Bus dispatching interval optimization system and method based on waiting negative emotion accumulation and sensing time expansion

Abstract

The invention relates to the field of bus management, and discloses a bus dispatching interval optimization system and method based on waiting negative emotion accumulation and sensing time expansion, and the system comprises a sensing waiting time quantification module, a data collection module, a parameter fitting module and a bus dispatching scheme optimization module. According to the invention, the subjective emotion experience of the passengers and the actual scheduling model are deeply fused for the first time, and the emotion experience target of the passengers is considered in parallel with the operation target in the mathematical level by quantifying the change of negative emotions in the waiting process of different passengers and sensing the expansion phenomenon of waiting time, so that the travel satisfaction degree of the passengers is improved, and the user experience is improved. And double balance is realized in cost and structure. Meanwhile, the method has extremely high adaptability and generalizability, can be suitable for different cities and different bus route types, and even can be popularized to operation optimization of other waiting scenes.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of bus management, and particularly relates to a bus departure interval optimization system and method based on negative emotion accumulation and perceived time expansion at bus stops. BACKGROUND

[0002] In daily bus system operation, the experience of passengers waiting for buses significantly affects their satisfaction with bus services. However, bus stops often face problems of passengers' boredom and anxiety due to long waiting times. As the waiting time prolongs, passengers' negative emotions such as anxiety and restlessness during waiting gradually increase, leading to passengers' subjective feeling of slower waiting time and perceived waiting time significantly longer than the actual waiting time. In addition, passengers' perceived waiting time will further lengthen with the accumulation of actual waiting time, and the gradual accumulation of negative emotions will make passengers feel time more slowly, resulting in the phenomenon of perceived waiting time expansion, which reduces passengers' travel experience of bus services. On the other hand, ignoring the phenomenon of perceived waiting time expansion caused by passengers' negative emotions during waiting cannot effectively reduce passengers' psychological cost, thereby reducing passengers' satisfaction and further reducing the overall service efficiency of the bus system.

[0003] Although there is a certain research basis in the field of bus optimization, the existing technology still has obvious deficiencies: (1) There is currently a lack of effective measurement methods for passengers' negative emotions and perceived waiting time length during waiting. Existing research generally calculates passengers' waiting time cost in a static way, and only evaluates according to the actual waiting time, ignoring the phenomenon of perceived waiting time expansion caused by the accumulation of passengers' negative emotions during service; (2) The existing optimization model does not fully consider the impact of passengers' perceived waiting time on the effectiveness of optimization strategies. Effectively measuring and incorporating passengers' perceived time cost can significantly improve the accuracy and effectiveness of bus optimization schemes, but existing methods often fail to achieve this goal, limiting the optimization effect. SUMMARY

[0004] To solve the technical problems in the above background, a bus line optimization system and method that comprehensively considers bus operation cost and passengers' perceived waiting time cost is developed, which is of great significance for improving bus service level, reducing passengers' waiting burden, and improving the overall efficiency of the transportation system. This system should be able to dynamically evaluate passengers' perceived waiting cost and provide precise vehicle scheduling and departure interval optimization strategies to achieve more precise resource allocation and overall improvement of system efficiency, meeting the changing needs of passengers and challenges of the transportation environment.

[0005] To achieve the above purpose, the present application provides a bus departure interval optimization system and method based on negative emotion accumulation and perceived time expansion at bus stops, thereby overcoming the limitations of existing technology in passenger experience and system efficiency.

[0006] Specifically, the following solutions are provided: A bus departure interval optimization system based on waiting negative emotion accumulation and perceived time expansion, comprising a perceived waiting time quantification module, a data acquisition module, a parameter fitting module, and a bus departure plan optimization module. The perceived waiting time quantification module is configured to construct a first mathematical model representing the relationship between actual waiting time and passenger negative emotion, and based on the first mathematical model, a second mathematical model representing the relationship between passenger negative emotion and passenger perceived waiting time is constructed. The data acquisition module is configured to obtain multi-dimensional data of the target bus line passenger waiting process through display preference surveys, including actual waiting time, subjective perceived waiting time, passenger negative emotion score, and unit time travel demand. The parameter fitting module is configured to fit the first mathematical model and the second mathematical model. The bus departure plan optimization module is configured to construct a mixed integer nonlinear optimization model based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, with the goal of minimizing the sum of passenger perceived waiting time cost and bus operation cost, and use the generalized Benders decomposition algorithm to solve the established mixed integer nonlinear optimization model, and output a bus departure plan that meets the operation constraints and service quality.

