A dynamic congestion pricing method considering herding effect

Abstract

The application discloses a dynamic congestion pricing method considering the herding effect, comprising the following steps: organizing traffic investigation, determining the traffic demand between each origin-destination and the initial link flow of the link, and setting the total number of congestion pricing implementation stages; generating the congestion pricing parameters of the corresponding link according to the link flow, and implementing the congestion pricing; after the implementation of the congestion pricing, updating the link reference flow according to the dynamic evolution model of the congestion pricing based on the herding effect; checking the convergence, if the reference flow converges to the link flow, the iteration is terminated; otherwise, returning to regenerate the parameters after updating the link flow according to the reference flow. The application considers the influence of the herding effect on the path selection behavior of travelers, can more accurately simulate the dynamic evolution of traffic flow, can flexibly implement the congestion pricing by setting irregular interval updating stages, is helpful to enhance the actual effect of the congestion pricing, optimize the traffic congestion condition, and is very consistent with the application requirement of the actual congestion pricing.

Description

Technical Field

[0001] This invention belongs to the field of road congestion pricing technology, specifically relating to a dynamic congestion pricing method that takes into account the bandwagon effect. Background Technology

[0002] Congestion pricing is one of the most effective economic means to alleviate traffic congestion and improve urban traffic efficiency. The key lies in determining a reasonable congestion pricing model, charging different fees based on road congestion levels to guide vehicles to choose off-peak travel times or other less congested routes, thereby reducing the number of vehicles on congested roads and alleviating traffic congestion. Traditional traffic flow dynamic evolution pricing models adjust tolls at fixed time intervals, such as daily or weekly, using observed road flow to formulate the congestion pricing model for the next stage, ultimately evolving the entire system to its optimal state. In this process, travelers can directly observe road flow and choose routes solely based on path travel time (i.e., impedance), without considering the impact of the herd effect on travelers' travel choices.

[0003] However, existing research indicates that conformity is widespread. [1] The bandwagon effect significantly influences travelers' route choices. During actual travel, travelers obtain route traffic information through various means, such as navigation apps or communication with other travelers at the same origin-destination (OD). Due to the bandwagon effect, travelers adjust their route choices, becoming more inclined to select routes chosen by the majority. Therefore, the results of traditional dynamic evolution models differ significantly from actual travel conditions, limiting their application and making them ill-suited to the complex changes in urban traffic.

[0004] References[1] Asch S E. Effects of group pressure upon themodification and distortion of judgments[J]. Organizational influenceprocesses, 1951, 58: 295-303. Summary of the Invention

[0005] Purpose of the invention: To address the above problems, this invention proposes a dynamic congestion pricing method that considers the herd effect. It studies the herd effect in the process of travelers' route selection, and based on the dynamic evolution model of traffic flow under the influence of the herd effect, it helps managers to automatically evolve the dynamic pricing parameters of road segments at each stage, implement congestion pricing, and improve the continuity of congestion pricing policy and its engineering feasibility.

[0006] Technical Solution: To achieve the objectives of this invention, the technical solution adopted is: a dynamic congestion pricing method considering the bandwagon effect, comprising the following steps:

[0007] Step 1: Construct the traffic network and initialize the parameters of the dynamic congestion pricing model that considers the bandwagon effect; the parameters include the traffic demand of travelers between each OD pair, the total number of stages for implementing congestion pricing, and the convergence accuracy.

[0008] Step 2, according to the Traffic generation of road segments Phased congestion pricing, updated congestion pricing model, and congestion pricing according to the new model.

[0009] Step 3, in After implementing the phased congestion pricing model, solve the optimization problem. Obtain the updated path flow vector when the road network traffic flow dynamically evolves to equilibrium. and reference traffic flow for road sections .

[0010] Step 4: Based on the reference traffic flow and travel impedance of the road segment, the traveler selects the travel route for the next stage and chooses the path with the minimum generalized travel impedance according to the generalized travel impedance function.

