CN103927890B - A Coordinated Signal Control Method for Arterial Lines Based on Dynamic O-D Matrix Estimation - Google Patents

Abstract

The invention discloses a kind of Trunk Road Coordination signal control method based on dynamic O-D Matrix Estimation, the method utilizes the link flow that on main line, each crossing turnover stomatodeum detects, Kalman filtering and reverse transmittance nerve network algorithm is adopted to estimate the dynamic O-D matrix at crossing respectively, and design the precision and stability that Bayes's combined method improves estimated result, set up single intersection Multiple Target Signals Controlling model on this basis, and using each crossing signals cycle maximal value of calculating as main line common period.Further design with main line vehicle not the rate of being obstructed be the Trunk Road Coordination signal control method of objective function to the maximum, solve the phase differential between split and adjacent intersection obtaining main line direction, each crossing, thus form Trunk Road Coordination signal timing plan.This method, under the prerequisite ensureing main line vehicle priority pass, takes into account the traffic efficiency of each single intersection, solves prior art cannot adjust control program in real time problem according to volume of traffic change, has the advantage such as high precision, application on site.

Description

A Coordinated Signal Control Method for Arterial Lines Based on Dynamic O-D Matrix Estimation

technical field

The invention belongs to the technical field of intelligent traffic control, and in particular relates to a method for controlling an arterial coordination signal based on dynamic O-D matrix estimation.

Background technique

As the core part of advanced traffic management system, real-time signal control system plays a vital role in alleviating urban traffic congestion. At the same time, because the control scheme of the real-time signal control system changes with time, it is necessary to use real-time traffic flow data as the basic data of the signal control scheme. As the basic unit of signal control, the real-time signal control of the intersection needs the dynamic flow of the entrance and exit of the intersection and the turning flow as input data. Under the condition of the existing flow detection system, the traffic flow of the intersection at each entrance and exit is easy to obtain , but real-time steering traffic cannot be detected. The intersection dynamic O-D matrix estimation model can obtain the intersection dynamic O-D matrix according to the time series of the detected entrance and exit flow, that is, the dynamic turning flow. With the development of intelligent transportation technology, this model has received widespread attention, and proposed recursive estimation algorithm (1987), Bell fleet diffusion method (1991), genetic algorithm (2005), Kalman filter algorithm (2006), backpropagation ( Backpropagation, referred to as BP) neural network algorithm (2007) and other intersection dynamic O-D matrix estimation methods, these methods can provide a good basic support for single intersection signal control.

In addition, in the urban road network, the intervals between intersections are generally not large, especially for multiple individual intersections on a certain arterial line, when implementing mutually independent signal control schemes, it often happens that the convoys between the intersections do not completely dissipate Or the situation that the motorcade always stops because of the red light, causing the vehicle queuing phenomenon to occur frequently and accumulate, thereby causing serious traffic congestion on the trunk line. In order to make most or even all vehicles on the arterial road pass smoothly during the green light time and avoid affecting the traffic of vehicles arriving in the next signal period, it is necessary to establish a coordinated control method for the arterial line that considers the fleet dissipation. In the existing coordinated control methods of trunk lines, the main parameters of coordinated control are public cycle, green signal ratio and phase difference. In order to obtain the optimal control parameters, scholars have proposed a variety of control methods, such as the maximum green wave band method and the phase difference optimization method based on the minimum delay.

The existing intersection dynamic O-D matrix estimation method and arterial coordination signal control method still have the following deficiencies:

Among the dynamic O-D matrix estimation methods at intersections, the recursive estimation algorithm and the Bell fleet diffusion method all use a linear model to derive and estimate the dynamic O-D matrix, which is suitable for the estimation of the traffic smoothing process for a long time, and it is difficult to estimate the dynamic O-D of real-time nonlinear changes. Matrix, not suitable for online applications; genetic algorithm is used in the dynamic O-D estimation of intersections to solve the optimization model that minimizes the sum of the absolute value of the error between the observed value and the estimated value, and iterates to make the result evolve to a state that contains or is close to the optimal solution , the efficiency is relatively low; the recursive nature of the Kalman filter algorithm determines its high efficiency but relatively poor accuracy; the BP neural network algorithm is trained and learned according to historical data, and compared with the actual data to get the error, through the reverse Propagate errors to continuously adjust the weights and thresholds of the network to minimize the sum of squared errors of the network, and realize the estimation of the current data under stable weights and thresholds, but it has shortcomings such as slow training speed and easy to fall into local optimum. .

