Section alternate response type urban and rural bus scheduling method considering autonomous selection of passengers

Abstract

The invention discloses a section alternate response type urban and rural bus scheduling method considering autonomous selection of passengers, and the method comprises the following specific steps: firstly, determining a demand response station, a section demarcation point and a demand station, secondly, if the demand station is within the service range of a DRT, defining the demand response station, otherwise, discarding the station, and finally, carrying out the next step; the method comprises the following steps: determining a corresponding relation between demand response sites and fixed sites through a vector product method, further dividing the demand response sites into site sets of two sections of a country according to the corresponding relation, then preprocessing an obtained order, setting a secondary selection mechanism and the like, and obtaining a demand response site set; according to the invention, passengers independently select instead of passively accept system decisions, which is closer to the psychology of the passengers and maximizes the decision right of the service to the passengers; the step of distributing train numbers for passengers through complex optimization is omitted, and the problems of resource waste, long calculation time and the like caused by inaccurate prediction or excessive optimization are avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of public transportation services, and in particular to a section alternating responsive urban and rural public transportation dispatching method taking into account passengers' autonomous selection. Background Art

[0002] Urban and rural buses are bridges between cities and villages, with the characteristics of long-term operation, mature routes, stable passenger flow, and high frequency of departure, but they also face bottlenecks such as unbalanced revenue and limited service scope. Compared with urban buses, urban and rural buses have a wider service scope, and it is difficult to transfer with other urban and rural bus routes. Residents have limited bus routes to choose from, and there are pain points such as long front-end and end-of-trip distances.

[0003] Continuous investment and improvement in the construction of urban and rural bus routes, station layout, vehicle configuration and other facilities have increased the coverage of urban and rural bus services and the accessibility of residents' travel. However, the low density and dispersed demand for bus travel in rural areas and limited transportation service capacity have led to lower departure frequency configuration and service level.

[0004] Demand Responsive Transit (DRT) is a representative of flexible public transportation. It flexibly adjusts service routes and stops based on passenger reservation information. It has the characteristics of intensive travel of traditional buses and high flexibility of taxis, and can meet the personalized and diversified travel needs of residents.

[0005] Demand-responsive customized public transportation (Subscription Bus or Customized Bus) aggregates individual travel needs and provides efficient, convenient, and personalized public transportation services for people with similar travel start and end points, travel time, and service level requirements. The service model is between regular buses and taxis, and it flexibly adjusts service routes and stations based on passenger reservation information. It has the characteristics of regular bus intensive travel and taxi high flexibility, and can meet the personalized and diversified travel needs of residents, effectively reduce the use of private cars during peak hours, and thus increase the public transportation share rate and alleviate urban traffic congestion. Transit cooperative research program (TCRP) in the United States [3] Demand-responsive bus services are divided into six categories: route-variable bus service, station-variable bus service, demand-responsive shuttle service, responsive station service, section-demand-responsive bus service and regional demand-responsive bus service.

[0006] It can be seen that one of the important differences between demand-responsive buses and fixed-route buses is that demand-responsive buses can provide customized services based on passengers' travel needs. The existing technical solutions improve service efficiency by changing the initial travel starting point and departure time window selected by passengers within a certain time and space threshold, and by concentrating potential passengers who can get on the bus at the same station through candidate stations. By setting a full service time window and partially transferring the decision-making power of the service level to passengers, it can flexibly adjust passenger travel time, boarding stations, and optimize passenger travel efficiency. However, passengers as travel subjects have limited right to choose. Passengers mostly passively accept the vehicles assigned to them by the system. The dispatching system ignores individual differences between passengers and their different preferences for trains. Summary of the invention

[0007] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0008] Therefore, the purpose of the present invention is to provide a segment alternating response urban and rural public transportation scheduling method that takes into account the autonomous selection of passengers on the basis of segment demand response. The present invention takes into account the autonomous selection of passengers from multiple alternative trains for the intended service, and considers their secondary selection behavior after being rejected by the system, thereby covering the entire travel process from the generation of demand to the end, avoiding their passive acceptance of system decisions. Combined with the actual situation of urban and rural public transportation, this paper adopts an instant processing method and also carries out dynamic scheduling in the first stage of the two-stage scheduling. The vector product method is used to determine the correspondence between demand response stations and fixed stations.

[0009] To solve the above technical problems, according to one aspect of the present invention, the present invention provides the following technical solutions:

[0010] A method for urban and rural bus dispatching with alternating sections and responsiveness considering passengers' autonomous selection, the steps are as follows:

[0011] S1. Model preparation stage:

[0012] Determine the demand response sections, section demarcation points, locations of demand sites, and the correspondence between demand response sites and fixed sites;

[0013] S2. Two-stage scheduling process:

[0014] S201, before departure, the first stage, determine whether there is a new reservation order, if yes, transfer to S3; otherwise, wait for the passenger to submit a new order in the reservation system;

[0015] S202: After the vehicle leaves, the system goes to the second stage. When the vehicle arrives at each stop, it determines whether there are passengers who have boarded the vehicle and submitted an order. If so, it goes to S3; otherwise, it continues to determine whether there are passengers who have boarded the vehicle and submitted an order when the vehicle arrives at the next stop. This step is repeated, and when the vehicle arrives at the first and last stops, the system ends.

[0016] S3, instant processing of orders and dynamic scheduling process:

[0017] S301, pre-processing the new order, that is, determining the intended service number selected by the passenger for the first time and calculating the fare;

[0018] S302. Determine whether the intended service train selected by the real-time passenger has remaining passenger capacity. If yes, proceed to S303; otherwise, proceed to S307.

[0019] S303, determine whether the passenger has made a second selection, if so, accept the order, include it in the dispatch range, and update the vehicle status. The order status is updated while booking the passenger, and the pre-processing is completed. Turn to S2, and the system continues to determine whether there is a new order; otherwise, turn to S304;

[0020] S304: The passenger does not make a second choice. The optimal path is obtained by combining enumeration method and genetic algorithm, and it is determined whether it meets the constraints. If so, the order is accepted, included in the dispatch range, and the vehicle status is updated. The order status of the reserved passenger is also updated. The preprocessing is completed and the system goes to S2 to continue to determine whether there is a new order; otherwise, it goes to S305.