[0011] Step 5: Perform a convergence check on the iterative results of the dynamic congestion pricing model considering the herding effect; if the path flow converges to the equilibrium flow and reaches the convergence accuracy, stop the iteration; otherwise, update the... Traffic flow in phased road sections ,make Return to step 2.

[0012] Furthermore, in step 1, the parameters of the dynamic congestion charging model that takes into account the herd effect are initialized.

[0013] Initialize the traffic network In a network, nodes represent intersections of road segments, and directed arcs represent road segments. (Definition) For the set of nodes in the network, It is a set of directed arcs in the network.

[0014] This represents the set of OD pairs generated by travel demand. For OD The set of paths between, For OD Traffic demand between; , Representing road segments The flow rate and impedance, and for A monotonically increasing function; determine the traffic demand of travelers between each OD pair. Road section Initial segment flow .

[0015] , They represent OD pairs Inter-path Path flow and path impedance, Indicates OD pair Inter-path The probability of being selected; and the correlation matrix between the path and the road segment. If the road section In OD Path between Above, then the indicator variable =1, otherwise It is 0.

[0016] Indicates OD pair Inter-path The generalized travel impedance makes The total number of stages for implementing congestion pricing. To improve convergence accuracy, dynamic congestion pricing phase .

[0017] This is a parameter relating the attractiveness of a route to its travel time, indicating the degree to which travelers rely on route flow information from the previous stage when the route reached a steady state. The larger the value, the greater the attractiveness of the path flow to travelers; the greater the attractiveness of a path, the smaller its corresponding generalized impedance. A parameter greater than 0 is used to describe the traveler's familiarity with the road network, and is inversely proportional to the traveler's familiarity with the road network.

[0018] Furthermore, in step 3, in After implementing the phased congestion pricing model, solve the optimization problem. Obtain the reference flow rate of road segments when the road network traffic flow dynamics to equilibrium. Optimization problem The solution steps are as follows:

[0019]

[0020]

[0021]

[0022]

[0023] In the formula, This represents the objective function of the dynamic congestion pricing model that considers the herd effect. For the decision variables of the model, Indicates OD pair The Traffic on the path For model decision variables The range of values ​​for , Indicates road segment The function for calculating travel time. and Let be constants, representing the th , respectively Phase and the After the phased congestion pricing system reaches a relatively stable level, the path traffic will be considered. As an indicator variable, if road segment In OD Path between Above, then the indicator variable =1, otherwise It is 0.

[0024] Step 3.1, for each OD pair According to the logit model ,Will Assigned to path In this process, the path flow vector is obtained. Set the number of iterations .

[0025] Step 3.2: Calculate the generalized travel impedance for each path using the generalized travel impedance function, which is defined as follows:

[0026]

[0027] In the formula, It is the first Phase Path Generalized travel impedance It is the first Phase Path The route travel time Indicates the first Phase Path The attraction; They are random terms and follow independent Gumbel distributions with the same parameter.

[0028] Step 3.3, under the generalized travel time of each current path, for each OD pair ,Will Assign to path according to the following formula In this process, the auxiliary path traffic flow vector is obtained. .

[0029]

[0030] Step 3.4, Convergence check: If If the iteration stops, then stop.

[0031] Step 3.5, along the direction The iteration step size is calculated using the Armijo line search method. .

[0032] Step 3.5.1, retrieve Armijo line search parameters , ,make .

[0033] Step 3.5.2, check if the following formula is true:

[0034]

[0035] In the formula , and Let each represent the objective function of the dynamic congestion pricing model considering the bandwagon effect. The function values ​​at each point and the first-order Taylor expansion.

[0036] Step 3.5.3: If the expression in step 3.5.2 is not true, then let... If not, return to step 3.5.2; otherwise, set the iteration step size. Step 3.5: Stop the iteration.

[0037] Step 3.6, Update path traffic: Let , Proceed to step 3.2.

[0038] Furthermore, in step 2, each road segment ,according to The congestion pricing model will be implemented.

[0039]

[0040] In the formula, Indicates the first Congestion charges for specific road sections Indicates the first Phase section Traffic, This represents the congestion charge coefficient function.

