Connection bus scheduling method during rail transit flow-limiting operation

Abstract

The invention discloses a connection bus scheduling method during rail transit current-limiting operation, and the method comprises the steps: constructing a connection bus candidate line generation model, and obtaining a connection bus candidate line set based on the connection bus candidate line generation model; constructing a connection bus route scheme and departure frequency joint decision model, and linearizing the connection bus route scheme and departure frequency joint decision model; and solving the linearized model to obtain a connection bus route layout scheme and the departure frequency of each route. According to the connection bus configuration and scheduling method in which passenger travel preferences, station service capabilities and passenger and enterprise benefit games are considered during rail transit flow-limiting operation, decision support is provided for a bus enterprise to plan and operate a connection bus line.

Description

Technical Field

[0001] The invention belongs to the technical field of public transportation, and in particular relates to a shuttle bus dispatching method when rail transit is running with limited current. Background Art

[0002] With the rapid development and network operation of urban rail transit systems, rail transit passenger volume continues to grow, network operation load is increasing, and some lines have entered an oversaturated operation state during peak passenger flow periods. In order to alleviate the crowded conditions of platforms and carriages and ensure the safety of line operation, cities such as Beijing, Shanghai, and Shenzhen have adopted a normalized flow control strategy for some large passenger flow rail transit stations. However, flow control measures cannot fundamentally solve the problem of mismatch between supply and demand of the rail transit system, and may significantly increase the travel time of some passengers and reduce the service level and attractiveness of public transportation. Therefore, in order to effectively alleviate the contradiction between supply and demand of rail transit during peak passenger flow periods and avoid the transfer of rail transit passengers to individual transportation modes, it is necessary to study the coordinated operation method of rail transit and shuttle buses, use shuttle buses to transport passengers from flow-restricted stations to surrounding non-flow-restricted stations, balance the passenger flow distribution within the rail transit network, give full play to the function of shuttle buses in relieving rail transit passenger flow, and improve 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 stranded passengers at rail transit flow-limited 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 dispatch methods around the evacuation of stranded passengers in the context of rail transit accidents. However, the research results related to emergency buses cannot be directly applied to the dispatch of feeder buses during rail transit flow-limited 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-limited operation requires consideration of passengers' acceptance of the combined travel mode of "feeder bus + rail transit" 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-limited strategies are often long-term management measures for rail transit systems to cope with normalized large passenger flows, requiring precise configuration of vehicles to reduce the number of vehicles and vehicle-kilometers used 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 shuttle bus scheduling method when rail transit is running with limited current. Summary of the invention

[0004] The present invention proposes a shuttle bus dispatching 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 object, the present invention provides a method for dispatching shuttle buses during rail transit current limiting 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 a feeder bus route plan and a departure frequency, and linearizing the joint decision-making model for a feeder bus route plan and a departure frequency;

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

[0009] Optionally, based on a given rail transit network layout and flow-limited stations, the feeder bus candidate line generation model is solved to obtain a feeder bus candidate line 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 both ends being flow-limited stations 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 limited rail transit stations, 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 of the shuttle bus route plan and the departure frequency is to minimize the total system cost, and the total system cost includes the passenger travel cost and the bus operation cost; 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 bus routes R = {1, 2, ..., r, ..., |R|}, where r represents a specific candidate 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 time in transit, 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 and k during the study period, f r is the departure frequency of the candidate connecting bus route r, W r The time required for passengers to walk to the corresponding rail transit station after getting off the candidate connecting bus line r. 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 of the connecting bus route plan and the 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 assigned to candidate routes only if and when they are included in the final feeder bus network plan, and the departure frequency of the candidate routes is not less than the minimum departure frequency of the acceptable feeder bus routes and not greater than the maximum departure frequency of the acceptable feeder bus routes;

[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 line and rail transit exceeds the upper limit of the detour time that passengers can accept, the passengers in the corresponding OD pair will give up choosing the corresponding candidate line.

[0023] Optionally, the connecting bus route plan and departure frequency joint decision model also includes calculating the number of passengers who failed to successfully board the connecting bus between all OD pairs.

[0024] Optionally, by introducing auxiliary variables, the constraints in the joint decision-making model of the shuttle 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, and the constraints in the objective function are linearized. 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 shuttle bus scheduling method during the current-limited operation of the rail transit are implemented.

[0026] The present invention also discloses a computer program product, including a computer program, which, when executed by a processor, implements the steps of the 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 shuttle bus configuration and scheduling method that takes into account passenger travel preferences, station service capabilities, and the game between passenger and enterprise interests when rail transit is running with limited flow. First, a shuttle bus candidate line generation model is constructed, and 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 model is constructed, and the shuttle bus line plan and departure frequency joint decision 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, so as to provide decision support for bus companies to plan and operate shuttle bus lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

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

[0031] Figure 2 The figure is a flow chart 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 in the embodiments of the present 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] Embodiment 1

