CN105427394A - Congestion charging optimal toll rate determining method based on trial-and-error method and motor vehicle flow - Google Patents

Abstract

The invention discloses a method for determining the optimal rate of congestion charging based on the trial and error method and motor vehicle flow. Only the traffic flow data of each entrance road section of the charging area is needed to adjust and obtain the optimal charging rate. For the optimal charging scheme, the present invention uses a set of strict mathematical proofs to establish a "trial and error method" for rate adjustment to ensure that the method can converge to the optimal charging rate, including: (1) using asymmetric The stochastic user balance theory of the link travel time equation is used to evaluate each available congestion charging model; (2) a monotonic, continuous variable inequality model is established to predict the network balance flow; (3) the projection of the solution variable inequality model is used Algorithm to determine the adjusted step size and the charging rate value of each step.

Description

Determination method of optimal rate of congestion charging based on trial and error method and motor vehicle flow

technical field

The invention relates to a method for determining the optimal charging rate of congestion charging according to the trial-and-error method and motor vehicle flow data at the entrance section of the charging area, belonging to the field of urban traffic management and control.

Background technique

Traffic congestion has always been the main problem of urban traffic operation. It not only makes many drivers frustrated with urban traffic, but also pollutes the urban environment and increases social costs. Traffic congestion increases travel time, increases travel time uncertainty, generates air and noise pollution and reduces social productivity. Congestion pricing is considered an important tool for urban traffic managers to manage traffic demand and divert bus ridership. Many existing studies focus on how to determine the optimal congestion charging rate. First (no restriction on charging location) and second (only charging on part of the network) optimal charging as two economic concepts have been widely studied as urban congestion charging strategies.

The practical application of urban traffic congestion charging is an important focus of the present invention, and three existing famous (Singapore, London, Stockholm) congestion charging embodiments all adopt the scheme of cordon charging. London uses cordon licences, and the other two cities use cordon entry tolls. As we all know, the charging method of the entrance section of the cordon is more effective and fair. Because it has two practical properties. First of all, when the cordon congestion charge was implemented, the traffic network managers were more concerned about the traffic conditions within the charge area; for example, when the congestion charge was first established in Singapore in 1975, the Singapore land traffic management The goal of the program is to reduce the total traffic flow entering the toll zone by 25% to 35%. That is, the total traffic flow entering a charging zone should be limited by a pre-determined threshold. Second, the toll value is the same for each entry into a certain toll area for easy driver identification and authority management.

In general, although the existing research has achieved good results in theory, many of the methods for determining the congestion charging rate are not suitable for practical applications, mainly because they require accurate data on many transportation network attributes, including the travel demand equation , the road segment travel time equation and the time value of traffic network users. For the entire transportation network, these data are difficult to obtain.

Contents of the invention

Technical problem: The present invention provides a method for determining the optimal rate of congestion charging based on trial and error and motor vehicle flow for cordon congestion charging and does not require a large amount of data.

Technical solution: The method for determining the optimal rate of congestion charging based on the trial and error method and motor vehicle flow of the present invention includes the following steps:

Step 1: Establish a traffic network topology map based on the point, line and partition data of the urban traffic network;

Step 2: Based on the topological map of the traffic network established in Step 1, determine the toll area and all entrances in the area, and determine each entrance as the toll location;

Step 3: Set the target total traffic flow limit value entering each toll area, and implement a set initial toll price scheme at the toll location;

Step 4: During the period during which the current toll price plan is implemented, observe and record the traffic flow entering each toll road section after the traffic flow is stable;

Step 5: Through the difference between the traffic flow of each toll road section observed in step 4 and the "target total traffic flow limit value" determined in step 3, a new toll price scheme is calculated according to the adaptive prediction and correction algorithm;

Step 6: Calculate the difference between the new charging price scheme and the old charging price scheme, and judge whether the difference is less than the judgment threshold. If so, output the new charging price scheme as the optimal result, otherwise return Step four.

