Method for predicting urban commuting cost and time under random changes of simulated external conditions

Abstract

The application provides a kind of prediction method for simulating the change of urban commuting cost and time under external conditions randomness variation.The method comprises the following steps: collecting the historical data of two random variables of commuting road capacity and traffic flow, fitting the joint probability density function of road capacity and traffic flow;Setting the working time and penalty cost coefficient;Simulate the travel cost and commuting mode under different external conditions and different correlation of external conditions without pre-trip information, predict the commuting time;Simulate the travel cost and commuting mode under different external conditions and different correlation of external conditions with pre-trip information, predict the commuting time.The application establishes a simple early commuting mathematical model under the random variation of road capacity and traffic flow, which can simulate the individual departure time selection behavior rule in urban morning peak period under different conditions, and the overall equilibrium travel cost and road congestion characteristics.

Description

Technical Field

[0001] This invention relates to the field of urban traffic management technology, and in particular to a method for predicting urban commuting costs and times under simulated random changes in external conditions. Background Technology

[0002] At the micro level, the main causes of urban traffic congestion include: first, a sudden increase in traffic volume, creating traffic bottlenecks; and second, traffic congestion caused by sudden road events reducing road capacity or attracting excessive traffic. In densely populated first- and second-tier cities, congestion during morning and evening rush hours severely impacts residents' quality of life, encroaches on their work and leisure time, and increases their living costs. Traffic congestion during morning rush hours has become a major problem plaguing cities and a key focus of urban traffic management. Simulating the departure time selection behavior of urban commuters during morning rush hour reveals its macro-level characteristics and underlying mechanisms, providing valuable insights for developing effective traffic control measures.

[0003] With the advent of the intelligent information age and the widespread deployment of information systems, the accuracy of traffic information prediction has gradually improved, making it possible to provide commuters with traffic condition information before they depart. For example, Advanced Pre-Travel Information Systems (ATIS) have shown significant effectiveness in alleviating traffic congestion and reducing uncertainty, and providing commuters with traffic condition information before departure has become one of the mainstream methods for solving traffic congestion. However, existing research indicates that providing pre-travel information does not necessarily reduce travel costs; the actual effect may be related to various factors such as the accuracy of the information, market penetration, and information heterogeneity. Therefore, simulating the departure time selection behavior of urban commuters during the morning rush hour after providing partial traffic condition information has practical significance.

[0004] In studies on urban morning rush hour commuting departure time selection, both domestic and international scholars have largely relied on Vickrey's bottleneck model for theoretical analysis and experimental verification. However, urban morning rush hour commuting systems are generally affected by many random, dynamic, and nonlinear uncertainties, and due to interference from various factors on both the supply and demand sides, the system's supply and demand can change throughout the day and / or daily. Currently, there are few methods capable of simulating commuting departure time selection under different external conditions and varying correlations of these conditions.

[0005] Currently, existing methods for predicting urban commuting departure times include: predicting commuting time based on information such as weather and traffic conditions through a training module, and then predicting commuting trajectories based on acquired historical trajectory data and map matching. The drawbacks of these existing methods include: not considering the correlation between external conditions, and not considering commuters' choice of departure time after being provided with pre-trip information. Summary of the Invention

[0006] The embodiments of the present invention provide a method for predicting urban commuting costs and times under simulated random changes in external conditions, so as to effectively simulate the macro-behavioral characteristics of urban commuting departure time selection and provide theoretical support for formulating effective commuting morning peak traffic management policies.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] A method for predicting urban commuting costs and times under simulated random variations in external conditions includes:

[0009] Historical data on commuting external conditions, including road capacity and traffic flow, are collected, and a joint probability density function of commuters under road capacity and traffic flow is fitted.

[0010] Set working hours and penalty cost coefficients;

[0011] Based on the probability density function of the random variable, the commute time, and the penalty cost coefficient, the commuting patterns of commuters under different external conditions and different correlations of external conditions are simulated without pre-trip information, and the commuting time of commuters is predicted.

[0012] Based on the probability density function of the random variable, the start time, and the penalty cost coefficient, the commuting patterns of commuters under different external conditions and different correlations of external conditions are simulated with pre-trip information, and the commuting time of commuters is predicted.