[0007] Preferably, the first mathematical model constructed includes: , wherein, is the real-time negative emotion intensity of the passenger waiting for a unit of time; is a continuous time variable from the starting point of waiting; , is the first estimated parameter.

[0008] Preferably, the second mathematical model constructed includes: , wherein, is the instantaneous perceived waiting time of the passenger waiting for a unit of time; is the second estimated parameter. Preferably, the perceived waiting time accumulates continuously with the increase of actual waiting time, and the perceived waiting time of a passenger during the entire waiting process is:

[0009] , The perceived waiting time cost of a single passenger is:​​ , where, is the perceived waiting time cost for a single passenger; represents the economic cost per unit of perceived waiting time.

[0010] Preferably, passengers arrive uniformly during the waiting process, and the perceived waiting time for all passengers is: , where, represents the headway of the bus within the time window represents the perceived waiting time for all passengers; represents the travel demand of passengers from stop to stop within the time window represents the length of the time window represents the number of passengers arriving at stop waiting for a bus to stop within the time window represents the number of times a bus arrives at stop within the time window is the integral variable representing the arrival time of passengers at represents the actual waiting time of passengers; The arrival time of each passenger will affect their actual waiting time, the outer integral traverses all waiting passengers within the time window, and the inner integral calculates the corresponding perceived waiting time of the passengers.

[0011] Preferably, the workflow of the parameter fitting module includes: First mathematical model parameter fitting: Determine parameters and by nonlinear least squares optimization, the optimization goal is to minimize the residual sum of squares of negative emotion observation and predicted value : , where the predicted value is defined by the integral model: , where, is the negative emotion value predicted by the model for passenger ; is the observed value of the negative emotion accumulated by passenger ;​​​​​ Passengers The actual waiting time; and These are the parameters that need to be fitted; Second mathematical model parameter fitting: Parameters are determined by nonlinear least squares optimization. The optimization objective is to minimize the observed perception wait time. and predicted value Sum of squared residuals: , The predicted value models include: , in, The predicted value of passengers' perceived waiting time; The observed value of passengers' perceived waiting time; Passengers The actual waiting time; This is the ratio of the intensity of negative emotions to perceived waiting time.

[0012] Preferably, the bus operating costs include: One-way bus departure frequency, within the time window Inside, the line The frequency of departures in one direction is: , in, Indicates time window Length; Indicates time window Internal lines Frequency of departures in one direction; Indicates time window Internal lines Bus departure intervals; Indicates time window After the departure interval scheduling is completed, there is not enough time to schedule the next bus. The calculation formula is: , The required frequency of bus departures for a given route, considering two-way operation, is calculated using the following formula: , in, Indicates the line Bus departure frequency; Operating fixed costs, routes The fixed operating cost model for public transportation operations is expressed as follows: , wherein, represents the line fixed cost of bus operation; represents the line fuel cost per unit distance of bus operation; represents the line fixed cost of a bus operation per day; represents the labor cost of a bus operation per day; represents the length of the line; represents the line number of buses in operation; fuel cost per unit distance of bus operation The calculation formula is: , wherein, represents the line fuel consumption per unit distance of bus operation, unit: liter; represents the oil price.

[0013] The application discloses a bus departure interval optimization method based on waiting negative emotion accumulation and perceived time expansion, which is applied to the above system and comprises the following steps: A first mathematical model representing the relationship between actual waiting time of passengers and negative emotions of passengers is constructed; meanwhile, a second mathematical model representing the relationship between negative emotions of passengers and perceived waiting time of passengers is constructed based on the first mathematical model; Multi-dimensional data of a waiting process of passengers of a target bus line are acquired through display preference investigation, and the multi-dimensional data include actual waiting time, subjective perceived waiting time, negative emotion score of passengers and travel demand per unit time; The first mathematical model and the second mathematical model are fitted; Based on the fitted first mathematical model, the fitted second mathematical model and the multi-dimensional data, a mixed integer nonlinear optimization model with the target of minimizing the sum of perceived waiting time cost of passengers and bus operation cost is constructed, and a generalized Benders decomposition algorithm is adopted to solve the established mixed integer nonlinear optimization model, so as to output a bus departure plan meeting operation constraints and service quality.

