CN107665581B - Main road fleet discrimination method considering incoming traffic flow - Google Patents

Main road fleet discrimination method considering incoming traffic flow Download PDF

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CN107665581B
CN107665581B CN201710913093.0A CN201710913093A CN107665581B CN 107665581 B CN107665581 B CN 107665581B CN 201710913093 A CN201710913093 A CN 201710913093A CN 107665581 B CN107665581 B CN 107665581B
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headway
critical
flow
branch
road
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CN107665581A (en
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宋现敏
李志慧
高雨虹
曲昭伟
魏巍
陶鹏飞
李达修
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Jilin University
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Jilin University
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    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/01Detecting movement of traffic to be counted or controlled
    • G08G1/0104Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0137Measuring and analyzing of parameters relative to traffic conditions for specific applications
    • G08G1/0145Measuring and analyzing of parameters relative to traffic conditions for specific applications for active traffic flow control
    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/07Controlling traffic signals
    • G08G1/08Controlling traffic signals according to detected number or speed of vehicles

Abstract

The invention discloses a trunk fleet judgment considering an imported traffic flowIn order to solve the problem that the influence of branch incoming traffic on the dispersion characteristic of the main road traffic is not considered in the existing vehicle fleet identification model, the main road vehicle fleet identification method considering the incoming traffic comprises the following steps: 1. determining a critical headway; 2. calculating the relation between the branch flow and the length of the trunk road section and the critical headway; 3. calculating the relation between the branch flow and the position of the branch and the critical headway; 4. calculating the relationship between the branch flow and the main flow and the critical headway time; 5. establishing a fleet discrimination index model: 1) calculating the relation between the critical headway and each influence factor, 2) determining a fleet discrimination model:in the formula: h iskIs the critical headway, unit.s; q. q.s0The flow rate of the main channel is unit veh/h; q. q.s1The unit is the branch flow rate, veh/h; a, b, c, d and e are undetermined parameters, and are obtained by calibrating the parameters according to actual data; 6) and (4) determining a fleet.

Description

Main road fleet discrimination method considering incoming traffic flow
Technical Field
The invention relates to a method for judging a trunk fleet in the field of traffic control, in particular to a method for judging a trunk fleet by considering an incoming traffic flow.
Background
Since fleet dispersion characteristics are objects that must be considered during traffic control system research, it is particularly necessary to study the impact of fleet dispersion characteristics on traffic control systems. At present, the economy and urban construction of China are continuously and rapidly developed, the traffic of China still shows a mixed phenomenon, and because of factors such as large distance between urban road networks, complex road structure and vehicle composition, poor traffic consciousness of citizens when going out and the like, the urban road fleet dispersion is greatly influenced. Therefore, the method is particularly important for researching and analyzing the influence of branch incoming traffic flow on the dispersion characteristic of main road traffic flow, and has important theoretical significance for establishing a fleet discrimination model.
At present, on the basis of the research result of discrete characteristics, the discrimination indexes of the motorcade discrimination method by domestic and foreign scholars can be roughly divided into three categories: the critical (key) headway (the maximum headway of the fleet is the critical headway when the headway is used as a judgment index to judge the fleet), the accumulated headway and the vehicle density. However, the influence factors of the dispersion characteristics of the main road traffic flow are less deeply researched, and the influence of the branch road incoming traffic flow on the dispersion characteristics of the main road traffic flow is less and less. Therefore, it is necessary to provide a new model algorithm for vehicle fleet determination from the viewpoint of the influence of the branch incoming traffic on the main road traffic.
Disclosure of Invention
The invention aims to solve the technical problem that the influence of branch incoming traffic on the dispersion characteristics of main road traffic is not considered in the conventional vehicle fleet identification model, and provides a main road vehicle fleet identification method considering the incoming traffic.
In order to solve the technical problems, the invention is realized by adopting the following technical scheme: the method for judging the trunk fleet considering the influx traffic flow comprises the following steps:
1) determining a critical headway:
(1) obtaining equivalent headway
Firstly, regarding a plurality of lanes on a certain road section as an equivalent lane, wherein traffic flow on the road section can be equivalent to a motorcade, then determining an equivalent section on a downstream equivalent lane, and then, the headway time distance measured on the section is the equivalent headway time distance;
(2) determining traffic flow concentration
The traffic flow concentration ratio refers to a measurement value used for representing the relative concentration degree of vehicles in one traffic flow on a road section; after the equivalent headway is acquired, fitting a function which can be obviously expressed as a curve change rule according to the relation between the total average accumulated headway probability and the headway; then, performing primary and secondary derivation on the fitting function to obtain the probability corresponding to the turning point of the curve, namely the traffic flow concentration;
(3) selecting critical headway
Drawing a cumulative headway probability curve chart under different conditions by taking the obtained traffic flow concentration as a standard, wherein the corresponding headway is the critical headway when the cumulative headway probability is the traffic flow concentration;
2) calculating the relationship between the branch flow and the length of the trunk road section and the critical headway:
(1) determining the relationship between branch flow and critical headway
By analyzing the variation trend and the law of the critical headway of each equivalent section along with the branch flow, the critical headway and the branch flow can be represented by a Gaussian function through fitting, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit s;
q1the branch flow is in unit veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(2) determining the relationship between the length of road section and critical headway
a. By analyzing the data obtained by simulation, the influence of the length of the trunk road section on the critical headway has no obvious influence on the change rule and the curve trend, and the main influence is that the extreme point of the curve and the change rate of the curve have obvious changes in different trunk road section lengths;
b. the change of data can obviously show that the critical headway is continuously reduced along with the increase of the length of the road section of the trunk road and obeys a linear relation;
(3) determining the relationship between the branch flow and the road section length of the trunk road and the critical headway