Among the arterial coordinated signal control methods, methods such as the maximum green wave band method and the phase difference optimization method based on the minimum delay have been widely used. There are strict restrictions on the arrival rules of vehicles at each intersection, and the obtained signal control scheme is fixed within a certain period of time, and cannot be adjusted in real time according to changes in traffic flow.

Contents of the invention

The technical problem to be solved by the present invention is that in the prior art, different methods of intersection dynamic O-D matrix estimation have different disadvantages, such as large estimation deviation, poor stability or low efficiency; The signal control scheme cannot be adjusted in real time according to changes in traffic conditions; and then a method for arterial coordinated signal control based on dynamic O-D matrix estimation is provided. Cycle, the green signal ratio of each intersection and the phase difference of adjacent intersections and other parameters can realize real-time coordinated signal control of the main line and improve traffic capacity.

In order to solve the above-mentioned technical problems, the present invention provides a kind of trunk coordination signal control method based on dynamic O-D matrix estimation:

The control method includes a method for calculating the public period of the trunk line based on dynamic O-D matrix estimation and a method for calculating the green signal ratio and phase difference of the trunk line based on the maximum unobstructed rate of vehicles. The two methods together constitute a coordinated signal control method for trunk lines based on dynamic O-D matrix estimation. According to the flow rate of the entrance and exit road sections of each intersection obtained by the flow detector, the optimal public cycle, green signal ratio and phase difference between adjacent intersections can be calculated at each intersection of the main line, and the coordinated control of the main line can be realized. The main steps are as follows:

(1) Traffic flow detection at the entrance and exit of the intersection: Run the road section flow detector at each intersection entrance and exit on the main line to detect the traffic flow of the section at the entrance and exit of the intersection at each time period;

(2) Estimation of the dynamic O-D matrix at the intersection: take the dynamic steering ratio of the intersection as an independent variable, and take the detected flow at the entrance and exit of the intersection as a known quantity, and run the dynamic steering ratio of the intersection based on Bayesian weighting in the remote computer Estimate the model program, solve the dynamic steering ratio of each intersection, and further obtain the dynamic O-D matrix of the intersection;

(3) Determination of the public period of the trunk line: Run the algorithm program of the multi-objective signal control model in the remote computer, take the dynamic O-D matrix of the intersection as the known quantity, and solve the problem with the minimum vehicle delay and average queuing length and the maximum effective traffic capacity of the road. The multi-objective signal control model of the target obtains the optimal signal timing period of each intersection, and selects the largest period value as the common period of the main line;

(4) Calculation of vehicle dissipation time: use the detector to judge whether the convoy at the next intersection of each pair of adjacent intersections has dissipated before the arrival of the convoy at the previous intersection, and divide them into two situations: undissipated and dissipated, and calculate the time of each intersection respectively vehicle dissipation time;

(5) Determination of the arterial coordinated control scheme: input the public period of the arterial line and the vehicle dissipation time at each intersection into the calculation model of the green signal ratio and phase difference of the main line based on the maximum unobstructed rate of vehicles, and take the maximum unobstructed rate of the arterial line as the objective function , to solve the green-signal ratio and phase difference of each intersection, the public cycle, green-signal ratio and phase difference three sets of parameters together constitute the arterial coordinated signal control scheme;

(6) Transmit the obtained control parameters to the signal machine for implementation, and realize the coordinated signal control of the main line.

On the basis of calculating the optimal period of each individual intersection on the arterial line by using the single intersection multi-objective signal control model based on dynamic O-D matrix estimation, the largest period value is selected as the common period C of the arterial line, and the arterial line based on the maximum unobstructed rate of vehicles is established Calculation method of green-signal ratio and phase difference to solve the green-signal ratio and phase difference of the coordinated control of the trunk line to ensure the smooth passage of vehicles in the direction of the trunk line;

Number of interval cycles required for a vehicle to travel between adjacent intersections:

In the formula, l is the distance between adjacent intersections on the arterial line; v is the average speed of vehicles traveling between adjacent intersections; C is the public period of the arterial line; INT() is a rounding function.

When the vehicles traveling on the main road section reach the intersection, there will be two situations: the first situation is that the intersection signal light is green, and the vehicle can pass directly through the intersection, that is, pass directly without hindrance; the second situation is that the intersection signal light is yellow light Or red light, the vehicle needs to wait for the signal light to turn green before passing through, that is, the vehicle is blocked from passing.