[0014] Compared with the prior art, the application has the following beneficial effects: The traditional bus route optimization model often focuses on the improvement of operation efficiency, ignores the subjective experience difference of passengers in the waiting process, and especially the phenomenon that the "perceived waiting time" is longer than the "actual waiting time" under negative emotions. The present application firstly deeply fuses the subjective emotional experience of passengers with the actual scheduling model, so that the emotional experience target of passengers can be considered on the mathematical level and the operation target, which improves the travel satisfaction of passengers and realizes the double balance of the cost structure.

[0015] Secondly, the present application firstly proposes the concept of "non-linear expansion of perceived time under negative emotions", models the relationship between the accumulated negative emotions of passengers in the waiting process and the waiting time, models the negative emotional state and the instantaneous perceived waiting time, and then models the relationship between the actual waiting time and the perceived waiting time, so as to realize the scientific measurement of the perceived time in the waiting scene.

[0016] Finally, the present application has strong adaptability and generalizability. Since the key parameters in the model can be fitted by local investigation data, this method can be applied to different cities, different types of bus lines (such as BRT, branch connecting bus, etc.), and even can be further extended to the quantification of perceived time in other scenes (such as train station ticket hall, airport security check, etc.), and then used for operation optimization (bus departure interval, queuing window, etc.) of different systems, which has high portability and operability. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed to be used in the embodiments, and obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0018] Figure 1 It is a system structure schematic diagram of the embodiment of the present application. Figure 2 It is a specific embodiment schematic diagram of the present application. Figure 3 It is an actual waiting time schematic diagram of the embodiment of the present application. Figure 4 It is a perceived waiting time schematic diagram of the embodiment of the present application. Figure 5 It is a bus line operation schematic diagram of the embodiment of the present application. Figure 6 It is a generalized benders decomposition algorithm solving flowchart of the embodiment of the present application. DETAILED DESCRIPTION

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Example 1: like Figure 1 The diagram shown is a schematic representation of the system structure of an embodiment of the present invention, including: a sensing waiting time quantification module, a data acquisition module, a parameter fitting module, and a bus departure scheme optimization module.

[0022] The following will describe in detail, with reference to this embodiment, how the present invention solves technical problems in real life, and the overall process is as follows: Figure 2 As shown.

[0023] Mechanisms by which passenger-perceived waiting time is generated: (1) The extended waiting time stimulates negative emotions in passengers: The Weber-Fechner Law, a fundamental principle in psychophysics, describes the relationship between the physical intensity of a stimulus and its perceived intensity. This law states that the perceived intensity of a stimulus increases logarithmically with increasing actual physical intensity. Mathematically, this can be expressed as: , in, Indicates perceived intensity. Indicates the physical intensity of the stimulus. 0 is a constant.

[0024] (2) The accumulation of negative emotions leads to a slower perceived waiting time: Depend on Figure 3 and Figure 4 It can be seen that as the waiting time increases, the perceived waiting time increases faster and faster, and the difference between the perceived waiting time and the actual time becomes larger and larger. In other words, the perceived waiting time inflates more and more, which shows that as the waiting time increases, the perceived waiting time seems to pass more slowly. At the same time, the perceived waiting cost increases more and more.

[0025] Based on the above, the embodiment utilizes the perceived waiting time quantification module to establish a first mathematical model representing the relationship between the actual waiting time of passengers and the negative emotions of passengers based on the Weber-Fechner law; based on the first mathematical model, a second mathematical model representing the relationship between the negative emotions of passengers and the perceived waiting time of passengers is established; based on the second mathematical model, the perceived waiting time cost of passengers is determined; and a nonlinear optimization model is established with the sum of the passenger perceived waiting time cost and the total operation cost of the public transport system as the objective function.

