CN109785624A - A kind of space-time analysis method of traffic capacity variation opposite with congestion ratio that studying section - Google Patents
A kind of space-time analysis method of traffic capacity variation opposite with congestion ratio that studying section Download PDFInfo
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Abstract
A kind of method of the climate resourcee variation opposite with congestion ratio for research the intensive traffic section that the present invention establishes, pass through the research method and research achievement of application patent application " a kind of space-time analysis method for studying traffic congestion qualitative change opposite with the traffic capacity " (application No. is 201811172485.7), under the guidance of novel traffic view of time and space, using theorem in Euclid space geometry and Min Shi space geometry as tool, deduce the relationship of the practical climate resourcee variation opposite with traffic congestion in section, for the traffic capacity of Scientific evaluation traffic route, find the control and solution of traffic congestion, provide a kind of new thinking.From application range, the section climate resourcee and congestion analysis that this method is carried out from cavitation angle can be widely applied to all kinds of traffic and transport fields and associated electrical message area, have great application value.
Description
Technical field
The present invention relates to a kind of space-time analysis methods of traffic capacity variation opposite with congestion ratio for studying section, are a kind of knots
Close traditional road Time-Space Occupancy, by patent application " a kind of opposite with the traffic capacity qualitative change of research traffic congestion when
The opposite change of climate resourcee and congestion ratio on channel cross-section is handed in research in empty analytic approach " (application No. is 201811172485.7)
The analysis method and research achievement of change relationship, applied to the intensive traffic section climate resourcee analysis in, establish section climate resourcee with
The opposite variation relation of congestion ratio is applicable in and traffic and transport field and associated electrical message area.
Background technique
A kind of patent application " space-time analysis method for studying traffic congestion qualitative change opposite with the traffic capacity " (patent application
Number be 201811172485.7, hereinafter referred to as macroscopical space-time analysis method) time by research traffic congestion and steric nature, ginseng
The newton view of time and space and space-time view in relativity for examining physics, establish the view of time and space of traffic characteristic, with Min Shi spacetime geometry, fortune
Etc. mathematical tools are raised, are disclosed on traffic cross section with the form of equations in space and time, traffic congestion and the cavitation traffic capacity
Between with respect to variation rule, reflect the macroscopic properties of traffic flow.
It is made of due to road network a section section, research is held in conjunction with traditional analysis macroscopic view road network below
Loading capability Louis horse still Time-Space Occupancy, by a kind of patent application " research traffic congestion variability opposite with the traffic capacity
Climate resourcee is opposite with congestion ratio on research traffic cross section in the space-time analysis method of matter " (application No. is 201811172485.7)
The rule of variation is generalized in the climate resourcee in section and the opposite mutation analysis of congestion.
Summary of the invention
A kind of patent application " space-time analysis method for studying traffic congestion qualitative change opposite with the traffic capacity " (patent application
Number in 201811172485.7), the main points of view of the novel traffic view of time and space of foundation is as follows:
A. time and space are independent of one another, unrelated, and are not influenced by substance or movement；
B. traffic capacity and time and space are all related, and it is opposite variation that value, which is not fixed,.
According to the above novel traffic view of time and space, cavitation road link speed is not fixed and invariable, and opposite variation.
To simplify the analysis, first the friendship passage fragments that port number is certain in section is selected to be analyzed.
The climate resourcee in section is analyzed
A kind of referenced patent application " space-time analysis method for studying traffic congestion qualitative change opposite with the traffic capacity " (patent application
Number for 201811172485.7) on traffic cross section climate resourcee and congestion ratio analysis method, to the climate resourcee in section
Analysis carries out from space and space-time angle respectively, and is assumed the practical climate resourcee of variation.
Theorem in Euclid space analysis
As shown in Figure 1, one section of traffic road is placed in the three-dimensional system of coordinate of European geometry, x-axis, z-axis unit are port number, y
Axis unit is the rice or km of the length International System of Units.Traffic road is longitudinally located on x/y plane, hands over channel cross-section flat positioned at xz
On face.A width can be described with a particle Q (x1, y1, z1) to be x1 lane, be highly that z1 lane, length are
Y1 meters of sections.