Further, in the method of the present invention, the traffic network topology map includes point, line and partition data of the urban traffic network, and the target total traffic volume limit value is determined according to the relative ratio of reducing congestion and optimizing the environment, and the described The initial charging price scheme is any price scheme, and the adaptive forecasting correction algorithm includes two processes of forecasting and correction.

Congestion charging measures are usually targeted, charging for areas prone to congestion in cities such as central business districts, expressways and outer ring roads, and urban business districts, and these cities usually have a relatively high proportion of private motor vehicle travel and have a sound environment. Roads or congested areas are easy to divide, and there are unsaturated road networks or well-developed public transportation outside the congestion charging area, which can bear the huge traffic volume diverted after the implementation of congestion charging.

In the preferred scheme of the present invention, assume that there are 1 toll areas in the network, determine to enter each toll area i according to the urban traffic network, i=1, 2, ..., I, all entrance road sections, and carry out these entrance road sections Charge and charge the same rate, denoted by τ _i . τ=(τ _i , i=1, 2, . . . I) ^T represents the charges for all areas, and the superscript "T" represents the transposition of the vector. H _i represents the limit value of the flow (total inbound flow) entering the predetermined toll area i.

A represents a collection of road segments in the network. Indicates the set of all entry road sections of area i, i=1, 2, . . . , I. Represents the collection of all toll entry road segments. if Then τ _a represents the toll amount on road section a, and if road section a is not an entrance road section of the toll area, then τ _a =0. Different charging schemes τ will affect the route selection of network users and lead to different balanced traffic flows. v _a (τ) represents the balanced traffic flow of road segment a∈A, and T _a (v, τ) represents the generalized road segment travel time function:

T _a (v, τ) = t _a (v) + τ _a /α, a∈A(1)

Among them, α represents the time value of network users. t _a (v) represents the asymmetric travel time function of the road segment a∈A, which is a non-negative, monotonically increasing and continuously derivable function about the traffic vector v of the road segment, and v represents the set of v _a (τ).

In the step 3 of the preferred scheme of the present invention, aiming at reducing congestion and optimizing the environment, the target total traffic flow limit value entering each toll area is set, for example, reducing the target traffic flow by half in order to reduce the congestion plan in a certain area of the urban area, then it can be Set the target total traffic flow limit value to half of the current value, and implement an arbitrary toll price scheme at the toll location, such as five yuan, which is the initial toll price vector

Step 4 of the preferred solution of the present invention: implement the current toll price scheme for one week, and observe and record the traffic flow entering each toll road section after the traffic flow is stable during the period during which the current toll price scheme is implemented.

The acquisition method of motor vehicle flow is closely related to the congestion charging method. For example, the traffic of motor vehicles can be counted through the video detectors installed at each toll entrance, or the electronic toll tags on each passing motor vehicle can be read based on roadside short-range wireless communication technology, and then the traffic of motor vehicles can be counted.

Step 5 of the preferred solution of the present invention: use the following mathematical formula to calculate the difference between the "observed motor vehicle flow" and the "motor vehicle flow threshold" to obtain a new charging price scheme.

The calculation process of the new charging price is as follows:

A. Build a model

Φ(τ ^* )(τ-τ ^* )≥0, τ∈Ω(2)

Where Ω={τ|τ _i ≥0, i=1, 2,...I} is a feasible set of τ, the superscript "*" represents the optimal solution, and the variable inequality function Φ(τ) is defined as follows:

in Represents a set of real numbers consisting of I elements.

B. Calculate the variable inequality equation Φ(τ ⁽ⁿ⁾ ), which is the difference between the "observed motor vehicle flow" and the "motor vehicle flow limit".

C. Find the auxiliary toll scheme vector through the projection operation, load the auxiliary toll scheme on the network, then observe the traffic flow of the corresponding entrance section, and then use the observed flow value to calculate the corresponding variable inequality equation value.