[0041] Furthermore, in step 5, the convergence conditions are set as follows:

[0042] .

[0043] Furthermore, in step 5, the traffic flow of the road segment is updated. Traffic flow in phased road sections Represented as:

[0044] ;

[0045] in .

[0046] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0047] This invention proposes a dynamic congestion pricing method that considers the bandwagon effect. This method incorporates the influence of the bandwagon effect into the dynamic evolution model of traffic flow, enabling a more accurate simulation of the dynamic evolution of road network traffic flow, reflecting the time-varying and random nature of traffic flow in the network, and adapting to the complex changes in urban traffic. Simultaneously, it uses irregular intervals to update the congestion pricing model in stages, and automatically evolves and generates the congestion pricing parameters for the next stage based on the traffic flow distribution of each stage of the congested road segment, dynamically adjusting the congestion pricing standard. Through this method, this invention provides strong support for governments to formulate more scientific and reasonable differentiated dynamic congestion pricing management methods, helping to implement congestion pricing to regulate traffic flow and thus optimize traffic conditions, which is highly consistent with the actual application needs of congestion pricing.

[0048] This invention considers the impact of the herd mentality on travelers' route selection behavior, thus enabling a more accurate simulation of the dynamic evolution of traffic flow and enhancing the practical effectiveness of congestion pricing. The dynamic congestion pricing method proposed in this invention can update the congestion pricing model at irregular time intervals. In other words, the charging period can be dynamically adjusted. This flexibility in updating the congestion pricing model at irregular intervals provides more options for practical implementation, perfectly meeting the application needs of congestion pricing. Therefore, this invention represents an exploration and innovation in road congestion pricing technology, possessing significant theoretical research value and practical guiding value. Attached Figure Description

[0049] Figure 1 This is a flowchart of the algorithm of the present invention.

[0050] Figure 2 This is the flowchart of the model solving algorithm in step 2.

[0051] Figure 3 This is a computational example network diagram.

[0052] Figure 4 This is a comparison of the convergence of different time interval charging schemes with the number of charges.

[0053] Figure 5 This is a comparison of the convergence of different time interval charging schemes with the cumulative number of iteration stages. Detailed Implementation

[0054] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0055] The present invention provides a dynamic congestion pricing method that considers the bandwagon effect. The symbols used in the dynamic congestion pricing method are defined as follows: Given a traffic network... , where defined It is the set of nodes (intersections of road segments) in the network. Let be the set of directed arcs (i.e., path segments) in the network. This represents the set of OD pairs generated by travel demand. For OD The set of paths between, For OD The traffic demand between them. , Representing road segments The flow rate and impedance, and for A monotonically increasing function. , They represent OD pairs Inter-path Path flow and path impedance, Indicates OD pair Inter-path The probability of being selected. Simultaneously, there is an association matrix between paths and road segments. If the road section In OD Path between Above, then the indicator variable =1, otherwise It is 0. Indicates OD pair Inter-path Generalized travel impedance A parameter greater than 0 is used to describe the traveler's familiarity with the road network, and is inversely proportional to the traveler's familiarity with the road network.

[0056] The foundation of traditional dynamic evolution models is the Stochastic User Equilibrium (SUE) model. Because road conditions in real-world transportation networks are random, travelers can only roughly estimate path impedance. Therefore, the SUE model assumes that travelers' estimates of path impedance on the road network have a certain margin of error compared to the actual values.

[0057] (1)

[0058] in, This represents the error term for perceived path impedance, i.e., the random term. In the stochastic user equalization model, travelers choose their travel routes based on perceived path impedance. The probability of (i.e., path) The probability that the perceived impedance is minimized is:

[0059] (2)

[0060] In the dynamic evolution model considering the bandwagon effect, travelers' route selection considers not only the travel impedance and the error term of the path impedance in equation (1), but also the route selection information of other travelers. Under the influence of the bandwagon effect, travelers observe and evaluate the traffic flow on each route from the perspective of group behavior. In this invention, these route flows are called "reference flows". Travelers will evaluate the "attractiveness" of each route based on the magnitude of the "reference flows" and tend to choose the route chosen by the majority.