① The first case: the time to travel through intersection n-1 to intersection n is less than the time for vehicles to dissipate under the accumulation of red lights at intersection n in the previous cycle, and vehicles need to queue up to pass through intersection n, namely:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&le;</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

In the formula, t′ _n is the time for the vehicle to travel from intersection n-1 to intersection n, t _n is the phase difference between intersection n and intersection n-1, λ _n is the green signal ratio of the green light phase in the direction of intersection n, k _n is the flow adjustment coefficient of intersection n, q _n (t) is the arrival rate function of vehicles at intersection n, and S _n is the traffic capacity of intersection n in the direction of the trunk line.

At this time, the dissipation time of vehicles at intersection n is:

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

The numerator in the above formula represents the total number of dissipated vehicles in the green light phase of the main line at the intersection n. This part of the vehicles consists of two parts. The first part is the queuing vehicles that have not dissipated at the intersection n in the previous cycle, and the second part is the vehicles traveling from the upstream intersection to Vehicles at intersection n.

②Second case: the time for the vehicle to travel from intersection n-1 to intersection n is longer than the time for the vehicle to dissipate under the accumulation of red lights in the previous cycle at intersection n, and the vehicle does not need to line up when it travels to intersection n, and passes directly, that is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&le;</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

At this time, the dissipation time of vehicles at intersection n is:

T _n =0

Define the unimpeded rate of straight-going vehicles in the direction of the arterial at intersection n:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

In the formula, Q′ _n is the flow that passes directly without delay due to light control within a certain cycle at the nth intersection in the trunk line, and Qn _is the total flow at the nth intersection within a certain cycle.

Taking the maximum sum of unobstructed rates of all intersections on the main line as the objective function, a coordinated signal control model of the main line is established: $\max f(t_{\mathrm{no}},{\mathrm{\&lambda;}}_{\mathrm{no}})=\underset{\mathrm{no}}{\&Sigma;}{m}_{\mathrm{no}}$

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right.$

In the formula, λ _{n, max} represents the maximum green signal ratio of intersection n on the trunk line.

Solve the arterial coordinated signal control model to obtain the green signal ratio λ _n in the direction of the main line at each intersection and the phase difference t _n of adjacent intersections. Combined with the common period C of the arterial line, the arterial coordinated signal control scheme can be obtained.

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

① The present invention uses the Kalman filter and BP neural network algorithm to estimate the dynamic O-D matrix of the intersection according to the section traffic obtained by the intersection entrance and exit detector, and then carries out weighted correction to the two estimated values through the Bayesian weighting algorithm to obtain an overall more accurate The optimal dynamic O-D matrix avoids excessive local errors in the estimation results, and improves the accuracy and stability of the dynamic O-D matrix estimation at intersections.

2. the present invention is aimed at single intersection signal control, with the dynamic O-D matrix estimated value of each intersection as input condition, has designed the multi-objective nonlinear optimization model with the minimum of each single intersection delay and queuing length, the maximum effective traffic capacity of the road, solves The signal period of each intersection is obtained, and the maximum value is used as the common period of the main line. While realizing the coordinated control of the main line, the traffic efficiency of each single intersection is taken into account.

③The present invention designs a coordinating signal control model of the main line that considers the dissipation of the fleet and aims at the minimum unobstructed rate of vehicles. traffic efficiency.

④ The trunk signal control parameters obtained by the present invention, such as the public period of the trunk line, the green signal ratio of each intersection and the phase difference of adjacent intersections, change in real time as the traffic conditions change, truly realizing the real-time trunk line coordination signal control, and the calculation efficiency is high , which can generate signal control schemes in real time to meet the accuracy and efficiency requirements of online applications.

Description of drawings

Figure 1 is a structure diagram of the arterial coordination signal control method based on dynamic O-D matrix estimation (intersection queuing is not dissipated)

Figure 2 is a structure diagram of the arterial coordination signal control method based on dynamic O-D matrix estimation (intersection queuing has dissipated)

Fig. 3 is a flow chart of a method for controlling trunk line coordination signals based on dynamic O-D matrix estimation

detailed description

Various details involved in the technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings. It should be pointed out that the described embodiments are only intended to facilitate the understanding of the present invention, rather than limiting it in any way.

