A method for joint control of bus speed and station parking speed

Abstract

This invention provides a method for joint control of Bus Rapid Transit (BRT) operating speed and station parking, belonging to the field of public transport management and control technology. The method includes the following steps: 1) Taking BRT operating reliability, intersection operating efficiency, and passenger comfort as optimization objectives, and customizing the weights of each indicator based on different needs, a nonlinear target programming model for BRT operating trajectory is established, using station parking time and interval speed as decision variables; 2) Solving the target programming model yields the BRT station parking time and interval operating speed guidance scheme, i.e., the BRT operating trajectory control scheme. This invention considers the optimization of multiple objectives related to the BRT operating service level, specifically considering its three-dimensional objectives of on-time arrival, intersection traffic efficiency, and interval passenger comfort. Different weights can be set for the three types of objectives based on different optimization needs, achieving the optimal comprehensive service level of BRT.

Description

Technical Field

[0001] This invention belongs to the field of public transport management and control technology, and in particular relates to a method for joint control of the speed and station parking of rapid transit buses. Background Technology

[0002] Prioritizing public transport is a crucial development strategy for addressing urbanization issues such as congestion, emissions, and fairness in travel. To implement this policy, governments invest heavily in public transport infrastructure. Bus Rapid Transit (BRT) systems, characterized by dedicated right-of-way, high controllability, platform fare collection, and higher passenger capacity than conventional buses, represent a high-quality ground-based public transport system with minimal modification requirements and transport capacity second only to rail transit. In recent years, with increasing demands for travel quality and the emergence of ride-hailing and bike-sharing services, public transport systems face challenges. Improving service levels is crucial for attracting more passengers. BRT operation is affected by traffic conditions, such as intersection signal control, and passenger boarding and alighting processes. Therefore, improving the punctuality, efficiency, and smoothness of BRT operations is an urgent issue to be addressed.

[0003] Common bus operation control optimization techniques include stop control and speed control. Stop control can improve the reliability of bus service, with existing technologies focusing on stop control based on headway. Stop-based control strategies can balance bus headway to some extent; however, because BRT routes pass through multiple intersections, vehicle efficiency is affected by intersection signal delays, limiting the effectiveness of stop control strategies. Speed ​​control can flexibly adjust bus speed within a section, further controlling bus arrival times at stops or intersections. Some technologies combine speed control and stop control to achieve better optimization results, improving operational efficiency while balancing headway.

[0004] However, existing speed control, station control, or combined speed and station control technologies are mostly focused on single objectives such as passenger waiting time and bus operating costs, and are still insufficient for comprehensive optimization of the service level of rapid transit, such as punctuality, efficiency, and comfort. Summary of the Invention

[0005] The purpose of this invention is to provide a method for joint control of the speed and station parking of Bus Rapid Transit (BRT) vehicles, characterized by the following steps:

[0006] S1: Taking the reliability of BRT operation, the efficiency of intersection operation and the comfort of passengers as optimization objectives, the weights of each indicator are customized based on different needs, and the station time and interval speed are used as decision variables to establish a nonlinear target programming model for BRT operation trajectory.

[0007] S2: Solve the objective programming model to obtain the bus rapid transit station dwell time and interval operation speed guidance scheme, i.e. the bus rapid transit operation trajectory control scheme.

[0008] Furthermore, in S1, different priority factors P1, P2, and P3 are set, along with a bias weight W. 11 W 12 w 31 and w 32 Establish a goal programming model as follows:

[0009]

[0010] In the above formula, P1, P2, and P3 are all priority factors in the goal programming model; >> indicates much greater than; W 11 Weighting of BRT vehicles arriving at stations early; W 12 Weighting of BRT vehicles arriving late at stations; For the deviation variable of BRT vehicles arriving at the station early; For BRT vehicles arriving late at stations, this is the deviation variable. e represents the deviation variable in BRT vehicle delays at intersections. 31 W represents the weight of the BRT vehicle's speed being lower than the desired speed in interval i; 32 The weight for the speed of the BRT vehicle in section i being higher than the expected speed; The deviation variable is the actual speed of the BRT vehicle being lower than the expected speed; This is the deviation variable where the actual speed of a BRT vehicle is higher than the expected speed.