[0061] Therefore, in a dynamic congestion pricing model that considers the bandwagon effect, travelers will observe that traffic flow reaches a relatively stable state after the implementation of congestion pricing in the previous stage (i.e., path flow converges to equilibrium flow with a convergence accuracy of 1). After considering the flow rate of each path, the next travel route is selected based on the "reference flow rate" of the path and the travel impedance. Let... For dynamic congestion pricing After phased implementation, once the traffic flow dynamic evolution model considering the herd effect reaches relative stability, the flow rates of each path can be determined by travelers within the same OD pair through observation or communication. Therefore, in the first phase... During the phase, travelers from the same OD pair according to The magnitude of the traffic flow determines the attractiveness of each path, while simultaneously weighing the travel time of each path (path travel time can vary with traffic fluctuations).

[0062] Based on the above discussion, the generalized travel impedance function under the herd effect is defined as:

[0063] (3)

[0064] in It is the first Phase Path ( Generalized travel impedance It is the first Phase Path ( The travel time along the route. Indicates the first Phase Path The "attractiveness" It is an important parameter relating the "attractiveness" of a route to the travel time of that route. It can also be understood as the degree to which travelers rely on route traffic information from the previous stage when the route reached a steady state. The larger the value, the more attractive the route traffic is to travelers. These are random terms and follow independent Gumbel distributions with the same parameter. The greater the attractiveness of a path, the smaller its corresponding generalized impedance; therefore, the coefficient before the second term in equation (3) is negative. Clearly, the... The actual path travel time of a stage is the path flow. The function, and the first The appeal of phased paths Then it is a constant value, the magnitude of which is determined by the first... The path flow is determined when the stage reaches a steady state.

[0065] If the If travelers in a given stage choose the path with the least impedance according to the generalized travel impedance function described by equation (3), then the traffic flow when the stage reaches a relatively stable state can be obtained by solving the following Logit-type stochastic user equilibrium model based on relative entropy:

[0066] [KL-SUE]

[0067] (4)

[0068]

[0069]

[0070]

[0071]

[0072] In the formula, Let the decision variables of the model represent OD pairs The Traffic on the path; For model decision variables The range of values ​​for; Indicates road segment The function for calculating travel time; The constant represents the first The path flow after the phased congestion pricing implementation has reached a relatively stable level.

[0073] Below are the detailed steps of a dynamic congestion pricing method that considers the bandwagon effect. The flowchart of the algorithm is shown below. Figure 1 As shown, the specific steps are as follows:

[0074] Step 1 (Initialization): Conduct a traffic survey to determine the traffic demand of travelers between each OD pair. Initial segment flow on the road segment ,make The total number of stages for implementing congestion pricing. To improve convergence accuracy, a dynamic congestion pricing phase is implemented. .

[0075] Step 2 (Generate congestion charges for each road segment) ,according to The congestion pricing model will be implemented.

[0076] (5)

[0077] In the formula, Indicates the first Congestion charges for specific road sections Indicates the first Traffic flow in each section of the road This represents the congestion charge coefficient function.

[0078] Step 3 (Update the "Reference Traffic Flow" for the road segment) ( After the implementation of the congestion pricing model in the initial stage, the path flow vector at the point where the road network traffic flow dynamically evolves to equilibrium... "Reference traffic flow" for road sections The following model was obtained by solving:

[0079] (6)

[0080]

[0081]

[0082]

[0083] Step 4: The traveler selects the route with the minimum generalized travel impedance according to the generalized travel impedance function described by equation (3).

[0084] Step 5 (Convergence Check) If

[0085] (7)

[0086] Then stop iterating; otherwise, update the... Traffic flow in phased road sections

[0087] (8)

[0088] in ;

[0089] Place Proceed to step 2.

[0090] By following the steps above, managers only need to adjust the congestion pricing model at each stage based on the dynamic evolution parameters of the road segments generated by the dynamic evolution model that takes into account the herd effect, and ensure that the traffic flow in the network automatically evolves to the system optimum.

