CN115376308A - Method for predicting automobile running time - Google Patents

Method for predicting automobile running time Download PDF

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CN115376308A
CN115376308A CN202210589772.8A CN202210589772A CN115376308A CN 115376308 A CN115376308 A CN 115376308A CN 202210589772 A CN202210589772 A CN 202210589772A CN 115376308 A CN115376308 A CN 115376308A
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葛乐
耿晓铭
崔莉
吴亦乐
郭朝辉
李曦
孙鼎
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Nanjing Institute of Technology
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Abstract

The invention discloses a method for predicting the automobile running time, which predicts the traffic speeds on different roads in the future time period by establishing an LSTM-GAN-based model, divides the roads into road sections with different speeds and time periods corresponding to the speeds of the different road sections according to the predicted traffic speeds, and calculates the total running time required by the automobile to reach a destination according to the speeds of the different road sections and the corresponding time periods; the model comprises a generator and a discriminator; the generator captures the time-space characteristics of traffic flow data and outputs the initially predicted traffic speed data to the discriminator; the discriminator simultaneously inputs corresponding actual traffic flow data to learn feature vectors of the two potential traffic flow data, finally constructs a classification model by using the feature vectors, judges the truth of the input initially predicted traffic flow data, and outputs the initially predicted traffic flow data judged to be true as predicted traffic flow data. The invention can improve the prediction precision.

Description

Method for predicting automobile running time
Technical Field
The invention relates to the technical field of path planning, in particular to a method for predicting automobile running time.
Background
Urban vehicle congestion causes a great deal of time to be spent on the road, which reduces the working efficiency of people. Energy consumption is in an increasing stage in the transportation industry and the transportation industry, and the fuel consumption is easily increased due to stop and go and low-gear running for a long time, and the unsmooth road becomes a main reason of the fuel consumption increase, so that the planning of the transportation route becomes more and more important.
The travel time of a car to a destination is an important factor for route selection, and the travel time can be calculated by predicting a traffic flow. The existing traffic flow prediction method ignores the space-time interaction between the traffic flows of adjacent roads and the traffic jam difference of different road sections, and the prediction error of the driving time influences the decision of path selection. In consideration of the space-time interaction of traffic flows among different roads, a long-short term memory-generative confrontation network (LSTM-GAN) deep learning algorithm is provided for predicting the traffic flows, and the prediction precision is improved.
Disclosure of Invention
1. The technical problem to be solved is as follows:
in order to solve the technical problems, the invention provides a method for predicting the automobile running time, which can accurately calculate the automobile running time, is favorable for calculating the energy consumption cost and is particularly favorable for planning the path of an electric automobile.
2. The technical scheme is as follows:
a method for predicting the running time of an automobile is characterized in that: predicting the traffic speed of a road in a future time period by establishing an LSTM-GAN-based model, dividing the road into road sections with different speeds and time periods corresponding to the speeds of the different road sections according to the predicted traffic speed, and calculating the total driving time required by the automobile to reach a destination according to the speeds of the different road sections and the corresponding time periods;
the LSTM-GAN model comprises a generator H and a discriminator D; the generator H captures the time-space characteristics of the input traffic flow data and outputs the initially predicted traffic speed data to the discriminator D; the discriminator D inputs the initially predicted traffic flow data and actual traffic flow data corresponding to the prediction of the initially predicted traffic flow data to learn the characteristic vectors of the two potential traffic flow data, and finally constructs a classification model by using the characteristic vectors, judges the truth of the input initially predicted traffic flow data and outputs the initially predicted traffic flow data which is judged to be true as predicted traffic flow data;
the traffic flow data adopts a traffic speed matrix sequence, and the traffic speed matrixes in different time periods on the same road are arranged according to a preset period; the generator H of the LSTM-GAN model is of a three-layer structure; inputting the traffic speed matrix sequence into a first CNN layer, and inputting the spatial characteristics of the traffic speed matrix sequence on all roads learned by the first CNN layer into a second LSTM layer by the first CNN layer; the second LSTM layer inputs the time characteristics of the captured continuous traffic speed matrix into the third CNN layer, and the third CNN layer generates initial prediction data of the traffic speed matrix in the next time period; the discriminator D has a three-layer structure; the initial prediction data of the traffic speed matrix of the next time period generated by the generator H and the real traffic speed matrix are input into the fourth CNN layer; the fourth CNN layer inputs the learned potential spatial features into the fifth bidirectional LSTM layer; the fifth bidirectional LSTM layer inputs the captured potential time characteristics to the sixth layer; and in the sixth layer, the global optimal solution is obtained through the precision of the loss function optimization generator and the precision of the discriminator, and the prediction result of the traffic speed is output.