[0011] Furthermore, in S1, to ensure the reliability of BRT operation, a punctuality constraint is adopted. Specifically, the actual arrival time of the BRT at the originating station is not optimized; instead, it is taken as the expected arrival time at that station, expressed as:

[0012]

[0013] In the above formula, t a1 This refers to the actual arrival time of the BRT at station 1. Let be the expected arrival time of the BRT at station 1. To optimize the reliability of BRT operation, the actual arrival times at other stations should be as close as possible to the expected arrival times given in the timetable, expressed as:

[0014]

[0015] In the above formula, t aj This represents the actual arrival time of the BRT at station j. Let t be the expected arrival time of the BRT at station j; where t ajComposed of the departure time of the upstream station, the travel time between stations, and the delay at the intersection, it is represented as:

[0016]

[0017] In the above formula, t d(j-1) L represents the departure time of the rapid transit bus from station j-1; i v is the length of interval i; i D represents the actual speed of the BRT in interval i; k The delay of the vehicle at intersection k; the expression for the BRT departure time is:

[0018] t dj =t aj +T j

[0019] In the above formula, T j Let be the dwell time of the BRT at station j, including passenger boarding and alighting time and additional dwell time; the corresponding constraint on the BRT departure time is expressed as:

[0020]

[0021] In the above formula, Let J be the passenger pick-up and drop-off time at station j.

[0022] Furthermore, in S1, regarding the intersection's operational efficiency, an intersection delay constraint is adopted. To minimize the intersection delay, the corresponding objective constraint is obtained, expressed as:

[0023]

[0024] If the BRT arrives at the intersection during the green light, the intersection delay is 0; if it arrives during the red light, it needs to stop and wait. In this case, the delay is the difference between the green light start time and the BRT arrival time, expressed as:

[0025]

[0026] In the above formula, The red light turns on at the δth signal cycle when the BRT arrives at intersection k. The green light turns on at the δ-th signal cycle when the BRT arrives at intersection k. The signal cycles for the two aforementioned green light activation times begin from the red light. ak The time when the BRT arrives at intersection k; Let be the time when the red light turns on in the next cycle of the δ-th signal cycle after the BRT arrives at intersection k; where, The calculation formula is expressed as:

[0027]

[0028] In the above formula, r k C is the moment when the red light turns on during the first signal cycle at intersection k; k The duration of signal k at the intersection; The calculation formula is expressed as:

[0029]

[0030] In the above formula, R k k is the red light duration at the intersection; t ak The calculation formula is expressed as:

[0031]

[0032] In the above formula, j is the upstream station of k; i is the upstream section of intersection k.

[0033] Furthermore, in S1, for the sake of passenger comfort, a BRT operating speed constraint is adopted at the section, expressed as:

[0034]

[0035] In the above formula, Let be the expected vehicle speed in interval i.

[0036] Furthermore, in S2, after linearizing the nonlinear terms in the target programming model, the existing solver is used to solve the problem, obtaining the actual bus speed and station dwell time for each section, thereby completing the rapid transit trajectory control scheme.

[0037] Furthermore, in S2, by introducing the auxiliary variable α, D k The expression is linearized and represented as:

[0038]

[0039] In the above formula, M is a sufficiently large positive number.

[0040] Furthermore, in S2, regarding the nonlinear term L... i and v i By fitting three piecewise functions, the velocity is divided into three intervals: [1, 5], [5, 20], and [20, 60]. The expression is:

[0041]

[0042] In the above formula, f σ For use Linearize the auxiliary continuous decision variables, σ = 1, 2, 3; z σ For use Linearized auxiliary 0-1 decision variables, σ = 1, 2, 3; the corresponding constraints are expressed as follows:

[0043]

[0044] Compared with the prior art, the beneficial effects of the present invention are mainly reflected in:

[0045] 1. This invention considers the optimization of multiple objectives of the rapid transit service level, specifically considering the three-dimensional objectives of on-time arrival, intersection traffic efficiency, and interval riding comfort. Different weights can be set for the three types of objectives according to different optimization needs, so as to achieve the optimal comprehensive service level of rapid transit.