[0021] S305: Determine whether the passenger is a reserved passenger. If so, the system does not accept the order, the reservation fails, and the passenger makes a new reservation; otherwise, the secondary selection mechanism is triggered to update the order status;

[0022] S306, determine whether the system has not accepted the order, if so, the pre-processing ends and the process goes to S2, where the system continues to determine whether there is a new order, otherwise, the process goes to S302;

[0023] S307. If the passenger has made a second selection, the order is not accepted, and the passenger chooses other alternative modes of travel, and the system updates the order status; otherwise, the second selection mechanism is triggered, the order status is updated, and the process proceeds to S306.

[0024] According to the rights, as a preferred scheme of the section alternating responsive urban and rural bus scheduling method considering the autonomous choice of passengers described in the present invention, in which, in step S1, the demand response section is set in the rural section that is the focus of the urban and rural bus operation line, and a section dividing point is set between the urban section and the rural section. In the rural section, the number of fixed stations and the operating mileage are comprehensively analyzed, and the appropriate fixed stations are set as the section dividing point to achieve a balance in the service intensity of the two rural sections, and the demand stations are arranged in the crowded places on both sides of the demand response section.

[0025] As a preferred solution of the section alternating responsive urban and rural public transportation scheduling method considering the autonomous selection of passengers according to the present invention, in step S1, the specific steps of determining the corresponding relationship between the demand response station and the fixed station by the vector product method are as follows:

[0026] Define a, b, and c as three consecutive fixed sites. In the fixed site set D, find the fixed site b closest to s and make the vector and

[0027] Calculating vectors and The product of and determine its sign, if it is non-negative, vector and The angle θ=α≤90°, G S1 =a,G S2 =b; otherwise, θ=β>90°, G S1 =b,G S2 =c;

[0028] Determine G S , let s and G S1 , G S2 The distances are s1 and s2 respectively, M is the ratio of s1 to s2, and the terminal travel distance coefficient ξ (ξ ≥ 1) is introduced. If M ≥ ξ, then G S =G S2 , service distance s f =s2; otherwise, G S =G S1 ,s f =s1;

[0029] Determine whether the demand station s is within the service range of DRT. Assume that DRT can only serve demand stations within L km of the fixed line, and two consecutive fixed stations run in a straight line. Let s, G S1 and G S2 The coordinates of are (x1, y1), (x2, y2) and (x3, y3), respectively. From the mathematical relationship, we can get: if s satisfies the relationship

[0030]

[0031] It is determined that the required site is within the service range of DRT;

[0032] Repeat the above steps for all sites in the demand site set. The demand sites that meet formula (1) are divided into the demand response site set, otherwise they are divided into the discarded site set. According to the service segments corresponding to each demand response site, the demand response sites in the set are further divided into the segment 1 and 2 site sets; in particular, if it is the dividing point between segments 1 and 2, the site is divided into the segment 1 set.

[0033] As a preferred solution of the section alternating responsive urban and rural bus dispatching method considering the autonomous selection of passengers according to the present invention, in step S301, the steps of pre-processing the acquired order are as follows:

[0034] Find the train number k that meets the passenger's travel needs;

[0035] The search model is as follows:

[0036]

[0037] Wherein, formula (1) represents the minimum number of trains; formula (2) represents the number of reservation orders Z for train k service. Yk Maximum booking volume Z not reached Ykmax , Formula (3) represents the order time of passenger c Earlier than the departure time of train number k F k , Formula (4) represents the time when passenger c arrives at the boarding station No later than the arrival time of train number k Formula (5) represents the segment Q where the passenger c gets off c Demand response zone Q served by train number k k same;

[0038] Determine whether the alternative trains k-1 and k-2 exist, and determine the intended train. After the passenger selects the intended train, the system recommends the best departure time for the passenger based on the time it takes for the passenger to arrive at the boarding station and the arrival time of the intended train. c , in order to reduce the waiting time of passengers at the station.

[0039] As a preferred solution of the section alternating responsive urban and rural public transportation dispatching method considering the autonomous selection of passengers according to the present invention, in step S303, the specific steps of the secondary selection mechanism are as follows:

[0040] If a passenger who is waiting at a station and wants to get off at a demand response station is rejected by the system because the time constraint is not met, he / she will immediately choose to arrive at the corresponding fixed station G. S Get off the bus and submit your ride request to the system again;

[0041] If the order is rejected because the vehicle is full, the passenger will immediately choose to take the next vehicle k+1. Passengers waiting at the station and expecting to get off at the demand response station will give up reaching the demand response station and choose to reach the corresponding fixed station G. S get off;

[0042] After the second selection, the system will only reject the order again if the vehicle is full. If the passengers are rejected again, it is assumed that these passengers will eventually choose to travel by alternative means.

[0043] As a preferred solution of the section alternating responsive urban and rural public transportation dispatching method considering the autonomous selection of passengers according to the present invention, in step S301, the calculation, updating and determination of the corresponding passenger fare are specifically as follows:

[0044] The corresponding fares are charged for different types of passengers, and the passenger fare is defined as the basic fare and the service fare. The fixed bus fare is recorded in the n×n dimensional matrix p n×n The basic fare for passengers who make online reservations in advance and wait at the station and expect to get off at a demand response station is calculated based on the fixed station G corresponding to the demand response station where they get off. S Calculate service fares is the additional cost caused by the vehicle detouring to meet the demand response station, which is determined by the service distance s f It was decided to introduce a service fee coefficient γ, whereby less than one kilometer will be counted as one kilometer. If the DRT operates during peak hours, an additional service fare of β times will be charged per kilometer, where β is the peak operation fare coefficient;

[0045] The service fare for passengers waiting at the station and getting off at a fixed station is 0, and the service fare for passengers of type 1 and 2 is for:

[0046]

[0047] Where: H k is a decision variable used to determine whether train number k is running during peak hours.

[0048] Total fare p for passenger c c for

[0049]

[0050] Total fare revenue U for train number k k for:

[0051]

[0052] Where: Whether the reservation order of passenger c is responded to by train k.