[0013] Preferably, the collected historical data of two random variables, commuter road capacity and traffic flow, and the fitted joint probability density function of road capacity and traffic flow include:

[0014] Historical data on commuting external conditions are collected, including road capacity and traffic flow. The range of historical commuting traffic flow variation on the main roads of the selected residential and work areas is defined as follows: , The historical road capacity variation range of the main roads in the selected residential and work areas is as follows: , And perform statistical analysis on the random variables;

[0015] Assuming all commuters are homogeneous, we choose an appropriate function type, calculate the relevant parameters in the function, and output the probability density function corresponding to the fitted random variable, road capacity. , Indicates condition The road capacity is set below; output the probability density function corresponding to the fitted random variable traffic flow. , Indicates condition Traffic flow rate; and the joint probability density function of the two random variables after fitting. ;

[0016] The commuting probability density function for a single commuter can be described as follows:

[0017] .

[0018] Preferably, the set working hours and penalty cost coefficient include:

[0019] Set work hours as Let γ be the cost coefficient for late arrival, β be the cost coefficient for early arrival, and α be the cost coefficient for travel time. Under the condition that γ > α > β > 0, and without congestion, the travel time required for each commuter to reach their workplace is... ;

[0020] Assuming that all commuters reach an equilibrium state, each individual will not reduce travel costs by changing their choices.

[0021] Preferably, the commuting patterns of commuters under different external conditions and different correlations of external conditions, simulated by the probability density function of the random variable "work time" and the penalty cost coefficient without pre-trip information, are used to predict commuter travel time, including:

[0022] Define road capacity , The range of variation is , Based on the set parameters and the fitted joint probability distribution, solve for... probability density function ;

[0023] Based on the Vickery bottleneck model, the expected travel cost for each commuter under user equilibrium is calculated:

[0024] E[ ]= =

[0025] Wherein, γ, β, and α represent the lateness penalty cost coefficient, early arrival penalty cost coefficient, and travel time cost coefficient, respectively.

[0026] According to the equilibrium condition E[ ]= E[ ] and Find the earliest departure time for commuters. Latest departure time ,in During working hours;

[0027] According to the equilibrium condition Solve for the departure time when the commuter arrives exactly on time. ;

[0028] Assuming in The space is divided into A discrete set of departure times, where the interval between two adjacent departure times is equal. Define the label for the discrete departure time set as , ..., , ..., According to the equilibrium condition E[ ] = E[ [Calculate the travel time of commuters at each time step under condition ω.] ,in , .

[0029] Preferably, based on the probability density function of the random variable, the start time, and the penalty cost coefficient, the commuting patterns of commuters under different external conditions and different correlations of external conditions are simulated with pre-trip information, and the commuting time of commuters is predicted, including:

[0030] When traffic flow information is known At that time, the commuter's commuting probability density function is described as follows: = When road capacity information is known At that time, the commuting probability distribution function of commuters is: = ,renew probability density function ;

[0031] Based on the Vickery bottleneck model, the expected travel cost for each commuter under user equilibrium is updated as follows:

[0032] E[ ]= =

[0033] Based on the updated probability density function and travel costs, the earliest departure time for commuters can be determined. Latest departure time ;

[0034] According to the equilibrium condition It calculates the departure time when commuters arrive exactly on time. ;

[0035] Based on the updated time points and probability density function, the expected cost for the earliest departing commuter is calculated. Calculate the expected cost for the commuter who departs latest. Calculate the expected travel cost for each commuter under user equilibrium: E[ ];

[0036] According to the equilibrium condition E[ ] = E[ ], calculate Travel time for commuters under condition ω As can be seen from the technical solutions provided by the embodiments of the present invention above, the present invention proposes a method for simulating urban commuting departure patterns. It fully considers the impact of heterogeneous traffic information before travel, external conditions, and the correlation between external conditions on the choice of departure time and departure pattern during the morning rush hour. It establishes a simple mathematical model for morning commuting under random changes in road capacity and traffic flow, which can simulate the behavior of individual departure time selection during the morning rush hour in cities under different conditions, and balance the overall travel cost and road congestion characteristics.

[0037] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0038] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments 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.

[0039] Figure 1 This is a flowchart of a preferred embodiment of a method for simulating urban commuting departure patterns provided in Embodiment 1 of the present invention.

[0040] Figure 2 This is a flowchart of another preferred embodiment of a method for simulating urban commuting departure patterns provided in Embodiment 2 of the present invention.