Further, the method specifically comprises the following steps:
the method comprises the following steps: acquiring historical traffic flow data, and preprocessing the traffic flow data into a traffic speed matrix sequence; the traffic speed matrix sequence is a traffic speed matrix sequence { v } of a road arranged in a preset period t }＝(v(t 0 ),v(t 1 ),…,v(t n ) The traffic speed matrix at the time t) is:
Figure BDA0003664643370000021
in the formula (A1), v n，1 Representing t time and the speed corresponding to the (n, 1) node in the road;
step two: inputting the traffic speed matrix sequence into a generator H of the LSTM-GAN model, and predicting and generating an initial predicted speed matrix sequence of a corresponding road at the moment t +1 after the generator H is trained for multiple times;
step three: and simultaneously inputting the initial prediction speed matrix sequence at the t +1 moment generated by the generator H and the real speed matrix sequence at the t +1 moment corresponding to the initial prediction speed matrix sequence into a discriminator D, and discriminating the initial prediction matrix sequence by the discriminator D. When the prediction is started, the discriminator firstly learns the distribution condition of real data and effectively identifies, if the probability output by the discriminator D is 1, the matrix sequence which is initially predicted is judged to be a real matrix sequence, and if the probability output by the discriminator D is 0, the matrix sequence which is initially predicted is judged to be a generated matrix sequence; the generator learns the probability distribution of traffic flow historical data on the basis of a large amount of data, the generated data is close to real data, and the traffic speed is obtained through identification and prediction of the discriminator.
Step four: and C, dividing the road into road sections with different traffic speeds and corresponding time periods according to the predicted traffic speed in the step three, and calculating the driving time of the automobile reaching the destination.
Further, in the second step, the generator H learns the probability distribution of the real traffic flow data through a large amount of historical data, and then predicts the future traffic flow by using the learned probability distribution; the generator H can not pass through the identification of the discriminator D when generating data in the initial learning stage and is identified as the generated data, and after the generator is subjected to repeated iterative training, the generated data is close to the real data and is identified by the discriminator D; the iterative optimization process improves the performance of the generator H and the discriminator D; when the discriminator D cannot correctly recognize the data generated by the generator and the real data, that is, the generator H has learned the distribution of the real data, the prediction accuracy is improved.
Further, the discriminator D in the third step adopts the cross entropy as a loss function to judge the similarity between the real traffic speed matrix sequence and the traffic speed matrix sequence distribution predicted in the second step; the cross entropy as a loss function is specifically:
Figure BDA0003664643370000031
(1) In the formula:
Figure BDA0003664643370000032
representing a real matrix sequence, wherein i, j represents a node number corresponding to the road;
Figure BDA0003664643370000033
true data distribution; p is a radical of v (v) Is a prior distribution; Δ t is the time interval;
Figure BDA0003664643370000034
is composed of
Figure BDA0003664643370000035
Probability taken from the real data; h (v) is the preliminary predicted data from the generator H output; d (H (v)) is the probability from H (v) to discriminator D;
Figure BDA0003664643370000036
representing an expectation of the initially predicted data distribution;
minimizing equation (1) by a generator H to obtain an optimal solution; in the continuous space, rewriting formula (1) to formula (2):
Figure BDA0003664643370000037
the expected output of discriminator D is between 0 and 1 when it inputs data
Figure BDA0003664643370000038
From the distribution of the real data, the discriminator D aims at making the probability of the output
Figure BDA0003664643370000039
As close to 1 as possible; when its input data comes from the generated data H (v), the discriminator D tries to correctly judge the data source so that D (H (v)) is as close to 0 as possible, while the generator H aims to make D (H (v)) as close to 1 as possible by iterative training; this means that the data generated by the generator H is closer and closer to the real data; i.e. by a zero-sum game between the generator H and the discriminator D, the loss function Obj of the generator H H (θ H )＝-Obj D (θ D ,θ H )；
Therefore, the objective function for establishing the whole LSTM-GAN model is shown as the formula (3):
Figure BDA00036646433700000310
