CN111932869A - Three-parameter analysis method based on traffic flow particle characteristics - Google Patents
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Abstract
The invention provides a three-parameter analysis method based on traffic flow particle characteristics, which refers to quantum theory methods of Planck and Einstein, and based on the fact that the transmission of traffic flow is carried out, the relation among three parameters of flow, space-time density and speed of the traffic flow on a cross section and the relation among the three parameters of the flow, the time occupancy and the speed are respectively obtained by applying the research results of Chinese patent application ' a space-time analysis method for researching the relative change property of traffic congestion and traffic capacity ' (application number 2018111724857), Chinese patent application ' a space-time analysis method for researching microscopic traffic flow ' (application number 2018112007160) and Newton's mechanics following theory. The verification effect by referring to the authoritative traffic data of the urban main road is good, and the speed-flow curve can well show the change trend of three stages of main road traffic flow. The method can be widely applied to various traffic and transportation fields and related electronic information fields, and has great application value.
Description
Technical Field
The invention provides a three-parameter analysis method based on traffic flow particle characteristics, which is based on a quantum theory method of Planck and Einstein, and based on the particle characteristics of the traffic flow, namely the fact that the traffic flow is transmitted, and provides a novel traffic flow three-parameter analysis method for researching the change relationship among three parameters of traffic flow, density and speed on a cross section by applying the research results of Chinese patent application ' a space-time analysis method for researching the relative change property of traffic congestion and traffic capacity ' (publication No. CN109410569A and application No. 2018111724857) and Chinese patent application ' a space-time analysis method for researching microscopic traffic flow ' (publication No. CN 109147332A and application No. 2018112007160) and Newton's mechanical heeling theory. The invention is suitable for the field of transportation and the field of related electronic information.
Background
The traditional traffic flow three-parameter analysis method is based on the fluctuation characteristics of traffic flow and the fluid mechanics fluctuation theory, and is used for analyzing the traffic flow q and the vehicle speed v of the cross section of a traffic road1And the traffic flow density k, the flow is formed by the space continuous distribution traffic flow wave, the interrelation of the three parameters can be expressed by the formula (1),
the traffic flow q represents the number of vehicles passing through a cross section of a road in unit time, the traffic density k represents the number of vehicles in unit length, and the vehicle speed v represents the distance traveled by the vehicles in unit time.
If a speed-model of the traffic flow at the cross section, such as the speed-density model of greenshiels shown in equation (2), for example, is obtained, as shown in equation (2),
wherein v isfFor smooth speed, kjIs the traffic jam density.
And substituting the speed-density model formula into the formula (1) to obtain a corresponding flow-density model and a corresponding speed-flow model.
In practical application, the time occupancy rate is often used to replace k/kjThe time occupancy is a ratio of time occupied when the vehicle body passes through the detector to total observation time within a certain observation time T.
In the book of urban road mixed traffic flow analysis model and method (hereinafter referred to as book one) compiled by the continental universities of Qinghua university and many people such as the inertia-Asia high-grade engineers of Beijing city public administration, chapter 1 to 12 of the first article are combined with a large amount of actual measurement data of Beijing city road traffic flow, and a traditional traffic flow three-parameter analysis method is applied to analyze speed-flow models of a branch trunk road and a express way. The following was analyzed in conjunction with the case of the book.
The fluid is considered to be in spatial continuous distribution by the fluid mechanics theory, but the fluid mechanics fluctuation theory is applied to the flow, density and speed three-parameter analysis of the traffic flow because the traffic flow is not fluid, under the condition of high-density and low-speed traffic flow, the theory is consistent with the reality, but under the condition of low-density and high-speed traffic flow, the theory has larger deviation with the reality.
Specifically, during speed-flow curve fitting, a situation of speed divergence of theoretical calculation often occurs, as shown by an express way traffic flow curve fitted in fig. 6.1 on page 42 in book, in the three fitted curves in the figure, the free flow speed fitting values are all higher at a low-density and high-speed free flow stage, that is, the speed divergence occurs.