[0041] Figure 3 This is a schematic diagram illustrating the statistical analysis results of historical data on urban morning rush hour commuting conditions in Embodiment 1 of the present invention.

[0042] Figure 4 This is a schematic diagram of the statistical analysis results of historical data on urban morning rush hour commuting conditions in Embodiment 2 of the present invention.

[0043] Figure 5 This is an embodiment of the present invention, showing the expected travel cost and travel time curves under different external conditions and without pre-trip information.

[0044] Figure 6 This is an embodiment of the present invention, showing the expected travel cost and travel time curves under different correlations of external conditions and road capacity information.

[0045] Figure 7 This is an embodiment of the present invention, showing the expected travel cost and travel time curves under different correlations of external conditions and traffic flow information.

[0046] Figure 8 This is a second embodiment of the present invention, showing the expected travel cost and travel time curves under different external conditions and without pre-trip information.

[0047] Figure 9 This is an embodiment of the present invention, showing the expected travel cost and travel time curves under different external conditions with road capacity information.

[0048] Figure 10 This is an embodiment of the present invention, showing the expected travel cost and travel time curves under different correlations of external conditions and traffic flow information. Detailed Implementation

[0049] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0050] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0051] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0052] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0053] This invention proposes a model for urban commuter departure time selection under stochastic variations in road capacity and traffic flow. It fully considers the impact of pre-trip information provided by advanced pre-trip information systems, external road conditions, and the correlation between these external conditions on departure time selection, establishing a simple mathematical model for early morning commuting. Based on historical data of external conditions and the nature of commuters' work, the model uses a bottleneck model to solve for the expected cost under stochastic conditions, then reverse-engineers commuters' departure time selection. Finally, through iterative simulation of the macro-equilibrium state of urban morning rush hour commuter departure patterns and road traffic conditions under different conditions, it provides strong theoretical support for formulating reasonable and effective traffic control measures.

[0054] The present invention provides a method for predicting urban commuting costs and times under simulated random changes in external conditions, comprising the following processing steps:

[0055] Step 1: Collect historical data on external conditions and fit the joint probability density function of the random variables.

[0056] Step 2: Setting parameters for the nature of work for commuting individuals.

[0057] Step 3: Simulate commuting patterns under different external conditions and different correlations of external conditions without prior travel information.

[0058] Step 4: Simulate commuting patterns under different external conditions and different correlations of external conditions, with pre-trip information available.

[0059] Step 5: Output the simulation results.

[0060] In any of the above schemes, it is preferred that the random variables in the joint probability density function fitted in step 1 include road capacity and traffic flow, and that the historical commuter traffic flow variation range of the main roads in the selected residential and work areas is defined as follows: , The historical road capacity variation range of the main roads in the selected residential and work areas is as follows: , We then perform statistical analysis on the random variables. We assume that all commuters are homogeneous. We select an appropriate function type, calculate the relevant parameters in the function, and output the probability density functions corresponding to the fitted random variables road capacity and traffic flow, respectively. and and the joint probability density of the two variables. .

[0061] Then, the commuting probability density function for each commuter can be described as:

[0062] In any of the above schemes, the preferred option is that the commuter's work nature setting in step 2 includes: the commuter's working hours. In the specific simulation, any time point can be selected; the lateness penalty cost coefficient γ for each commuter Early arrival penalty cost coefficient β ) and travel time cost coefficient α ( In the specific simulation, any value that satisfies the condition γ>α>β>0 can be selected; under congestion-free conditions, the travel time required for each commuter to reach their workplace is... . For cost units.

[0063] The mathematical model for early morning commuting under stochastic variations in road capacity and traffic flow first calculates the expected travel costs under different conditions. The system reaches an equilibrium state, where no individual will reduce their travel costs by changing their choices. Based on the expected travel costs, the choice of commuting departure time can be derived in reverse, including the earliest departure time, the latest departure time, and the on-time arrival time. Based on the equilibrium condition, the travel time of commuters at each moment under condition ω can be further obtained as the simulation result output.