The flow detector at each intersection judges whether the vehicles queue at the intersection dissipate when the vehicle arrives at the intersection, and divides the main line coordination signal control method into two situations: the queue at the intersection has not dissipated, and the queue at the intersection has dissipated.

When the queuing at the intersection has not dissipated, the structure diagram of the arterial coordinated signal control method based on dynamic O-D matrix estimation is shown in Figure 1. At this time, the queuing vehicles at the intersection need a certain amount of time to dissipate and pass through the intersection after the green light is turned on. Vehicles also need to wait in line. The upper part of Figure 1 shows the relationship between each intersection on the trunk line. Through the section flow detectors buried under the entrance and exit roads of each intersection, the flow of the entrance and exit road sections of the intersection is obtained as known data and transmitted to the remote end computer. The lower part of Fig. 1 shows the principle of the arterial coordinated signal control method based on dynamic O-D matrix estimation. According to the detected flow of the road section at the entrance and exit of each intersection, the Bayesian combination method is used to estimate the dynamic O-D matrix of each intersection, and its Input it into the single-intersection multi-objective signal control model to solve the optimal signal period of each intersection, and use the maximum value as the common period of the main line; at the same time, when the queuing vehicles at the intersection have not dissipated, calculate the dissipation time of the queuing vehicles and combine it with the main line The public period is input into the arterial control model that minimizes the unobstructed rate, and the green signal ratio of each intersection and the phase difference of adjacent intersections are solved; The trunk coordination signal control scheme.

When the queue at the intersection has dissipated, the structure diagram of the arterial coordination signal control method based on dynamic O-D matrix estimation is shown in Figure 2. At this time, the queued vehicles at the intersection have dissipated when the upstream vehicle arrives, and the arriving vehicles can pass without waiting. . The structure of Figure 2 is basically the same as that of Figure 1, the only difference is that the dissipation time of vehicles queuing at the intersection should be 0.

The flow chart of the method for controlling the coordinated signal of the trunk line based on dynamic O-D matrix estimation is shown in Fig. 3 . The whole process consists of the following six steps: (1) Flow detection at the entrance and exit of the intersection, (2) Estimation of the dynamic O-D matrix of the intersection, (3) Determination of the public period of the trunk line, (4) Calculation of vehicle dissipation time, (5) Determination of trunk line coordination control scheme, (6) transmission to application of signal control system. Specific steps include:

Step 1: Flow detection at the entrance and exit of the intersection

Utilize the flow detectors of each lane installed at the entrance and exit road sections of the intersection to detect the traffic flow of the entrance and exit roads within the time interval k, that is, Q _i (k), i=1, 2,..., r represents the time period k from the entrance The flow of road i flowing into the intersection, Y _j (k), j=1, 2, ..., s represents the flow of time period k flowing out of the intersection from exit road j, and at the same time judge whether there is a queuing vehicle at the intersection, and transmit it to the remote computer for processing .

Step 2: Estimation of the intersection dynamic O-D matrix

According to the time series of the traffic flow at the entrance and exit of the intersection detected, the dynamic steering ratio B _ij (k) of period k is used as the state variable to estimate the dynamic steering ratio of the intersection, including the estimation of the historical period and the current period.

Obviously, the intersection dynamic steering ratio should meet the following constraints:

①B _ij (k)≥0, i=1, 2, ..., r; j = 1, 2, ..., s

② $\underset{j=1}{\overset{\mathrm{the\; s}}{\&Sigma;}}{B}_{ij}\left(k\right)=1,i=1,2,...,r$

First, the Kalman filter algorithm is used to estimate the dynamic steering ratio, and the state space model is established as follows:

Equation of state: B(k)=B(k-1)+W(k)

Observation equation: Y(k)=Q(k)*B(k)+e(k)

In the formula, B(k), Q(k), and Y(k) are the matrix or vector form of B _ij (k), Q _i (k), and Y _j (k) respectively, and W(k) is the mean value of 0 Gaussian white noise vector, e(k) is the observed Gaussian white noise vector with mean 0.

The existing sequential Kalman filter algorithm is used to solve the problem, and the initial value of the dynamic steering ratio in the modified algorithm process is as follows:

In the formula, L _ij is the number of lanes that turn from entrance i to exit j. For mixed lanes, the average value of each turn is taken.

The dynamic steering ratio calculated by the sequential Kalman filter algorithm is cut and standardized to make it meet the inherent constraints of the steering ratio.