Page one of the book 27 to 30, three-segment mathematical formula is used to fit curves of free flow, steady flow and crowding stage in the speed-flow relation of the urban main road traffic flow, and the curve is difficult to fit by using the fluid mechanics fluctuation theory.
These practical cases show that the fluid mechanics fluctuation theory is applied to analyze the relation among the flow rate, the density and the speed of the traffic flow, and the defects that the low-density and high-speed traffic flow state is difficult to describe exist.
When the technology is applied, the data of the relationship among the flow, the density and the speed of the main road traffic flow combined with the book I are analyzed and verified.
In the history of physics, a case also relates to the problem that a physical theoretical value curve diverges relative to an actual value and is perfectly solved, and the case is a famous ultraviolet disaster problem of black body radiation, namely a scientific Wuyun in recent physics history. Experimental data on black body radiation energy show that the energy radiated by a black body is not continuous, and its distribution in wavelength is related only to the temperature of the black body. Classical physics cannot explain this phenomenon, and the formula established by the german physicist wien based on thermodynamics only fits experimental facts when the wavelength is short and the temperature is low. British physicist Rayleigh, physicist and astronomer King think that energy is a continuously variable physical quantity based on electromagnetic field theory, and establish a blackbody radiation formula which is in accordance with experimental facts when the wavelength is relatively long and the temperature is relatively high. However, it is not possible at all to deduce from the rayleigh-kings formula that the radiation intensity can be increased endlessly as the wavelength becomes shorter in the short wavelength region (ultraviolet region), i.e., the radiation energy dispersion phenomenon, which is different from experimental data by hundreds of thousands of miles. This failure is called the "ultraviolet disaster" by the erfenfiti.
The Planck creatively provides an energy quantum viewpoint, namely, the emission and the absorption of energy by an object are carried out by one part, for radiation with a certain frequency v, the object can only absorb or emit by taking hv as an energy unit, and an improved formula perfectly fits a black body radiation curve.
The Planck's energy quantum viewpoint seriously impacts classical physics, and Einstein also uses a quantization method to establish a light quantum theory and successfully explain the photoelectric effect phenomenon. Further research is carried out by later people, and finally a quantum mechanics theory is established.
Disclosure of Invention
The invention provides a novel traffic flow three-parameter analysis method for researching the relation between traffic flow, density and speed on a cross section by referring to a quantum theory method of Planck and Einstein based on the particle characteristics of traffic flow, namely the transmission of the traffic flow is one part. The specific method comprises the following steps:
the method comprises the following steps: time and space management of traffic road cross section by using space-time analysis method
The chinese patent application "a space-time analysis method for studying the relative change nature of traffic congestion and trafficability" (publication No. CN109410569A, application No. 2018111724857) uses the traditional mathematical tools-european spatial geometry and relativistic mathematical tools-minch spatial geometry, and describes trafficability of traffic channel cross section by a space-time analysis method combining the spatio-temporal method and the queuing theory. If the observation time is 1 hour, the cross section has s lanes, the maximum space-time capacity of the cross section is s channels per 1 hour, namely s channels per hour, and the space-time capacity of each lane is 1 channel per hour.
The temporal and spatial management of the cross section of the traffic road by referring to the spatio-temporal analysis method of the patent is defined as follows, including:
defining 1 time traffic T0: time traffic T0The total time of occupation of s lanes of the traffic cross section by the vehicle during a certain time T is described, expressed by the following equation (3),
wherein, t0iThe length of time spent by the ith vehicle passing through the cross-section.
Defining 2 traffic volume a, describing the proportion of s lanes occupied in the traffic cross section in unit time, as shown in formula (4),
it can be seen that traffic is a dimensionless unit, and the unit in the queuing theory is Ireland. 1 Ireland indicates that one channel is occupied for one hour.
Definition of 3 space-time Density p0Reflecting the proportion of each traffic channel occupied on average per unit time, as represented by the following formula (5),
where a is traffic volume and s is the number of lanes.
