Differentiated travel cycle formulating method based on IPASOR network model
By using the IPASOR network model to analyze the evolution of traveler types and calculate revenue, the problem of traveler policy adaptation in differentiated pricing schemes is solved, achieving revenue maximization and traffic flow optimization, and promoting a win-win situation for all parties.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-01-11
- Publication Date
- 2026-04-10
AI Technical Summary
Existing technologies fail to effectively consider travelers' understanding and adaptation process to policies when formulating differentiated pricing schemes, leading to discrepancies between predicted and actual policy effects. Furthermore, the lack of scientific research on the length of the time frame affects the optimality of the policy and the maximization of benefits.
By adopting the IPASOR network model, historical travel data is acquired, travel cycles are divided, a traveler attribute classification model is established, traveler types evolve, the number of people and revenue for each type are calculated, the travel cycle corresponding to the maximum total revenue is determined, and a differentiated pricing policy is formulated.
It increases the revenue of highway management, optimizes traffic flow distribution, reduces exhaust emissions, lowers freight costs, alleviates congestion, improves the utilization rate of highway network resources, and achieves a win-win situation for investors, freight companies and the environment.
Smart Images
Figure CN121836408A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of highway management technology, specifically to a method for determining differentiated travel cycles based on the IPASOR network model. Background Technology
[0002] The main reasons for charging tolls on highways are to achieve the following objectives: recover costs, repay loans and maintain the daily upkeep and repair expenses of the highway, ensure that the builders who invested initial capital receive a certain return in the future, and improve the efficiency of highway traffic through economic leverage, so that the advantages of highways can be better utilized. However, in the current economic situation and with trucks gradually becoming larger, the relatively high tolls charged to heavy trucks on highways will force them to abandon highways and turn to toll-free roads, triggering various problems such as exhaust pollution, traffic congestion, and a decline in the debt repayment capacity of highways.
[0003] Differential tolling refers to a policy of charging different tolls for different types of vehicles using highways. This can take various forms, including different tolls based on vehicle type, road segment, and time of day. A reasonable differential tolling policy can lead to a more rational distribution of traffic flow in time and space, thereby achieving multiple objectives such as increasing investor revenue, reducing road network emissions, lowering freight costs, and alleviating traffic pressure on national and provincial highways. It has strong applicability and acceptability. The plan stipulates that differential tolling schemes should be formulated according to local conditions without increasing user travel costs. Therefore, differential tolling schemes can only offer positive discounts. Given that some highways' revenue is insufficient to support the debts incurred during construction, aiming for the highest possible net revenue for highway management is justifiable.
[0004] Currently, when formulating differentiated pricing schemes, it is assumed that all travelers will be fully aware of and adapt to the policy at the beginning of its implementation. This differs from the actual situation, and the model's prediction of the policy's effect differs from the actual value. Consequently, the policy scheme may not be optimal. Furthermore, there is a lack of research methods on the length of the differentiated pricing policy cycle, and most studies simply stipulate a cycle length of six months or one year. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides a differentiated travel cycle determination method based on the IPASOR network model. The method includes: acquiring historical travel data of the target highway and dividing it into multiple travel cycles; establishing an IPASOR network model based on the attribute information of travelers within each travel cycle, classifying travelers within each travel cycle into multiple categories; dividing each travel cycle into multiple time periods and establishing an evolutionary model of the number of travelers in each category; solving for the model parameters of the IPASOR network model based on the evolutionary model and substituting them into the evolutionary model to obtain the number of travelers in each category; obtaining the total revenue for each travel cycle; and using the travel cycle corresponding to the maximum total revenue as the travel cycle of the target highway. This invention can increase the revenue of highway management without increasing the burden on travelers, thereby effectively improving the comprehensive utilization rate of highway network resources.
[0006] This invention adopts the following technical solution: a differentiated travel cycle formulation method based on the IPASOR network model, comprising:
[0007] Obtain historical travel data for the target highway, divide the historical travel data into multiple travel cycles of different time lengths, and obtain the attribute information of travelers within each travel cycle;
[0008] An IPASOR network model is established based on the attribute information of travelers in each travel cycle, and the IPASOR network model is used to classify travelers in each travel cycle into multiple categories.