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

[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 terminals 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 the historical automatic ticket vending and checking 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 shuttle bus and rail transit to reach their destination can be calculated based on the questionnaire survey results, so it is assumed that the travel demand for selecting a shuttle bus between each OD pair in G(N,A) is given and fixed. In summary, the core problem of the shuttle bus scheduling during the limited flow operation of rail transit is: given the bus travel demand, candidate routes, available vehicles, and rail transit station service capacity, the modeling decision is made on the final shuttle 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 limited-flow stations with non-limited-flow stations, passengers may choose different routes to complete their trips between the same departure and arrival points. Figure 1 The passenger queuing outside the rail transit station 3 originally planned to take the train to the rail transit station 11. When multiple connecting bus lines are provided outside the limited flow station, the passenger can choose to take the connecting bus line 1 to the rail transit station 2 first, and then directly enter the station to take the train to the rail transit station 11 (the order of passing the rail transit stations is 2-3-4-5-10-11); or choose to take the connecting bus line 2 to the rail transit station 10 first, and then directly enter the station to take the train to the destination (the order of passing the rail transit stations is 10-11); or choose to take the connecting bus line 3 to the rail transit station 9 and then directly enter the station to take the train (the order of passing the rail transit stations is 9-5-10-11). Therefore, when there are multiple travel paths in the network, it is necessary to consider the allocation of travel demand among different paths. In actual situations, passengers may give up some combined travel mode paths with too long detour time and choose to queue outside the limited flow station to wait for entry. Therefore, when modeling and allocating passenger flow demand, it is also necessary to consider the longest 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] Candidate route generation model for connecting buses

[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 network G(N,A) are included in the set of candidate feeder bus routes. Constraint (2) indicates that directed arcs with both ends of limited flow stations cannot be used as candidate feeder bus routes. Constraint (3) ensures that the one-way travel time of candidate feeder bus routes does not exceed B. max . Constraints (4) define the range of decision variables.

[0047] Joint decision-making model of 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 layout of feeder bus routes 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 take 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 successfully take 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 available vehicles of the enterprise. Constraints (8) and (9) indicate that vehicles can be allocated to the candidate route r only if and when it is included in the final feeder bus network plan, and it is necessary to ensure that the departure frequency of route r is not 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 shuttle 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 shuttle bus. 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 that period. In order to avoid excessive passenger flow at unrestricted stations caused by the introduction of shuttle bus services, constraints (16) and (17) are set to ensure that the number of passengers added to the corresponding rail transit station at the terminal of the shuttle bus candidate route r 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 acceptable to passengers, P max , then OD pair k passengers will give up on candidate route r. Constraints (19) and (20) define the 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 shuttle 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 transformed 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 an 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 Substitute, the linearization results are shown in equations (25)-(27).

[0060]

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

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

[0063]

[0064]

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

[0066] This embodiment 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 shuttle bus scheduling method when the rail transit is operating with limited flow are implemented.

[0067] This embodiment also discloses a computer program product, including 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 operating with limited current.

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

Claims

1. A method for dispatching shuttle buses during rail transit current limiting 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 a feeder bus route plan and a departure frequency, and linearizing the joint decision-making model for a feeder bus route plan and a departure frequency; The linearized model is solved to obtain the layout plan of the connecting bus lines and the departure frequency of each line.

2. The method for dispatching shuttle buses during rail transit current limiting operation according to claim 1, characterized in that: Based on the given rail transit network layout and flow-limited stations, the feeder bus candidate line generation model is solved to obtain a feeder bus candidate line set.

3. The method for dispatching shuttle buses during rail transit current limiting operation according to claim 2, characterized in that: 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 both ends being flow-limited stations 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; wherein, 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 limited rail transit stations, 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.

4. The method for dispatching shuttle buses during rail transit current limiting operation according to claim 1, characterized in that: The objective function of the joint decision-making model of the shuttle bus route plan and departure frequency is to minimize the total system cost, which includes the passenger travel cost and the bus operation cost; the objective function is as follows: In the formula, the set of OD pairs 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 bus routes R = {1, 2, ..., r, ..., |R|}, where r represents a specific candidate 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 time in transit, 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 and k during the study period, f r is the departure frequency of the candidate connecting bus route r, W r The time required for passengers to walk to the corresponding rail transit station after getting off the candidate connecting bus line r. 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.

5. The method for dispatching shuttle buses during rail transit current limiting operation according to claim 4, characterized in that: The constraints of the joint decision-making model of the connecting 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 assigned to candidate routes only if and when they are included in the final feeder bus network plan, and the departure frequency of the candidate routes is not less than the minimum departure frequency of the acceptable feeder bus routes and not greater than the maximum departure frequency of the acceptable feeder bus routes; 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 line and rail transit exceeds the upper limit of the detour time that passengers can accept, the passengers in the corresponding OD pair will give up choosing the corresponding candidate line.

6. The method for dispatching shuttle buses during rail transit current limiting operation according to claim 4, characterized in that: By introducing auxiliary variables, the constraints in the joint decision-making model of the shuttle 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.

7. 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 current-limited operation of rail transit as described in any one of claims 1 to 6 are implemented.

8. 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 current-limited operation of rail transit as described in any one of claims 1 to 6 are implemented.

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