding rail transit station of the connecting bus candidate route r terminal during the study period does not exceed U r Constraint (18) indicates that if the detour time generated by the OD for k-way bus candidate line r and rail transit exceeds the upper limit of the detour time P that the passenger can accept, max , then OD pair k passengers will give up choosing candidate route r. Constraints (19) and (20) define the value range of each decision variable.

[0052] Model linearization and solution

[0053] By introducing auxiliary variables, the constraints in the joint decision-making model of the connecting bus route plan and the departure frequency, which include the absolute value function and the product of the binary variable and the integer variable, are linearized. Perform linearization. It is equivalently converted into a mixed integer linear programming model. The linearization process is as follows:

[0054] (1) Linearization of absolute value function.

[0055] Constraint (11) contains an absolute value function, so the auxiliary variable is introduced and Linearize it, let The linearization results are shown in equations (21)-(24).

[0056]

[0057] Constraint (16) contains absolute values Similarly, it can be linearized by introducing auxiliary variables, so I will not go into details.

[0058] (2) Linearization of the product of binary variables and integer variables.

[0059] For the integer variable in constraint (17) With the binary variable d r,r′ The product of , introduces auxiliary variables Substitute, the linearization results are shown in Equations (25)-(27).

[0060]

[0061] (3) Linearization of the product of an integer variable and the reciprocal of an integer variable.

[0062] is the linearized expression in formula (5) Introduce a set based on the range of the integer variable departure frequency Represents the inverse of the departure frequency The value range of Then the objective function (5) Can be converted into In order to further linearize, auxiliary variables are introduced Then in formula (5) Eventually converted to The corresponding linearization process is shown in Equations (28)-(31).

[0063]

[0064]

[0065] The linearized model can be used to obtain the optimal solution using commercial solvers such as CPLEX and GUROBI.

[0066] This embodiment further discloses a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned method for dispatching shuttle buses when rail transit is operating with limited flow are implemented.

[0067] This embodiment also discloses a computer program product, including a computer program. When the computer program is executed by a processor, the steps of the above-mentioned method for scheduling shuttle buses when the rail transit is operating with limited current are implemented.

[0068] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for dispatching shuttle buses during rail transit flow-limited operation, characterized in that: The following steps are involved: Constructing a feeder bus candidate route generation model, and obtaining a feeder bus candidate route set based on the feeder bus candidate route generation model; Constructing a joint decision-making model for feeder bus route plans and departure frequencies, and linearizing the joint decision-making model for feeder bus route plans and departure frequencies; Solve the linearized model to obtain the layout plan of the connecting bus routes and the departure frequency of each route; The objective function of the feeder bus candidate route generation model is to maximize the number of feeder bus candidate routes. The constraints include: directed arcs with flow-limited stations at both ends cannot be used as feeder bus candidate routes, and the one-way travel time of the feeder bus candidate routes does not exceed the maximum one-way travel time of the feeder bus that passengers can accept. The objective function is as follows: Where N is the set of rail transit stations and their corresponding feeder bus stations, S is the set of rail transit stations with limited flow, and when the directed arc connecting stations i and j is a candidate feeder bus route, then a i，j =1, otherwise it is 0, where i, j∈N; The objective function of the joint decision-making model of the feeder bus route plan and departure frequency is to minimize the total system cost, which includes passenger travel costs and bus operating costs. The objective function is as follows: In the formula, the set of OD pairs in the rail transit network K = {1, 2, ..., k, ..., |K|}, where k represents a specific OD pair and They represent the starting station and the terminal station of OD pair k respectively, The set of candidate feeder bus routes R = {1, 2, ..., r, ..., |R|}, where r represents a specific candidate feeder bus route, and its starting station and terminal station are represented by and express, α w is the unit economic value of passenger waiting time, α m is the unit economic value of the passenger's travel time, α p is the penalty cost for failing to serve passengers, α o is the bus operating cost, is the number of passengers who successfully boarded the connecting bus candidate route r between OD pairs k during the study period, is the number of passengers who failed to take the connecting bus line between OD pairs k during the study period, f r is the departure frequency of the candidate bus route r, W r The time required for passengers to walk to the corresponding rail transit station after getting off the connecting bus candidate line r terminal. is the time required for k passengers to take a train from the corresponding rail transit station of the connecting bus candidate line r terminal to their destination, E k is the time required for k passengers to complete their trip by rail transit, v r represents the number of vehicles configured for the candidate bus route r, T r The round trip running time of the vehicle connecting to the candidate bus route r; The constraints of the joint decision-making model for the feeder bus route plan and departure frequency include: The total number of vehicles allocated to each feeder bus route shall not exceed the number of vehicles available to the enterprise; Vehicles can be allocated to candidate routes only if they are included in the final feeder bus network plan, and the candidate route's departure frequency is no less than the acceptable minimum departure frequency of the feeder bus route and no more than the acceptable maximum departure frequency of the feeder bus route; If and only if the candidate route is included in the final connecting bus network plan and the starting station of the candidate route is consistent with the starting station of the OD pair, the candidate route can serve the corresponding passengers between the OD pairs; The total number of passengers assigned to a single candidate route during the study period does not exceed the passenger capacity of the candidate route during that period; The number of additional passengers at the corresponding rail transit station at the terminal of the candidate bus route during the study period shall not exceed the upper limit; If the detour time between an OD pair and a connecting bus candidate route and rail transit exceeds the upper limit of the detour time that passengers can accept, the passengers of the corresponding OD pair will give up choosing the corresponding candidate route.

2. The method for dispatching shuttle buses during rail transit current-limited operation according to claim 1, characterized in that: The process of obtaining a set of feeder bus candidate routes based on the feeder bus candidate route generation model includes: solving the feeder bus candidate route generation model based on a given rail transit network layout and flow-limited stations to obtain a set of feeder bus candidate routes.

3. The method for dispatching shuttle buses during rail transit current-limited operation according to claim 1, characterized in that: By introducing auxiliary variables, the constraints in the joint decision-making model of the connecting bus route plan and the departure frequency, which include the absolute value function and the product of the binary variable and the integer variable, are linearized. Perform linearization.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a method for dispatching shuttle buses during rail transit current-limited operation according to any one of claims 1 to 3 are implemented.

5. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of a method for dispatching shuttle buses during rail transit current-limited operation according to any one of claims 1 to 3 are implemented.

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