By analyzing the data obtained by simulation, the critical headway time has an obvious functional relationship with the length of the trunk road section and the branch flow; the relation between the critical headway and the branch flow accords with a Gaussian formula, and the relation between the critical headway and the length of the trunk road section accords with a negative correlation, so that the relation between the critical headway and the trunk road section is integrated, the following functional relation is obtained through fitting, and the specific formula is as follows:
hk=i+j*l1+k*exp(-0.5*((q1-m)/n)2) (5)
in the formula: l1Is the length of the road section of the trunk road in the unit of m;
q1the branch flow is in unit veh/h;
i, j, k, m and n are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
3) calculating the relationship between branch flow and the position of the branch and the critical headway:
(1) determining the relationship between branch flow and critical headway
Analyzing the variation trend and the law of the critical headway of each equivalent section along with the branch flow, and fitting to obtain the critical headway and the branch flow which can be expressed by a Gaussian function, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit s;
q1the branch flow is in unit veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(2) determining the relation between the branch position and the critical headway;
a. recording a main road flow of 2100veh/h and a main road section length of 500m as a condition A, and recording a main road flow of 2350veh/h and a main road section length of 300m as a condition B;
b. respectively simulating the two conditions to obtain a critical headway time;
c. analyzing the data obtained by simulation, wherein the branch position and the critical headway are in a negative correlation linear relationship, and the critical headway is continuously reduced along with the increase of the branch position;
(3) determining the relation between branch flow and the position of the branch and the critical headway;
comprehensively considering the relationship among the three, and obtaining the functional relationship among the three through fitting as follows:
hk=o+p*l2+q*exp(-0.5*((q1-r)/s)2) (6)
in the formula: l2Is the branch position, unit m;
q1the branch flow is in unit veh/h;
o, p, z, r and s are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
4) calculating the relationship between the branch flow and the main flow and the critical headway:
(1) determining the relationship between branch flow and critical headway
Through fitting, the obtained critical headway and branch flow can be represented by a Gaussian function, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit s;
q1the branch flow is in unit veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(2) determining the relationship between the main road flow and the critical headway
The functional relation between the critical headway and the main road flow is obtained through fitting, and the specific formula is as follows:
hk=u*exp(-0.5*((q0-v)/w)2) (7)
in the formula: q. q.s0The flow rate of the main channel is in unit veh/h;
u, v and w are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(3) determining the relationship between branch flow and main flow and critical headway
Critical headway hkRespectively decreases along with the increase of the main road flow and the branch road influx flow, and the critical headway h is obtained through the fitting analysis of the relationship of the main road flow, the branch road influx flow and the branch road influx flowkThe relationship between the main flow and the branch inflow can be expressed by a gaussian formula, which is as follows:
hk=a1*exp(-0.5*(((q0-b1)/c1)2+((q1-d1)/e1)2)) (8)
in the formula: a is1,b1,c1,d1,e1The undetermined parameters can be obtained by calibrating the parameters according to actual data;
5) establishing a fleet discrimination index model:
(1) calculating the relation between the critical headway and each influence factor
The fleet discrimination model is comprehensively considered and expressed as a functional relation among branch position, trunk road section length, branch flow, trunk flow and critical locomotive time distance, and the specific formula is as follows:
hk=f(l1,l2,q0,q1) (9)
in the formula: h iskIs the critical headway, unit s; l1Is the length of the road section of the trunk road in the unit of m; l2Is the branch position, unit m; q. q.s1The branch flow is in unit veh/h; q. q.s0The flow rate of the trunk line is in unit veh/h;
(2) determination of fleet discrimination model
According to the actual condition of the road, for a specific passing road, the position of the branch road and the length of the trunk road section which are connected with the road are fixed and unchanged, so that the action values of the two influencing factors of the position of the branch road and the length of the trunk road section are indirectly replaced by constants, and the judgment model of the motorcade is the critical headway time hkFlow q of trunk line0And branch flow q1Is a function ofShown below:
hk=f(q0,q1) (10)
namely:
in the formula: h iskIs the critical headway, unit s;
q0the flow rate of the main channel is in unit veh/h;
q1the branch flow is in unit veh/h;
a, b, c, d and e are undetermined parameters, and are obtained by calibrating the parameters according to actual data;
6) determination of the fleet:
(1) parameter calibration of fleet discrimination model
Calibrating parameters according to actual data of the investigation place; when the parameter calibration is carried out, the minimum Root Mean Square Error (RMSE) of a calculated value and an actual value of the model is taken as a judgment standard to calibrate the parameter, namely when the root mean square error is minimum, the corresponding parameter value is the model parameter value under the condition of the road;
during parameter calibration, MATLAB software is used, and a minimum gradient method is used for carrying out iteration for multiple times, so that a corresponding parameter value when a Root Mean Square Error (RMSE) is minimum is obtained;
(2) fleet determination
Substituting the calibrated parameters into a formulaAnd obtaining a fleet judgment model under the road condition, obtaining the critical headway of the road section, and obtaining the fleet with the parameter value of the equivalent headway between different equivalent sections, wherein the fleet is different fleets.
Compared with the prior art, the invention has the beneficial effects that:
1. the method for judging the trunk road fleet by considering the incoming traffic flow comprehensively considers the influence of the branch incoming traffic flow on the discrete characteristics of the trunk road traffic flow, establishes a new fleet judgment index model by taking the critical headway time interval as a judgment index, and ensures the feasibility and the effectiveness of the method for judging the fleet;
2. the method for judging the trunk motorcade by considering the converged traffic flow is vital to the judgment of the motorcade, can ensure that when the flow of an upstream vehicle is larger, the phenomenon of traffic jam caused by overlong downstream queuing motorcade can be avoided, the waste of green light time of a downstream intersection is avoided, the vehicle delay is increased, and the method avoids the waste of space-time resources of a signal intersection while ensuring the passing efficiency and the safety of the vehicle;
3. the trunk line motorcade distinguishing method considering the confluent traffic flow overcomes the problem of insufficient motorcade distinguishing influence factors in the conventional method, comprehensively discusses various factors which can influence motorcade distinguishing, can better realize effective recognition of motorcade, provides theoretical basis for a traffic control system, provides theoretical support for improving urban traffic efficiency, and plays a positive role in rapid development and construction of cities.