[0046] 2. This invention adopts a combined stationing and speed control strategy, taking into account the differences in passenger flow at different stations and the impact of intersection signal timing on stationing time and interval speed. This can balance the BRT headway, reduce the average travel time of buses and passengers, and improve the trajectory control effect. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the interval operation according to an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the route and sections according to an embodiment of the present invention;

[0049] Figure 3 This is a trajectory comparison diagram before and after the implementation of the combined station parking and vehicle speed control in an embodiment of the present invention;

[0050] Figure 4 This is a comparison diagram of trajectories for different control strategies in embodiments of the present invention;

[0051] Figure 5 This is a graph showing the station dwell time results for each site according to an embodiment of the present invention;

[0052] Figure 6 This is a comparison chart of the deviation effects of different control strategies in embodiments of the present invention;

[0053] Figure 7 This is a comparison chart of average passenger travel time under different control strategies according to embodiments of the present invention;

[0054] Figure 8 This is a comparison chart of average passenger travel time under different combinations of priority factors according to an embodiment of the present invention;

[0055] Figure 9 This is a graph showing the variation of deviation under different green light ratio increments in an embodiment of the present invention. Detailed Implementation

[0056] The following will describe in more detail a method for joint control of bus speed and station parking according to the present invention with reference to schematic diagrams, which illustrate preferred embodiments of the invention. It should be understood that those skilled in the art can modify the invention described herein while still achieving the beneficial effects of the invention. Therefore, the following description should be understood as being of general knowledge to those skilled in the art and is not intended to limit the invention.

[0057] Example

[0058] This application proposes a method for joint control of bus speed and station parking for punctual, efficient, and comfortable rapid transit systems, including:

[0059] S1. Considering the issues of punctuality, efficiency, and comfort of Bus Rapid Transit (BRT) at stations, intersections, and intervals, a target system is designed based on three indicators: arrival punctuality deviation, intersection delay, and interval speed deviation. The weights of each indicator are customized based on different needs. With station dwell time and interval speed as decision variables, a nonlinear target programming model for BRT operation trajectory is established.

[0060] S2. A linearization method for the target programming model is proposed to solve the bus rapid transit station dwell time and interval operation speed guidance scheme, i.e. bus rapid transit operation trajectory control scheme.

[0061] In this invention, the BRT's interval operation is as follows: Figure 1 As shown, i = 1, 2, ... I represents the interval index, j = 1, 2, ... J represents the bus stop index, and k = 1, 2, ... K represents the intersection index. The expected arrival times for stops j and j+1 are respectively... and Passenger pick-up and drop-off time at station j is

[0062] The BRT departs station j without making an additional stop after picking up and dropping off passengers. It then travels at the desired speed along section i to stop at intersection k at a red light. If the BRT employs a stop control strategy at station j, the stop time is T. j , and then t aj Once you leave station j, you can travel at the desired speed in section i to intersection k and pass through after the green light turns on.

[0063] BRT operates at the desired speed in interval i+1. When the light turns green at intersection k+1, the actual vehicle speed is v. i+1 The value can be taken according to the desired vehicle speed. Within the interval i+2, at the desired speed... Running to station j+1 will be later than the scheduled time. To ensure on-time arrival at the station, the vehicle speed in section i+2 is adjusted by controlling the actual vehicle speed v. i+2 With expected speed To minimize deviations, ensure that the BRT arrives at downstream stations as punctually as possible while maintaining a reasonable speed.

[0064] Based on the above-mentioned section operation control concept, this invention is applied to an embodiment of the Shanghai Fengpu Expressway BRT line in the upbound direction, such as... Figure 2 As shown in the figure. This embodiment passes through 13 stations, with a total route length of 20.31km and 44 intersections, which can be divided into 56 sections. GPS data and departure timetables from the morning peak hours (7:00-9:00) of five working days (October 11th to October 15th, 2021) of BRT vehicles were used to calculate the expected arrival time at each station. Passenger boarding and alighting times at each station were calculated by combining this data with passenger card swipe data. Signal timing at each intersection was obtained through surveys.