[0064] In any of the above solutions, step 3 preferably includes the following sub-steps:

[0065] Sub-step 31: Assume α, γ, β, These are parameters describing the nature of an individual's work during commuting; the probability density function of the fitted random variables (road capacity and traffic flow). and Based on the probability density function of the random variable, the commuting probability density function for each commuter can be described as follows: ;

[0066] Sub-step 32: Road capacity. Based on long-term observed road capacity and traffic flow, fit the joint probability distribution function of the two random variables. ;in

[0067] Sub-step 33: Define a new variable: , The range of variation is .in , The solution can be obtained based on the set parameters and joint probability distribution. probability density function ;

[0068] Sub-step 34: Based on the Vickery bottleneck model, the expected travel cost for each commuter under user equilibrium can be calculated:

[0069] E[ ]= =

[0070] Sub-step 35: Based on the equilibrium condition E[ ]= E[ ] and The earliest departure time can be calculated. Latest departure time ;

[0071] Sub-step 36: For commuters who arrive just on time, the longest queue has no planned delay costs, according to the equilibrium condition... This can be used to calculate the departure time when commuters arrive exactly on time. ;

[0072] Sub-step 37: Assume that in The space is divided into A discrete set of departure times, where the interval between two adjacent departure times is equal. Define the label for the discrete departure time set as , ..., , ..., According to the equilibrium condition E[ ] = E[ This allows us to calculate the travel time of commuters at each moment under condition ω. ,in , ;

[0073] In any of the above schemes, step 4 preferably simulates the commuting pattern when traffic flow information or road capacity information is provided before departure. Since the traffic flow information or road capacity information is known before departure, the joint probability distribution function is updated, and the earliest departure time, latest departure time, and on-time arrival departure time are also updated. Based on the equilibrium condition, the travel time of commuters at each time point under condition ω can be further obtained as the simulation result output.

[0074] Sub-step 41: When traffic flow information is known When, the new joint probability distribution function is = When road capacity information is known When, the new joint probability distribution function is = Update based on the new joint probability distribution function. probability density function θ is a ratio, i.e., θ = N / s.

[0075] Sub-step 42: Based on the Vickery bottleneck model, update the expected travel cost for each commuter under user equilibrium:

[0076] E[ ]= =

[0077] Sub-step 43: Update the earliest departure time based on the updated probability density function and equilibrium condition. Latest departure time ;

[0078] Sub-step 44: Based on the equilibrium condition Update the departure time of commuters who arrive exactly on time. ;

[0079] Sub-step 45: Based on the updated time points and probability density function, update the expected travel costs of the earliest and latest departing commuters and the expected travel cost of each commuter under user equilibrium: , E[ ].

[0080] Sub-step 46: Based on the equilibrium condition E[ ] = E[ [Can be updated] Travel time for commuters under condition ω According to the equilibrium condition E[ ] = The solution is obtained, where γ, β, and α are the penalty costs for each commuter being late, the penalty costs for arriving early, and the commuting costs, respectively. Ideal time for commuters to reach their workplace. From sub-step 44, we obtain that for t∈[ , At any given moment, the equilibrium equations can be used to solve for the condition at that moment. .

[0081] Earliest departure time Latest departure time and the departure time to arrive at the workplace on time The results are obtained in sub-steps 43 and 44 respectively.

[0082] In any of the above schemes, it is preferred that step 5 outputs simulation results including: calculating the expected travel cost of the system under different degrees of correlation of random variables and the commuting time selection of each commuter. Based on the equilibrium condition, the travel time of commuters at each time point under condition ω can be further obtained as the simulation result output.

[0083] Example 1

[0084] like Figure 1 As shown, step 100 involves collecting data on external conditions for urban commuting, including historical data on road capacity and traffic flow. It is assumed that the commuting traffic flow variation range of the main roads in the selected residential and work areas is as follows: , The range of road capacity variation for the main roads in the selected residential and work areas is as follows: , This forms the sample data space X. Statistical analysis is then performed on the random variables, such as... Figure 3 As shown.

[0085] Perform step 110, select Bernoulli distribution as the fitting function type, and solve for the mean of historical road capacity and traffic flow data. , Calculate the relevant parameters in the Bernoulli function: the probability that the road capacity is in a good state. The probability that traffic flow is in good condition Where X=300 is the total number of samples. This represents the number of samples where the road capacity is greater than the mean. This represents the number of samples with traffic flow greater than the mean. The probability density function of the fitted random variable. and Based on the probability density function of the fitted random variable and The commuting probability density function that can be fitted to commuters is: ,make .