[0009] Each travel cycle is divided into multiple time periods. The IPASOR network model is used to analyze the evolution of travelers of each category in each time period and to establish an evolution model of the number of travelers of each category.
[0010] The model parameters of the IPASOR network model are solved based on the evolution model of the number of travelers of each category in each time period.
[0011] Substitute the model parameters into the evolution model of the number of travelers in each category to obtain the number of travelers in each category in each time period.
[0012] The revenue for each time period is calculated based on the number of travelers in each category; the total revenue for each travel cycle is calculated based on the revenue from all time periods within each travel cycle.
[0013] The travel period corresponding to the maximum total revenue is taken as the toll period for the target highway.
[0014] Furthermore, the IPASOR network model is specifically as follows:
[0015] The traveler's inherent attributes S, O, R and real-time attributes I, P, A, where:
[0016] S attribute indicates that the individual is sensitive to behavior and easily influences those around them; O attribute indicates that the individual is sensitive to behavior but not easily influences those around them; R attribute indicates that the individual is insensitive.
[0017] The I attribute indicates complete ignorance of travel policies; the P attribute indicates partial understanding of travel policies; and the P attribute indicates complete knowledge of travel policies.
[0018] Furthermore, the IPASOR network model is used to categorize travelers within each travel cycle into multiple classes, including:
[0019] Based on both inherent and real-time attributes of travelers, travelers are categorized into: Type I travelers, Type P travelers, Type A travelers, and Type R travelers. Among them, Type P travelers include Type PO travelers and Type PS travelers; Type A travelers include Type AO travelers and Type AS travelers.
[0020] Type I travelers are individuals who are completely unaware of the pricing policy; Type PO travelers are individuals who are aware of some of the pricing policy but have no intention of disseminating their knowledge; Type PS travelers are individuals who are aware of some of the pricing policy and have the intention of disseminating their knowledge to other travelers; Type AO travelers are individuals who are fully aware of the pricing policy but have no intention of disseminating their knowledge; Type AS travelers are individuals who are fully aware of the pricing policy and are willing to disseminate their knowledge to other travelers; and Type R travelers are individuals who are insensitive to the pricing policy and have an inherent choice.
[0021] Furthermore, the IPASOR network model is used to analyze the evolution of travelers in each time period for each category, including:
[0022] When a Type I traveler receives information from a Type P or Type A traveler, the Type I traveler transforms into a Type P traveler.
[0023] When a Type P traveler receives information from a Type A traveler, the experience value of the Type P traveler is calculated based on the number of Type P travelers at the current time and the average social range of the travelers. When the experience value is greater than a set threshold, the Type P traveler is converted into a Type A traveler.
[0024] Furthermore, an evolutionary model for the number of travelers in each category is established as follows:
[0025]
[0026]
[0027]
[0028]
[0029]
[0030] Among them, C I (n) represents the number of Type I travelers in the nth time period. This indicates the probability that Type I travelers did not receive any information. P3 represents the probability that a type I traveler receives only information disseminated by a type P traveler; P4 represents the average social range per person; P3 represents the proportion of travelers with type S among all travelers after excluding type R travelers; P4 represents the proportion of travelers with type O among all travelers after excluding type R travelers; experience and influence (AS) are model parameters; experience represents the experience value obtained by type P individuals from point T; influence (AS) represents the influence of type AS travelers on type P travelers; and J represents the set threshold for type P travelers.
[0031] Furthermore, the method for determining the revenue for each time period based on the number of travelers in each category is as follows:
[0032] N a (n)=C I (n)·P a (I)+[C AS (n)+C AO (n)]·P a (A)+[C PS (n)+C PO (n)]·P a (P)+C R ·P a (R)
[0033] M(n) = N a (n)·E·(1-Y k )
[0034] Where, N a (n) represents the number of six types of trucks traveling on the highway in the nth time period, C I (n) represents the number of Type I travelers in the nth time period, C AS (n) represents the number of AS-type travelers in the nth time period, C AO (n) represents the number of AO type travelers in the nth time period, C PS (n) represents the number of PS-type travelers in the nth time period, C PO (n) represents the number of PO type travelers in the nth time period, CR (n) represents the number of type R travelers in the nth time period, Y k Let P(I) represent the discount rate of the toll policy corresponding to the k-th period, P(A) represent the probability that a type I traveler will choose to travel on the highway, P(P) represent the probability that a type P traveler will choose to travel on the highway, and P(R) represent the probability that a type R traveler will choose to travel on the highway.