D. By further calculating the ratio r ⁽ⁿ⁾ and the step value π ⁽ⁿ⁾ , a new charging rate scheme is obtained.

Specific solution steps (adaptive prediction and correction algorithm):

Step 1 initialization;

Set three constants κ ₁ , κ ₂ , γ, where 0<κ ₂ <κ ₁ <1, γ∈(0, 2), and set the initial step size η ⁽¹⁾ >0. Set the iteration number to n=1.

Step 2 prediction process;

Step 2.1: Set the toll scheme τ ⁽ⁿ⁾ in the network, and then observe the traffic flow at the entrance section of each toll area, determined by i=1, 2,...I to represent, and then calculate the variable inequality equation

$\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&Element;</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Step 2.2: Operation via projection

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Find ancillary fee scheme vector Among them, P _Ω [τ′] represents the projection operation of projecting the vector τ′ onto the feasible set Ω of the charging scheme, and its value is expressed by the following formula:

P _Ω [τ′]=(max(0,τ′ _i ), i=1, 2, ..., I) ^T (6)

Step 2.3: Add ancillary fee schemes Load it to the network, and then observe the traffic flow of the corresponding entrance segment i = 1, 2, ... I, and then use the observed flow values to calculate the corresponding variable inequality equation values

$\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&Element;</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Step 2.4: Calculate the ratio r ⁽ⁿ⁾ by the following equation,

${\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

If r ⁽ⁿ⁾ ≤ κ ₁ , go to step 3, otherwise according to

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Decrease the step size value and proceed to step 2.2.

Step 3 correction process;

Based on τ ⁽ⁿ⁾ , η ⁽ⁿ⁾ , calculate a step value π ⁽ⁿ⁾ for the correction process, and then get the updated charging scheme vector τ ⁽ⁿ⁺¹⁾ .

Step 3.1: Calculate the step size value π ⁽ⁿ⁾ of the correction process according to the following equation:

${\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&rsqb;</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

in

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Step 3.2: Update the charging scheme vector τ ⁽ⁿ⁺¹⁾ by the following projection operation:

${\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Step 3.3: Determine whether the following conditions are true:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&kappa;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

If the above formula is established, increase the step size η ⁽ⁿ⁾ according to the following scheme, and then proceed to step six:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

Otherwise, go to step six directly.

Step 6: Calculate the difference between the new charging price scheme and the old charging price scheme, and judge whether the difference is less than the judgment threshold. If so, output the new charging price scheme as the optimal result, otherwise return Step four.

if Then terminate, ε is a positive limit value set in advance. Otherwise, let n=n+1, go to step 4.

Beneficial effect: compared with the prior art, the present invention has the following advantages:

Although the existing studies have achieved good results in theory, many of the methods for determining the congestion charge rate are not suitable for practical applications, mainly because they require accurate data on many attributes of the transportation network, including travel demand equations, road segment travel time equations and the time value of transportation network users. For the entire transportation network, these data are difficult to obtain. Therefore, the present invention proposes a decision-making method aiming at cordon congestion charges and avoiding the charging rates of the aforementioned data that are difficult to obtain, while considering the two practical properties of cordon congestion charges, that is, the total traffic volume entering a certain charging area. Traffic should be limited by a pre-determined threshold and the toll value should be the same for each entry into a toll zone for easy driver identification and authority management. Judging from the proposed trial-and-error method, only the motor vehicle flow data on the toll road section is needed, and these data are easily obtained from toll booths or vehicle detection coils.

The method of the invention has strong operability, and can automatically adjust and obtain the optimal toll rate that meets the objectives of reducing congestion and optimizing the environment, etc. only by recording the traffic flow data of the entrance road section of the congested toll area.

Description of drawings

Figure 1 is a topology diagram of the road network.

Fig. 2 is a flow chart of the method for determining the optimal rate.

detailed description

Below in conjunction with example and accompanying drawing, the present invention will be further described.

This part further clarifies the present invention in conjunction with embodiment, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after reading the present invention, those skilled in the art should deal with various equivalents of the present invention Modifications in form all fall within the scope defined by the appended claims of this application.