[0065] The optimization objectives of the goal programming model in step S1 are threefold: first, the reliability of Bus Rapid Transit (BRT) operation, represented by the deviation between the expected and actual arrival times; second, the efficiency of BRT operations at intersections, represented by the delays of BRT vehicles at intersections; and third, the comfort of the ride, represented by the deviation between the actual and expected speeds of BRT vehicles within a given section. Based on the priority order of reliability, efficiency, and comfort, different priority factors P1, P2, and P3, and a deviation weight W, are set. 11 W 12 W 31 and W 32 Establish a goal programming model, as shown in the following equation:

[0066]

[0067] In the formula: P1, P2, and P3 are priority factors of the goal programming model, and the symbol ">>" indicates that they are much greater than; W 11 W 12 These represent the weights of the early and late arrival stations for BRT vehicles, respectively. These represent the deviation variables of BRT vehicles arriving at stations early and late, respectively, in seconds (s). This represents the deviation of BRT vehicle delays at intersections, in seconds (s); W 31 and W 32 These represent the weights of the BRT vehicle's speed being lower and higher than the expected speed in interval i, respectively; These represent the deviation variables where the actual speed of the BRT vehicle is lower than and higher than the expected speed, respectively, in km / h.

[0068] The model's constraints take into account the operation of the Bus Rapid Transit (BRT) system at three aspects: stations, intersections, and sections.

[0069] (1) Punctuality constraint

[0070] The actual arrival time of the BRT at the originating station is not optimized; instead, the expected arrival time at that station is used.

[0071]

[0072] In the formula: t a1 This indicates the actual arrival time of the BRT at station 1; This indicates the expected arrival time of the BRT at station 1.

[0073] To optimize the reliability of Bus Rapid Transit (BRT) operations, the actual arrival times at other stations should be as close as possible to the expected arrival times given in the timetable.

[0074]

[0075] In the formula: t represents the expected arrival time of the BRT at station j; aj This indicates the actual arrival time of the BRT at station j.

[0076] t aj It consists of the departure time of the upstream station, the travel time between stations, and the delay at the intersection:

[0077]

[0078] In the formula: t d(j-1) Indicates the departure time of the BRT from station j-1; L i v represents the length of interval i, in km; i D represents the actual speed of the BRT in interval i, in km / h; k This indicates the delay of a vehicle at intersection k, measured in seconds (s).

[0079] The BRT departure time expression and corresponding constraints are as follows:

[0080] t dj =t aj +T j

[0081]

[0082] In the formula: T j This indicates the BRT's dwell time at station j, including passenger boarding and alighting time and additional dwell time for the BRT to pass through the intersection on green light; This indicates the passenger pick-up and drop-off time at station j.

[0083] (2) Intersection delay constraints

[0084] To minimize intersection delays, the following objective constraints are obtained:

[0085]

[0086] If the BRT arrives at the intersection during the green light, the intersection delay is 0; if it arrives during the red light, it needs to stop and wait, and the delay is the difference between the green light start time and the BRT arrival time, as shown in the following formula:

[0087]

[0088] In the formula: These represent the times when the red and green lights turn on in the δ-th signal cycle when the BRT arrives at intersection k, respectively. The signal cycle starts from the red light; t ak This indicates the time when the BRT arrives at intersection k; This indicates the moment when the red light turns on in the next cycle of the δth signal cycle when the BRT arrives at intersection k.

[0089] The calculation method is as follows:

[0090]

[0091] In the formula: r k Indicates the moment when the red light turns on at intersection k in the first signal cycle; C k R represents the duration of the k-signal cycle at the intersection, in seconds. k This indicates the duration of the red light at intersection k, in seconds.

[0092] t ak The calculation method is as follows:

[0093]

[0094] In the formula, j is the upstream station of k, and i is the upstream section of intersection k.

[0095] (3) Intersection running speed constraints

[0096] To optimize the smoothness of BRT operation, the design speed for each section should be as close as possible to the desired speed.

[0097]

[0098] In the formula: Let i represent the expected vehicle speed in interval i.

[0099] Model Solving

[0100] Due to the established model D k Since the expression is a piecewise function, it cannot be solved directly using linear programming. Therefore, by introducing an auxiliary variable α, D is solved... k Linearization:

[0101]

[0102] In the formula: M is a sufficiently large positive number.