[0035] Furthermore, the method for obtaining the total revenue corresponding to each travel cycle is as follows:
[0036]
[0037] Where M represents the total revenue for each travel cycle, m represents the number of months in the travel cycle, f represents the time required for a single information transmission, M(n) represents the revenue for the nth time segment of each travel cycle, and D k This represents the number of days in the k-th cycle. `int` indicates rounding down, and `mod` indicates taking the remainder.
[0038] The beneficial effects of this invention are as follows: By establishing an IPASOR network model to evolve traveler types, and combining the number of travelers of each type under different cycles to calculate revenue, this invention determines the travel cycle with the highest revenue. This can make the distribution of traffic flow in time and space more reasonable, thereby achieving multiple objectives such as increasing investor income, reducing road network exhaust emissions, reducing freight costs, and alleviating peak-hour congestion. It promotes a win-win situation for investors, freight companies, other travelers, and the ecological environment, and effectively improves the comprehensive utilization rate of highway network resources. Attached Figure Description
[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0040] Figure 1 This is a schematic diagram of a method for formulating a differentiated pricing policy based on the IPASOR network model according to an embodiment of the present invention;
[0041] Figure 2 This is a schematic diagram of an IPASOR network model structure according to an embodiment of the present invention;
[0042] Figure 3 This is a schematic diagram illustrating the evolution of traveler types according to an embodiment of the present invention;
[0043] Figure 4 This is a schematic diagram comparing the periodic revenue of highway management under different preferential rates according to an embodiment of the present invention. Detailed Implementation
[0044] 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.
[0045] Because travelers' sensitivity to and familiarity with road toll policies influence their travel choices, changes in toll policies will cause fluctuations in road network traffic flow for a period before stabilizing. This fluctuation reflects the process of different travelers becoming familiar with and adapting to the policy. Furthermore, changes in various factors throughout the year, such as total travel volume, supply and demand, types of transported goods, and climate, can lead to changes in the most suitable policy for the current situation. Therefore, the shorter the cycle of a differentiated toll policy, the more targeted it will be, and the better its stabilizing effect will be. However, this also leads to a higher proportion of fluctuating periods and decreased policy stability. Policy formulation should balance targeting and stability. This invention uses a network model to assess travelers' understanding and adaptation to the policy. The network model categorizes individuals within a group according to their attributes or behavioral logic and studies the changing trends of the proportion of each category over time. This, combined with the proposed IPASOR network model, allows for the formulation of differentiated toll policies that better align with travelers' travel patterns, providing a theoretical basis for determining differentiated travel cycles.
[0046] A flowchart illustrating a differentiated travel cycle formulation method based on the IPASOR network model according to an embodiment of the present invention is shown below. Figure 1 As shown, it includes:
[0047] Obtain historical travel data for the target highway, divide the historical travel data into multiple travel cycles of different time lengths, and obtain the attribute information of travelers within each travel cycle;
[0048] Historical travel data includes information on the target highway and its surrounding road network, as well as survey data on travelers within the target road network. Information on the target highway and its surrounding road network includes traffic volume, vehicle type ratio, directional unevenness coefficient, number of lanes, design speed, and longitudinal gradient. This basic survey helps in selecting differentiated tolling methods and serves as an important basis for cost analysis and benefit calculation. The survey data on travelers within the target road network can be divided into two aspects: personal attribute surveys and travel attribute surveys. Personal attribute surveys include investigations into travelers' gender, age, driving experience, income, social characteristics, and information sensitivity. Travel attribute surveys include investigations into the type of vehicle driven, type of goods transported, travel frequency, and toll payment method. The personal attribute survey serves as the basis for classifying travelers, while the travel attribute survey is a crucial foundation for calibrating parameters in the travel prediction model.