Step 1: Input the relevant data (points, lines and partitions) of the target city's traffic network to obtain the topological map of the traffic network.

Figure 1 is the network structure of the embodiment, and Table 1 shows the origin-end pairs and travel demands of the network. This example contains 7 vertices, 11 road segments and a toll area. The travel time equation uses a BPR type equation,

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.0</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.15</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Table 1 Traffic demand of origin and destination

origin-destination pair Traffic demand (vehicle/hour) 1→7 6000 2→7 5000 3→7 5000 6→7 4000

in Represents the free flow travel time, and C _a represents the link allowance. At the same time, the effect of converging links is considered, for example, the traffic on links 1 and 7 converges to link 3, so the traffic flow on link 1 will affect the travel time of link 7. There are two pairs of confluence links in this example: links 1 and 7, and links 2 and 6. Therefore, for these two pairs of road segments, their travel time equations take the following type:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.15</span>}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}}_{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}}{\mathrm{<span\; class="notranslate">\; 1.5</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Represents the traffic on road segment a ∈ A in a pair of road segments. For example, for segment 1, Represents the traffic on segment 7. This type of equation results in an asymmetric link travel time function. Table 2 provides the and the specific value of C _a .

Table 2 Parameters of road segment travel time function

Step 2: Determine the toll area and all entrances in the area based on the traffic network map in step 1, and then determine each entrance as the toll location.

This toll area is bounded by its vertices 1, 4, 5, 7. Tolls are charged on sections 5, 6, and 7 of the three regional entrances. The optimal toll value is the same on all area entry links.

Step 3: set the target total motor vehicle flow limit value entering each toll area (to reduce congestion, optimize the environment and other goals to determine the total motor vehicle flow limit value), the present embodiment adopts three kinds of limit values as contrast, which are respectively 6000 vehicles /hour, 5000 vehicles/hour and 4000 vehicles/hour, and implement an initial charging price of 5 yuan at the charging position, that is, the initial charging price vector

Step 4: Implement the current toll price plan for one week. During the period of implementation of the current toll price plan, observe and record the traffic flow entering each toll road section after the traffic flow is stable.

A. For the initial toll scheme, it is necessary to observe the section flow of each entrance section corresponding to it. In this embodiment, we solve a probit-based stochastic user balance problem, and use the obtained balanced link flow of the entrance link to estimate these motor vehicle flow data. Here, we assume that the travel behavior of Internet users obeys the random user balance theory based on probit, and the proposed methodology is also applicable to other types of random user balance theory. We also assume that the time value of network users is 0.6 yuan/minute. In practice, the user's time value is not needed in the trial and error method.

B. In the embodiment, we use the continuous average method to solve this probit-based random user balance problem. Among them, Monte Carlo simulation is used to estimate the random network loading process, that is, the first step is to initialize and set the iteration count l=1; the second step is to sample from T _a ~ N(t _a , βt _a ) for each road section a Sampling; the third step is all-or-nothing allocation, that is, based on the obtained Assign {q _w } to the shortest path connecting each origin-destination pair, q _w represents the travel demand of the origin-destination pair w∈W. This step produces the segment traffic flow set The fourth step is to average the traffic, so that The fifth step is to detect the termination condition, so that ${\mathrm{\&sigma;}}_a^{\left(l\right)}=\sqrt{\frac{1}{l(l-1)}\underset{m=1}{\overset{l}{\&Sigma;}}{\&lsqb;V_a^{\left(m\right)}-v_a^{\left(l\right)}\&rsqb;}^2},\&ForAll;a,$ if ${\max }_a\{{\mathrm{\&sigma;}}_a^{\left(l\right)}/v_a^{\left(l\right)}\}\&le;\mathrm{\&kappa;},$ then terminate, the solution is Otherwise, let l=l+1, go to the second step.