[0053] As a preferred solution of the section alternating responsive urban and rural bus dispatching method considering the autonomous selection of passengers according to the present invention, in step S304, the objective function of the dispatching model is:

[0054]

[0055] Where: Z is the mileage of all vehicles in the system, X ijk is a decision variable to determine whether train number k stops at stations i, j, d consecutively ij is the distance between site i and site j;

[0056] The constraints of the scheduling model include:

[0057] Service zone constraints:

[0058] Each train can only provide service in one demand response section during a one-way operation, namely:

[0059]

[0060] Where: Q k The demand response section serving train number k;

[0061] Among two consecutive DRT trains, only one train serves a specific demand response section, namely:

[0062]

[0063] Where: is the decision variable, and the judgment section q Whether it is served by train number k;

[0064] Vehicle capacity constraints

[0065] The remaining passenger capacity R of train number k leaving the current station j jk is the remaining passenger capacity R leaving the previous station i ik Subtract the net number of people boarding at the current stop Right now:

[0066]

[0067] The type 1 passengers served by train k have successfully made reservations before departure, and the capacity needs to be reserved for this type of passengers. Therefore, when train k departs, the remaining capacity of the first station is R 1k The maximum passenger capacity R minus the total number of reservations for train number k Right now:

[0068]

[0069] Run time constraints:

[0070] In order to avoid a long one-way running time and ensure the frequency and punctuality of two-way departure, the time tolerance coefficient λ is introduced. The one-way running time T of train number k is k No more than λ times the fixed line operation time T0, that is

[0071]

[0072] Where: T nk represents the time when train number k arrives at the terminal station, F k is the departure time of train number k;

[0073] Assume that the last station number of the urban section is g, the first and last stations of the demand response section served by train number k are l,m, the urban driving speed is v1, and the rural driving speed is v2. In addition, the average speed during peak hours is affected by the time when passengers get on and off the bus and the degree of road congestion. The peak operation time coefficient μ is introduced, and the time T when train number k arrives at the stop i is ik for:

[0074]

[0075] Where: R k is the stopover site of train number k, D ijk is the distance between the next stop j of train number k and the current stop i;

[0076] Time constraints in transit:

[0077] Where: is the time for fixed-line train number k to arrive at each stop i.

[0078] Compared with the prior art, the present invention has the following beneficial effects:

[0079] 1. The present invention takes into account passengers' autonomous choices rather than passively accepting system decisions, is closer to passengers' psychology, and maximizes the decision-making power of services to passengers; it eliminates the step of allocating train numbers to passengers through complex optimization, and avoids problems such as waste of resources and long calculation time caused by inaccurate prediction or over-optimization.

[0080] 2. The present invention only needs to determine the farthest distance that DRT can serve from the fixed line, the fixed site and the coordinates of the demand site, and can use the vector product method to quickly and accurately determine the corresponding relationship between the demand response site and the fixed site. The location, number and model parameters of the demand site can be flexibly and dynamically adjusted according to the acceptance of urban and rural residents in various places and the actual operation conditions, and has strong universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0082] Figure 1 A flow chart of the section alternating responsive urban and rural public transportation dispatching method considering passengers' autonomous selection according to the present invention;

[0083] Figure 2 A schematic diagram of the vehicle dispatching process provided by the present invention;

[0084] Figure 3 A schematic diagram of the travel process for passengers making reservations provided by the present invention;

[0085] Figure 4 and Figure 5 A schematic diagram of the order placement process of the reservation system provided by the present invention;

[0086] Figure 6 The travel process of passengers waiting at the station provided by the present invention;

[0087] Figure 7 A schematic diagram of determining whether a demand site provided by the present invention is within the DRT service range;

[0088] Figure 8 A schematic diagram of a solution strategy combining the enumeration method and the genetic algorithm provided by the present invention. DETAILED DESCRIPTION

[0089] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0090] Secondly, the present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention in detail, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0091] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0092] (1) The present invention provides a section-alternating responsive urban and rural public transportation dispatching method that takes into account passengers' autonomous choices, such as Figure 1 As shown, the specific steps are as follows:

[0093] S1. Model preparation stage:

[0094] Determine the demand response sections, section demarcation points, locations of demand sites, and the correspondence between demand response sites and fixed sites;

[0095] S2. Two-stage scheduling process:

[0096] S201, before departure, the first stage, determine whether there is a new reservation order, if yes, transfer to S3; otherwise, wait for the passenger to submit a new order in the reservation system;

[0097] S202: After the vehicle leaves, the system goes to the second stage. When the vehicle arrives at each stop, it determines whether there are passengers who have boarded the vehicle and submitted an order. If so, it goes to S3; otherwise, it continues to determine whether there are passengers who have boarded the vehicle and submitted an order when the vehicle arrives at the next stop. This step is repeated, and when the vehicle arrives at the first and last stops, the system ends.

[0098] S3, instant processing of orders and dynamic scheduling process:

[0099] S301, pre-processing the new order, that is, determining the intended service number selected by the passenger for the first time and calculating the fare;

[0100] S302. Determine whether the intended service train selected by the real-time passenger has remaining passenger capacity. If yes, proceed to S303; otherwise, proceed to S307.

[0101] S303, determine whether the passenger has made a second selection, if so, accept the order, include it in the dispatch range, and update the vehicle status. The order status is updated while booking the passenger, and the pre-processing is completed. Turn to S2, and the system continues to determine whether there is a new order; otherwise, turn to S304;

[0102] S304: The passenger does not make a second choice. The optimal path is obtained by combining enumeration method and genetic algorithm, and it is determined whether it meets the constraints. If so, the order is accepted, included in the dispatch range, and the vehicle status is updated. The order status of the reserved passenger is also updated. The preprocessing is completed and the system goes to S2 to continue to determine whether there is a new order; otherwise, it goes to S305.

[0103] S305: Determine whether the passenger is a reserved passenger. If so, the system does not accept the order, the reservation fails, and the passenger makes a new reservation; otherwise, the secondary selection mechanism is triggered to update the order status;

[0104] S306, determine whether the system has not accepted the order, if so, the pre-processing ends and the process goes to S2, where the system continues to determine whether there is a new order, otherwise, the process goes to S302;

[0105] S307. If the passenger has made a second selection, the order is not accepted, and the passenger chooses other alternative modes of travel, and the system updates the order status; otherwise, the second selection mechanism is triggered, the order status is updated, and the process proceeds to S306.