[0049] An IPASOR network model is established based on the attribute information of travelers in each travel cycle, and the IPASOR network model is used to classify travelers in each travel cycle into multiple categories.
[0050] The IPASOR network model includes travelers' inherent attributes S, O, R and real-time attributes I, P, A, where: S indicates that the individual is sensitive to the travel policy and can easily influence the surrounding individuals; O indicates that the individual is sensitive to the travel policy but cannot easily influence the surrounding individuals; R indicates that the individual is insensitive; I indicates that the individual is completely unaware of the travel policy; P indicates that the individual has some understanding of the travel policy; and P indicates that the individual is fully aware of the travel policy.
[0051] The IPASOR network model is used to classify travelers within each travel cycle into multiple categories, including: combining inherent and real-time attributes, travelers are divided into: Type I travelers, Type P travelers, Type A travelers, and Type R travelers. Specifically, Type P travelers include Type PO and Type PS travelers; Type A travelers include Type AO and Type AS travelers. The specific meanings of these traveler categories in the IPASOR network model are shown in Table 1 in this embodiment.
[0052] Table 1. Illustration of Individual Categories in the IPASOR Network Model
[0053]
[0054]
[0055] Each travel cycle is divided into multiple time periods. The IPASOR network model is used to analyze the evolution of travelers of each category in each time period and to establish an evolution model of the number of travelers of each category.
[0056] In one specific embodiment, the evolution process of the IPASOR network model is shown in Table 2:
[0057] Table 2. Schematic diagram of the evolution process of the IPASOR network model.
[0058]
[0059]
[0060] The basic data given in Table 2 and the specific meanings of other parameters in the IPASOR network model are shown in Table 3:
[0061] Table 3. IPASOR Network Model Parameter Diagram
[0062]
[0063]
[0064] In the IPASOR model, B, The values of the five parameters P1, P2, P3, and P4 can be obtained from the questionnaire survey data, while the network model also includes the parameters Influence (AS) and μ. A (x), μ P The values of (x) and experience need to be calculated based on historical travel data.
[0065] In one specific embodiment, considering practical application scenarios, the present invention does not set a restraint mechanism or a forgetting mechanism for the established IPASOR network model. Furthermore, to avoid the influence of extreme individuals, the network model state is stipulated to evolve in a probabilistic expectation manner, and the number of travelers in the network model is constant within the same period. That is, the initial state of travelers in the system for each period is:
[0066] The IPASOR network model, after evolving the number of travelers in each category at each time stage, is illustrated in the diagram below. Figure 2 As shown, the transformation of Type I individuals (Type I travelers) can be viewed as the dissemination of information. Once a Type I traveler learns about relevant information, they can transform into a Type P individual (Type P traveler). The information they can access can be divided into two types: one is information containing only the new cycle's toll policy, called Type P information. This information mainly comes from official information sources M, PS individuals in their social networks, and discoveries made during their own travels; the other is information containing both the new cycle's toll policy and information from the mature experiences of Type A individuals, called Type A information. This information comes from AS individuals in their social networks. The probability that a Type I traveler receives Type A information and Type P information at each stage is:
[0067]
[0068]
[0069] Therefore, the parameters in the network model can be calculated as follows:
[0070]
[0071]
[0072] The speed at which a Type P traveler transforms into a Type A traveler is determined not only by the understanding and adaptation of other travelers in their social network to the policy and their willingness to influence it, but also by their own attributes such as education level and driving experience. Therefore, it is not appropriate to discuss them in the same way as Type I travelers. This embodiment distinguishes travelers' ability to acquire and transform experience by randomly assigning a precise threshold to each traveler. When a Type P individual's experience value from various channels reaches their precise threshold, they can transform into a Type A individual. The formula for the evolution of a Type P individual into a Type A individual is:
[0073]
[0074] Where J is a set precision threshold. When the evolution formula of a P-type individual meets the condition, the state of the P-type individual is updated, that is:
[0075] Under the differentiated pricing policy, the perceived total cost for Type A travelers is the sum of all costs under the current discount package, while the perceived total cost for Type I travelers is the sum of all perceived costs under the original discount amount. Changes in the discount amount under the current differentiated pricing policy will not affect their choice behavior, but their numbers will continue to decrease to an extremely low level.