Step two: analyzing the consumption duration of the traffic unit based on the particle characteristics and the statistical characteristics
The Chinese patent application 'a space-time analysis method for researching microscopic traffic flow' (publication number CN 109147332A, application number 2018112007160) refers to quantum theory viewpoints of Planck and Einstein, integrates the existing microscopic traffic flow theory, namely Newton mechanics car-following theory, and analyzes the space-time traffic volume occupied by a traffic unit on the cross section, thereby establishing a space-time volume submodel of the traffic unit.
The traffic flow is composed of traffic units, taking the road traffic as an example, the traffic flow is composed of a traffic vehicle, and the consumed time t is determined by referring to the space-time capacity submodel and the Newton mechanics following theory when the traffic flow passes through the cross section0Is one part, and each part time length can be represented by the following formula (6),
wherein, t0Representing the length of time spent by the vehicle passing through the cross-section, r0Indicates the duration of the driver's reaction,/1Is the length of the car body, /)2V is the vehicle speed for the safe distance after parking.
Let us assume that equation (6) is still valid in the statistical case, i.e. r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking, v is the average speed of the vehicle, t0Is represented by r0、l1、l2The elapsed time when v is averaged, it should be noted that t is generally the time t0Is not equal to t0iAverage value of (a). Substituting the formula (6) into the formula (3) to obtain the formula (7),
wherein, T0Representing time traffic, t0iThe length of time spent for the ith vehicle passing through the cross section, t0Represents r in the formula (3)0、l1、l2V is averaged with t0Correspondingly, N represents r in the formula (3)0、l1、l2V, the number of vehicles passing through the cross section in the observation time T, i.e. the traffic flow q, are averaged.
Step three: analyzing the variation relation among the flow, space-time density and speed of traffic flow
The formula (3) and the formula (4) are substituted into the formula (5) to obtain the product,
where ρ is0For space-time density, T denotes the observation duration, T0Representing time traffic, s being the number of lanes, t0Represents r in the formula (3)0、l1、l2V is averaged and N represents the number of vehicles passing through the cross section, i.e. the flow q.
Substituting the formula (6) into the formula (8) to obtain,
in formula (9), ρ0For space-time density, T represents the observation duration, s represents the number of lanes, and N represents the number of vehicles passing through the cross-section, i.e., the flow rate q, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2V is the average safe distance after parking and v is the average vehicle speed.
The formula (9) can be used to calculate the number of vehicles N passing through the cross section, i.e., the flow rate q, i.e.
In the formula (10), q is the traffic flow, i.e., the number of vehicles N passing through the cross section, v is the average speed of the vehicles passing through the cross section, ρ0For space-time density, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking.
Thus, from the perspective of traffic particle characteristics, we obtain formula (10) reflecting the relationship among the three parameters of flow rate, space-time density and speed of the cross-section traffic flow. The formula is the same as the formula (1) in the fluid mechanics fluctuation theory, and can reflect the change relation of flow, density and speed parameters of the cross flow on the cross section.
Step four: analyzing the change relation of three parameters of flow, time occupancy and speed of traffic flow
In formula (9), let
In the formula (11), T represents the observation period, s is the number of lanes, and N represents the number of vehicles passing through the cross section, i.e., the flow rate q, l1Is the average length of the body, v is the average speed of the vehicle, l1And/v represents the average length of time that the vehicle body passes through the cross section.
It can be found from the observation of the formula (11) which represents the ratio of the time taken for the vehicle body to pass through the cross section to the total time of observation, ρ1Indicating time occupancy, i.e. often used as a substitute for k/k as described in the backgroundjTime occupancy parameter of (1).
The formula (11) gives the calculation formula of the number of vehicles N passing through the cross section, i.e., the vehicle flow q, i.e.
In the formula (12), q is the traffic flow, i.e., the number of vehicles N passing through the cross section, v is the average speed of the vehicles passing through the cross section, ρ1Is the time occupancy, in addition, s is the number of lanes, T represents the observation time length, l1Is the average length of the car body.
From the viewpoint of traffic granularity, the formula (12) reflecting the relationship of change between the flow rate, the time occupancy, and the speed of the traffic flow on the cross section is also obtained. The formula can reflect the variation relation of the flow, density and speed parameters of the cross-section flow as well as the formula (1) and the formula (10).