[0106] (2) Vehicle dispatch process Figure 2 As shown in the figure, the existing urban and rural bus fixed lines are used to carry out the section alternating response service organization mode, and two fixed stations are selected as the section demarcation points, and the line is divided into three sections 0, 1, and 2. Section 0 is in the city (town), and sections 1 and 2 are in the countryside. Demand stations are arranged at the crowded places on both sides of the rural section line. Section 0 maintains the fixed line operation mode within the city; Sections 1 and 2 are in the rural operation section, and respond alternately. For example, when Section 1 operates with DRT, Section 2 operates with a fixed line. The dotted lines in the figure represent the vehicle paths when responding to Sections 1 and 2, respectively, and the bold dotted lines specifically mark the running trajectory of the current train in the demand response section.

[0107] (3) Passenger travel process

[0108] 1) The process of booking a passenger's trip is as follows Figure 3 As shown, the ordering process of the reservation system is as follows Figure 4 and Figure 5 As shown in the figure, the passenger selects a fixed bus stop in the city as the boarding point in the system, and selects a demand response stop in the countryside as the alighting point, fills in the departure time and the time required to reach the boarding point, and the system searches for alternative trains k, k-1, and k-2 in the planned trains. The system calculates the arrival times of these three trains and returns them to the passengers. After the passengers independently select the intended train, the system calculates the fare and recommends the best departure time to the passengers based on the arrival time of the intended train to avoid long waiting at the platform. Ultimately, it is up to the passengers to decide whether to place an order.

[0109] After the passenger places an order, the system interface retains information such as boarding and alighting stations, fares and recommended departure times, and further feeds back vehicle information and boarding codes to the passenger, including: license plate number, vehicle location, distance, estimated arrival time (updated in real time) and boarding QR code.

[0110] 2) The travel process for passengers waiting at the station is as follows Figure 6 As shown in the figure, there are many rural residents and students among the passengers, and some passengers do not have the ability to make online reservations. Therefore, in addition to responding to online reservation needs, it is also necessary to meet the travel needs of passengers waiting at fixed stations. Based on this, the passengers are divided into three categories:

[0111] Type 1: Passengers who have made online reservations in advance;

[0112] Type 2: passengers waiting at the station and expecting to get off at the demand response station;

[0113] Type 3: Passengers who wait at the station and get off at a fixed station.

[0114] In order to improve operational efficiency, fully meet the travel needs of type 2 and 3 passengers, and ensure travel fairness for passengers getting off at fixed stops, four reservation conditions are set as follows:

[0115] Condition 1: Limit the maximum number of reservations for each trip;

[0116] Condition 2: You cannot make a reservation for a train that has already departed;

[0117] Condition 3: The time of arrival at the boarding station shall not be later than the arrival time of the scheduled train;

[0118] Condition 4: You can only book drop-off at demand response stations.

[0119] In response to the needs of different types of passengers, a two-stage dispatching process is designed: the first stage serves type 1 passengers who submit travel needs in the reservation system before departure. The system searches for alternative trains in the planned trains. After the passenger selects the intended train, the system calculates the fare and recommends the best departure time for the passenger. The passenger ultimately decides whether to place an order. The second stage serves type 2 and 3 passengers after departure. When the urban and rural buses arrive at each stop, the passengers get on the bus and submit the get-off location to the system. The system receives the order in real time and determines whether it is included in the dispatching range. Each order is processed in turn through instant processing, thereby achieving real-time response and dynamic dispatch.

[0120] The method of searching for alternative trains is: in the first stage of vehicle dispatch, in addition to providing train k that meets all reservation conditions based on the reservation information, the first two trains k-1 and k-2 are also provided so that passengers can depart in advance when time permits. In the second stage of vehicle dispatch, the first train k and the next train k+1 that arrive after arriving at the boarding station are provided to passengers. If the passenger is not served by train k, he or she can choose a subsequent train to travel. Passengers with personalized choices refer to passengers who choose other than train k, that is, passengers who choose the previous, subsequent, and secondary choices.

[0121] 1.2 Determine the correspondence between demand response sites and fixed sites

[0122] In order to explore whether each station in the demand station set S' is within the DRT service range and further divide the demand response stations into corresponding demand response sections, it is necessary to determine the correspondence between the demand response stations and the fixed stations, that is, to find the fixed station G where passengers who get off at the demand station s get off when taking a fixed route bus. S This paper uses the vector product method to achieve this process, such as Figure 7 As shown, a, b, and c are three consecutive fixed sites. The specific process is as follows:

[0123] Step 1: Find the fixed site b closest to s in the fixed site set D and make vector and

[0124] Step 2: Calculate the vector and The product of and determine its sign. If it is non-negative, the vector and The angle θ=α≤90°, G S1 =a,G S2 =b; otherwise, θ=β>90°, G S1 =b,G S2 =c.

[0125] Step 3: Determine G S . Let s and G S1 , G S2 The distances are s1 and s2 respectively, M is the ratio of s1 to s2, and the terminal travel distance coefficient ξ (ξ ≥ 1) is introduced. If M ≥ ξ, then G S =G S2 , service distance s f =s2; otherwise, G S =G S1 ,s f =s1.

[0126] Step 4: Determine whether the demand station s is within the service range of the DRT. Assume that the DRT can only serve demand stations within L km of the fixed line, and that the distance between two consecutive fixed stations is a straight line. Let s, G S1 and G S2 The coordinates of are (x1, y1), (x2, y2) and (x3, y3), respectively. From the mathematical relationship, we can get: if s satisfies the relationship

[0127]

[0128] It is determined that the required site is within the service range of DRT.

[0129] Step 5: Repeat Steps 1 to 4 for all sites in the demand site set S′, and divide the demand sites that meet formula (1) into the demand response site set S, otherwise they are divided into the discarded site set. S2 The service segment where G is located further divides the demand response sites in S into the set of sites in segments 1 and 2. In particular, if G S2 It is the dividing point between sections 1 and 2, and the site is divided into the section 1 set.

[0130] 1.3 Order pre-processing strategy and passenger secondary selection mechanism

[0131] (1) Define order and vehicle status

[0132] The order state space S is defined as

[0133] S:{P,P Q ,P J ,P B ,P R} (2)

[0134] Where: P is the basic information of the order, and type 1 passengers include the order time starting point end Departure Time Time required to reach the boarding point Type 2 and 3 passengers including starting point end Arrival time at the boarding point P Q Derived from P, including segment Q c , basic fare Service fares Total fare p c ;P J Rejection related information, including whether the order is rejected. c and the reasons for rejection. The specific reasons for rejection are shown in Table 1; B The system calculates the alternative train number and returns it to the passenger. R The order result is determined by the passenger's choice, including the intended service number. and passenger type Type 1 passengers also include a suggested departure timeJ c .