On the basis of detecting the flow, use the M language programming of Matlab software to realize the Kalman filter algorithm, and output the real-time estimated value of the dynamic steering ratio, including the historical estimated value and current estimates

Then, use the BP neural network algorithm to estimate the dynamic steering ratio, and the algorithm flow is as follows:

Design a three-layer BP neural network, including input layer, hidden layer and output layer:

Input layer: 3 neurons, corresponding to the import flow of each lane upstream of the entrance road, when the number of lanes upstream of the entrance road is different, the number of neurons will change accordingly;

Hidden layer: 15 neurons, the transfer function adopts a logarithmic S-type function, and its output value is in the interval range of [0, 1], which is consistent with the steering ratio range;

Output layer: using a linear transfer function, with a total of 3 neurons, corresponding to the steering ratio of the 3 directions of turning left, going straight, and turning right, and a total of 3 output values.

In order to make the output value of each neuron after the initial weighting close to zero, ensure that the weight of each neuron can be adjusted at the place where their S-type activation function changes the most, and the initial weight is (- 1, a random number between 1).

The momentum-adaptive learning rate adjustment algorithm is used to correct the weight and threshold in the error backpropagation process, so that the BP neural network algorithm can not only find the global optimal solution, but also shorten the training time.

Use the M language programming of Matlab to realize the solution of the BP neural network, and output the real-time estimated value of the dynamic steering ratio, including the historical estimated value and current estimates

Comparing the historical estimated value of Kalman filter and BP neural network with the corresponding historical real value of dynamic steering ratio, the average absolute percentage error is obtained, and then the probability Pr(H ^KF ), the probability of choosing the BP neural network algorithm Pr(H ^N ):

$\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; EH</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; EH</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; EH</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

$\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; EH</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; EH</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; EH</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

Among them, EH ^KF and EH ^N are the average absolute percentage errors between the historical estimated values of the Kalman filter algorithm and the BP neural network algorithm and the corresponding historical true values, respectively.

Calculation method of mean absolute percentage error: in is the estimated value, B _ij (k) is the real value.

Further consider the estimated deviation of the day, in order to improve the accuracy and dynamically update the weight of the combined method, the deviation between the estimated value of the first five periods of the current estimated period of the Kalman filter and BP neural network algorithm and the estimated value of the combined method in the corresponding period is used as the current estimate deviation, so that under the premise of historical estimation deviation, the probability Pr(D|H ^KF ) of selecting the Kalman filter algorithm and the probability Pr(D|H ^N ) of selecting the BP neural network algorithm are obtained according to the current estimation deviation:

$\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

$\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

Among them, E ^KF and E ^N are the average absolute percentage error between the estimated value of the Kalman filter algorithm and the BP neural network algorithm in the first five periods and the corresponding Bayesian combined estimated value.

Solve the Bayesian weights W ^KF and W ^N of the Kalman filter algorithm and BP neural network algorithm:

Pr(D)＝Pr(D|H ^KF )Pr(H ^KF )+Pr(D|H ^N )Pr(H ^N )

${\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}$

${\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; PR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}$

Using the dynamic steering ratio estimated by Kalman filter and BP neural network, according to the Bayesian weighting formula, the final estimated value of dynamic steering ratio in the current period can be obtained:

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>$

The deviation between the Kalman filter and BP neural network estimation results of the current period and the Bayesian weighted correction value of the current period is stored in the current deviation database as the deviation of the current period, which is used to calculate the current estimated deviation of the next estimation period, and update Estimated time period.

Dynamic Steering Scale Estimated from Bayesian Combination Method And the section flow Q _i (k) of each intersection entrance road, the dynamic OD matrix estimation value of each intersection can be obtained.

Step 3: Determination of trunk public period

A nonlinear optimization model is established with the intersection signal control period as the independent variable, and the minimum vehicle delay and queuing length and the maximum effective road capacity as the objective function.

Define the weight coefficients K _x ¹ , K _x ² , and K _x ³ of the three evaluation indicators of delay, queuing length, and effective road capacity:

K _x ¹ =2s _x p _x (1-P); K _x ² =s _x p _x (1-P)T; K _x ³ =2(3600/T)P;

In the formula, s _x is the saturated flow of the xth phase, p _x is the ratio of the traffic flow of the xth phase to the saturated flow, P is the sum of the ratios of the traffic flow of each phase to the saturated flow, and T is the signal period of the intersection.