[0103] It is also a nonlinear term, represented by a piecewise function fitting, dividing the velocity into three intervals: [1, 5], [5, 20], and [20, 60]. The expression is:

[0104]

[0105] In the formula: f σ Indicates used for Linearized auxiliary continuous decision variables, σ = 1, 2, 3; z σ Indicates used for Linearized auxiliary 0-1 decision variables, σ = 1, 2, 3.

[0106] The corresponding constraints are:

[0107]

[0108] After linearizing the model, it can be solved using existing solvers to obtain the actual bus speeds and station dwell times for each section.

[0109] In this embodiment, the weight parameters in the objective function are P1 = 1000, P2 = 1, P3 = 0.001, and W... 11 =0.2, W 12 =0.8, W 31 =0.6, W 32 =0.4, other parameters v max =60km / h, v min = 1km / h.

[0110] The BRT trajectory comparison diagram before and after the implementation of the combined station parking and vehicle speed control method adopted in this invention is shown in the figure below. Figure 3 As shown. Figure 3 Images (a) and (b) respectively show 18 trajectory lines, representing 18 buses departing at different times during peak hours. Figure 3(a) It is evident that during peak hours, the vehicle operation was unstable. The fourth bus overtook the third bus after passing Jinhui Station and arrived at the terminal station earlier than the third bus, affecting passengers' arrival time. Furthermore, frequent stops at intersections affected the bus speed, resulting in uneven intervals between the eighth and fifteenth buses and the buses in front and behind them, increasing travel time. After optimizing the station-stop strategy and speed control strategy, overtaking disappeared, ensuring passengers could board smoothly and reach the terminal station. Vehicles could pass through intersections on green lights, and the intervals during operation were more uniform, facilitating smoother travel at higher speeds. The average travel time was reduced by 5.69% after optimization.

[0111] To further illustrate the advantages of the method of the present invention, the trajectories of station-only control and speed-only control are compared with those of the method of the present invention, such as... Figure 4 As shown, when only station control is used, BRT will experience delays at intersections, resulting in a longer total travel time and difficulty in arriving at stations on time; when only speed control is used, the BRT's operating speed fluctuates more, and the operation is not smooth enough; the method of this invention can not only avoid BRT stopping at intersections at red lights, but also reduce its operating speed fluctuations, indicating that the combined speed and station control strategy is superior to the speed control strategy and the station control strategy alone.

[0112] The results of calculating the average dwell time of buses at various stops during peak hours are as follows: Figure 5 As shown. Station dwell time consists of the passenger pick-up and drop-off time at each station and additional dwell time; the dwell time at the terminal station is calculated based on the passenger pick-up and drop-off time at that station. Figure 5 It can be seen that, except for the terminal station, the dwell time of other stations is within 90 seconds, and 92% of the stations have an average additional dwell time of less than 60 seconds.

[0113] The punctuality deviations, intersection delays, and section running speed deviations of non-optimized, station-only, and speed-only control methods are compared with the results of the method of this invention, respectively. Figure 6 (a), (b), (c). From Figure 6 It can be seen that, compared with the actual situation, adopting a station-only control strategy can reduce bus punctuality deviation by 69.27% ​​and intersection delay by 79.18%. The reasons for punctuality deviation are twofold: first, the bus speed cannot be adjusted during operation, and the vehicle may arrive at the station early (represented by negative numbers in the diagram); second, if... Figure 6 As shown in (b), excessive red light delays at certain intersections caused buses to arrive late (represented by positive numbers in the figure) to downstream stops. Adopting a speed-only control strategy and a combined speed and station control strategy can further reduce on-time deviations at each stop and intersection delays to zero, and speed deviations to within 20 km / h. Compared to speed-only control, the combined speed and station control strategy can improve the smooth operation range (speed deviation of 0) by 19.64%. (Summary) Figure 6Therefore, the station-only control strategy cannot meet the goals of on-time vehicle arrival and non-stop waiting at intersections, while the speed-only control strategy makes it difficult to keep the vehicle speed close to the desired speed.