Step five: analyzing the proportional relation between the space-time density and the time occupancy of the traffic flow
The proportional relationship between the space-time density and the time occupancy can be obtained by dividing the formula (9) by the formula (10), that is,
in the formula (13), ρ0Is the space-time density, p1For time occupancy, v is the average speed of the vehicle through the cross section, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking.
Step six: obtaining the speed-density (or time occupancy) change relation of traffic flow
In the study related to traffic capacity, a speed-density formula of the traffic flow on the cross section as shown in formula (2) can be obtained from the observed data, and k/k is replaced by rhojThe latter f () functional form represents, the velocity-density formula is shown as equation (14),
in the formula (14), v represents the average speed of the vehicle passing through the cross section, and ρ represents the space-time density ρ0Or time occupancy ρ1，vfRepresenting the free flow velocity. The f () function may be any one of a linear function, an exponential function, a logarithmic function, and the like.
From the formula (14), the density-speed formula of the traffic flow on the cross section can be obtained, and the inverse function f of f () is used-1() Is shown, i.e.
In the formula (15), ρ represents the space-time density ρ0Or time occupancy ρ1V denotes the average speed of the vehicle through the cross section, vfRepresenting the free flow velocity.
Step seven: analyzing the change relation between the flow and the space-time density of the traffic flow
If ρ = ρ of formula (14)0Substituting the speed-density formula of the formula (14) into the formula (10) can obtain a formula for describing the relation between the traffic flow and the space-time density on the cross section,
in the formula (16), q is a vehicle flow rate, i.e., the number of vehicles N, ρ passing through the cross section0For space-time density, f () is a velocity-space-time density relationship function, and, in addition, vfIs the free flow velocity, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking.
Step eight: analyzing the change relation of the traffic flow and the time occupancy
If ρ = ρ of formula (14)1By substituting the speed-density formula of formula (14) into formula (12), the traffic flow can be described in the cross sectionA formula of flow-time occupancy relationship on the surface;
in the formula (17), q is a traffic flow rate, i.e., the number of vehicles N, ρ passing through the cross section1F () is a speed-time occupancy relation function for time occupancy, and vfFor free flow velocity, s is the number of lanes, T represents the observation duration, l1Is the average length of the car body.
Step nine: analyzing speed-flow variation relation of traffic flow
If ρ = ρ of formula (14)0Substituting the density-speed formula of the formula (15) into the formula (10) can obtain a formula for describing the flow-speed relation of the traffic flow on the cross section under the condition of space-time density,
in the formula (18), q is the flow rate, i.e., the number of vehicles passing through the cross section N, v is the average speed of the vehicles passing through the cross section, f-1() For describing the inverse of the velocity-space-time density relationship, i.e. the space-time density-velocity relationship, and, in addition, vfIs the free flow velocity, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking.
If ρ = ρ of formula (14)1Substituting the density-speed formula of the formula (15) into the formula (12) can obtain a formula describing the flow-speed relation of the traffic flow on the cross section under the condition of time occupancy,
formula (19) Where q is the flow rate, i.e. the number of vehicles N passing through the cross-section, v is the average speed of the vehicles passing through the cross-section, f-1() For describing the inverse of the velocity-space-time density relationship, i.e. the time occupancy-velocity relationship, and, in addition, vfFor free flow velocity, s is the number of lanes, T represents the observation duration, l1Is the average length of the car body.
In summary, the present invention provides a novel traffic flow three-parameter analysis method based on the particle characteristics of traffic flow by referring to the quantum theory viewpoint of planck and einstein, based on the fact that traffic flow is a share of transmission, referring to the research results of the chinese patent application "a space-time analysis method for studying microscopic traffic flow" (publication No. CN 109147332a, application No. 2018112007160) and the chinese patent application "a space-time analysis method for studying the relative change property of traffic congestion and traffic capacity" (publication No. CN109410569A, application No. 2018111724857), applying newton mechanics following theory, and based on the particle characteristics of traffic flow, which can describe the relationship among traffic flow, density and speed on the cross section, and the specific research results include:
obtaining a new formula (10) describing the relationship among the flow, the space-time density and the speed of the cross-section flow, and respectively obtaining a formula (16) describing the relationship between the flow and the space-time density and a formula (18) describing the relationship between the flow and the speed by using a formula (14) and a formula (15) describing the relationship between the speed and the space-time density;
obtaining a new formula (12) describing the flow, time occupancy and speed correlation of the cross-section flow, and obtaining a formula (17) describing the flow-time occupancy relation and a formula (19) describing the flow-speed relation by using a formula (14) and a formula (15) describing the speed and space-time density relation respectively;
equation (13) describing the space-time density versus time occupancy ratio is obtained.