[0076] Therefore, based on the IPASOR network model, the evolutionary model of the number of travelers of various types is established as follows:
[0077]
[0078]
[0079]
[0080]
[0081]
[0082] Among them, C I (n) represents the number of Type I travelers in the nth time period. This indicates the probability that Type I travelers did not receive any information. P3 represents the probability that a type I traveler receives only information disseminated by a type P traveler; P4 represents the average social range per person; P3 represents the proportion of travelers with type S among all travelers after excluding type R travelers; P4 represents the proportion of travelers with type O among all travelers after excluding type R travelers; experience and influence (AS) are model parameters; experience represents the experience value obtained by type P individuals from point T; influence (AS) represents the influence of type AS travelers on type P travelers; and J represents the set threshold for type P travelers.
[0083] The model parameters of the IPASOR network model are solved by calculating the evolutionary model of the number of travelers of each category in each time period. By simultaneously solving the above formulas, the Influence (AS) and μ values in the network model can be obtained. A (x), μ P The values of the four parameters (x), experience, etc. are used to input the model parameters into the evolution model of the number of travelers in each category, so as to obtain the number of travelers in each category in each time period.
[0084] The revenue for each time period is calculated based on the number of travelers in each category; the total revenue for each travel cycle is calculated based on the revenue from all time periods within each travel cycle.
[0085] In this embodiment, after determining the number of travelers of each type in each time period, the revenue generated by these travelers for highway investors is calculated using the expression: M(n) = N a (n)·E·(1-Y k Furthermore, by statistically analyzing the total returns for investors during the corresponding period, the following can be calculated: Where M represents the total revenue for each travel cycle, m represents the number of months in the travel cycle, f represents the time required for a single information transmission, M(n) represents the revenue for the nth time segment of each travel cycle, and D k This represents the number of days in the k-th period. `int` indicates rounding down, and `mod` indicates taking the remainder. Y k This represents the discount rate of the charging policy corresponding to the k-th period.
[0086] The present invention aims to maximize the investor's returns. In one specific embodiment, the length of the travel cycle can be divided into 1, 2, 3, 4, 6, and 12 months, thereby calculating the total revenue corresponding to different cycle lengths. The travel cycle corresponding to the maximum total revenue is taken as the travel cycle of the target highway.
[0087] This invention establishes an IPASOR network model to evolve traveler types and calculates revenue based on the number of travelers of each type in different cycles, thereby determining the travel cycle with the highest revenue. This can make the distribution of traffic flow in time and space more reasonable, thereby achieving multiple objectives such as increasing investor income, reducing road network exhaust emissions, reducing freight costs, and alleviating peak-hour congestion. It promotes a win-win situation for investors, freight companies, other travelers, and the ecological environment, and effectively improves the comprehensive utilization rate of highway network resources.
[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A differentiated travel cycle formulation method based on the IPASOR network model, characterized in that, include: Obtain historical travel data for the target highway, divide the historical travel data into multiple travel cycles of different time lengths, and obtain the attribute information of travelers within each travel cycle; An IPASOR network model is established based on the attribute information of travelers in each travel cycle, and the IPASOR network model is used to classify travelers in each travel cycle into multiple categories. Each travel cycle is divided into multiple time periods. The IPASOR network model is used to analyze the evolution of travelers of each category in each time period and to establish an evolution model of the number of travelers of each category. The model parameters of the IPASOR network model are solved based on the evolution model of the number of travelers of each category in each time period. Substitute the model parameters into the evolution model of the number of travelers in each category to obtain the number of travelers in each category in each time period. The revenue for each time period is calculated based on the number of travelers in each category; the total revenue for each travel cycle is calculated based on the revenue from all time periods within each travel cycle. The travel period corresponding to the maximum total revenue is taken as the toll period for the target highway.