further, the road segments with different traffic speeds in step four are compared with the historical average speed of the road, specifically: defining the road sections with the queued vehicles and the road sections with the speed less than the historical average speed as downstream road sections, the road sections with the speed greater than the historical average speed as upstream road sections, and the intersections needing to pass through traffic lights as waiting road sections; the method comprises the steps that at least one road is arranged on the route of an automobile to a destination, the required driving time of each road of the route is calculated, and the sum of the required time of each road is the predicted total required time of the automobile to reach the destination; the step of calculating the required travel time of each road of the route specifically comprises the following steps:
s41: dividing the driving time of the automobile on a corresponding road into free driving time, queuing waiting time and crossing time; the free-driving time is the driving time of an upstream road section on the road; the queuing waiting time is the time required for waiting for traffic lights on the downstream road section on the road; the crossing time is the average time required for a vehicle to enter the next road through the crossing, and one road corresponds to the crossing time; the expression is specifically shown in the following formula (4):
Figure BDA0003664643370000041
(4) In the formula: (t) represents a function over time;
Figure BDA0003664643370000042
as a function of the time required to travel on the road;
Figure BDA0003664643370000043
and
Figure BDA0003664643370000044
the time periods respectively include free driving time, queuing waiting time and crossing passing time;
s42: wherein free running time
Figure BDA0003664643370000045
As shown in formula (5):
Figure BDA0003664643370000046
(5) In the formula: d is a radical of i，j The total distance of the road to be driven;
Figure BDA0003664643370000047
queuing the length of the vehicle for the middle and lower reaches of the road;
Figure BDA0003664643370000048
is the predicted average speed on the link;
length of queued vehicles in said downstream stretch
Figure BDA0003664643370000049
As shown in the following formula (6):
Figure BDA00036646433700000410
(6) In the formula: n is a radical of i,j (t) number of vehicles on road;
Figure BDA00036646433700000411
the average headway distance of the queued vehicles; mu.s i,j Maximum vehicle flow for the road; lambda i,j Is the split of the intersection;
the road blockage density is determined by the maximum vehicle flow mu on the road i,j And limiting the speed of the vehicle
Figure BDA00036646433700000412
Obtaining the ratio of (A) to (B); according to the relation between the road jam density and the average speed; the number of vehicles N on the road i,j (t) is represented by the formula (7):
Figure BDA00036646433700000413
according to formulae (5), (6) and (7),
Figure BDA00036646433700000414
and
Figure BDA00036646433700000415
as shown in formulas (8) and (9), respectively:
Figure BDA0003664643370000051
Figure BDA0003664643370000052
s43: wherein the queue waiting time
Figure BDA0003664643370000053
When the vehicle arrives at the intersection with the traffic lights, the queuing waiting time is the green light waiting time
Figure BDA0003664643370000054
Or waiting for red light time
Figure BDA0003664643370000055
As shown in (10) and (11), respectively:
Figure BDA0003664643370000056
Figure BDA0003664643370000057
(10) In the formula: alpha (alpha) ("alpha") i,j Indicating a signal period at a road intersection;
queue waiting time
Figure BDA0003664643370000058
The following equation (12) is approximated:
Figure BDA0003664643370000059
(12) In the formula, p j The probability of the vehicle reaching the intersection during the green light period;
S44, wherein, the time of passing the intersection
Figure BDA00036646433700000510
The average time for the vehicle to pass through the intersection is shown as equation (13):
Figure BDA00036646433700000511
in the formula: beta is a j And (t) is preset turn ending time of the intersection obtained based on the statistical data.
3. Has the beneficial effects that:
(1) The invention establishes a traffic flow prediction model through a long-term and short-term memory-generation confrontation network (LSTM-GAN) deep learning algorithm. The prediction model can obtain more accurate prediction results when the traffic speed changes in different periods are faced, the prediction accuracy is effectively improved, and meanwhile, the important role of the time-varying characteristic in traffic speed prediction is proved.
(2) According to the prediction result of the traffic flow prediction model, the road is divided into different road sections, so that the time of the automobile reaching the destination is calculated. The effectiveness of the method is proved through simulation verification, the method is beneficial to accurate calculation of the running time, and the prediction of the running time is closely related to the traffic jam degree.
Drawings
FIG. 1 is a schematic structural diagram of the LSTM-GAN model in the present invention;
FIG. 2 is a flow chart of traffic speed prediction using the LSTM-GAN model according to the present invention;
FIG. 3 is a schematic illustration of road segment division in the present invention;
fig. 4 is a traffic network diagram in a specific embodiment.