[0026] The first mathematical model representing the relationship between the actual waiting time of passengers and the negative emotions of passengers is: , wherein, is the real-time negative emotion intensity of passengers in a unit of waiting time; is a continuous time variable from the starting point of waiting; , is a first estimated parameter. The second mathematical model representing the relationship between the negative emotion intensity of passengers and their perceived waiting time is:

[0027] , wherein, is the instantaneous perceived waiting time of passengers in a unit of waiting time; is a second estimated parameter. Since the perceived waiting time accumulates with the increase of the actual waiting time, the perceived waiting time of passengers in the entire waiting process is:

[0028] , The perceived waiting time cost of a single passenger is: , wherein, is the perceived waiting time cost of a single passenger; represents the economic cost of a unit of perceived waiting time. After that, the data collection module obtains the multi-dimensional data of the waiting process of passengers on the target public transport line through the display preference survey method, and the main process includes: recording the actual waiting time of passengers on site; obtaining the subjective perception value of passengers on the waiting time through a questionnaire survey; setting four types of negative emotion items, using a Likert 5-level scale for scoring, which is used for parameter fitting of the first mathematical model and the second mathematical model.

[0029] The data collection module mainly includes the following dimensions:

[0030] The data collection module mainly includes the following dimensions: ​(1) Actual waiting time record: The actual waiting time of passengers from arriving at the platform to boarding is recorded by observation and passengers' self-reports. All time records are in the unit of "minutes". The travel demand of passengers is also recorded.

[0031] (2) Perception of waiting time acquisition: After the passengers complete waiting and boarding, the "subjective feeling of waiting time" is inquired by questionnaire. The perceived time is often longer than the actual waiting time, which is used to describe the emotional regulation and psychological magnification effect of passengers.

[0032] (3) Negative emotion intensity score design: In order to quantify the psychological burden of passengers during waiting, this questionnaire specially sets four typical negative emotion items, covering the most common emotional reactions of passengers, including: Anxiety (such as worrying about missing the bus, and the bus coming late); Irritation (such as annoyance to the noisy environment or long waiting time); Uneasiness (such as worrying about not being able to board the bus due to too many people); Helplessness (such as psychological stress when encountering unexpected situations).

[0033] Each item of emotion is scored by Likert five-level scale, specifically: 1=none, 2=slightly, 3=average, 4=strong, 5=very strong.

[0034] Passengers are required to give scores according to the feelings during waiting. The average value of the scores of the four items of each passenger is calculated to form the "negative emotion index", which is used as the input parameter of the emotional-perceived time conversion function in the subsequent model.

[0035] Through the above systematic and structured data collection method, a solid empirical basis is provided for parameter fitting and algorithm design of this embodiment, and the proposed optimization method has good practical applicability and generalizability.

[0036] The first mathematical model and the second mathematical model are fitted by using the parameter fitting module.

[0037] (1) Parameter fitting of the first mathematical model: The parameters and are determined by nonlinear least squares optimization, and the optimization objective is to minimize the residual sum of squares of the observed value and the predicted value of the negative emotion: , wherein the predicted value is defined by the integral model: , where, is the model predicted negative emotion value of the passenger ; is the observed value of the negative emotion accumulated by the passenger ; is the actual waiting time of the passenger ; and are parameters to be fitted.

[0038] Fitting method: Nonlinear least squares : Because the model is a nonlinear function, it cannot be solved directly by simple linear algebra, and an iterative optimization algorithm needs to be used. The commonly used algorithm is the Levenberg-Marquardt (LM) algorithm, which combines the advantages of gradient descent and Gauss-Newton methods, and can better handle nonlinear problems and has faster convergence speed. The algorithm needs a set of initial values , then the algorithm will automatically adjust and , and at the same time calculate the residual sum of squares at this time, until the change of the residual sum of squares is less than a certain threshold or reaches the maximum number of iterations, at this time the and with the smallest residual sum of squares are found. It should be noted that the selection of initial values is important, and poor initial values may lead to convergence to local minimum or failure to converge. It can be set according to the physical meaning of the problem or by trying several different values.

[0039] (2) Second mathematical model parameter fitting: Determine parameters by nonlinear least squares optimization, the optimization goal is to minimize the residual sum of squares of the observed value and the predicted value of the perceived waiting time: , where the predicted value model is as follows: , where, is the predicted value of the perceived waiting time of the passenger; is the observed value of the perceived waiting time of the passenger; is the actual waiting time of the passenger ; is the proportionality coefficient of the negative emotion intensity converted into the perceived waiting time.