[0135] Table 1 Reasons for rejection

[0136]

[0137] The state space S of train number k k Defined as

[0138] S k :{F k ,Q k ,Z Yk ,Z Sk ,Z k ,Z ik ,U k ,R k ,D ijk ,D k ,T ik ,T k} (3)

[0139] Where: F k is the departure time; Q k Demand response section for service; Z Yk , Z Sk They represent the number of passengers served in the first and second phases of vehicle dispatching respectively; Z k is the total number of passengers carried, which is Z Yk With Z Sk and; Z ik is the remaining passenger capacity when arriving at stop i; U k is the total fare revenue; R k D is the stopover site; ijk is the distance between the next stop j and the current stop i; D k is the total driving distance; T ik is the time to arrive at stop i; T k is the total travel time.

[0140] (2) First-stage preprocessing strategy

[0141] The system gives priority to reservation orders and processes them in the order in which they are placed. After the Type 1 passenger fills in the basic order information in the system, the system starts the first stage of preprocessing without violating reservation condition 4. The specific process is as follows:

[0142] Step 1: Find the train number k that meets the passenger's travel needs

[0143] The search model is as follows:

[0144] mink(4)

[0145] Z Yk <Z Ykmax (5)

[0146]

[0147] Q c =Q k (8)

[0148]

[0149] Formula (4) represents the minimum number of trains; Formula (5) represents the number of reservation orders Z for train k Yk Maximum booking volume Z not reached Ykmax (Booking condition 1); Formula (6) represents the order time of passenger c Earlier than the departure time of train number k F k (Booking condition 2); Formula (7) represents the time when passenger c arrives at the boarding station No later than the arrival time of train number k (Booking condition 3); Formula (8) represents the segment Q where the passenger c gets off c Demand response zone Q served by train number k k If no train number k that meets the conditions is found, the rejection reason 2 is triggered.

[0150] Step 2: Determine whether the alternative trains k-1 and k-2 exist

[0151] Refer to the four reservation conditions to determine whether the passenger can reserve train k-2. If yes, both trains k-1 and k-2 exist. Otherwise, determine whether the passenger can catch train k-2 after immediate departure. If yes, both trains k-1 and k-2 exist. However, if the passenger chooses train k-2, the passenger type changes from 1 to 2. Otherwise, determine whether the passenger can catch train k-1 after immediate departure. If yes, train k-1 exists. Otherwise, neither of them exists. The time when the passenger leaves immediately to arrive at the boarding station Order time The time required to reach the boarding point However, considering that the passengers may not expect to depart immediately, the system gives passengers a certain amount of preparation time. but

[0152]

[0153] Step 3: Determine the train number you want

[0154] Since there are few applications of urban and rural public transportation demand response services and there is no historical order data, the "roulette" idea is used to simulate passenger selection. The specific numerical setting analysis is as follows: ① Passengers have a high intention and preference for the departure time they first choose; ② If the train number k-1 exists, since the service section of this train number does not cover the passenger's target getting-off station, if the passenger chooses this train number, he will have to get off at a fixed station, which will cause inconvenience to the terminal travel; on the contrary, if the train number k-2 exists, the passenger's preference and choice intention for this train number will be significantly enhanced. Based on the above analysis, the train numbers with the strongest and weakest passenger selection intentions are k and k-1 respectively. In addition, the probability of passengers giving up public transportation (rejection reason 3) is set to 5%, and the specific probability of passengers choosing different results autonomously is shown in Table 2.

[0155] Table 2 The probability of passengers choosing different results on their own

[0156]

[0157] Note: “√” represents existence, “×” represents non-existence.

[0158] Step 4: Calculate the passenger's recommended departure time

[0159] After the passenger selects the train they want, the system recommends the best departure time for the passenger based on the time it takes the passenger to reach the boarding station and the arrival time of the train they want. c , in order to reduce the waiting time of passengers at the station. Considering that passengers usually wait in advance, the advance waiting time parameter is introduced but

[0160]

[0161] Where: The time when the intended train selected by passenger c arrives at his boarding station, is the time required for passenger c to arrive at the boarding station.

[0162] (3) Second-stage preprocessing strategy

[0163] Real-time orders are processed first for the trains that depart first, and orders for the same train are processed in order of the boarding stations. When passengers of type 2 and 3 are waiting at the station, basic order information is generated, and the system starts the second stage of preprocessing. The specific process is as follows:

[0164] Step 1: Use equations (4), (7) and (9) to find the first train k that arrives after the passenger arrives at the boarding station. If no train k that meets the conditions is found, the rejection reason 2 is triggered.

[0165] Step 2: If the passenger type is 3, the intended train number is k and the preprocessing ends; otherwise, determine whether equation (7) is satisfied. If so, the intended train number of the passenger of type 2 is k; otherwise, proceed to Step 3.

[0166] Step 3: Determine the alternative bus number k+1 from bus number k. Based on the analysis of the passenger's intended bus number in the first stage of preprocessing, the probabilities of different choices for type 2 passengers are determined as follows: 15% probability of choosing bus number k, 80% probability of choosing bus number k+1, and 5% probability of terminating the bus trip.

[0167] (4) Passenger Second Selection Mechanism

[0168] The first stage dispatches the passengers who have made reservations. This type of passengers will only fail to make reservations if they give up on public transportation. During the second stage dispatch, if the passenger's first selected intended bus is rejected by the system, the secondary selection mechanism will be triggered, specifically:

[0169] Mechanism 1: If the passenger of type 2 is rejected by the system because the time constraint is not met, the passenger immediately chooses to arrive at the corresponding fixed station G S Get off the bus and submit your ride request again.

[0170] Mechanism 2: If the order is rejected because the vehicle is full, the passenger immediately chooses to take the next vehicle k+1, and the passenger of type 2 gives up reaching the demand response station and chooses to reach the corresponding fixed station G. S get off.

[0171] After the second selection, the system will only reject the order again if the vehicle is fully loaded. However, in practice, taking into account alternative modes of travel such as taxis and private cars, if the passenger is rejected again, it is assumed that these passengers will eventually choose alternative modes of travel.