Detailed Description
As shown in fig. 1 to 3, a method for predicting a driving time of an automobile, comprising: predicting traffic speeds on different roads in a future time period by establishing an LSTM-GAN-based model, dividing the road into road sections with different speeds and time periods corresponding to the speeds of the different road sections according to the predicted traffic speeds, and calculating the total driving time required by the automobile to reach the destination according to the speeds of the different road sections and the corresponding time periods;
the LSTM-GAN model comprises a generator H and a discriminator D; the generator H captures the time-space characteristics of the input traffic flow data and outputs the initially predicted traffic speed data to the discriminator D; the discriminator D inputs the initially predicted traffic flow data and actual traffic flow data corresponding to the prediction of the initially predicted traffic flow data to learn the characteristic vectors of the two potential traffic flow data, and finally constructs a classification model by using the characteristic vectors, judges the truth of the input initially predicted traffic flow data and outputs the initially predicted traffic flow data which is judged to be true as predicted traffic flow data;
the traffic flow data adopts a traffic speed matrix sequence, and the traffic speed matrixes in different time periods on the same road are arranged according to a preset period; the generator H of the LSTM-GAN model is of a three-layer structure; inputting the traffic speed matrix sequence into a first CNN layer, and inputting the spatial characteristics of the traffic speed matrix sequence on all roads learned by the first CNN layer into a second LSTM layer by the first CNN layer; the second LSTM layer inputs the time characteristics of the captured continuous traffic speed matrix into the third CNN layer, and the third CNN layer generates initial prediction data of the traffic speed matrix in the next time period; the discriminator D has a three-layer structure; the initial prediction data of the traffic speed matrix of the next time period generated by the generator H and the real traffic speed matrix are input into the fourth CNN layer; the fourth CNN layer inputs the learned potential spatial features into the fifth bidirectional LSTM layer; the fifth bidirectional LSTM layer inputs the captured potential time characteristics to the sixth layer; and in the sixth layer, the global optimal solution is obtained through the precision of the loss function optimization generator and the precision of the discriminator, and the prediction result of the traffic speed is output.
The specific embodiment is as follows: the starting point of the car in this embodiment is node 43 and the end point is node 17 as shown in fig. 4, which needs to predict the speed of different road segments in the future and the corresponding average speed after every 15 minutes by taking the dotted line part of 7 roads as an example. The road-related parameters are shown in table 1:
TABLE 1
Figure BDA0003664643370000071
In order to verify the effectiveness of the proposed LSTM-GAN model in predicting traffic speeds on different roads in a future time period, the average absolute error (MAE), the average relative error (MRE), and the Root Mean Square Error (RMSE) are used as evaluation examples in this embodiment. The LSTM-GAN model using the present application is compared to predictive methods including LSTM, ARIMA and SVR. And because LSTM is a kind of RNN, RNN-GAN is added as a comparison method to verify whether the combination of LSTM and GAN has significant advantages. The average speed of the future 15 minutes is predicted by these methods, and the result of the prediction accuracy is shown in table 2. It is clear that the proposed LSTM-GAN yields the lowest MAE, MRE and RMSE values with the highest prediction accuracy.
TABLE 2
Figure BDA0003664643370000072
Although the present invention has been described with reference to the preferred embodiments, it should be understood that the invention is not limited thereto, and various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention.

Claims (5)

1. A method for predicting the running time of an automobile is characterized in that: predicting the traffic speed of a road in a future time period by establishing an LSTM-GAN-based model, dividing the road into road sections with different speeds and time periods corresponding to the speeds of the different road sections according to the predicted traffic speed, and calculating the total driving time required by an automobile to reach a destination according to the speeds of the different road sections and the corresponding time periods;
the LSTM-GAN model comprises a generator H and a discriminator D; the generator H captures the time-space characteristics of the input traffic flow data and outputs the initially predicted traffic speed data to the discriminator D; the discriminator D inputs the initially predicted traffic flow data and actual traffic flow data corresponding to the prediction of the initially predicted traffic flow data to learn the feature vectors of the two potential traffic flow data, and finally constructs a classification model by using the feature vectors, judges the truth of the input initially predicted traffic flow data and outputs the initially predicted traffic flow data judged to be true as predicted traffic flow data;
the traffic flow data adopts a traffic speed matrix sequence, and the traffic speed matrixes in different time periods on the same road are arranged according to a preset period; the generator H of the LSTM-GAN model is of a three-layer structure; inputting the traffic speed matrix sequence into a first CNN layer, and inputting the spatial characteristics of the traffic speed matrix sequence on all roads learned by the first CNN layer into a second LSTM layer by the first CNN layer; the second LSTM layer inputs the time characteristics of the captured continuous traffic speed matrix into the third CNN layer, and the third CNN layer generates initial prediction data of the traffic speed matrix in the next time period; the discriminator D has a three-layer structure; the initial prediction data of the traffic speed matrix of the next time interval generated by the generator H and the real traffic speed matrix are input into the fourth CNN layer; the fourth CNN layer inputs the learned potential spatial features into the fifth bidirectional LSTM layer; the fifth layer bidirectional LSTM layer inputs its captured potential temporal characteristics to the sixth layer; and in the sixth layer, the global optimal solution is obtained by optimizing the precision of the generator and the discriminator through the loss function, and the prediction result of the traffic speed is output.