Drawings
The invention is further described with reference to the accompanying drawings in which:
FIG. 1 is a block flow diagram of a method for determining a fleet of arterial roads that considers incoming traffic in accordance with the present invention;
FIG. 2 is a schematic diagram of obtaining an equivalent headway time interval in the trunk fleet determination method considering the incoming traffic flow according to the present invention;
FIG. 3 is a schematic diagram illustrating a fitting functional relationship between a total headway and a total average headway cumulative probability in the arterial road fleet determination method considering incoming traffic flows according to the present invention;
FIG. 4 is a schematic diagram of a total average cumulative probability function, a first derivative function and a second derivative function curve of headway time interval in the method for discriminating the trunk fleet considering the incoming traffic flow according to the present invention;
FIG. 5 is a schematic diagram illustrating the calculation of a critical headway in the method for determining a fleet of arterial roads in consideration of incoming traffic flow according to the present invention;
FIG. 6-a is a schematic diagram illustrating a relationship between an incoming road traffic and a critical headway for a road under a road length of 300 meters in the method for determining a fleet of thoroughfares in consideration of incoming traffic according to the present invention;
FIG. 6-b is a schematic diagram illustrating a relationship between an incoming road traffic and a critical headway for a road with a road length of 350m in the method for determining a trunk fleet considering incoming traffic according to the present invention;
FIG. 6-c is a schematic diagram illustrating a relationship between an incoming road traffic and a critical headway for a road under a road length of 400 meters in the method for determining a trunk fleet considering incoming traffic according to the present invention;
FIG. 6-d is a schematic diagram illustrating a relationship between an incoming road traffic and a critical headway for a sub-road junction at a road length of 450 meters in the method for determining a fleet of main roads considering incoming traffic according to the present invention;
FIG. 6-e is a schematic diagram illustrating a relationship between an incoming road traffic and a critical headway for a road under a road section length of 500 meters in the method for determining a trunk fleet considering incoming traffic according to the present invention;
FIG. 6-f is a schematic diagram illustrating a relationship between an incoming road flow and a critical headway for a road under a road length of 550 meters in the method for determining a trunk fleet considering incoming traffic according to the present invention;
FIG. 6-g is a schematic diagram of a relationship between an incoming road traffic and a critical headway for a road under a road section length of 600 meters in the method for determining a trunk fleet considering incoming traffic according to the present invention;
FIG. 7 is a schematic diagram illustrating a relationship between a critical headway, a road section length and a branch road flow in the method for determining a main road fleet considering incoming traffic flow according to the present invention;
FIG. 8-a shows the main road flow q in the method for determining the fleet of main roads considering the incoming traffic according to the present invention02350veh/h and road length l1A schematic diagram of the relationship between the branch position, the branch flow and the critical headway under the condition of 300 m;
FIG. 8-b shows the trunk flow q in the method for determining a fleet of trunk lines considering incoming traffic according to the present invention02100veh/h and link length l1A schematic diagram of the relationship between the branch position, the branch flow and the critical headway under the condition of 500 m;
FIG. 9-a is a schematic diagram illustrating a relationship between a trunk line flow and a critical headway time when a branch line flow is 0veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
FIG. 9-b is a schematic diagram illustrating a relationship between a trunk line flow and a critical headway time when a branch line flow is 100veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
FIG. 9-c is a schematic diagram of a relationship between a trunk line flow and a critical headway time when a branch line flow is 200veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
FIG. 9 d is a schematic diagram illustrating a relationship between a trunk line flow and a critical headway time when a branch line flow is 300veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
FIG. 9-e is a schematic diagram illustrating a relationship between a trunk line flow and a critical headway time when a branch line flow is 400veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
FIG. 9-f is a schematic diagram of a relationship between a trunk line flow and a critical headway time when a branch line flow is 500veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
FIG. 9-g is a schematic diagram of a relationship between a trunk line flow and a critical headway time distance when a branch line flow is 600veh/h in the trunk line fleet determination method considering the influx traffic flow according to the present invention;
fig. 10-a is a schematic diagram of a relationship between a critical headway time span, a trunk road flow and a branch road flow under the condition that the length of a road segment is 300 meters in the trunk road fleet determination method considering the influx traffic flow according to the present invention;
fig. 10-b is a schematic diagram of a relationship between a critical headway time span, a trunk road flow and a branch road flow under the condition that the length of a road segment is 400 meters in the trunk road fleet determination method considering the influx traffic flow according to the present invention;
FIG. 11 is a schematic diagram of a channelized graph of data acquisition sites and camera placement positions in a method for determining a fleet of thoroughfares that takes into account incoming traffic flow in accordance with the present invention;
FIG. 12 is a schematic diagram illustrating a fitting functional relationship between calculated headway and average accumulated headway probability in the arterial road fleet determination method considering incoming traffic flows according to the present invention;
FIG. 13 is a schematic diagram of a headway function, a first derivative function and a second derivative function curve in the method for determining a main road fleet considering incoming traffic flow according to the present invention;
fig. 14 is a schematic diagram of a relationship between a critical headway time, a main road flow and a branch road flow obtained according to a survey in the main road fleet determination method considering the incoming traffic;
fig. 15-a is a schematic diagram of a residual error value between a critical headway time interval actually obtained and a critical headway time interval obtained according to the model of the present invention, according to a change in branch road traffic in the trunk fleet determination method considering the influx traffic;
fig. 15-b is a schematic diagram illustrating a residual variation trend of a critical headway actually obtained according to a variation of branch road traffic in the method for determining a trunk fleet considering incoming traffic flow according to the present invention and a critical headway obtained according to the model of the present invention;
fig. 16-a is a schematic diagram of a residual error value between an actual critical headway and a critical headway time interval obtained according to a model in the method for judging the trunk fleet considering the influx traffic according to the present invention, the residual error value varying with the flow of the trunk;
fig. 16-b is a schematic diagram of a residual variation trend of an actual critical headway and a critical headway time interval obtained according to a model and varying with a trunk road flow in the trunk road fleet determination method considering the influx traffic;
FIG. 17-a is a schematic diagram of a critical headway, a trunk flow and a branch flow fitting condition actually investigated in the method for discriminating a trunk fleet considering incoming traffic according to the present invention;
fig. 17-b is a schematic diagram of a difference between an actual critical headway and a critical headway distribution obtained according to a model in the arterial road fleet determination method considering the influx traffic stream.