[0172] 1.4 Total fare calculation considering service fares

[0173] The corresponding fares are charged for different types of passengers, and the passenger fare is defined as the basic fare and the service fare. The fixed bus fare is recorded in the n×n dimensional matrix p n×n The base fare for type 1 and 2 passengers is calculated based on the fixed station G corresponding to the demand response station where they get off. S Calculate. Service fares is the additional cost caused by the vehicle detouring to meet the demand response station, which is determined by the service distance s f It is decided to introduce a service fee coefficient γ, and calculate it as one kilometer for every kilometer less than one kilometer. If the DRT operates during peak hours, an additional service fare of β times will be charged per kilometer, where β is the peak operation fare coefficient.

[0174] The service fare for type 3 passengers is 0, and the service fare for type 1 and 2 passengers is 0 for

[0175]

[0176] Where: H k is a decision variable used to determine whether train number k is running during peak hours.

[0177] Total fare p for passenger c c for

[0178]

[0179] Total fare revenue U for train number k k for

[0180]

[0181] Where: Whether the reservation order of passenger c is responded to by train k.

[0182] 2 Scheduling Model

[0183] 2.1 Model establishment

[0184] (1) Model assumptions

[0185] The dynamic dispatching model of alternating response of urban and rural bus sections is based on the following assumptions: ① The road conditions are good and there are no external factors that cause vehicle operation interruptions; ② The average driving speed of vehicles in rural areas is faster than that in cities; ③ The detour speed of vehicles in rural demand response sections is the same as that in cities; ④ Vehicles travel at a constant speed in each section; ⑤ Each order corresponds to one passenger; ⑥ Except for passengers who are rejected or voluntarily give up bus travel, the travel information of other passengers will not change midway; ⑦ The distance between stations is Euclidean distance.

[0186] (2) Objective function

[0187] From the perspective of urban and rural public transportation serving the people, we maximize the interests of passengers and maximize the choices of passengers in different situations through order pre-processing and secondary selection mechanisms. On this basis, we take the shortest mileage of urban and rural public transportation as the goal, that is,

[0188]

[0189] Where: Z is the mileage of all vehicles in the system, X ijk is a decision variable to determine whether train number k stops at stations i, j, d consecutively ij is the distance between site i and site j.

[0190] (3) Constraints

[0191] ① Service section constraints

[0192] Each train can only provide service in one demand response section during one-way operation, i.e.

[0193]

[0194] Where: Q k The demand response section serving train number k.

[0195] Of the two consecutive DRT trains, only one train serves a specific demand response section, that is,

[0196]

[0197] Where: is the decision variable, and the judgment section q Whether it is served by train number k.

[0198] ② Vehicle passenger capacity constraints

[0199] The remaining passenger capacity R of train number k leaving the current station j jk is the remaining passenger capacity R leaving the previous station i ik Subtract the net number of people boarding at the current stop Right now

[0200]

[0201] The type 1 passengers served by train k have successfully made reservations before departure, and the capacity needs to be reserved for this type of passengers. Therefore, when train k departs, the remaining capacity of the first station is R 1k The maximum passenger capacity R minus the total number of reservations for train number k Right now

[0202]

[0203] ③Run time constraints

[0204] In order to avoid a long one-way running time and ensure the frequency and punctuality of two-way departure, the time tolerance coefficient λ is introduced. The one-way running time T of train number k is k No more than λ times the fixed line operation time T0, that is

[0205]

[0206] Where: T nk represents the time when train number k arrives at the terminal station, F k is the departure time of train number k.

[0207] Assume that the last station number of the urban section is g, the first and last stations of the demand response section served by train number k are l,m, the urban driving speed is v1, and the rural driving speed is v2. In addition, the average speed during peak hours is affected by the time when passengers get on and off the bus and the degree of road congestion. The peak operation time coefficient μ is introduced, and the time T when train number k arrives at the stop i is ik for

[0208]

[0209] Where: R k is the stopover site of train number k, D ijk is the distance between the next stop j of train number k and the current stop i.

[0210] ④Transit time constraints

[0211] Although increasing demand-response stations can bring convenience to more passengers, vehicle detours will affect the travel experience of type 3 passengers. Therefore, the time required to reach each fixed station is set to no more than α times the original time, where α is the transit time coefficient.

[0212]

[0213] Where: is the time for fixed-line train number k to arrive at each stop i.

[0214] 2.2 State Transfer

[0215] (1) Order status transfer

[0216] Order status transfer occurs during order preprocessing and secondary selection.

[0217] When passengers of type 1 select a train, the system gives them a recommended departure time, so the departure time shifts; when they select train k-1, the alighting station shifts; when they select train k-1 or k-2, the passenger type shifts. The shift equations are (23) to (25).

[0218]

[0219] Where: is the departure time of passenger c, J c is the suggested departure time for passenger c, is the alighting stop for passenger c, The fixed stop where passenger c gets off when taking a fixed-route bus. is the type of passenger c, This is the train number that passenger c intends to take.

[0220] When passengers of type 2 and 3 trigger the secondary selection mechanism, the intended service number is transferred, and at the same time, the alighting station and passenger type of passengers of type 2 are transferred. The transfer equations are as follows: (26) to (28).

[0221]

[0222] (2) Vehicle state transfer

[0223] Since the system processes each order immediately, the vehicle state transfer occurs immediately after the system receives each order. If the demand response station is included in the service station of train number k, then this station and other fixed stations have been or will be served by train number k, and can be regarded as a "temporary fixed station". The system determines whether the relevant constraints are met when it first receives the demand to get off at this station. Subsequent demands only need to determine whether there is remaining passenger capacity.

[0224] Define the vehicle transfer action σ k , k , specifically:

[0225] σ k :{Z Yk ,Z Sk ,Z k ,U k} (29)

[0226] ρ k :{R k ,D ijk ,D k ,T ik ,T k} (30)

[0227] Then the state space S of train number k k It can be further expressed as: S k :{F k ,Q k ,σ k ,ρ k ,Z ik}.

[0228] ① When passenger c of train number k asks to get off at a stop that has been served, that is, The system pre-processes and determines whether to reject the order based on the constraints, and updates σ k and Z ik ,Right now

[0229]

[0230] {σ k ,Z ik The update equations of} are (32) to (36).

[0231]

[0232] Z k =Z k +1=Z Yk +Z Sk (33)

[0233] U k =U k +p c (34)

[0234]

[0235] In formula (36), train number k stops at stations u and w in sequence.