C. In order to ensure accuracy, we use 1000 simulations. In each Monte Carlo simulation, there are three tasks: first, use pseudorandom numbers to sample the cognitive error term of the normal distribution; second, Search for the shortest path between each origin-destination pair; finally, assign all origin-destination requirements to the searched shortest path. Since the cognitive error of travel time is usually defined based on the path, in order to avoid enumerating the path, we define the cognitive error on each road segment, that is, the generalized road segment travel time recognized by the user is equal to:

Where T _a represents a generalized link travel time function, and it is assumed that the cognitive error ξ _a of link travel time is a normal distribution with a mean of 0 and a constant variance.

Step 5: According to the difference between the "observed motor vehicle flow" and the "motor vehicle flow limit value", according to the adaptive prediction and correction algorithm, a new charging price scheme is obtained.

Step 1 initialization;

κ ₁ = 0.9, κ ₂ = 0.1, γ = 1.8, η ⁽⁰⁾ = 1.0. And set the iteration number as n=1.

Step 2 prediction process;

Step 2.1: Set the toll scheme τ ⁽ⁿ⁾ in the network, and then observe the traffic flow at the entrance of each toll area, given by v _a (τ ⁽ⁿ⁾ ), i = 1, 2, ... I to represent, and then calculate the variable inequality equation $\mathrm{\&Phi;}\left({\mathrm{\&tau;}}^{\left(\mathrm{no}\right)}\right)={(h_i-\underset{a\&Element;{\stackrel{\&OverBar;}{A}}_i}{\&Sigma;}{v}_a\left({\mathrm{\&tau;}}^{\left(\mathrm{no}\right)}\right),i=1,2,\mathrm{...},I)}^T,,$ That is, the difference between "observed motor vehicle flow" and "motor vehicle flow threshold".

Step 2.2: Operation via projection Find ancillary fee scheme vector The projection operation P _Ω [τ′]=(maX(0, τ′ _i ), i=1, 2, . . . , I) ^T represents the projection of the vector τ′ onto the feasible set Ω of the charging scheme.

Step 2.3: Add ancillary fee schemes Load it to the network, and then observe the traffic flow of the corresponding entrance segment i=1, 2, ... I, then use the observed flow value to calculate the corresponding variable inequality equation value $\mathrm{\&Phi;}\left({\stackrel{\&OverBar;}{\mathrm{\&tau;}}}^{\left(\mathrm{no}\right)}\right)={(h_i-\underset{a\&Element;{\stackrel{\&OverBar;}{A}}_i}{\&Sigma;}{v}_a\left({\stackrel{\&OverBar;}{\mathrm{\&tau;}}}^{\left(\mathrm{no}\right)}\right),i=1,2,\mathrm{...},I)}^T.$

Step 2.4: Calculate the ratio r ⁽ⁿ⁾ by the following equation,

${\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}$

If r ⁽ⁿ⁾ ≤ κ ₁ , go to step 3, otherwise according to Decrease the step size value and proceed to step 2.2.

Step 3 correction process;

Based on τ ⁽ⁿ⁾ , η ⁽ⁿ⁾ , calculate a step value π ⁽ⁿ⁾ for the correction process, and then get the updated charging scheme vector τ ⁽ⁿ⁺¹⁾ .

Step 3.1: Calculate another step size value π ⁽ⁿ⁾ according to the following equation

${\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&rsqb;</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

in $h_i^{\left(\mathrm{no}\right)}=({\mathrm{\&tau;}}_i^{\left(\mathrm{no}\right)}-{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_i^{\left(\mathrm{no}\right)})-{\mathrm{\&eta;}}^{\left(\mathrm{no}\right)}\left({\mathrm{\&Phi;}}_i\right({\mathrm{\&tau;}}^{\left(\mathrm{no}\right)})-{\mathrm{\&Phi;}}_i({\stackrel{\&OverBar;}{\mathrm{\&tau;}}}^{\left(\mathrm{no}\right)}\left)\right),$ i=1,2,...,I

Step 3.2: Update the charging scheme vector τ ⁽ⁿ⁺¹⁾ by the following projection operation