[0086] Execute step 120 to set the work nature of the commuter. Assume the commuter's working hours are... In the specific simulation, any time point can be selected; the lateness penalty cost coefficient γ = 15.21 ( The early arrival penalty cost coefficient β = 3.9 ) and travel time cost coefficient α = 6.4 ( In the specific simulation, any value that satisfies the condition γ>α>β>0 can be selected; the travel time required for each commuter to reach their workplace under congestion-free conditions. =0.

[0087] Proceed to step 130. If commuters are not provided with pre-trip information, proceed to step 140. If commuters are provided with pre-trip information, proceed to step 150.

[0088] Execute step 140 to simulate commuting patterns under different external conditions and varying correlations of these conditions, without prior travel information. Let the expected travel cost under these conditions be E[ The earliest departure time for commuters is The latest departure time is And the best departure time is Specifically, it includes the following sub-steps:

[0089] Execution step 141: Based on the set parameters and the probability distribution of the random variables, fit the joint probability distribution function of the random variables when the correlation coefficient is r:

[0090] ;

[0091] in This describes the correlation between random road capacity and random demand, with a range of values:

[0092] Step 142: Define a new variable: , The range of variation is ,in , Based on the set parameters and the fitted joint probability distribution, we obtain... ;

[0093] Step 143: Based on the Vickery bottleneck model, the expected costs of the earliest and latest departing commuters and the expected travel cost of each commuter under user equilibrium can be calculated:

[0094] E[ ]=

[0095] in Conditions must be met: Assume there are and and , , E must be satisfied. ]=min According to the equilibrium condition E[ ]= E[ From this, we can deduce that the earliest departure time for commuters is... According to the equilibrium condition E[ ]= E[ From this, we can deduce that the latest departure time for commuters is... For the best moment Commuters who have already started queuing have the longest lines but have no planned delay costs. This can be used to calculate the departure time when commuters arrive exactly on time. ;

[0096] Table 1. Calculation results of the earliest departure time, latest departure time, and best departure time without pre-trip information.

[0097]

[0098] Execute step 144: Based on the equilibrium condition E[ ] = E[ This allows us to calculate the travel time of commuters at each moment under condition ω. ,in , ;

[0099] Step 150 simulates commuting patterns under different external conditions and varying correlations of these conditions, given pre-trip information. Since traffic flow or road capacity information is known before departure, the joint probability distribution function needs to be updated, along with the earliest departure time, latest departure time, and optimal departure time. The expected travel cost of the system and the commuting departure time selection for each individual commuter are calculated under different degrees of correlation of random variables. Based on the equilibrium condition, the travel time of commuters at each moment under condition ω can be further obtained. Specifically, the following sub-steps are included:

[0100] Step 151: Based on the given settings and the probability distribution of the random variables, and assuming prior knowledge of traffic flow or road capacity information, update the joint probability distribution function calculation formula:

[0101] 1) The road capacity is known to be in good condition. Joint probability distribution function:

[0102]

[0103] 2) The road capacity is known to be in poor condition. Joint probability distribution function:

[0104]

[0105] 3) Traffic flow is known to be in good condition. Joint probability distribution function:

[0106]

[0107] 4) Traffic flow is known to be in a bad state. Joint probability distribution function:

[0108]

[0109] in The correlation between random road capacity and random demand is still described, and its value range is: ;

[0110] Execution step 152: Update the probability distribution function The road capacity is known to be in good condition. hour, , , The road capacity is known to be in poor condition. hour, , , Traffic flow is known to be in good condition. hour, , , Traffic flow is known to be in a poor state. hour, , , ;

[0111] Step 153: Based on the Vickery discrete bottleneck model, the expected cost of the earliest departure when equilibrium is reached is calculated using the formula: E[ ]= When commuters are provided with road capacity information and traffic flow information respectively, the formula for calculating the expected travel cost at user equilibrium is:

[0112] 1) When the known road capacity is in good condition At this time, there are two possible states: GG, BG; when the known road capacity is in a bad state. There are two possible states: GB and BB. The first and second letters represent the states of traffic flow and road capacity, respectively (G represents a good state, and B represents a bad state). Given road capacity information, the expected travel cost for commuters at user equilibrium is:

[0113] E[ ]=

[0114] in The expected costs for the four scenarios are calculated using the following formulas:

[0115]

[0116]

[0117] in and It can be derived from the formula and The solution is obtained. Based on the equilibrium condition E[ ]= E[ ] and The specific formulas for calculating the earliest and latest departure times of commuters when road capacity information is known can be derived as follows:

[0118]

[0119]

[0120] For the best moment Commuters who have already started queuing have the longest lines but have no planned delay costs. The departure time when the commuter arrives exactly on time can be calculated. It can be deduced that, given the road capacity, the departure time for arriving exactly on time is...