Detailed Description
The invention is described in detail below with reference to the attached drawing figures:
the invention aims to solve the technical problem that the influence of branch incoming flow on the dispersion characteristic of main road traffic flow is not considered in the prior art, and the critical headway time is used as a judgment index to realize effective judgment of a motorcade. The method utilizes the related technology in the traffic control field to research and consider the discrimination problem of the main road fleet which converges traffic flow. In the main road fleet discrimination method considering the imported traffic flow: firstly, determining a critical headway, then calculating the relationship between branch flow and the length of a trunk road section and the critical headway, further calculating the relationship between the branch flow and the position of the branch and the critical headway, then calculating the relationship between the branch flow and the trunk flow and the critical headway, and finally determining the critical headway by using the parameter relationship obtained in the previous four steps, thereby establishing a fleet judgment index model. Therefore, the method comprises the following specific operation steps:
1. determining critical headway
1) Obtaining equivalent headway
Referring to fig. 2, a schematic diagram of a certain road section is shown, assuming that the road section is four lanes from west to east, and the length is about 1000m, first, the four lanes of the road section are regarded as an equivalent lane, the traffic flow on the road section can be equivalent to a fleet, then an equivalent section is determined on the downstream equivalent lane, and the headway measured on the section is the equivalent headway.
The equivalent lane means that a plurality of lanes on a certain road section are regarded as one lane, and the lane is the equivalent lane; the equivalent section is a section of an equivalent lane, and one or more vehicles may be contained in the vehicle headway data measured by taking the equivalent section as the data detection point; the headway refers to the time interval, unit.s, of two continuous vehicle headways passing through a certain section in a vehicle queue running on the same lane; the equivalent headway refers to the headway, unit.s, when the vehicle passes through a certain section of the equivalent lane.
2) Determining traffic flow concentration
The traffic flow concentration ratio refers to a measurement value used for indicating the relative concentration degree of vehicles in a traffic flow on a road section. Since the size limit of the fleet is fuzzy, a critical threshold for the minimum fleet needs to be set. According to the existing research, the vehicles contained in the traffic flow with 5 continuous headway distances less than or equal to the critical headway distance are regarded as the minimum fleet.
(1) Obtaining a fitting curve
Firstly, based on actual data of a Jilin road in Changchun city of Jilin and a road section in the direction from east to west at an intersection of a river street, simulation is carried out by using Vissim software. Assuming that the distance between the branch road converging position and the upstream intersection is 200m, the main road flow is 2450veh/h, the branch road is a one-way lane, the flow is increased in 25veh/h increments within the range of (0-600veh/h), data acquisition points are respectively arranged at the cross section positions of 300m, 350m, 400m, 450m, 500m, 550m and 600m at the downstream, and equivalent headway time is acquired. Then, a function capable of obviously expressing the curve change rule can be fitted according to the relation between the total average accumulated headway probability (the average value of the sum of the headway probabilities corresponding to the same road section passing through different traffic flows) and the headway, and the specific function is shown in fig. 3.
As can be seen from fig. 3, the overall average cumulative headway probability fitting function is:
f(x)=a*xb+c (1)
wherein, a is-0.4354, b is-0.9485, and c is 1.016;
(2) first and second order derivation of a function
Then, the fitting function is subjected to primary and secondary derivation:
first derivative function:
f′(x)=a*b*xb-1 (2)
second derivative function:
f″(x)=a*b(b-1)*xb-2 (3)
TABLE 1 calculation of the function, first and second derivatives
In a mathematical sense, a minimum point is found when the first derivative is equal to zero and the second derivative is greater than zero; the maximum point is when the first derivative is equal to zero and the second derivative is less than zero. Referring to fig. 4 and table 1, it can be seen that f '(x) is 0.01 and gets closer to zero after x is 5.5s, so f' (x) at this time can be approximated to 0; and f "(x) is negative at this time, then this point can be taken as the maximum point of the function, i.e., f (x) increases approximately zero (only to illustrate that the increase is relatively slow after x is 5.5 s). Finally, the comprehensive knowledge is that: and x is 5.5s, which is the turning point of the curve, and the corresponding probability is 93%, so that the traffic flow concentration ratio is 93%.
3) Selecting critical headway
Referring to fig. 5, a graph of cumulative headway probability under different conditions is plotted with 93% traffic flow concentration as a standard, and the headway corresponding to the situation where the cumulative headway probability (the sum of the headway probabilities corresponding to the same road section passing through different traffic flows) is 0.93 is the critical headway (h)k). And in the same way, the h of each section under the condition that different branches are converged into the flow is determined by analogyk
2. Calculating the relationship between the branch flow and the road section length of the trunk road and the critical headway
1) Determining the relationship between branch flow and critical headway
When the main road flow and the branch road position are fixed, the branch road flow has a relatively obvious influence on the judgment of the motorcade. Based on the Vissim simulation, the critical headway time h of each section under different branch flows is obtained by sorting and researching the actual data of the Jilin road, the river crossing and the crossing western-way direction road section in Jilin province, Changchun cityk. The data specifically used is consistent with the data in the step of "determining the traffic flow concentration".
Referring to FIGS. 6-a to 6-g, h is obtained by analyzing each equivalent cross sectionkH is obtained by fitting along with the variation trend and the law of the branch flowkThe bypass flow can be expressed by a gaussian function, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit.s;
q1the unit is the branch flow rate, veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data.