[0040] Fitting method: Nonlinear least squares , and Using the results of the first mathematical model parameter fitting, also using the Levenberg-Marquardt (LM) algorithm, find the minimum residual sum of squares .

[0041] Finally, the bus departure scheme optimization module is used to construct a mixed integer nonlinear optimization model based on the fitted first mathematical model, the fitted second mathematical model and multi-dimensional data, with the goal of minimizing the sum of passenger perceived waiting time cost and bus operation cost.

[0042] The single passenger perceived waiting time cost is: , wherein, is the single passenger perceived waiting time cost; represents the economic cost of unit perceived waiting time.

[0043] Considering that passengers are evenly arrived during waiting, the perceived waiting time of all passengers is: , wherein, represents the departure interval of the bus within the time window ; and represents the perceived waiting time of all passengers. represents the travel demand of passengers from the station to the station within the time window ; and represents the length of the time window. represents the number of passengers arriving at the station waiting for the bus to the station within the unit time of the time window ; and represents the number of times of the bus arriving at the station within the time window. is the integral variable representing the arrival time of the passenger at ; and represents the actual waiting time of the passenger. Passengers are evenly arrived during waiting, and the arrival time of each passenger will affect their actual waiting time. The outer integral traverses all waiting passengers within the time window, and the inner integral calculates the corresponding perceived waiting time of the passenger.

[0044] The bus operation cost is determined by the frequency of vehicle use and the daily operation cost of each vehicle, and the bus operation cost is: (1) The one-way bus departure frequency within the time window , the line The one-way bus frequency is: , wherein, represents the length of the time window . represents the line one-way bus frequency in the time window . represents the headway of the line in the time window . represents the time after the headway scheduling ends, which is not enough for scheduling the next bus, The calculation formula is: .

[0045] (2) The bus frequency of the line, considering the two-way operation, the required bus frequency of the line, the calculation formula is: , wherein, represents the bus frequency on the line .

[0046] (3) The fixed cost of operation, the fixed operation cost model of the line bus operation, the expression is: , wherein, represents the fixed cost of the line bus operation; represents the fuel cost per unit distance of the line bus operation; represents the fixed cost generated by a bus in a day on the line ; represents the labor cost generated by a bus in a day; represents the length of the line; represents the number of buses operating on the line . The fuel cost per unit distance of the bus operation The calculation formula is: , wherein, represents the fuel consumption per unit distance of the bus on the line , unit: liter; represents the oil price.

[0047] The objective function of the finally established mixed integer nonlinear optimization model is to minimize the total cost total cost is expressed as: , wherein, denotes the economic cost per unit of perceived waiting time; denotes the total perceived waiting time of all passengers; denotes the length of the time window ; denotes the headway of the buses on the route within the time window ; denotes the length of the bus route .

[0048] The constraint conditions of the mixed integer nonlinear optimization model are: , wherein, denotes the time required for a bus to travel from the departure point to the start of the return journey; denotes the standard passenger capacity of the bus on the route ; denotes the maximum demand of passengers at the site within the time window ; denotes the maximum demand of passengers at the site within the time window

[0049] . Figure 5 As shown in the following table, the lower limit of the headway depends on the number of buses arranged for the route, and the number of buses that depart at the headway within the time window is , and the number of buses arranged for the route should not be less than this number; the upper limit of the headway depends on the passenger carrying capacity of the buses on the route, and the passenger carrying capacity of the buses on the route within the time window is , and accordingly the maximum demand of passengers for uplink and downlink should not be greater than this value.

[0050] Considering the specific route conditions, the optimization objective function is integrated as: , wherein, denotes the travel demand of passengers who depart from the site and arrive at the site within a certain time window .

[0051] For the above bus optimization problem, since the model contains integer variables (vehicle number) and continuous variables (headway), it belongs to the MINLP problem which is difficult to solve. In order to improve the solving efficiency and scalability, the generalized Benders decomposition algorithm is used for efficient iterative solution in this embodiment.

[0052] The core idea of GBD is to decompose the original problem into two levels: the master problem and the sub-problem, and handle the integer decision and continuous variable optimization respectively. In the iteration, the optimal solution is approached through "Benders cut". The specific solving process is as follows: Step 1 Problem decomposition: The decision variables are divided into: the master problem, i.e. integer variables (number of bus lines ) and auxiliary variables ; the sub-problem, i.e. continuous variables (bus departure interval in each time window).