[0121] ;

[0122] Table 2 shows the calculation results of the earliest departure time, latest departure time, and best departure time with road capacity information.

[0123]

[0124] 2) When the known traffic flow is in a good state At this time, there are two possible states: GG, GB; when the traffic flow is known to be in a bad state. There are two possible states: BG and BB. The first and second letters represent the traffic flow and road capacity states, respectively (G represents a good state, and B represents a bad state). Given the traffic flow information, the expected travel cost for commuters at user equilibrium is:

[0125] E[ ]=

[0126] in The expected costs for the four scenarios are calculated using the following formulas:

[0127]

[0128]

[0129] in and It can be derived from the formula and The solution is obtained. Based on the equilibrium condition E[ ]= E[ ] and The specific formulas for calculating the earliest and latest departure times of commuters when road capacity information is known can be derived as follows:

[0130]

[0131]

[0132] For the best moment Commuters who have already started queuing have the longest lines but have no planned delay costs. The departure time when the commuter arrives exactly on time can be calculated. It can be deduced that, given the traffic flow, the departure time that ensures a precise arrival on time is...

[0133] ;

[0134] Table 3 shows the calculation results of the earliest departure time, latest departure time, and best departure time with traffic flow information.

[0135]

[0136] Execute step 154: Based on the equilibrium condition E[ ] = E[ This allows us to calculate the travel time of commuters at each moment under condition ω. ,in , ;

[0137] Perform step 160 and output the simulation results. Calculate the expected travel cost and commuting time selection of the system under different degrees of correlation of random variables. Based on the equilibrium condition, the travel time of commuters at each time step under condition ω can be further obtained as the simulation results output.

[0138] Example 2

[0139] This invention proposes a simulation method for choosing urban morning rush hour commuting departure time based on a bottleneck model and stochastic variations in road capacity and traffic flow. Figure 2 As shown, the specific steps include:

[0140] Step S1: Collect data on external conditions for urban commuting, including historical data on road capacity and traffic flow. Assume the range of traffic flow variation on the main roads of the selected residential and work areas is as follows: , The range of road capacity variation for the main roads in the selected residential and work areas is as follows: , This forms the sample data space X. Statistical analysis is then performed on the random variables, such as... Figure 3 As shown.

[0141] Step S2: Select the Gumbel distribution as the fitting function type, and base it on traffic flow. The sample data, the known commuting probability density function of commuters can be described as follows: Solve for the mean of road capacity and commuting probability data. , and standard deviation , The relevant parameters (positional parameters) in the Günbel fitting function , and scale parameters , The formula for calculating ) is: 3825, 4275; , .in, This is the Euler-Mascheroni constant, approximately equal to 0.577. The probability density functions for the fitted random road capacity and traffic flow are: and .

[0142] Step S3: Set the work nature of commuting individuals. In this embodiment, the working hours are taken as... =9:00, the penalty cost coefficient for being late is γ=15.21 ( The early arrival penalty cost coefficient β = 3.9 ) and travel time cost coefficient α = 6.4 ( Select the option that satisfies the condition γ>α>β>0. Determine the travel time required for each commuter to reach their workplace under congestion-free conditions. =0.

[0143] Step S4: Determine whether to provide pre-trip information. If pre-trip information is not provided to commuters, proceed to step S5; if pre-trip information is provided to commuters, proceed to step S6.

[0144] Step S5: Simulate commuting patterns under different external conditions and varying correlations of these conditions, without prior travel information. Let the expected travel cost under these conditions be E[ The earliest departure time for commuters is The latest departure time is And the best departure time is Specifically, it includes the following sub-steps:

[0145] S501) Based on the set parameters and the probability distribution of the random variables, solve for the joint distribution function and joint probability density function when the correlation coefficient of the random variables is m:

[0146]

[0147]

[0148] Where m represents the correlation parameter between random road capacity and random traffic flow, and its calculation formula is: , The correlation coefficient between random road capacity and random traffic flow. .