2. The method for predicting a travel time of an automobile according to claim 1, wherein: the method specifically comprises the following steps:
the method comprises the following steps: acquiring historical traffic flow data, and preprocessing the traffic flow data into a traffic speed matrix sequence; the traffic speed matrix sequence is a traffic speed matrix sequence { v } of a road arranged in a preset period t }＝(v(t 0 ),v(t 1 ),…,v(t n ) The traffic speed matrix at the time t) is:
Figure FDA0003664643360000011
in the formula (A1), v n，1 Representing t time and the speed corresponding to the (n, 1) node in the road;
step two: inputting the traffic speed matrix sequence into a generator H of the LSTM-GAN model, and predicting and generating an initial predicted speed matrix sequence of a corresponding road at the moment t +1 after the generator H is trained for multiple times;
step three: simultaneously inputting the initial prediction speed matrix sequence at the t +1 moment generated by the generator H and the real speed matrix sequence at the t +1 moment corresponding to the initial prediction speed matrix sequence into a discriminator D, and discriminating the initial prediction matrix sequence by the discriminator D; when the prediction is started, the discriminator firstly learns the distribution condition of real data and effectively identifies, if the probability output by the discriminator D is 1, the matrix sequence which is predicted at first is judged to be a real matrix sequence, and if the probability output by the discriminator D is 0, the matrix sequence which is predicted at first is judged to be a generated matrix sequence; the generator learns the probability distribution of the traffic flow historical data on the basis of a large amount of data, the generated data is close to the real data, and the traffic speed is obtained through the identification of the discriminator in a prediction mode;
step four: and C, dividing the road into road sections with different traffic speeds and corresponding time periods according to the predicted traffic speed in the step three, and calculating the driving time of the automobile reaching the destination.
3. The method for predicting the travel time of an automobile according to claim 2, wherein: in the second step, a generator H learns the probability distribution of real traffic flow data through a large amount of historical data, and then predicts the future traffic flow by using the learned probability distribution; the generator H can not pass through the identification of the discriminator D when generating data in the initial learning stage and is identified as the generated data, and after the generator is subjected to repeated iterative training, the generated data is close to the real data and is identified by the discriminator D; the iterative optimization process improves the performance of the generator H and the discriminator D; when the discriminator D cannot correctly recognize the data generated by the generator and the real data, that is, the generator H has learned the distribution of the real data, the prediction accuracy is improved.