Technical application
In contents of 38 to 40 pages of a book of 'urban road mixed traffic flow analysis model and method' (hereinafter, referred to as book one) written by the university of Qinghua and many people such as the inertia Asia and high-grade engineers in Beijing public administration of China, original data scatter diagrams reflecting three parameter relationships of urban main road flow density are provided, namely a speed-density relationship scatter diagram, a flow-density relationship scatter diagram and a speed-flow relationship scatter diagram, wherein a curve of the speed-flow relationship scatter diagram of 39 pages is similar to a speed-flow relationship scatter diagram of a bidirectional 2-lane of 27 pages, and an author uses three sections of mathematical functions to respectively fit curves of traffic flow in three stages, namely a free flow stage, a stable flow stage, a congestion stage and a dissipation stage on 27 pages.
Since the inventors have no raw data, fitting an actual curve is difficult. Only a few data can be assumed to obtain the trend of the curve.
Assuming that the average reaction time of the driver is 1 second, the average vehicle length is 5 meters, and the average safe distance after parking is 2 meters.
(1) Calculating the maximum value of the time occupancy:
space-time density ρ as the average velocity over the cross-section approaches 00The time occupancy ρ is obtained by referring to the formula (13) toward 11Maximum of, i.e.
Thus, in the velocity-density scattergram shown in FIG. 5.5 of page 38 of the book, the vertical axis is an index of time occupancy which is 100 times the original value, the horizontal axis is velocity in km/h, and the free flow velocity v isfEqual to 80 km/h;
(2) speed-time occupancy formula and fitting curve of urban main road
For the velocity-time occupancy scatterplot shown in FIG. 5.5 of page 38 of the book, the present invention uses a conventional May velocity-density model for fitting to obtain the following velocity-time occupancy calculation formula, i.e.
The unit of the velocity v in the formula (21) is kilometer per hour, and the time occupancy is between 0 and 0.71.
Accordingly, the formula of time occupancy rate-speed can be obtained from the formula (21),
the time occupancy-speed graph corresponding to equation (22) is shown in fig. 1.
(3) Flow-time occupancy calculation formula and fitting curve of urban main road
Under the condition that the number of lanes s is 1 and the observation time is 1 hour, the flow-time occupancy calculation formula when the number of unidirectional lanes s is 1, namely the flow-time occupancy calculation formula when the unit kilometer and hour is converted into meter and second simultaneously by utilizing the formula (17) for describing the flow-time occupancy relation
The graph of the flow rate-time occupancy corresponding to the formula (23) is shown in fig. 2, and the curve shows that the variation of the fitted flow rate curve is consistent with the fluctuation trend of the corresponding scatter diagram at the low density stage and the high density stage.
(4) Speed-flow formula and fitting curve of urban main road
Under the condition that the number of lanes s is 1 and the observation time is 1 hour, the flow-speed formula of the traffic flow, namely the traffic flow is obtained by utilizing the formula (19) for describing the flow-speed relation under the condition of time occupancy of the invention and converting the unit kilometer and hour into meter and second
The velocity-flow curve corresponding to equation (23) is shown in fig. 3.
Compared with the curve of the speed-flow relation scatter diagram on page 39 and the speed-flow relation scatter diagram on the bidirectional 2-lane on page 27, the speed-flow relation curve fitted in the graph 3 not only has no speed divergence of a hydrodynamics fluctuation theory, but also perfectly presents the trend of the traffic flow changing in three stages of a free flow stage, a stable flow stage, a crowding stage and a dissipation stage, and truly reflects the rule of the traffic flow change of the urban main road.