[0149] S502) Define a new variable: Its range is ,in , Based on the set parameters and joint probability distribution, we can obtain... ;

[0150] S503) Based on the Vickery discrete bottleneck model, the expected cost to reach theoretical equilibrium is calculated using the following formula:

[0151] E[ ]= =

[0152] in It can be derived from the formula Solving for the equilibrium condition E, we get... ]= E[ ] and The earliest departure time can be calculated. The latest departure time is For commuters who arrive exactly on time, based on the equilibrium condition... This allows us to calculate the departure time that arrives exactly on time. ;

[0153] Table 4. Calculation results of the earliest departure time, latest departure time, and best departure time without pre-trip information.

[0154]

[0155] S504) According to the equilibrium condition E[ ] = E[ This allows us to calculate the travel time of commuters at each moment under condition ω. ,in , ;

[0156] Step S6: Simulate commuting patterns under different external conditions and varying correlations of these conditions, given pre-trip information. Since traffic flow or road capacity information is known before departure, the joint probability distribution function needs to be updated, including the earliest departure time, latest departure time, and optimal departure time. Based on the equilibrium condition, the travel time of commuters at each time point under condition ω can be further obtained as the simulation result output. This includes the following sub-steps:

[0157] (S601) Based on the set parameters and the probability distribution of random variables, when traffic flow information or road capacity information is known before departure, update the joint probability density function. The formula for calculating the joint probability density function when road capacity information is known is: The formula for calculating the joint probability density function when traffic flow information is known is: .

[0158] in, 'm' still describes the correlation parameter between stochastic road capacity and stochastic demand, and its calculation formula is: , The correlation coefficient between random road capacity and random traffic flow. .

[0159] S602) Assumption Its range is ,in , Update based on the set parameters and joint probability distribution. The probability density function. When road capacity information is known. The formula for calculating the probability density function is: When traffic flow information is known The formula for calculating the probability density function is: .

[0160] S603) Based on the Vickery discrete bottleneck model, the formula for calculating the expected cost of the earliest departure when reaching equilibrium is: E[ ]= and E[ ]= When commuters are provided with road capacity information and traffic flow information respectively, the formula for calculating the expected travel cost at user equilibrium is:

[0161] E[ ]=

[0162] E[ ]=

[0163] 1) According to the equilibrium condition E[ ]= E[ ]and The formulas for calculating the earliest and latest departure times when road capacity information is known are as follows: , .in, It can be calculated by formula The solution is obtained.

[0164] 2) According to the equilibrium condition E[ ]= E[ ]and The formulas for calculating the earliest and latest departure times when traffic flow information is known are as follows: , .in, It can be calculated by formula The solution is obtained.

[0165] (S604) For commuters who arrive just on time, the longest queue has no planned delay costs, according to the equilibrium condition... This allows us to determine the departure time at which commuters will arrive exactly on time, given road capacity information. When traffic flow information is known, the departure time at which commuters arrive exactly on time. .

[0166] Table 5 shows the calculation results of the earliest departure time, latest departure time, and best departure time with road capacity information.

[0167]

[0168] Table 6 shows the calculation results of the earliest departure time, latest departure time, and best departure time with traffic flow information.

[0169]

[0170] S605) According to the equilibrium condition E[ ] = E[ When updating known road capacity or traffic flow information, the travel time of commuters at each time point under condition ω can be calculated. .

[0171] Step S7: Output simulation results. Calculate the expected travel cost of the system under different degrees of correlation of random variables and the commuting departure time choice for each individual commuter. Based on the equilibrium condition, the travel time of commuters at each time step under condition ω can be further obtained as the simulation results output.

[0172] In summary, this invention proposes a simulation method for urban morning rush hour commuting departure patterns under stochastic variations in road capacity and traffic flow, based on a bottleneck model. This method considers the impact of external conditions and their correlations on urban morning rush hour commuting departure patterns. By simply fitting the probability distribution function of the external conditions and the joint probability distribution function of multiple conditions, the travel time of commuters at each time point under condition ω can be simulated. Furthermore, the heterogeneity of commuters' work nature is considered, and the parameters in the model do not require modification after initial determination. This invention also considers the impact of providing heterogeneous traffic condition information on urban morning rush hour commuting departure patterns, which is of great significance for high-quality information delivery solutions in real-world information systems. This invention can effectively simulate the macro-behavioral characteristics of urban commuter departure time selection, providing theoretical support for formulating effective morning rush hour traffic management policies.