[0053] Take a single time window for example, establish a hierarchical optimization framework: (1) Master problem: , (2) Sub-problem: , , where represents the bus operation cost, represents the approximate estimate value of the passenger perceived waiting cost, represents the passenger perceived waiting time cost.

[0054] Step 2 Iterative solving core process: The solving process flow chart is shown in Figure 6 .

[0055] Step 3 Key technical features: Generation mechanism of cut: When the sub-problem is feasible, the optimal cut is generated: , where , is the dual variable.

[0056] When the sub-problem is not feasible, the feasible cut is generated: , Convergence criterion: , where is the preset tolerance.

[0057] Step 4 Scheme output: Generate an executable bus departure scheme: .

[0058] The optimized bus scheduling scheme sets different bus scheduling intervals for different time windows (such as a pre-peak time window, a peak time window, a daytime time window, a late-peak time window, and a nighttime time window).

[0059] Through the above complete modeling and algorithm solving process, not only the passenger demand changes of the bus line in different time periods are accurately described, but also the optimal number of bus vehicles and the bus scheduling interval required by each line in each time window are accurately calculated by means of the close coupling between the mathematical model and the actual data. The result has clear engineering implementability and provides a data-driven decision basis for the dispatching management system.

[0060] Compared with the traditional static scheduling mode mainly based on fixed bus scheduling intervals, the scheme proposed by the present application not only guarantees the economic benefits and resource utilization efficiency of the bus enterprise, but also fundamentally improves the passenger satisfaction and travel experience, thereby establishing a virtuous feedback mechanism between passengers and bus operators. In the future, the present application can be expanded to various scenarios such as subway connection, cross-line joint operation, and nighttime circulating line, and even extended to other scenarios with waiting time cost (such as train station ticket office and airport security check).

[0061] Embodiment Two The embodiment also provides a bus scheduling interval optimization method based on waiting negative emotion accumulation and perceived time expansion, and the steps include: constructing a first mathematical model representing the relationship between actual waiting time of passengers and negative emotions of passengers; at the same time, based on the first mathematical model, constructing a second mathematical model representing the relationship between negative emotions of passengers and perceived waiting time of passengers; obtaining multi-dimensional data of the waiting process of passengers of the target bus line through display preference investigation, the multi-dimensional data including: actual waiting time, subjective perceived waiting time, passenger negative emotion score, and unit time travel demand; fitting the first mathematical model and the second mathematical model; based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, constructing a mixed integer nonlinear optimization model with the objective of minimizing the sum of passenger perceived waiting time cost and bus operation cost, and using generalized Benders decomposition algorithm to solve the established mixed integer nonlinear optimization model, and outputting a bus scheduling scheme meeting the operation constraints and service quality.

[0062] The above-described embodiments are only descriptions of the preferred modes of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. A bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, characterized in that, include: The system includes a module for quantifying perceived waiting time, a data acquisition module, a parameter fitting module, and a bus departure plan optimization module. The perceived waiting time quantification module is used to construct a first mathematical model representing the relationship between passengers' actual waiting time and passengers' negative emotions; at the same time, based on the first mathematical model, a second mathematical model representing the relationship between passengers' negative emotions and passengers' perceived waiting time is constructed. The data acquisition module is used to obtain multi-dimensional data on the waiting process of passengers on the target bus route through a display preference survey. The multi-dimensional data includes: actual waiting time, subjectively perceived waiting time, passenger negative emotion rating, and travel demand per unit time. The parameter fitting module is used to fit the first mathematical model and the second mathematical model; The bus departure scheme optimization module is used to construct a mixed integer nonlinear optimization model based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, with the goal of minimizing the sum of passenger perceived waiting time cost and bus operating cost. The module then uses the generalized Benders decomposition algorithm to solve the established mixed integer nonlinear optimization model and outputs a bus departure scheme that satisfies operational constraints and service quality.

2. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation as described in claim 1, characterized in that, The first mathematical model constructed includes: ， in, Passengers wait continuously Real-time intensity of negative emotions at any given time unit; It is a continuous time variable calculated from the starting point of the wait; , This is the first parameter to be estimated.

3. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, as described in claim 2, is characterized in that... The second mathematical model constructed includes: ， in, Passengers wait continuously Instantaneous perceived waiting time within a unit of time; This is the second parameter to be estimated.

4. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, as described in claim 3, is characterized in that... The perceived waiting time accumulates as the actual waiting time increases. The passenger's perceived waiting time throughout the entire waiting process is: ， The perceived waiting time cost per passenger is: ， in, For each individual passenger, the perceived cost of waiting time; This represents the economic cost of perceived waiting time per unit.

5. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, as described in claim 4, is characterized in that... Passengers arrive at a uniform rate while waiting for the vehicle, and the perceived waiting time for all passengers is: ， in, Indicates time window The interval between bus departures within the city; This represents the perceived waiting time for all passengers. Indicates time window Passengers inside the station to station The travel demand; Indicates time window Length; Indicates time window Arrival time at the station per unit of time Waiting to be sent to the station The number of passengers on the bus; Indicates the bus arrival station within the time window. The number of times; The integral variable represents the passenger's... Arrival time; Indicates the actual waiting time for passengers; The arrival time of each passenger will affect their actual waiting time. The outer integral iterates through all waiting passengers within the time window, while the inner integral calculates the perceived waiting time for each passenger.

6. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation as described in claim 1, characterized in that, The workflow of the parameter fitting module includes: First mathematical model parameter fitting: Parameters are determined by nonlinear least squares optimization. and The optimization objective is to minimize the observed negative sentiment values. and predicted value Sum of squared residuals: ， The predicted value is defined by the integral model: ， in, The model predicts passengers The negative emotion value; For passengers Observations of accumulated negative emotions; Passengers The actual waiting time; and These are the parameters that need to be fitted; Second mathematical model parameter fitting: Parameters are determined by nonlinear least squares optimization. The optimization objective is to minimize the observed perception wait time. and predicted value Sum of squared residuals: ， The predicted value models include: ， in, The predicted value of passengers' perceived waiting time; The observed value of passengers' perceived waiting time; Passengers The actual waiting time; This is the ratio of the intensity of negative emotions to perceived waiting time.

7. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation as described in claim 1, characterized in that, The bus operating costs include: Frequency of one-way bus departures, within the time window Inside, the line The frequency of departures in one direction is: ， in, Indicates time window Length; Indicates time window Internal lines Frequency of departures in one direction; Indicates time window Internal lines Bus departure intervals; Indicates time window After the departure interval scheduling is completed, there is not enough time to schedule the next bus. The calculation formula is: ， The required frequency of bus departures for a given route, considering two-way operation, is calculated using the following formula: ， in, Indicates the line Bus departure frequency; Operating fixed costs, routes The fixed operating cost model for public transportation operations is expressed as follows: ， in, Indicates the line Fixed costs of public transportation operation; Indicates the line Fuel costs for the distance covered by the bus operating unit; Indicates the line The fixed costs incurred by a bus operating for one day; This represents the labor costs incurred by a bus operator in one day. Indicates the length of the line; Indicates the line The number of buses in operation; Fuel costs for bus operating units The calculation formula is: ， in, Indicates the line Fuel consumption per unit distance for bus operation, unit: liters; This indicates the price of oil.

8. A method for optimizing bus departure intervals based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, the method being applied to the system described in any one of claims 1-7, characterized in that the steps include... include: A first mathematical model is constructed to characterize the relationship between passengers' actual waiting time and passengers' negative emotions; at the same time, based on the first mathematical model, a second mathematical model is constructed to characterize the relationship between passengers' negative emotions and passengers' perceived waiting time. Multi-dimensional data on passenger waiting processes for target bus routes were obtained through a display preference survey. The multi-dimensional data included: actual waiting time, subjectively perceived waiting time, passenger negative emotion rating, and travel demand per unit time. Fit the first mathematical model and the second mathematical model; Based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, a mixed-integer nonlinear optimization model is constructed with the goal of minimizing the sum of passenger perceived waiting time cost and bus operating cost. The generalized Benders decomposition algorithm is used to solve the established mixed-integer nonlinear optimization model, and the bus departure scheme that satisfies operational constraints and service quality is output.

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