As can be seen from Table 2, the coefficients were determined(ratio of regression sum of squares to total sum of squares of data) R2The values are all above 0.85, so that the Gaussian formula can represent the relationship of two variables under strong correlation, and the fitting effect is good.
TABLE 2 values of the parameters for different road section lengths
2) Determining the relationship between the length of road section and critical headway
Referring to fig. 7, by analyzing the data obtained by simulation, the influence of the length of the trunk road section on the critical headway has no obvious influence on the change rule and the curve trend, and the main influence is that the extreme point of the curve and the change rate of the curve have obvious changes in different lengths of the trunk road section; meanwhile, the change of data can obviously show that the critical headway is continuously reduced along with the increase of the length of the road section of the trunk road and obeys a linear relation.
3) Determining the relationship between the branch flow and the road section length of the trunk road and the critical headway
Referring to fig. 7, by analyzing the data obtained by simulation, the critical headway has a significant functional relationship with the length of the trunk road section and the branch flow. The relation between the critical headway and the branch flow accords with a Gaussian formula, and the relation between the critical headway and the length of the trunk road section accords with a negative correlation. Therefore, the relationship among the three is synthesized, and the following functional relationship is obtained through fitting, and the specific formula is as follows:
hk=i+j*l1+k*exp(-0.5*((q1-m)/n)2) (5)
in the formula: l1Is the length of the road section of the main road in unit m;
q1the unit is the branch flow rate, veh/h;
and i, j, k, m and n are undetermined parameters and can be obtained by calibrating the parameters according to actual data.
As can be seen from Table 3, R2Above 0.85, therefore, the formula can represent three variables with strong correlationThe fitting effect is better.
TABLE 3 values of the parameters
3. Calculating the relationship between branch flow and branch position and critical headway
1) Determining the relationship between branch flow and critical headway
Referring to fig. 6-a to 6-g, the relationship between the branch flow and the critical headway can be obtained from step 1) in "calculating the relationship between the branch flow and the trunk section length and the critical headway" in step 2, and the two obey the gaussian function relationship.
2) Determining the relationship between branch position and critical headway
Referring to fig. 8-a and 8-B, the critical headway time interval is obtained by respectively simulating the position where the main road flow is 2100veh/h, the length of the main road section is 500m (recorded as condition a), the main road flow is 2350veh/h and the length of the main road section is 300m (recorded as condition B); as shown in fig. 6-a to 6-g, the branch flow and the critical headway are subject to gaussian distribution, and it can be seen from fig. 8-a and 8-b that there is an obvious linear relationship between the branch position and the critical headway, and the critical headway is continuously decreased as the branch position increases.
3) Determining the relationship between branch flow and branch position and critical headway
Referring to fig. 8-a and 8-b, by analyzing the data obtained from the simulation, there is a certain functional relationship between the branch flow and the branch position and the critical headway. According to the formula 4, the critical headway and the branch flow are in accordance with Gaussian distribution and can be expressed by a first-order Gaussian function; the branch position and the critical headway are in a linear relationship of negative correlation, so the relationship among the three is comprehensively considered, the functional relationship among the three can be obtained through fitting, and the specific formula is as follows:
hk=o+p*l2+q*exp(-0.5*((q1-r)/s)2) (6)
in the formula: l2Is the branch position, unit.m;
q1the unit is the branch flow rate, veh/h;
and o, p, z, r and s are undetermined parameters and can be obtained by calibrating the parameters according to actual data.
As can be seen from Table 4, R2All are above 0.85, therefore, the formula can represent the relationship of three variables under strong correlation, and the fitting effect is good.
TABLE 4 flow rate of different main road and road section length of different main road
4. Calculating the relationship between the branch flow and the main flow and the critical headway
1) Determining the relationship between branch flow and critical headway
Referring to fig. 6-a to 6-g, the relationship between the branch flow and the critical headway can be obtained by the step 1) of calculating the relationship between the branch flow and the trunk section length and the critical headway in the step 2, and the two obey the gaussian function relationship.
2) Determining the relationship between the main road flow and the critical headway
Referring to FIGS. 9-a to 9-g, the length l of the road section is shown1Taking 300m as an example, the main road flow is in the range of 1450veh/h-2450veh/h, the main road flow is in the range of 0-600veh/h, the branch road flow is in the range of 100veh/h as the variable quantity, the data acquisition points are arranged at the 300m section to count the headway time, and the critical headway time h under various conditions can be obtained after arrangement calculationk
Through analyzing the data obtained by simulation, the change rule of the critical headway time interval along with the main road flow under different branch flows is discussed respectively, and the change trend of the data shows that the critical headway time interval is continuously reduced along with the increase of the main road flow all the time, and the change trends under different branch flow conditions are similar. Therefore, a functional relation between the main road flow and the critical headway is obtained through fitting, and a specific formula is as follows:
hk=u*exp(-0.5*((q0-v)/w)2) (7)
in the formula: q. q.s0The flow rate of the main channel is unit veh/h;
u, v and w are undetermined parameters and can be obtained by calibrating the parameters according to actual data.
As can be seen from table 5, the gaussian function can completely and significantly express the relationship between the main road flow and the critical headway, that is, the critical headway is continuously reduced with the increase of the main road flow, and conforms to the change rule of the gaussian function.
TABLE 5 values of parameters at different branch flows
3) Determining the relationship between branch flow and main flow and critical headway
Referring to fig. 10-a and 10-b, it can be seen from the analysis of the data obtained by the simulation that under the condition that the length of the trunk road section is changed, the relationship between the branch flow, the trunk flow and the critical headway time interval is similar, and the critical headway time interval is respectively reduced along with the increase of the trunk flow and the branch influx flow. In summary, through fitting analysis of the relationship among the three, the relationship between the critical headway, the trunk flow and the branch inflow flow can be expressed by a gaussian formula, and the specific formula is as follows:
hk=a1*exp(-0.5*(((q0-b1)/c1)2+((q1-d1)/e1)2)) (8)
in the formula: a is1,b1,c1,d1,e1The undetermined parameters can be obtained by calibrating the parameters according to actual data.