[0236] ② When passenger c of train number k requests to get off at an unserved demand response station, that is, The system pre-processes and determines whether to reject the order based on the constraints, and updates σ k , k and Z ik ,Right now

[0237]

[0238] Among them, σ kThe update equations are (32) to (34), {ρ k ,Z ik The update equations of} are (21), (38) to (44).

[0239]

[0240] D ijk =X ijk d ij (39)

[0241]

[0242] T k =T ik -F k (41)

[0243]

[0244] Z wk =Z vk -1=Z uk -2 (44)

[0245] In formula (44), the train number k originally stops at stations u and w in sequence, but now a new stop is added Formula (42) assigns it to parameter v. After scheduling, the train now stops at stations u, v, and w in sequence and satisfies formula (44).

[0246] 3 Solution Algorithm

[0247] 3.1 Solution strategy combining enumeration method and genetic algorithm

[0248] When a new demand response station is added to the stop of bus number k, the change of the driving route is limited to the demand response section, and no global replanning is required. Therefore, this paper focuses on the route adjustment of urban and rural buses in the demand response section. When serving fewer demand response stations, efficient and precise algorithms such as enumeration methods can be used to quickly determine the optimal solution. However, as the number of response stations increases, the solution space of the enumeration method will expand exponentially. Therefore, heuristic algorithms such as genetic algorithms can be used to solve it.

[0249] When the number of stations to be adjusted is higher than a certain critical value, a genetic algorithm is used to solve it, otherwise an enumeration method is used to solve it, and this critical value is defined as the selection coefficient. To determine the specific value of the selection coefficient, it is necessary to conduct an experimental comparison of the time efficiency of the enumeration method and the genetic algorithm when solving the same order and the same station scale, and select the number of stations with roughly the same solution time for the two. In the actual decision-making process, the determination of the selection coefficient also needs to be flexibly adjusted based on the setting of the genetic algorithm parameters, the tolerance of drivers and passengers for waiting calculation time and other factors. The solution strategy is as follows: Figure 8 As shown, where l and m These are the first and last stops in the demand response section served by the current train.

[0250] 3.2 Genetic Algorithm Design

[0251] The sequential coding rule is adopted to code the fixed stations of the urban and rural bus fixed routes in sequence. The last fixed station, i.e. the terminal station, is coded as n, and the demand response stations are coded in sequence from n+1. When a demand response station is added to the stop of bus number k, the first and last fixed stations in the demand response section of the service, i.e. the section demarcation point l, m Construct a path within the demand response segment for the starting and ending points, and add the fixed station coding sequence of the remaining segments before and after it to form a complete stop sequence for train number k. The value of the objective function, that is, the shortest vehicle path, is used as a measure of individual fitness. When selecting operations, the elite preservation strategy is combined with the roulette wheel selection strategy to perform survival of the fittest operations. Considering that the first and last digits in the population represent the first and last fixed stations of the segment, which cannot be changed, the range of crossover and mutation is between the second and second to last chromosomes in the population. Using the rule of random two-point crossover and mutation, the number of chromosomes for crossover and mutation is

[0252] Although the present invention has been described above with reference to the embodiments, various modifications may be made thereto and parts thereof may be replaced by equivalents without departing from the scope of the present invention. In particular, as long as there is no structural conflict, the various features in the embodiments disclosed in the present invention may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A section alternating responsive urban and rural public transportation dispatching method considering passengers' autonomous selection, characterized in that: Here are the steps: S1. Model preparation stage: Determine the demand response sections, section demarcation points, locations of demand sites, and the correspondence between demand response sites and fixed sites; S2. Two-stage scheduling process: S201, before departure, the first stage, determine whether there is a new reservation order, if yes, transfer to S3; otherwise, wait for the passenger to submit a new order in the reservation system; S202, after the start, enter the second stage; When the vehicle arrives at each stop, it determines whether there are passengers boarding the vehicle to submit an order. If so, it proceeds to S3; Otherwise, when the vehicle arrives at the next stop, continue to determine whether there are passengers who have boarded and submitted an order; repeat this step, and when the vehicle arrives at the first or last stop, the system ends; S3, instant processing of orders and dynamic scheduling process: S301, pre-processing the new order, that is, determining the intended service number selected by the passenger for the first time and calculating the fare; S302, determining whether there is remaining passenger capacity in the intended service number selected by the real-time passenger, if yes, proceeding to S303; otherwise, proceeding to S307; S303, determine whether the passenger has made a second selection, if so, accept the order, include it in the dispatch range, and update the vehicle status. The order status is updated while booking the passenger. The pre-processing is completed and the system goes to S2, where it continues to determine whether there is a new order; Otherwise, go to S304; S304: The passenger does not make a second choice; the optimal path is obtained by using a solution strategy combining enumeration method and genetic algorithm, and it is determined whether it meets the constraints. If so, the order is accepted, included in the dispatch range, and the vehicle status is updated. The order status of the reserved passenger is also updated at the same time. The preprocessing is completed and the system goes to S2, where it continues to determine whether there is a new order. Otherwise, go to S305; S305, determining whether the passenger is a reserved passenger, if so, the system does not accept the order, the reservation fails, and the passenger makes a new reservation; Otherwise, the secondary selection mechanism is triggered to update the order status; S306, determine whether the system has not accepted the order, if so, the pre-processing ends and the process goes to S2, where the system continues to determine whether there is a new order, otherwise, the process goes to S302; S307: If the passenger has made a second choice, the order is not accepted, and the passenger chooses another alternative mode of travel, and the system updates the order status; Otherwise, the secondary selection mechanism is triggered, the order status is updated, and the process proceeds to S306.

2. The section alternating responsive urban and rural public transportation dispatching method considering passengers' autonomous selection according to claim 1 is characterized in that: In step S1, the demand response section is set in the rural section that is the focus of the urban and rural bus operation line, and a section boundary point is set between the urban section and the rural section. In the rural section, the number of fixed stations and the operating mileage are comprehensively analyzed, and the appropriate fixed stations are set as the section boundary point to achieve a balance in service intensity between the two rural sections, and demand stations are arranged in places with dense traffic on both sides of the desired response section.