${\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>$

Step 3.3: Judgment Conditions ${\mathrm{\&eta;}}^{\left(\mathrm{no}\right)}\left|\right|\mathrm{\&Phi;}\left({\mathrm{\&tau;}}^{\left(\mathrm{no}\right)}\right)-\mathrm{\&Phi;}\left({\stackrel{\&OverBar;}{\mathrm{\&tau;}}}^{\left(\mathrm{no}\right)}\right)|{|}_2/||{\mathrm{\&tau;}}^{\left(\mathrm{no}\right)}-{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}^{\left(\mathrm{no}\right)}|{|}_2\&le;{\mathrm{\&kappa;}}_2$ Whether it is established, and if it is established, then Go to step 6 again; otherwise, go to step 6 directly.

Step 6: Use the difference between the new charging price scheme and the old charging price scheme to judge whether to terminate the algorithm and output the optimal result. If it does not stop, return to step 4 for loop iteration.

That is, if Then terminate, ε=1×10 ^-4 . Otherwise, let n=n+1, go to step 4.

The benefit evaluation of the trial-and-error method for solving the optimal charging rate of congestion charging based on motor vehicle flow data according to the present invention:

The purpose of congestion charging based on motor vehicle flow data is to maintain the traffic conditions in the charging area, and this goal can be achieved by limiting the inbound traffic flow into the charging area not to exceed a certain threshold value set in advance. Table 3 gives the optimal charging scheme in three different situations. The termination condition is 1×10 ^-4 , and the parameter values are κ ₁ =0.9, κ ₂ =0.1, γ=1.8, and η ⁽⁰⁾ =1.0. The third row in Table 3 provides the value of the output optimal toll scheme, and the fourth row shows that the total inbound traffic flow in the toll area is equal to the predetermined threshold value, implying that its solution satisfies the aforementioned three mathematical conditions, that is, the obtained The toll scheme can successfully limit the total inbound traffic flow to no greater than a predetermined threshold. From cases 1 to 3, the toll value of the toll area becomes larger and larger as a smaller predetermined threshold value is set, that is to say better traffic conditions in the toll area are required. This also shows that network users need to pay more to achieve and maintain better traffic conditions.

Table 3 Three schemes of threshold value and optimal charging value

The foregoing embodiments are only preferred implementations of the present invention. It should be pointed out that those skilled in the art can make several improvements and equivalent replacements without departing from the principle of the present invention. Technical solutions requiring improvement and equivalent replacement all fall within the protection scope of the present invention.

Claims (2)

1., based on a congestion-pricing optimum toll rate defining method for trial and error and motor vehicle flow, it is characterized in that, the method comprises the following steps:

Step one: according to the point of urban traffic network, line and partition data, set up transportation network topological diagram;

Step 2: based on the transportation network topological diagram set up in step one, determine all entrances in area of charge and this region, and each entrance is defined as toll collection location;

Step 3: the total vehicle flowrate boundary value of target entering each area of charge is set, and implement the initial charge price plan of a setting at toll collection location;

Step 4: current tariff price plan implement during this period of time in, observe and record the vehicle flowrate entering each charging section after vehicle flowrate is stablized;

Step 5: the difference between " the total vehicle flowrate boundary value of target " that the vehicle flowrate of each charging section observed by step 4 and step 3 are determined, according to adaptive prediction algorithm for correction, calculates new paying price scheme;

Step 6: calculate the difference between new paying price scheme and old paying price scheme, judges whether this difference is less than decision threshold, in this way, then the new paying price scheme finally obtained is exported as optimal result, otherwise returns step 4.

2. the congestion-pricing optimum toll rate defining method based on trial and error and motor vehicle flow according to claim 1, it is characterized in that, described transportation network topological diagram comprises the point of urban traffic network, line and partition data, the total vehicle flowrate boundary value of described target be block up according to reducing, the relative ratio of optimizing the environment determines, described initial charge price plan is arbitrary price plan, and described adaptive prediction algorithm for correction comprises prediction and corrects two processes.