In the calculation of weight coefficients K _x ¹ , K _x ² , and K _x ³ , the acquisition of p _x and P requires the estimated value of the intersection dynamic OD matrix as known data.

The multi-objective signal control model of a single intersection is as follows:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; \&lsqb;</span>{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; \&rsqb;</span>$

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\left\{\begin{array}{c}\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}\\ \mathrm{<span\; class="notranslate">\; 0.9</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; \&le;</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1.1</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; e</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; e</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}\\ \underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}\end{array}\right.$

In the formula:

d _x : the average delay time of vehicle arrival at the xth phase;

L _x : the average vehicle queuing length of the xth phase;

Q _x : the effective traffic capacity of the road at the xth phase;

G _x : Effective green light time of the xth phase;

A _x : the yellow light time of the xth phase, which is taken as 3 seconds;

R _x : the full red time of the xth phase, which is taken as 3 seconds;

m: number of signal phases;

green _{x, min} , green _{x, max} : the minimum effective green light time and the maximum effective green light time of the xth phase of the intersection, which are taken as 15 seconds and 60 seconds respectively;

L: Total lost time of signal cycle, Take it as 16 seconds;

l _x : The vehicle start-up loss time of the xth phase, which is taken as 3 seconds;

I _x : Green light interval time of the xth phase, I _x ＝A _x +R _x ;

J: The maximum cycle time, which is taken as 180 seconds;

The three performance evaluation indicators of delay, queuing length and effective road capacity are defined as follows:

The average delay time of vehicles: the difference between the time required for vehicles to be obstructed and unimpeded at the approach road at the intersection entrance, the average delay time of vehicles in the xth phase:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; T</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\frac{\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}}$

Average queuing length of vehicles: within a signal period, the average value of the maximum queuing length of each lane at the beginning of the green light phase, and the average queuing length of vehicles in the xth phase:

L _x =2q _x R _x

In the formula, q _x represents the vehicle arrival flow rate of the xth phase, which can be taken as a Poisson distribution according to the actual situation.

Effective traffic capacity of the road: the sum of the number of vehicles passing through the stop line of all entrances at an intersection within a certain period of time. For signal intersections, the effective traffic capacity of the road at the xth phase:

Q _x =λ _x s _x

In the formula, λ _x represents the green signal ratio of the xth phase.

Input the intersection dynamic O-D matrix obtained in step 2 into the multi-objective signal control model of single intersection, and use Lingo programming to solve it, and obtain the signal timing parameters and evaluation indicators of single intersection, and take the largest signal period of each intersection as the common period C of the trunk line.

Step 4: Calculation of Vehicle Dissipation Time

Calculate the number of interval cycles required for a vehicle to travel between adjacent intersections:

In the formula, l is the distance between adjacent intersections on the arterial line; v is the average speed of vehicles traveling between adjacent intersections, which can be obtained according to the floating vehicle system or other existing vehicle speed prediction methods; INT() is the whole function;

When the vehicles traveling on the main road section reach the intersection, there will be two situations: the first situation is that the intersection signal light is green, and the vehicle can pass directly through the intersection, that is, pass directly without hindrance; the second situation is that the intersection signal light is yellow light Or red light, the vehicle needs to wait for the signal light to turn green before passing through, that is, the vehicle is blocked from passing.

① The first case: the time to travel through intersection n-1 to intersection n is less than the time for vehicles to dissipate under the accumulation of red lights at intersection n in the previous cycle, and vehicles need to queue up to pass through intersection n, namely:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&le;</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

In the formula, t′ _n is the time for the vehicle to travel from intersection n-1 to intersection n, t _n is the phase difference between intersection n and intersection n-1, λ _n is the green signal ratio of the green light phase in the direction of intersection n, k _n is the flow adjustment coefficient of intersection n, S _n is the traffic capacity in the direction of the main line of intersection n, and q _n (t) is the arrival rate function of vehicles at intersection n, which can be taken as a Poisson distribution according to the actual situation.

At this time, the dissipation time of vehicles at intersection n is:

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

The numerator in the above formula represents the total number of dissipated vehicles in the green light phase of the main line at the intersection n. This part of the vehicles consists of two parts. The first part is the queuing vehicles that have not dissipated at the intersection n in the previous cycle, and the second part is the vehicles traveling from the upstream intersection to Vehicles at intersection n.