3. The section alternating responsive urban and rural public transportation dispatching method considering passengers' autonomous selection according to claim 1 is characterized in that: In step S1, the specific steps of determining the corresponding relationship between the demand response site and the fixed site by the vector product method are as follows: Define a, b, and c as three consecutive fixed sites. In the fixed site set D, find the fixed site b closest to s and make the vector and Calculating vectors and The product of and determine its sign, if it is non-negative, vector and The angle θ=α≤90°, G S1 =a,G S2 =b; otherwise, θ=β>90°, G S1 =b,G S2 =c; Determine G S , let s and G S1 , G S2 The distances are s1 and s2 respectively, M is the ratio of s1 to s2, and the terminal travel distance coefficient ξ (ξ ≥ 1) is introduced. If M ≥ ξ, then G S =G S2 , service distance s f =s2; otherwise, G S =G S1 ,s f =s1; Determine whether the demand station s is within the service range of DRT. Assume that DRT can only serve demand stations within L km of the fixed line, and two consecutive fixed stations run in a straight line. Let s, G S1 and G S2 The coordinates of are (x1, y1), (x2, y2) and (x3, y3), respectively. From the mathematical relationship, we can get: if s satisfies the relationship It is determined that the required site is within the service range of DRT; Repeat the above steps for all sites in the demand site set. The demand sites that meet formula (1) are divided into the demand response site set, otherwise they are divided into the discarded site set. According to the service segments corresponding to each demand response site, the demand response sites in the set are further divided into the segment 1 and 2 site sets; in particular, if it is the dividing point between segments 1 and 2, the site is divided into the segment 1 set.

4. The method for urban and rural public transportation dispatching in section alternating response mode considering passengers' autonomous selection according to claim 1 is characterized in that: In step S301, the steps of preprocessing the acquired order are as follows: Find the train number k that meets the passenger's travel needs; The search model is as follows: Wherein, formula (1) represents the minimum number of trains; formula (2) represents the number of reservation orders Z for train k service. Yk Maximum booking volume Z not reached Ykmax , Formula (3) represents the order time of passenger c Earlier than the departure time of train number k F k , Formula (4) represents the time when passenger c arrives at the boarding station No later than the arrival time of train number k Formula (5) represents the segment Q where the passenger c gets off c Demand response zone Q served by train number k k same; Determine whether the alternative trains k-1 and k-2 exist, and determine the intended train. After the passenger selects the intended train, the system recommends the best departure time for the passenger based on the time it takes for the passenger to arrive at the boarding station and the arrival time of the intended train. c , in order to reduce the waiting time of passengers at the station.

5. The section alternating responsive urban and rural public transportation dispatching method considering passengers' autonomous selection according to claim 1 is characterized in that: In step S303, the specific steps of the secondary selection mechanism are as follows: If a passenger who is waiting at a station and wants to get off at a demand response station is rejected by the system because the time constraint is not met, he / she will immediately choose to arrive at the corresponding fixed station G. S Get off the bus and submit your ride request to the system again; If the order is rejected because the vehicle is full, the passenger will immediately choose to take the next vehicle k+1. Passengers waiting at the station and expecting to get off at the demand response station will give up reaching the demand response station and choose to reach the corresponding fixed station G. S get off; After the second selection, the system will only reject the order again if the vehicle is full. If the passengers are rejected again, it is assumed that these passengers will eventually choose to travel by alternative means.

6. The method for dispatching urban and rural public transportation in sections alternating in response to passengers' autonomous choices according to claim 1, characterized in that: In step S301, the corresponding passenger fare is calculated, updated and determined as follows: The corresponding fares are charged for different types of passengers, and the passenger fare is defined as the basic fare and the service fare. The fixed bus fare is recorded in the n×n dimensional matrix p n×n The basic fare for passengers who make online reservations in advance and wait at the station and expect to get off at a demand response station is calculated based on the fixed station G corresponding to the demand response station where they get off. S Calculate service fares is the additional cost caused by the vehicle detouring to meet the demand response station, which is determined by the service distance s f It was decided to introduce a service fee coefficient γ, whereby less than one kilometer will be counted as one kilometer. If the DRT operates during peak hours, an additional service fare of β times will be charged per kilometer, where β is the peak operation fare coefficient; The service fare for passengers waiting at the station and getting off at a fixed station is 0, and the service fare for passengers of type 1 and 2 is for: Where: H k is a decision variable used to determine whether train number k is running during peak hours. The total fare p for passenger c c for Total fare revenue U for train number k k for: Where: Whether the reservation order of passenger c is responded to by train k.

7. The section alternating responsive urban and rural public transportation dispatching method considering passengers' autonomous selection according to claim 1 is characterized in that: In step S304, the objective function of the scheduling model is: Where: Z is the mileage of all vehicles in the system, X ijk is a decision variable to determine whether train number k stops at stations i, j, d consecutively ij is the distance between site i and site j; The constraints of the scheduling model include: Service zone constraints: Each train can only provide service in one demand response section during a one-way operation, namely: Where: Q k The demand response section serving train number k; Among two consecutive DRT trains, only one train serves a specific demand response section, namely: Where: is the decision variable, and the judgment section q Whether it is served by train number k; Vehicle capacity constraints The remaining passenger capacity R of train number k leaving the current station j jk is the remaining passenger capacity R leaving the previous station i ik Subtract the net number of passengers boarding at the current stop Right now: The type 1 passengers served by train k have successfully made reservations before departure, and the capacity needs to be reserved for this type of passengers. Therefore, when train k departs, the remaining capacity of the first station is R 1k The maximum passenger capacity R minus the total number of reservations for train number k Right now: Run time constraints: In order to avoid a long one-way running time and ensure the frequency and punctuality of two-way departure, the time tolerance coefficient λ is introduced. The one-way running time T of train number k is k No more than λ times the fixed line operation time T0, that is Where: T nk represents the time when train number k arrives at the terminal station, F k is the departure time of train number k; Assume that the last station number of the urban section is g, the first and last stations of the demand response section served by train number k are l,m, the urban driving speed is v1, and the rural driving speed is v2. In addition, the average speed during peak hours is affected by the time when passengers get on and off the bus and the degree of road congestion. The peak operation time coefficient μ is introduced, and the time T when train number k arrives at the stop i is ik for: Where: R k is the stopover site of train number k, D ijk is the distance between the next stop j of train number k and the current stop i; Time constraints in transit: Where: is the time for fixed-line train number k to arrive at each stop i.

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