[0114] The method of the present invention will now be evaluated from the perspective of passengers.

[0115] Passenger travel time includes waiting time at the platform and time spent on the vehicle. Assuming passengers arrive uniformly within 5 minutes of the timetable, and disregarding passenger congestion at bus stops, the total waiting time at the platform during peak hours is:

[0116]

[0117] In the formula: T wait This represents the total waiting time for passengers at the bus stop; n represents the bus number during peak hours; N represents the total number of BRT departures during peak hours; r j This represents the passenger arrival rate at station j; d n,j This indicates the departure time of bus n at station j. During peak hours, the total number of BRT buses is 18.

[0118] Compare the average passenger travel time after optimization (no optimization, only station control, only speed control) with the method of this invention. Figure 7 As shown, the average passenger travel time can be obtained from the total number of passengers during peak hours, the total waiting time, and the total time spent on the train. Compared with the actual situation, station control alone can reduce passenger waiting time and on-train time by 28.65% and 13.50% respectively, while speed control alone can reduce passenger waiting time and on-train time by 9.55% and 14.16% respectively. The combined station and speed control can shorten passenger platform waiting time by 29.78% and on-train travel time by 14.47%. At the same time, the average passenger travel time is 16.15% lower than without control, 1.16% lower than with station control alone, and 2.89% lower than with speed control alone. This shows that the combined speed and station control strategy can effectively reduce passenger travel time and is superior to the speed-only and station-only control strategies.

[0119] Passenger travel time varies depending on different combinations of priority factors, for example Figure 8As shown, in combinations 1 (P2>P3>P1), 2 (P3>P2>P1), and 4 (P3>P1>P2), passenger travel times are relatively high. This is because the speed deviation weight is greater than the punctuality deviation weight (P3>P1) in these combinations, the bus cannot effectively adjust its speed, leading to late arrivals and uneven intervals, thus increasing passenger waiting time and travel time. In contrast, combinations 3 (P2>P1>P3), 5 (P1>P2>P3), and 6 (P1>P3>P2) have lower speed deviation weights than punctuality deviation weights, effectively coordinating speed control and station control, resulting in higher bus punctuality and reduced passenger travel time. In combination 6, the speed priority factor is greater than the delay priority factor (P3>P2), resulting in reduced bus stop time and red light delays at intersections. Some passengers arriving during the stop period need to wait for the next bus, increasing waiting time. In combinations 3 and 5, the speed deviation priority factors are both the smallest (P3 is the smallest), the bus arrival times are the same, and there is only a deviation in departure times at a few stops. The average travel time for passengers is not much different in the two cases.

[0120] Using the method of this invention, after simultaneously and proportionally changing the green ratio of all intersections based on the existing signal timing green ratio at intersections, the changes in punctuality deviation, intersection delay, and speed deviation are as follows: Figure 9 As shown in (a), (b), and (c). From Figure 9 The results show that all three types of deviation values ​​decrease with increasing green light ratio, indicating that the control effect of the speed and station-based joint control strategy improves with increasing green light ratio. Intersection delays show relatively little change with increasing green light ratio, while punctuality is more sensitive to green light ratio; a 5% increase in green light ratio is needed to ensure sufficient adjustment space for bus punctuality. When the green light ratio decreases by 15%, punctuality deviation increases rapidly. This is because excessively long red light times significantly reduce the time window for buses to pass through intersections. When this exceeds the bus speed adjustment range, punctuality becomes difficult to guarantee, and delays at upstream stops also prevent buses from arriving at downstream stops on time, thus significantly reducing the overall punctuality of the route.