[0091] As the theoretical basis of this invention, the following two propositions prove that the Kuhn-Tucker condition in equation (6) can derive the traveler generalized travel impedance function in equation (3), which shows that the traveler generalized travel impedance function under the herd effect has an inherent consistency with the [KL-SUE] model.

[0092] Proposition 1: The [KL-SUE] problem is a convex programming problem. The optimal solution to this problem is... It is unique.

[0093] Proof: The feasible region formed by the linear equality constraints is a convex set, and nonnegative constraints do not change this property. Therefore, the constraint set of the [KL-SUE] problem is convex, and the first term of the objective function of the [KL-SUE] problem is... A convex function.

[0094] Let the second term of the objective function for the [KL-SUE] problem be:

[0095] (9)

[0096] The partial derivatives can be calculated as follows:

[0097] (10)

[0098] (11)

[0099] but The Hessian matrix is

[0100] (12)

[0101] It can be observed that It is a diagonal matrix, and all diagonal elements are positive. Therefore, The Hessian matrix is ​​positive definite, from which we can conclude that for A strictly convex function.

[0102] In summary, the first term of the objective function for the [KL-SUE] problem is: The convex function, the second term of the objective function for A strictly convex function, the sum of the two terms is The strictly convex function, i.e., the objective function of [KL-SUE], is path flow. If the function is strictly convex and the constraint set of the problem is convex, then the [KL-SUE] problem is a convex programming problem, and its optimal solution is... It is unique.

[0103] Proposition 2: Let If it is the optimal solution for [KL-SUE], then Satisfy the following expression:

[0104] (13)

[0105] Proof: As stated in Proposition 1, the [KL-SUE] problem is a convex programming problem, and the optimal solution to this problem... It is unique.

[0106] The [KL-SUE] model is a minimization problem with linear equality and nonnegativity constraints, and its Lagrangian function is:

[0107] (14)

[0108] in, It corresponds to the constraint conditions. Lagrange operators, It corresponds to the constraint conditions. The Lagrange operator. The first-order condition of the [KL-SUE] model is equivalent to... The minimal KKT conditions, the KKT conditions for the Lagrange function are:

[0109] (15)

[0110] (16)

[0111] (17)

[0112] (18)

[0113] (19)

[0114] OD to The set of valid paths between them is And any middle, Then, from equations (17), (18) and (19), we can obtain .

[0115] Therefore, from the Lagrange function, i.e., equation (14), we can obtain:

[0116] (20)

[0117] Since the actual travel impedance of a route is equal to the sum of the travel impedances of all the road segments it traverses, that is... From equations (15) and (20), we can obtain:

[0118] (twenty one)

[0119] From equation (21), we can obtain

[0120] (twenty two)

[0121] Substituting equation (22) into equation (22) We can obtain:

[0122] (twenty three)

[0123] Then, from equations (22) and (23), the path flow solution of the model can be obtained as follows:

[0124] (twenty four)

[0125] Equation (24) is clearly the Logit path selection formula. Therefore, if the first... If travelers choose the path with the minimum generalized travel impedance according to the generalized travel impedance function described by equation (3), then the traffic flow solution when the system reaches a steady state at the end of the stage is the minimum point of [KL-SUE].

[0126] As can be seen from equation (24) of Proposition 2, the generalized travel impedance function of travelers under the herd effect (i.e., equation (3)) is inherently consistent with the [KL-SUE] model.

[0127] As a further improvement of the present invention, the solution to the optimization problem in step 3 is obtained by the following 6 sub-steps:

[0128] Based on steps 3.1–3.6 below, we can obtain the result at... ( After the implementation of the congestion pricing model in the initial stage, the path "reference flow" at which the road network traffic flow dynamically evolves to equilibrium is calculated using the following algorithm: Figure 2 As shown:

[0129] Step 3.1 (Initialization) Given the allowable convergence accuracy For each OD pair According to the logit model ,Will Assigned to path In this process, the initial path flow vector is obtained. Set the number of iterations .