The success of speed-flow curve fitting proves that the new method based on the particle characteristics of the traffic flow can better analyze the relation among three parameters of flow, density and speed of the traffic flow than the fluid mechanics fluctuation theory.
Drawings
Fig. 1 is a time occupancy-speed curve graph according to the formula (22), which corresponds to fig. 5.5 on page 38 of "urban road mixed traffic flow analysis model and method" written by the university of qinghua and university general teaching in continental china and many people such as the super engineers in the inertia and asia of the beijing city public security bureau, that is, a speed-density relation scatter diagram of an urban main road.
Fig. 2 is a flow-time occupancy curve diagram plotted according to the formula (23), which corresponds to fig. 5.6 on page 39 of "urban road mixed traffic flow analysis model and method" written by the university of qinghua and university general education and many people such as the super engineer in the inertia and asia of the beijing city public security bureau, that is, a flow-density relation scatter diagram of an urban main road. The fitted flow-density relationship curve in fig. 2 is consistent with the fluctuation trend of the corresponding scatter plot at both low-density and high-density stages.
Fig. 3 is a speed-flow curve diagram according to the formula (24), which corresponds to fig. 5.7 on page 39 of "urban road mixed traffic flow analysis model and method" written by the university of qinghua and university general education and many people such as the third engineer in the inertia and asia of the beijing city public security bureau, i.e., a speed-flow relation scatter diagram of an urban main road. The fitted speed-flow relation curve in fig. 3 not only does not have the speed divergence of the hydrodynamics fluctuation theory, but also perfectly presents the trend of the traffic flow changing in three stages of a free flow stage, a steady flow stage, a crowding stage and a dissipation stage, and truly reflects the rule of the traffic flow change of the urban main road.
Claims (5)
1. A three-parameter analysis method based on the particle characteristics of traffic flow refers to the quantum theory method of Planck and Einstein, and based on the fact that the traffic flow is transmitted in one part, a novel traffic flow three-parameter analysis method is provided by applying the research results of Chinese patent application ' a space-time analysis method for researching the relative change property of traffic congestion and traffic capacity ' (publication No. CN109410569A, application No. 2018111724857) and Chinese patent application ' a space-time analysis method for researching microscopic traffic flow ' (publication No. CN 109147332A, application No. 2018112007160) and Newton's mechanics following theory, and is characterized by comprising the following steps of:
the method comprises the following steps: time and space management of traffic road cross section by using space-time analysis method
The chinese patent application "a space-time analysis method for studying the relative change property of traffic congestion and traffic capacity" (publication No. CN109410569A, application No. 2018111724857) describes the traffic capacity of a traffic channel cross section by a space-time analysis method fusing physical time, space and queuing theory, and defines the traffic volumes such as time traffic volume, space-time density and the like and corresponding calculation methods thereof by referring to the management mode of the space-time analysis method of the patent on the time and space of the traffic road cross section, that is,
defining 1 time traffic T0: time traffic T0The total time of occupation of s lanes of a traffic cross section by a vehicle within a certain time T is described, and is expressed by the following formula (1),
wherein, t0iThe time length consumed when the ith vehicle passes through the cross section;
defining 2 traffic volume a, describing the proportion of s lanes occupied in the traffic cross section in unit time, as shown in formula (2),
it can be seen that the traffic volume is a dimensionless unit, the unit in the queuing theory is ireland, and 1 ireland means that one channel is occupied for one hour;
definition of 3 space-time Density p0Reflecting the proportion of each traffic channel occupied on average per unit time, as represented by the following formula (3),
wherein a is traffic volume and s is the number of lanes;
step two: analyzing the consumption duration of traffic units on the cross section based on the particle and statistical characteristics of the traffic flow