As can be seen from Table 6, R2All are above 0.85, therefore, the formula can represent the relationship of three variables under strong correlation, and the fitting effect is good.
TABLE 6 parameter values for different road section lengths
5. Establishing motorcade discrimination index model
1) Calculating the relation between the critical headway and each influence factor
Referring to fig. 1, according to steps 1, 2, 3 and 4 of the trunk fleet determination method, it can be known that the relationships between the branch position and the critical headway distance and between the length of the trunk section and the critical headway distance can be represented by a linear function with negative correlation, and the relationships between the branch flow and the critical headway distance and between the trunk flow and the critical headway distance conform to gaussian distribution. Therefore, the comprehensive consideration fleet identification model can be expressed as branch position, trunk road section length, branch flow, trunk flow and critical headway time hkThe specific formula of the functional relationship is as follows:
hk=f(l1,l2,q0,q1) (9)
in the formula: h iskIs the critical headway, unit.s; l1Is the length of the road section of the main road in unit m; l2Is the branch position, unit.m; q. q.s1The unit is the branch flow rate, veh/h; q. q.s0The flow rate of the trunk line is in unit veh/h;
2) determination of fleet discrimination model
According to the actual condition of the road, for a specific passing road, the position of the branch road connected with the road and the length of the trunk road section are fixed and unchanged, so that the action values of the two influencing factors of the position of the branch road and the length of the trunk road section can be indirectly replaced by a constant, and the judgment model of the motorcade is the critical headway time hkFlow q of trunk line0And branch flow q1The specific formula of the functional relationship is as follows:
hk=f(q0,q1) (10)
namely:
in the formula: h iskIs the critical headway, unit.s;
q0the flow rate of the main channel is unit veh/h;
q1the unit is the branch flow rate, veh/h;
a, b, c, d and e are undetermined parameters and can be obtained by calibrating the parameters according to actual data.
6. Fleet determination
1) Calibrating parameters of a fleet discrimination model;
and calibrating parameters according to actual data of the investigation place. When the parameter calibration is performed, the minimum Root Mean Square Error (RMSE) between the calculated value and the actual value of the model is used as a judgment standard to calibrate the parameter, that is, when the root mean square error is minimum, the corresponding parameter value is the model parameter value under the condition of the road.
During parameter calibration, MATLAB software is used for carrying out multiple iterations by using a minimum gradient method, so that a corresponding parameter value when the Root Mean Square Error (RMSE) is minimum is obtained.
2) Fleet determination
And (3) according to a formula 11, the calibrated parameters are introduced into the model to obtain a fleet judgment model under the road condition, namely the critical headway of the road section, and the fleet with the equivalent headway between different equivalent sections as the value is different fleets.
Examples
In order to verify the effect of the invention, videos are shot on road sections between the city of Changchun and the intersection of the east China road and between the city of Tongxiang and the intersection of the releasing road at two time periods of 11:00-13:00 and 14:30-16:30 respectively on days 3 and 4 of 7 months in 2016, and the following experiments are completed.
Referring to fig. 11, the experimental road section is 345m long, and four lanes in both north and south directions; on the road section from north to south, a branch of a bidirectional single lane, namely a wicker road, is arranged at a position 85m away from the upstream, and the road can only turn right when entering a main road at the intersection, so the road environment and conditions are ideal; meanwhile, in order to ensure the validity of the collected data, a high-definition camera C1 is erected at an upstream intersection, a high-definition camera C2 is erected at a branch junction, and a high-definition camera C3 is erected at a downstream 195m section for data collection. The upstream camera C1 is used for determining traffic flow in each period, the branch junction camera C2 is used for determining traffic flow in each period of entering the branch and entering the main road, and the downstream cross-section camera C3 is used for collecting headway.
1. Determining critical headway
1) Obtaining equivalent headway
Referring to fig. 11, first, two lanes of the survey road section are regarded as an equivalent lane, traffic flow on the road section can be equivalent to a fleet, and then the headway of a downstream equivalent section is measured, which is the equivalent headway of the road section.
2) Determining traffic flow concentration
(1) Obtaining a fitting curve
Referring to fig. 12, in order to unify the determination criteria, the accumulated headway probabilities of each period are added and then averaged to obtain an average accumulated headway probability; concentration is then determined based on the average cumulative headway probability. A curve with good fitting can be obtained by averagely accumulating the headway probability.
(2) First and second order derivation of a function
Referring to fig. 13, the function f (x) can significantly represent the relationship between the average cumulative headway probability and the headway. Then, first order derivation and second order derivation are performed on the function, which is specifically shown in the following formula:
f′(x)=-a0b0*exp-(c0x) (12)
f″(x)=a0b0 2*exp(-c0x) (13)
in the formula: x is the headway, unit.s;
a0,b0,c0is a constant, respectively0=-1.07,b0=0.3334,c0=0.9533。
Referring to fig. 13 and table 7, the values of the first and second derivatives at different headway are obtained according to equations (12) and (13).
From the mathematical meanings represented by the different function values, it can be seen in table 6 that: after x is 9.5s, f '(x) is 0.02 and gets closer to zero, so looking f' (x) at approximately 0 and f "(x) at a negative value, this point approximates the maximum point as a function, i.e. the increase in f (x) is approximately zero. In conclusion: and x is 9.5s, which can be used as the turning point of the curve, and the corresponding probability is 91%, namely the concentration of the traffic flow is 91%.
TABLE 7 values of functions at different headway
3) Selecting critical headway
As can be seen from step 2, if the concentration ratio is 91%, that is, 91% of the vehicles in the traffic flow are relatively concentrated, the cumulative probability curve under the condition is calculated by using the concentration ratio as a standard, the critical headway time interval corresponding to the point is estimated when the cumulative probability is 0.91, and the critical headway time interval of each equivalent section under the condition that different branches converge into the flow is estimated by analogy. The specific values of the critical headway obtained through calculation are shown in the table 8 and the table 9.