[0130] Step 3.2 (Update the generalized travel impedance function) is from

[0131]

[0132] Calculate the generalized travel impedance function for each path.

[0133] Step 3.3 Under the generalized travel time of each current path, for each OD pair ,Will Assign to path according to formula (25) In this process, the auxiliary path traffic flow vector is obtained. .

[0134] (25)

[0135] Step 3.4 Convergence check: If If the iteration stops, then stop.

[0136] Step 3.5 (Calculate the iteration step size) along the direction The iteration step size is calculated using the Armijo line search method. :

[0137] Step 3.5.1 Obtain Armijo line search parameters , , step length .

[0138] Step 3.5.2 Check if the following formula is true:

[0139] (26)

[0140] In the formula , and Let each represent the objective function of the dynamic congestion pricing model considering the bandwagon effect. The function values ​​at each point and the first-order Taylor expansion are obtained using the Armijo step size, which is a commonly used step size method.

[0141] Step 3.5.3 If equation (26) does not hold, then let Proceed to step 3.5.2; otherwise, let... Step 3.5: Stop the iteration.

[0142] Step 3.6 Update path traffic, making , Proceed to step 3.2.

[0143] Through the above steps, the administrator automatically evolves the road segment dynamic charging parameters based on the dynamic congestion charging model that takes into account the herd effect, and changes the congestion charging mode once in each stage. The traffic flow in the network automatically evolves to the system optimum. In the dynamic congestion charging model that takes into account the herd effect, travelers observe the traffic flow of each path after the traffic flow reaches a relatively stable state after the implementation of congestion charging in the previous stage, and comprehensively select the travel route for the next stage based on the reference flow of the path and travel impedance.

[0144] The model and algorithm of this invention are verified using a computational example below. The computational example network is as follows: Figure 3 As shown, the network consists of 11 road segments, 7 nodes, and 4 OD pairs. The travel time of each road segment is calculated using the BPR function.

[0145] (34)

[0146] in , Each is a road segment Free-flow travel time and road sections The capacity. Figure 3 In this context, the specific values ​​of these two parameters are determined by the road segment. The adjacent binary pair Provided.

[0147] The demand for OD is as follows: The OD demand is evenly distributed across all feasible paths of the OD pair, and the resulting traffic distribution is used as the initial state of the network.

[0148] To evaluate the impact of the congestion charging phase interval on the algorithm's convergence speed, a case study was conducted on three different charging phase intervals: , and , This refers to the number of stages in the implementation of congestion pricing for road sections.

[0149] like Figure 4 As shown, it can be seen that regardless of whether the charging interval is a variable (i.e. ) or fixed (i.e. or This demonstrates that the method proposed in this invention can achieve convergence even when updating tolls at irregular time intervals. Furthermore, by Figure 5 It can be seen that it has The performance of the imprecise method is better than Variants, too, The variant is superior A variant of 3. This means that to achieve the same level of solution accuracy, methods with longer time intervals require fewer trials. The reason behind this phenomenon is that methods with longer time intervals allow travelers more time to understand traffic conditions and adjust their route choices. Therefore, the network traffic observed at the end of each tolling phase is closer to equilibrium. Consequently, the search directions generated under longer time intervals will more effectively improve the convergence speed of the tolling method.