2. The differentiated travel period formulation method based on the IPASOR network model according to claim 1, characterized in that: The IPASOR network model is specifically as follows: The traveler's inherent attributes S, O, R and real-time attributes I, P, A, where: S attribute indicates that the individual is sensitive to behavior and easily influences those around them; O attribute indicates that the individual is sensitive to behavior but not easily influences those around them; R attribute indicates that the individual is insensitive. The I attribute indicates complete ignorance of travel policies; the P attribute indicates partial understanding of travel policies; and the P attribute indicates complete knowledge of travel policies.
3. The differentiated travel cycle formulation method based on the IPASOR network model according to claim 2, characterized in that: The IPASOR network model is used to categorize travelers within each travel cycle into multiple classes, including: Based on both inherent and real-time attributes of travelers, travelers are categorized into: Type I travelers, Type P travelers, Type A travelers, and Type R travelers. Among them, Type P travelers include Type PO travelers and Type PS travelers; Type A travelers include Type AO travelers and Type AS travelers. Type I travelers are individuals who are completely unaware of the pricing policy; Type PO travelers are individuals who are aware of some of the pricing policy but have no intention of disseminating their knowledge; Type PS travelers are individuals who are aware of some of the pricing policy and have the intention of disseminating their knowledge to other travelers; Type AO travelers are individuals who are fully aware of the pricing policy but have no intention of disseminating their knowledge; Type AS travelers are individuals who are fully aware of the pricing policy and are willing to disseminate their knowledge to other travelers; and Type R travelers are individuals who are insensitive to the pricing policy and have an inherent choice.
4. The differentiated travel period formulation method based on the IPASOR network model according to claim 3, characterized in that: The IPASOR network model is used to analyze the evolution of travelers in each time period for each category, including: When a Type I traveler receives information from a Type P or Type A traveler, the Type I traveler transforms into a Type P traveler. When a Type P traveler receives information from a Type A traveler, the experience value of the Type P traveler is calculated based on the number of Type P travelers at the current time and the average social range of the travelers. When the experience value is greater than a set threshold, the Type P traveler is converted into a Type A traveler.
5. The differentiated travel period formulation method based on the IPASOR network model according to claim 1, characterized in that: The evolutionary model for the number of travelers in each category is established as follows: Among them, C I (n) represents the number of Type I travelers in the nth time period. This indicates the probability that Type I travelers did not receive any information. P3 represents the probability that a type I traveler receives only information disseminated by a type P traveler; P4 represents the average social range per person; P3 represents the proportion of travelers with type S among all travelers after excluding type R travelers; P4 represents the proportion of travelers with type O among all travelers after excluding type R travelers; experience and influence (AS) are model parameters; experience represents the experience value obtained by type P individuals from point T; influence (AS) represents the influence of type AS travelers on type P travelers; and J represents the set threshold for type P travelers.
6. The differentiated travel period formulation method based on the IPASOR network model according to claim 1, characterized in that: The method for determining revenue based on the number of travelers in each category during each time period is as follows: N a (n)=C I (n)·P a (I)+[C AS (n)+C AO (n)]·P a (A)+[C PS (n)+C PO (n)]·P a (P)+C R ·P a (R) M(n)=N a (n)·E·(1-Y k ) Where, N a (n) represents the number of six types of trucks traveling on the highway in the nth time period, C I (n) represents the number of Type I travelers in the nth time period, C AS (n) represents the number of AS-type travelers in the nth time period, C AO (n represents the number of AO-type travelers in the nth time period, C) PS (n) represents the number of PS-type travelers in the nth time period, C PO (n) represents the number of PO type travelers in the nth time period, C R (n) represents the number of type R travelers in the nth time period, Y k Let P(I) represent the discount rate of the toll policy corresponding to the k-th period, P(A) represent the probability that a type I traveler will choose to travel on the highway, P(P) represent the probability that a type P traveler will choose to travel on the highway, and P(R) represent the probability that a type R traveler will choose to travel on the highway.
7. The differentiated travel period formulation method based on the IPASOR network model according to claim 1, characterized in that: The method for obtaining the total revenue for each travel cycle is as follows: Where M represents the total revenue for each travel cycle, m represents the number of months in the travel cycle, f represents the time required for a single information transmission, M(n) represents the revenue for the nth time segment of each travel cycle, and D k This represents the number of days in the k-th cycle. `int` indicates rounding down, and `mod` indicates taking the remainder.