TABLE 8 day h of the first daykValue (C represents period)
TABLE 9 actual h daykValue (C represents period)
2. Fleet determination
The steps 2, 3, 4 and 5 in the method are not required to be repeated when the model is verified, and the four steps only provide basis for finally determining the motorcade, so that the model is not required to be repeated, and the calculation can be directly carried out by using the motorcade discrimination model obtained in the step 6.
1) Parameter calibration of model
And calibrating parameters according to the actual data of the first day of the survey site. When the parameter calibration is performed, the minimum Root Mean Square Error (RMSE) between the calculated value and the actual value of the model is used as a judgment standard to calibrate the parameter, that is, when the root mean square error is minimum, the corresponding parameter value is the model parameter value under the condition of the road.
Referring to fig. 14, the parameter calibration at this time is performed by using MATLAB software and performing multiple iterations by using the minimum gradient method, and the corresponding parameter value when the Root Mean Square Error (RMSE) is minimum is obtained, as shown in table 10.
TABLE 10 parameter calibration values
2) Fleet determination
The calibrated parameters are introduced into the formula 11, and the fleet identification model under the road condition is obtained as follows:
in the formula: h iskIs the critical headway, unit.s;
q0the flow rate of the main channel is unit veh/h;
q1the unit is the branch flow rate, veh/h.
Thus, the motorcades with the equivalent headway time distance between different equivalent sections being the value are different motorcades.
3. Validation of fleet discrimination models
Referring to fig. 15-a, 15-b, 16-a and 16-b, model validation was performed based on actual data of the next day of the survey site. When the effectiveness of the model is verified, the variation trends of the residual value when the flow changes along with the main road and the branch road are discussed respectively by comparing the residual between the actual data and the calculated value of the model.
Referring to fig. 16-a and 16-b, the residual error is decreased with the increase of the main flow rate, and the larger the main flow rate, the more stable the residual error value. The reduction of the residual value is relatively rapid in the range of 0-400veh/h (the number of lanes is two lanes), and after 400veh/h, the reduction speed of the residual value is more and more slow and tends to be a constant value. As can also be seen from fig. 15-a, 15-b, the residual error decreases with increasing bypass flow, but the rate of decrease is slower. Therefore, in general, the residual error is influenced by the main flow rate to a relatively large extent, and is influenced by the branch flow rate to a relatively small extent. Therefore, the effectiveness of the model can be discussed based on the influence of the main-line flow.
Referring to FIG. 17-a, the model results are shown for the curved surface, with black dots representing actual data. The theoretical model analysis shows that the amplitude of the change of the critical headway is larger in the direction of the change of the main road flow, the critical headway is continuously reduced along with the increase of the flow, the change is obvious particularly when the main road flow is 0-500veh/h, and the change is slow and tends to a stable value after the main road flow is 1000 veh/h; in addition, the critical headway is also continuously reduced along with the increase of the branch flow, but the reduction speed is slower.
Referring to fig. 16-a, 17-a and 17-b, the main flow is used as a leading factor for analysis, the actual data are distributed uniformly on the upper side and the lower side of the model, and the model can be distributed in the middle of the actual data remarkably. Through data statistics, 84% of residual values in the total data are (-1.8), and then when the data in the range is selected for verification, the correlation coefficient is 0.72. However, the main road flow is in the range of 0-400veh/h, and the deviation between actual data and theoretical data is larger, because when the main road traffic is smaller, the arrival randomness of the vehicles is larger, the dispersion degree between the vehicles in the fleet is higher, and the influence on theoretical research is larger. But most of the traffic is concentrated in the range after the trunk flow is 400veh/h, the actual data values can be well distributed above and below the curved surface after the trunk flow is 400veh/h, the residual error value is small, about 83% of the actual data values are in the range of (-1.5 to-1.5), the data in the range are selected for verification, the obtained correlation coefficient is 0.76, the critical headway tends to be a stable value along with the reduction of the branch incoming flow and the trunk flow, and the ideal fitting effect can be achieved.
In summary, the optimization method for judging the main motorcade by considering the branch incoming traffic flow comprehensively considers the safety, the high efficiency and the full utilization of space-time resources in the driving process of the motorcade, reasonably optimizes the main motorcade judging technology on one hand, provides theoretical support for improving the urban traffic efficiency, provides theoretical basis for a traffic control system on the other hand, and plays a positive role in the rapid development and construction of cities. Therefore, the method can provide theoretical reference and technical support for effective discrimination of the motorcade, and has a good application prospect.