Claims

1. A dynamic congestion pricing method considering the bandwagon effect, characterized in that, Includes the following steps: Step 1: Construct the traffic network and initialize the parameters of the dynamic congestion pricing model considering the bandwagon effect. These parameters include the traffic demand of travelers between each origin-destination (OD) pair, the total number of stages for implementing congestion pricing, and the convergence accuracy. Specifically, this involves initializing the traffic network. In a network, nodes represent intersections of road segments, and directed arcs represent road segments. (Definition) For the set of nodes in the network, It is a set of directed arcs in the network; This represents the set of OD pairs generated by travel demand. For OD The set of paths between, For OD Traffic demand between; , Representing road segments The flow rate and impedance, and for A monotonically increasing function; road segment Initial segment flow ; , They represent OD pairs Inter-path Path flow and path impedance, Indicates OD pair Inter-path The probability of being selected; and the correlation matrix between the path and the road segment. If the road section In OD Path between Above, then the indicator variable =1, otherwise =0; Indicates OD pair Inter-path The generalized travel impedance makes The total number of stages for implementing congestion pricing. To improve convergence accuracy, dynamic congestion pricing phase ; This is a parameter relating the attractiveness of a route to its travel time, indicating the degree to which travelers rely on route flow information from the previous stage when the route reached a steady state. The larger the value, the greater the attractiveness of the path flow to travelers; the greater the attractiveness of a path, the smaller its corresponding generalized impedance. A parameter greater than 0 is used to describe the traveler's familiarity with the road network, and is inversely proportional to the traveler's familiarity with the road network. Step 2, according to the Traffic generation of road segments Phased congestion pricing, updated congestion pricing model, and congestion pricing according to the new model; Step 3, in After implementing the phased congestion pricing model, solve the optimization problem. Obtain the path flow vector when the road network traffic flow evolves to equilibrium. and reference traffic flow for road sections Among them, the optimization problem The solution steps are as follows: ， ， ， ， In the formula, This represents the objective function of the dynamic congestion pricing model that considers the herd effect. For model decision variables The range of values ​​for , Indicates road segment The function for calculating travel time. and Let be constants, representing the th , respectively Phase and the Path flow after the phased congestion pricing implementation reaches a relatively stable level; Indicates OD pair Inter-path Path impedance; Indicates the first Congestion charges for specific road sections; Step 4: Based on the reference traffic flow and travel impedance of the road segment, the traveler comprehensively selects the travel route for the next stage and chooses the path with the minimum generalized travel impedance according to the generalized travel impedance function. Step 5: Perform a convergence check on the iterative results of the dynamic congestion pricing model considering the herding effect; if the path flow converges to the equilibrium flow and reaches the convergence accuracy, stop the iteration; otherwise, update the... Traffic flow in phased road sections ,make Return to step 2.

2. The dynamic congestion pricing method considering the bandwagon effect according to claim 1, characterized in that, Step 3 specifically includes: Step 3.1, for each OD pair According to the logit model ,Will Assigned to path In this process, the path flow vector is obtained. Set the number of iterations ; Step 3.2: Calculate the generalized travel impedance for each path using the generalized travel impedance function, which is defined as follows: ， In the formula, It is the first Phase Path Generalized travel impedance It is the first Phase Path The route travel time, Indicates the first Phase Path The attraction; These are random terms and follow independent Gumbel distributions with the same parameter; Step 3.3, under the generalized travel time of each current path, for each OD pair ,Will Assign to path according to the following formula In this process, the auxiliary path traffic flow vector is obtained. ; ， Step 3.4, Convergence check: If If the iteration stops, then stop. Step 3.5, along the direction The iteration step size is calculated using the Armijo line search method. ; Step 3.5.1, retrieve Armijo line search parameters , ,make ; Step 3.5.2, check if the following formula is true: ， In the formula , and Let each represent the objective function of the dynamic congestion pricing model considering the bandwagon effect. The function values ​​at each point and the first-order Taylor expansion; Step 3.5.3: If the expression in step 3.5.2 is not true, then let... If not, return to step 3.5.2; otherwise, set the iteration step size. Step 3.5: Stop the iteration. Step 3.6, Update path traffic: Let , Proceed to step 3.

2.

3. A dynamic congestion pricing method considering the bandwagon effect according to claim 1 or 2, characterized in that, In step 2, each road segment ,according to Congestion pricing will be implemented using a new pricing model. ， In the formula, Indicates the first Congestion charges for specific road sections Indicates the first Phase section Traffic, This represents the congestion charge coefficient function.

4. A dynamic congestion pricing method considering the bandwagon effect according to claim 1 or 2, characterized in that, In step 5, the convergence conditions are set as follows: 。 5. A dynamic congestion pricing method considering the bandwagon effect according to claim 2, characterized in that, In step 5, the traffic flow of the road segment is updated. Traffic flow in phased road sections Represented as: ； in .

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