[0121] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A method for joint control of bus speed and station parking speed of rapid transit, characterized in that, The steps include: S1: Taking the reliability of BRT operation, the efficiency of intersection operation and the comfort of passengers as optimization objectives, the weights of each indicator are customized based on different needs, and the station time and interval speed are used as decision variables to establish a nonlinear target programming model for BRT operation trajectory. S2: Solve the target programming model to obtain the bus rapid transit station dwell time and interval operation speed guidance scheme, i.e. bus rapid transit operation trajectory control scheme; In S1, different priority factors P1, P2, and P3, and a deviation weight W are set. 11 W 12 W 31 and W 32 Establish a goal programming model as follows: P1>>P2>>P3 In the above formula, P1, P2, and P3 are all priority factors in the goal programming model; >> indicates much greater than; W 11 Weighting of BRT vehicles arriving at stations early; W 12 Weighting of BRT vehicles arriving late at stations; For the deviation variable of BRT vehicles arriving at the station early; For BRT vehicles arriving late at stations, this is the deviation variable. W represents the deviation of BRT vehicle delays at intersections. 31 W represents the weight of the BRT vehicle's speed being lower than the desired speed in interval i; 32 The weight for the speed of the BRT vehicle in section i being higher than the expected speed; The deviation variable is the actual speed of the BRT vehicle being lower than the expected speed; The deviation variable is the actual speed of the BRT vehicle being higher than the expected speed. In S1, to ensure the reliability of the BRT operation, a punctuality constraint is adopted. Specifically, the actual arrival time of the BRT at the originating station is not optimized, but taken as the expected arrival time at that station, expressed as: In the above formula, t a1 This refers to the actual arrival time of the BRT at station 1. Let be the expected arrival time of the BRT at station 1. To optimize the reliability of BRT operation, the actual arrival times at other stations should be as close as possible to the expected arrival times given in the timetable, expressed as: In the above formula, t aj This represents the actual arrival time of the BRT at station j. Let t be the expected arrival time of the BRT at station j; where t aj Composed of the departure time of the upstream station, the travel time between stations, and the delay at the intersection, it is represented as: In the above formula, t d(j-1) L represents the departure time of the rapid transit bus from station j-1; i v is the length of interval i; i D represents the actual speed of the BRT in interval i; k The delay of the vehicle at intersection k; the expression for the BRT departure time is: t dj =t aj +T j In the above formula, T j Let be the dwell time of the BRT at station j, including passenger boarding and alighting time and additional dwell time; the corresponding constraint on the BRT departure time is expressed as: In the above formula, The passenger pick-up and drop-off time at station j; In S1, an intersection delay constraint is adopted to improve the intersection's operational efficiency. To minimize the intersection delay, the corresponding target constraint is obtained, expressed as follows: If the BRT arrives at the intersection during the green light, the intersection delay is 0; if it arrives during the red light, it needs to stop and wait. In this case, the delay is the difference between the green light start time and the BRT arrival time, expressed as: In the above formula, The red light turns on at the δth signal cycle when the BRT arrives at intersection k. The green light turns on at the δ-th signal cycle when the BRT arrives at intersection k. The signal cycles for the two aforementioned green light activation times begin from the red light. ak The time when the BRT arrives at intersection k; Let be the time when the red light turns on in the next cycle of the δ-th signal cycle when the BRT arrives at intersection k; where, The calculation formula is expressed as: In the above formula, r k C is the moment when the red light turns on during the first signal cycle at intersection k; k The duration of signal k at the intersection; The calculation formula is expressed as: In the above formula, R k k is the red light duration at the intersection; t ak The calculation formula is expressed as: In the above formula, j is the upstream station of k; i is the upstream section of intersection k; In S1, for the sake of passenger comfort, the BRT operating speed constraint at the section is adopted, which is expressed as: In the above formula, Let be the expected vehicle speed in interval i; In step S2, after linearizing the nonlinear terms in the target programming model, the existing solver is used to solve the problem, thereby obtaining the actual bus speed and station dwell time for each section, and thus completing the rapid transit trajectory control scheme.

2. The method for joint control of bus speed and station parking according to claim 1, characterized in that, In S2, D is adjusted by introducing an auxiliary variable α. k The expression is linearized and represented as: In the above formula, M is a sufficiently large positive number.

3. The method for joint control of bus speed and station parking according to claim 2, characterized in that, In S2, for the nonlinear term By fitting three piecewise functions, the velocity is divided into three intervals: [1, 5], [5, 20], and [20, 60]. The expression is: In the above formula, f σ For use Linearize the auxiliary continuous decision variables, σ = 1, 2, 3; z σ For use Linearized auxiliary 0-1 decision variables, σ = 1, 2, 3; the corresponding constraints are expressed as follows:

Images