[0173] This invention can simulate the departure time selection behavior of urban commuters under different conditions and with different correlations by adjusting parameters. It can simulate the individual departure time selection behavior patterns during the morning rush hour in cities under different conditions. The method is simple and practical, and it balances travel costs and road traffic flow characteristics.

[0174] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0175] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0176] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0177] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting urban commuting costs and times under simulated random changes in external conditions, characterized in that, include: Historical data on commuting external conditions, including road capacity and traffic flow, are collected, and a joint probability density function of road capacity and traffic flow is fitted. Set working hours and penalty cost coefficients; Based on the joint probability density function, work time and penalty cost coefficient, the commuting patterns of commuters under different external conditions and different correlations of external conditions are simulated without pre-trip information, and the commuting time of commuters is predicted. Based on the joint probability density function, work time and penalty cost coefficient, the commuting patterns of commuters under different external conditions and different correlations of external conditions are simulated with pre-trip information, and the commuting time of commuters is predicted. The aforementioned collection of historical data on commuting external conditions, including road capacity and traffic flow, and fitting of the joint probability density function of road capacity and traffic flow, includes: Historical data on commuting external conditions are collected, including road capacity and traffic flow. The range of historical commuting traffic flow variation on the main roads of the selected residential and work areas is defined as follows: The historical road capacity variation range of the main roads in the selected residential and work areas is as follows: And perform statistical analysis on the random variables; Assuming all commuters are homogeneous, we choose an appropriate function type, calculate the relevant parameters in the function, and output the probability density function corresponding to the fitted random variable, road capacity. , Indicates condition The road capacity is set below; output the probability density function corresponding to the fitted random variable traffic flow. , Indicates condition Traffic flow rate; and the joint probability density function of the two random variables after fitting. ; The commuting probability density function for a single commuter can be described as follows: ; The set working hours and penalty cost coefficients include: Set work hours as Let γ be the cost coefficient for late arrival, β be the cost coefficient for early arrival, and α be the cost coefficient for travel time. Under the condition that γ > α > β > 0, and without congestion, the travel time required for each commuter to reach their workplace is... ; Assuming that all commuters can reach an equilibrium state, each individual will not reduce travel costs by changing their choices; The method of simulating commuter travel patterns under different external conditions and different correlations of external conditions without pre-trip information, based on the joint probability density function, work hours, and penalty cost coefficients, and predicting commuter travel time, includes: Define flow-capacity ratio , The range of variation is , Based on the set parameters and the fitted joint probability distribution, solve for... probability density function ; Based on the Vickery bottleneck model, the expected travel cost for each commuter under user equilibrium is calculated: E[ ]= = Wherein, γ, β, and α represent the lateness penalty cost coefficient, early arrival penalty cost coefficient, and travel time cost coefficient, respectively; From the formula Solving for the equilibrium condition E, we get... ]= E[ ] and Find the earliest departure time for commuters. Latest departure time ,in During working hours; According to the equilibrium condition Solve for the departure time when the commuter arrives exactly on time. ; Assuming in The space is divided into A discrete set of departure times, where the interval between two adjacent departure times is equal. Define the label for the discrete departure time set as , ..., , ..., According to the equilibrium condition E[ ] = E[ [Calculate the travel time of commuters at each time step under condition ω.] ,in , ; The method of simulating commuter commuting patterns under different external conditions and different correlations of external conditions based on the joint probability density function, work time, and penalty cost coefficient, with pre-trip information, and predicting commuter commuting time, includes: When traffic flow information is known At that time, the commuter's commuting probability density function is described as follows: = When road capacity information is known At that time, the commuting probability distribution function of commuters is: = ,renew probability density function ; Based on the Vickery bottleneck model, the expected travel cost for each commuter under user equilibrium is updated as follows: E[ ]= = ； Based on the updated probability density function and travel costs, the earliest departure time for commuters can be determined. Latest departure time ; According to the equilibrium condition It calculates the departure time when commuters arrive exactly on time. ; Based on the updated time points and probability density function, the expected cost for the earliest departing commuter is calculated. Calculate the expected cost for the commuter who departs latest. Calculate the expected travel cost for each commuter under user equilibrium: E[ According to the equilibrium condition E[ ] = E[ ], calculate Travel time for commuters under condition ω .

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