②Second case: the time for the vehicle to travel from intersection n-1 to intersection n is longer than the time for the vehicle to dissipate under the accumulation of red lights in the previous cycle at intersection n, and the vehicle does not need to line up when it travels to intersection n, and passes directly, that is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&le;</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; C</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}$

At this time, the dissipation time of vehicles at intersection n is:

T _n =0

Step 5: Determination of trunk line coordinated control scheme

Input the public period of the trunk line obtained in step 3 and the vehicle dissipation time obtained in step 4 into the trunk line coordination signal control model:

$\mathrm{<span\; class="notranslate">\; max</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}$

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right.$

In the formula, λ _{n, max} represents the maximum green signal ratio of intersection n on the trunk line, which is taken as 0.75 in the present invention.

Using the M language programming of Matlab, the arterial coordination signal control model is solved. Taking the intersection n as an example, the green signal ratio λ _n of the green light phase in the direction of the arterial line at the intersection n and the phase difference t _n of the intersection n relative to the intersection n-1 are obtained.

The trunk line public period, the green signal ratio of each intersection in the direction of the trunk line, and the phase difference between adjacent intersections constitute the trunk line control scheme. By updating the time period, a real-time trunk line coordination signal control scheme can be obtained.

Step 6: Transmission to application of signal control system

Real-time coordinated signal control of the trunk can be realized by transmitting the real-time public period of the trunk line, the green signal ratio of the trunk line at each intersection, and the phase difference of adjacent intersections to the signal control system.

The present invention compares the results of the trunk line coordination signal control method based on dynamic O-D matrix estimation in specific trunk line cases with the commonly used maximum green wave band method through traffic investigation, and the trunk line coordination signal control method based on dynamic O-D matrix estimation can be based on Time-varying traffic flow, providing a real-time arterial control scheme, the three indicators of delay, queue length and parking times are obviously due to the maximum green wave band method, which has a good effect and can meet the requirements of accuracy and efficiency. Next, improve the traffic efficiency of the trunk line.

The embodiment of the present invention has been specifically described above, it should be understood that for a person with ordinary skills in the technical field, any modification or partial replacement without departing from the scope of the present invention belongs to the protection scope of the claims of the present invention.

Claims (1)

1. a kind of main line coordination signal control method based on dynamic O-D matrix estimation, it is characterized in that: The control method includes the calculation method of the public period of the trunk line based on dynamic O-D matrix estimation and the calculation method of the green signal ratio and phase difference of the trunk line based on the maximum unobstructed rate of vehicles. The optimal public period of each intersection, the green signal ratio and the phase difference between adjacent intersections to realize the coordinated control of the main line, the main steps are as follows: (1) Traffic flow detection at the entrance and exit of the intersection: Run the road section flow detector at each intersection entrance and exit on the main line to detect the traffic flow of the section at the entrance and exit of the intersection at each time period; (2) Estimation of the dynamic O-D matrix at the intersection: take the dynamic steering ratio of the intersection as an independent variable, and take the detected flow at the entrance and exit of the intersection as a known quantity, and run the dynamic steering ratio of the intersection based on Bayesian weighting in the remote computer Estimate the model program, solve the dynamic steering ratio of each intersection, and further obtain the dynamic O-D matrix of the intersection; (3) Determination of the public period of the trunk line: Run the algorithm program of the multi-objective signal control model in the remote computer, take the dynamic O-D matrix of the intersection as the known quantity, and solve the problem with the minimum vehicle delay and average queuing length and the maximum effective traffic capacity of the road. The multi-objective signal control model of the target obtains the optimal signal timing period of each intersection, and selects the largest period value as the common period of the main line; (4) Calculation of vehicle dissipation time: use the detector to judge whether the convoy at the next intersection of each pair of adjacent intersections has dissipated before the arrival of the convoy at the previous intersection, and divide them into two situations: undissipated and dissipated, and calculate the time of each intersection respectively vehicle dissipation time; (5) Determination of the arterial coordinated control scheme: input the public period of the arterial line and the vehicle dissipation time at each intersection into the calculation model of the green signal ratio and phase difference of the main line based on the maximum unobstructed rate of vehicles, and take the maximum unobstructed rate of the arterial line as the objective function , to solve the green-signal ratio and phase difference of each intersection, the public cycle, green-signal ratio and phase difference three sets of parameters together constitute the arterial coordinated signal control scheme; (6) Transmit the obtained control parameters to the signal machine for implementation, and realize the coordinated signal control of the main line.