Referring to the quantum theory viewpoint of Planck and Einstein, namely that the emission and absorption of energy by an object are carried out by one part, the particle characteristics of the traffic flow are analyzed by combining the actual situation of the traffic flow, taking the road traffic as an example, the traffic flow is composed of one traffic vehicle, and when the traffic flow passes through the cross section, the consumed time t is long0Is one part, and referring to Newton's mechanics following theory, the duration of each part can be expressed by the following formula (4),
wherein, t0Representing the length of time spent by the vehicle passing through the cross-section, r0Indicates the duration of the driver's reaction,/1Is the length of the car body, /)2V is the safe distance after parking, and v is the vehicle speed;
the traffic flow also has statistical characteristicsUsing t0Represents r in the formula (4)0、l1、l2And v are averaged to obtain the time consumption duration of the traffic unit, and the time traffic T can be obtained by the formula (4)0Is calculated by the formula (i)
Wherein, T0Representing time traffic, t0iThe length of time spent for the ith vehicle passing through the cross section, t0Represents r in the formula (4)0、l1、l2V is averaged, and N represents r in the formula (4)0、l1、l2V is the number of vehicles passing through the cross section within the observation time T when the average value is obtained, namely the vehicle flow q;
step three: analyzing the variation relation among the flow, space-time density and speed of traffic flow
And analyzing the flow q and the space-time density rho of the traffic flow by combining the traffic volume such as the time traffic volume, the traffic volume, the space-time density and the like of the cross section of the traffic channel defined in the step one and a consumption time calculation formula of traffic units on the cross section obtained on the basis of the particle characteristics and the statistical characteristics of the traffic flow in the step two0The variation relation between the three parameters of the speed v can be obtained,
in the formula (6), ρ0For space-time density, T represents the observation duration, s represents the number of lanes, and N represents the number of vehicles passing through the cross-section, i.e., the flow rate q, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2The average safe distance after parking is shown, and v is the average speed of the vehicle;
from the formula (6), the calculation formula of the number of vehicles N passing through the cross section, i.e., the vehicle flow q, can be obtained, i.e.
In the formula (7), q is the traffic flow, i.e. the number of vehicles N passing through the cross section, v is the average speed of the vehicles passing through the cross section, ρ0For space-time density, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2The average safe distance after parking;
thus, from the perspective of traffic particle performance and statistics, a formula (7) reflecting the variation relationship among three parameters of flow rate, space-time density and speed of the traffic flow on the cross section is obtained;
step four: analyzing the change relation of three parameters of flow, time occupancy and speed of traffic flow
In the formula (6) of the third step, let
Another formula for calculating the number of vehicles N passing through the cross section, i.e. the flow rate q, can be obtained, i.e.
In the formula (9), q is the traffic flow, i.e., the number of vehicles N passing through the cross section, v is the average speed of the vehicles passing through the cross section, ρ1Is the time occupancy, in addition, s is the number of lanes, T represents the observation time length, l1Is the average length of the car body;
thus, from the viewpoint of traffic particle characteristics and statistics, the flow rate q and the time occupancy ρ reflecting the traffic flow on the cross section are obtained1And the speed v is in a variable relation of a formula (9);
step five: analyzing the proportional relation between the space-time density and the time occupancy of the traffic flow
The space-time density ρ is obtained by dividing equation (7) by equation (9)0And time occupancy ratio rho1The ratio of (a) to (b), i.e.,
in the formula (10), ρ0Is the space-time density, p1For time occupancy, v is the average speed of the vehicle through the cross section, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2The average safe distance after parking;
step six: obtaining the speed-density (or time occupancy) change relation of traffic flow
Replacing k/k by ρ with reference to the velocity-density equation in the traffic capacity correlation studyjThe latter f () functional form represents, the velocity-density formula is shown as equation (11),
in the formula (11), v represents the average speed of the vehicle passing through the cross section, and ρ represents the space-time density ρ0Or time occupancy ρ1，vfThe function f () can be any one of linear function, exponential function, logarithmic function, etc.;
from the formula (11), the density-speed formula of the traffic flow on the cross section can be obtained, and the inverse function f of f () is used-1() Is shown, i.e.