Claims (1)

1. A method for judging a trunk fleet considering an imported traffic flow is characterized by comprising the following steps of:
1) determining a critical headway:
(1) obtaining equivalent headway
Firstly, regarding a plurality of lanes on a certain road section as an equivalent lane, wherein traffic flow on the road section can be equivalent to a motorcade, then determining an equivalent section on a downstream equivalent lane, and then, the headway time distance measured on the section is the equivalent headway time distance;
(2) determining traffic flow concentration
The traffic flow concentration ratio refers to a measurement value used for representing the relative concentration degree of vehicles in one traffic flow on a road section; after the equivalent headway is acquired, fitting a function which can be obviously expressed as a curve change rule according to the relation between the total average accumulated headway probability and the headway; then, performing primary and secondary derivation on the fitting function to obtain the probability corresponding to the turning point of the curve, namely the traffic flow concentration;
(3) selecting critical headway
Drawing a cumulative headway probability curve chart under different conditions by taking the obtained traffic flow concentration as a standard, wherein the corresponding headway is the critical headway when the cumulative headway probability is the traffic flow concentration;
2) calculating the relationship between the branch flow and the length of the trunk road section and the critical headway:
(1) determining the relationship between branch flow and critical headway
By analyzing the variation trend and the law of the critical headway of each equivalent section along with the branch flow, the critical headway and the branch flow can be represented by a Gaussian function through fitting, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit s;
q1the branch flow is in unit veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(2) determining the relationship between the length of road section and critical headway
a. By analyzing the data obtained by simulation, the influence of the length of the trunk road section on the critical headway has no obvious influence on the change rule and the curve trend, and the main influence is that the extreme point of the curve and the change rate of the curve have obvious changes in different trunk road section lengths;
b. the change of data can obviously show that the critical headway is continuously reduced along with the increase of the length of the road section of the trunk road and obeys a linear relation;
(3) determining the relationship between the branch flow and the road section length of the trunk road and the critical headway
By analyzing the data obtained by simulation, the critical headway time has an obvious functional relationship with the length of the trunk road section and the branch flow; the relation between the critical headway and the branch flow accords with a Gaussian formula, and the relation between the critical headway and the length of the trunk road section accords with a negative correlation, so that the relation between the critical headway and the trunk road section is integrated, the following functional relation is obtained through fitting, and the specific formula is as follows:
hk=i+j*l1+k*exp(-0.5*((q1-m)/n)2) (5)
in the formula: l1Is the length of the road section of the trunk road in the unit of m;
q1the branch flow is in unit veh/h;
i, j, k, m and n are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
3) calculating the relationship between branch flow and the position of the branch and the critical headway:
(1) determining the relationship between branch flow and critical headway
Analyzing the variation trend and the law of the critical headway of each equivalent section along with the branch flow, and fitting to obtain the critical headway and the branch flow which can be expressed by a Gaussian function, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit s;
q1the branch flow is in unit veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(2) determining the relation between the branch position and the critical headway;
a. recording a main road flow of 2100veh/h and a main road section length of 500m as a condition A, and recording a main road flow of 2350veh/h and a main road section length of 300m as a condition B;
b. respectively simulating the two conditions to obtain a critical headway time;
c. analyzing the data obtained by simulation, wherein the branch position and the critical headway are in a negative correlation linear relationship, and the critical headway is continuously reduced along with the increase of the branch position;
(3) determining the relation between branch flow and the position of the branch and the critical headway;
comprehensively considering the relationship among the three, and obtaining the functional relationship among the three through fitting as follows:
hk=o+p*l2+q*exp(-0.5*((q1-r)/s)2) (6)
in the formula:l2is the branch position, unit m;
q1the branch flow is in unit veh/h;
o, p, z, r and s are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
4) calculating the relationship between the branch flow and the main flow and the critical headway:
(1) determining the relationship between branch flow and critical headway
Through fitting, the obtained critical headway and branch flow can be represented by a Gaussian function, namely:
hk=f*exp(-0.5*((q1-g)/h)2) (4)
in the formula: h iskIs the critical headway, unit s;
q1the branch flow is in unit veh/h;
f, g and h are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(2) determining the relationship between the main road flow and the critical headway
The functional relation between the critical headway and the main road flow is obtained through fitting, and the specific formula is as follows:
hk=u*exp(-0.5*((q0-v)/w)2) (7)
in the formula: q. q.s0The flow rate of the main channel is in unit veh/h;
u, v and w are undetermined parameters and can be obtained by calibrating the parameters according to actual data;
(3) determining the relationship between branch flow and main flow and critical headway
Critical headway hkRespectively decreases along with the increase of the main road flow and the branch road influx flow, and the critical headway h is obtained through the fitting analysis of the relationship of the main road flow, the branch road influx flow and the branch road influx flowkThe relationship between the main flow and the branch inflow can be expressed by a gaussian formula, which is as follows:
hk=a1*exp(-0.5*(((q0-b1)/c1)2+((q1-d1)/e1)2)) (8)
in the formula: a is1,b1,c1,d1,e1The undetermined parameters can be obtained by calibrating the parameters according to actual data;
5) establishing a fleet discrimination index model:
(1) calculating the relation between the critical headway and each influence factor
The fleet discrimination model is comprehensively considered and expressed as a functional relation among branch position, trunk road section length, branch flow, trunk flow and critical locomotive time distance, and the specific formula is as follows:
hk=f(l1,l2,q0,q1) (9)
in the formula: h iskIs the critical headway, unit s; l1Is the length of the road section of the trunk road in the unit of m; l2Is the branch position, unit m; q. q.s1The branch flow is in unit veh/h; q. q.s0The flow rate of the trunk line is in unit veh/h;
(2) determination of fleet discrimination model
According to the actual condition of the road, for a specific passing road, the position of the branch road and the length of the trunk road section which are connected with the road are fixed and unchanged, so that the action values of the two influencing factors of the position of the branch road and the length of the trunk road section are indirectly replaced by constants, and the judgment model of the motorcade is the critical headway time hkFlow q of trunk line0And branch flow q1The specific formula of the functional relationship is as follows:
hk=f(q0,q1) (10)
namely:
in the formula: h iskIs the critical headway, unit s;
q0the flow rate of the main channel is in unit veh/h;
q1the branch flow is in unit veh/h;
a, b, c, d and e are undetermined parameters, and are obtained by calibrating the parameters according to actual data;
6) determination of the fleet:
(1) parameter calibration of fleet discrimination model
Calibrating parameters according to actual data of the investigation place; when the parameter calibration is carried out, the minimum Root Mean Square Error (RMSE) of a calculated value and an actual value of the model is taken as a judgment standard to calibrate the parameter, namely when the root mean square error is minimum, the corresponding parameter value is the model parameter value under the condition of the road;
during parameter calibration, MATLAB software is used, and a minimum gradient method is used for carrying out iteration for multiple times, so that a corresponding parameter value when a Root Mean Square Error (RMSE) is minimum is obtained;
(2) fleet determination
Substituting the calibrated parameters into a formulaAnd obtaining a fleet judgment model under the road condition, obtaining the critical headway of the road section, and obtaining the fleet with the parameter value of the equivalent headway between different equivalent sections, wherein the fleet is different fleets.
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