4. A method for predicting a travel time of an automobile according to claim 3, wherein:
in the third step, the discriminator D adopts the cross entropy as a loss function to judge the similarity between the real traffic speed matrix sequence and the traffic speed matrix sequence distribution predicted in the second step; the cross entropy as a loss function is specifically:
Figure FDA0003664643360000021
(1) In the formula:
Figure FDA0003664643360000022
representing a real matrix sequence, wherein i, j represents a node number corresponding to the road;
Figure FDA0003664643360000023
true data distribution; p is a radical of v (v) Is a prior distribution; Δ t is the time interval;
Figure FDA0003664643360000024
is composed of
Figure FDA0003664643360000025
Probability taken from the real data; h (v) is the preliminary predicted data from the output of generator H; d (H (v)) is the probability from H (v) to discriminator D;
Figure FDA0003664643360000026
representing an expectation of the initially predicted data distribution;
minimizing equation (1) by generator H to obtain an optimal solution; in the continuous space, rewriting formula (1) to formula (2):
Figure FDA0003664643360000031
the expected output of discriminator D is between 0 and 1 when it inputs data
Figure FDA0003664643360000032
From the distribution of the real data, the discriminator D aims at making the probability of the output
Figure FDA0003664643360000033
As close to 1 as possible; when its input data comes from the generated data H (v), the discriminator D tries to correctly judge the data source, bringing D (H (v)) as close to 0 as possible, while the generator H aims to bring D (H (v)) as close to 1 as possible by iterative training; this means that the data generated by the generator H is getting closer to the real data; i.e. by a zero-sum game between the generator H and the discriminator D, the loss function Obj of the generator H H (θ H )＝-Obj D (θ D ,θ H )；
Therefore, the objective function for establishing the whole LSTM-GAN model is shown as the formula (3):
Figure FDA0003664643360000034
5. the method for predicting a travel time of an automobile according to claim 1, wherein: the road sections with different traffic speeds in the fourth step are compared with the historical average speed of the road, and the method specifically comprises the following steps: defining the road sections with queued vehicles and the road sections with the speed less than the historical average speed as downstream road sections, defining the road sections with the speed more than the historical average speed as upstream road sections, and defining the intersections needing to pass through traffic lights as waiting road sections; the method comprises the following steps that at least one road is arranged for the automobile to reach a destination, the required driving time of each road in the route is calculated, and the sum of the required time of each road is the predicted total required time for the automobile to reach the destination; the step of calculating the required driving time of each road of the route specifically comprises the following steps:
s41: dividing the driving time of the automobile on a corresponding road into free driving time, queuing waiting time and crossing passing time; the free-driving time is the driving time of an upstream road section on the road; the queuing waiting time is the time required for waiting for traffic lights on the downstream road section on the road; the crossing time is the average time required for a vehicle to enter the next road through the crossing, and one road corresponds to the crossing time; the expression is specifically shown in the following formula (4):
Figure FDA0003664643360000035
(4) In the formula: (t) represents a function over time;
Figure FDA0003664643360000036
as a function of the time required to travel on the road;
Figure FDA0003664643360000037
and
Figure FDA0003664643360000038
the time periods respectively include free driving time, queuing waiting time and crossing passing time;
s42: wherein free running time
Figure FDA0003664643360000039
As shown in formula (5):
Figure FDA0003664643360000041
(5) In the formula: d i，j The total distance of the road to be driven;
Figure FDA0003664643360000042
queuing the length of the vehicle for the downstream section of the road;
Figure FDA0003664643360000043
is the predicted average speed on the link;
length of queued vehicles in said downstream stretch
Figure FDA0003664643360000044
As shown in the following formula (6):
Figure FDA0003664643360000045
(6) In the formula: n is a radical of i,j (t) the number of vehicles on the road;
Figure FDA0003664643360000046
the average headway distance of the queued vehicles; mu.s i,j Maximum vehicle flow for the road; lambda i,j Is the split of the intersection;
the road blockage density is determined by the maximum vehicle flow mu on the road i,j And limiting the speed of the vehicle
Figure FDA0003664643360000047
Obtaining the ratio of (A) to (B); according to the relation between the road jam density and the average speed; the number of vehicles N on the road i,j (t) is represented by the formula (7):
Figure FDA0003664643360000048
according to the formulae (5), (6) and (7),
Figure FDA0003664643360000049
and
Figure FDA00036646433600000410
as shown in formulas (8) and (9), respectively:
Figure FDA00036646433600000411
Figure FDA00036646433600000412
s43: wherein the queue waiting time
Figure FDA00036646433600000413
When the vehicle arrives at the intersection with the traffic light, the queuing waiting time is the green light waiting time
Figure FDA00036646433600000414
Or waiting for red light time
Figure FDA00036646433600000415
As shown in (10) and (11), respectively:
Figure FDA00036646433600000416
Figure FDA00036646433600000417
(10) In the formula: alpha is alpha i,j Indicating a signal period at a road intersection;
queue waiting time
Figure FDA00036646433600000418
The following equation (12) is approximated:
Figure FDA0003664643360000051
(12) In the formula, p j Is the probability of the vehicle reaching the intersection during the green light;
s44, wherein, the crossing passing time
Figure FDA0003664643360000052
The average time for the vehicle to pass through the intersection is shown as equation (13):
Figure FDA0003664643360000053
in the formula: beta is a j And (t) is preset turn ending time of the intersection obtained based on the statistical data.
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