In the formula (12), ρ represents the space-time density ρ0Or time occupancy ρ1V denotes the average speed of the vehicle through the cross section, vfRepresenting the free flow velocity;
step seven: analyzing the change relation between the flow and the space-time density of the traffic flow
If ρ = ρ of velocity-density equation (11)0Substituting equation (11) into equation (7) yields equation (13) describing the traffic flow-space-time density relationship over a cross section, i.e., equation (11) is
In the formula (13), q is a vehicle flow rate, i.e., the number of vehicles N, ρ passing through the cross section0For space-time density, f () is a velocity-space-time density relationship function, and, in addition, vfIs the free flow velocity, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2The average safe distance after parking;
step eight: analyzing the change relation of the traffic flow and the time occupancy
If ρ = ρ of velocity-density equation (11)1Substituting equation (11) into equation (9) can give equation (14) describing the traffic flow-time occupancy relationship on the cross section, that is
In the formula (14), q is a traffic flow rate, i.e., the number of vehicles N, ρ passing through the cross section1F () is a speed-time occupancy relation function for time occupancy, and vfFor free flow velocity, s is the number of lanes, T represents the observation duration, l1Is the average length of the car body;
step nine: analyzing speed-flow variation relation of traffic flow
If ρ = ρ of the density-velocity equation (12)0Substituting equation (12) into equation (7) yields equation (15) describing the flow-velocity relationship of traffic flow over a cross-section, i.e.
In the formula (15), q is the flow rate, i.e., the number of vehicles passing through the cross section N, v is the average speed of the vehicles passing through the cross section, f-1() For describing the inverse of the velocity-space-time density relationship, i.e. the space-time density-velocity relationship, and, in addition, vfIs the free flow velocity, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2The average safe distance after parking;
if ρ = ρ of the density-velocity equation (12)1Substituting equation (12) into equation (9) yields equation (16) describing the flow-velocity relationship of traffic flow over a cross-section, i.e.
In the formula (16), q is the flow rate, i.e., the number of vehicles passing through the cross section N, v is the average speed of the vehicles passing through the cross section, f-1() For describing the inverse of the velocity-space-time density relationship, i.e. the time occupancy-velocity relationship, and, in addition, vfFor free flow velocity, s is the number of lanes, T represents the observation duration, l1Is the average length of the car body.
2. The analysis method according to claim 1, wherein the time traffic calculation method comprises obtaining the total time consumed by the traffic flow on the cross section, i.e. the time traffic T, based on the particle and statistical characteristics of the traffic flow in the step two0Is shown in formula (5), wherein T0Representing time traffic, t0iThe length of time spent for the ith vehicle passing through the cross section, t0Representing the driver reaction time period r in equation (4)0Length l of vehicle body1Safety distance after parking2The vehicle speed v is leveled offConsumption time at mean value, N represents the driver reaction time r in equation (4)0Length l of vehicle body1Safety distance after parking2The number of vehicles passing through the cross section within the observation time T, i.e., the vehicle flow q, when the vehicle speed v is averaged.
3. The analysis method according to claim 1, wherein a calculation formula reflecting the relationship among the three parameters of the flow rate, the space-time density and the velocity of the cross-sectional flow is obtained, wherein the calculation formula is represented by formula (7), wherein q is the flow rate of the vehicle, i.e., the number of vehicles passing through the cross-sectional area N, v is the average velocity of the vehicle passing through the cross-sectional area p0For space-time density, s is the number of lanes, T represents the observation duration, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking.
4. The analysis method according to claim 1, wherein a calculation formula reflecting the relationship among the three parameters of the flow rate, the time occupancy and the speed of the cross-sectional flow is obtained, wherein the calculation formula is represented by formula (9), wherein q is the flow rate of the vehicle, i.e., the number of vehicles passing through the cross-sectional area, N, v is the average speed of the vehicle passing through the cross-sectional area, p1Is a time occupancy, s is a number of lanes, T represents an observation time period, l1Is the average length of the car body.
5. The analysis method according to claim 1, wherein a calculation formula reflecting the relation between the space-time density and the time occupancy of the cross-sectional flow is obtained, wherein the calculation formula is represented by formula (10), wherein ρ0Is the space-time density, p1For time occupancy, v is the average speed of the vehicle through the cross section, r0Indicating the average driver reaction duration,/1Is the average length of the car body, /)2Is the average safe distance after parking.
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