When analyzing plane communications and transportation, z1 is fixed as the 3 D stereo coordinate system of European geometry shown in 1, Fig. 1, can convert
For two-dimensional plane coordinate system shown in Fig. 2, channel cross-section is handed over to translate into the traffic road transversal of x-axis direction, traffic road is indulged
To for y-axis direction, wherein x-axis unit is port number, and y-axis unit is the rice or km of the length International System of Units.At this moment, Ke Yiyong
One particle Q (x1, y1) is come to describe a width be x1 lane, length is y1 meters of sections.
Min Shi spatial analysis
Plane the intensive traffic section in theorem in Euclid space shown in Fig. 2 is placed in the three-dimensional system of coordinate of Min Shi space-time and is analyzed, such as Fig. 3 institute
Show,
The setting of Min Shi space-time coordinates is as follows, and x-axis, y-axis and time shaft t axis constitute three reference axis of Min Shi space-time, x-axis
Unit is port number, and y-axis unit is the rice or km of the length International System of Units, and t axis unit is the second of the time International System of Units, divides
Clock or hour.
Section particle Q (x1, y1) is straight line with the world line of time change, if initial time is 0, by
Time is t1, then the maximum climate resourcee of section particle Q (x1, y1, t1) is occupied climate resourcee C1 and section, such as formula
(1) shown in,
(1)。
The deficiency of traditional Time-Space Occupancy
For the Time-Space Occupancy of French Louis horse still when calculating the climate resourcee of road network, one-dimensional model is with effective fortune of road
Space-time total resources of the product of battalion commander's degree and service time as section, two dimensional model is with the Effective Operation area of road and operation
Space-time total resources of the product of time as section.
The analytic process of the Time-Space Occupancy of Louis horse still is described using Min Shi spacetime geometry shown in Fig. 3, such as
Shown in Fig. 4, when analyzing section climate resourcee, the Effective Operation length (area) of shadow representation road in figure is first calculated,
Then it is integrated according to time orientation.This method is disadvantageous in that, when can only obtain the section as shown in formula (1)
Spatial capacity maximum value cannot obtain section climate resourcee relative value corresponding with Congestion Level SPCC.
The practical climate resourcee in section is analyzed
Assuming that section apart from long enough, with the increase of section Congestion Level SPCC, section provide climate resourcee C2 be variation,
As shown in formula (2),
(2)
Wherein, k is road link speed coefficient undetermined, and dimensionless, numerical value is greater than 0, and is less than or equal to 1.
In formula (2), when k is equal to 1, the climate resourcee C2 in section is equal to maximum value C1, exactly Louis horse still
Road link speed in Time-Space Occupancy, i.e. formula (2) become formula (1).
It is assumed that
(3)
In formula (3), k is nondimensional coefficient, and numerical value is between 0 to 1, and the unit of k*x1*t1 is the space * time, and a2 is just
It is represented by the space-time flow by cross section any in the section.
Formula (3) is converted, when t1 is equal to 1, as shown in formula (4),
(4)
In formula (3), a2 is the space-time flow by any cross section in the section, and x1 is the width of cross section, and unit is vehicle
Road number, a kind of referenced patent application " space-time analysis method for studying traffic congestion qualitative change opposite with the traffic capacity " (patent Shen
Please be number for 201811172485.7), at this moment, k is equivalent to the space-time density p on road cross section.
Formula (3) are substituted into formula (2), then shown in the climate resourcee C2 such as formula (5) in section,
(5)
In formula (5), C2 is the climate resourcee in section, and a2 is the space-time flow by any cross section in the section, and y1 is road
The length of section.
Formula (5) illustrates that the calculating of the intensive traffic section climate resourcee can be converted into and hand over the cavitation current energy of channel cross-section
The long product in the road Li Yu calculates, and analytic process is indicated using Min Shi space-time diagram shown in Fig. 3, as shown in figure 5, i.e. formula (4) exists
When analyzing section climate resourcee, the cavitation traffic capacity in shadow representation road cross section in figure is first calculated, then multiplied by section
Longitudinal length.
The calculating of section congestion ratio
Assuming that the cavitation queuing service system of any cross section is all that M/M/s waits queuing service system processed in the intensive traffic section,
Average arrival rate is λ, average service rate μ, and the Poisson process that parameter is λ, each traffic list are obeyed in the arrival of traffic unit
Member service time obey parameter be μ quantum condition entropy, then traffic unit need wait probability (also known as time delays rate,
Or congestion ratio) and the traffic capacity between opposite changing rule, patent application " a kind of research traffic congestion and traffic capacity phase
To the space-time analysis method of qualitative change " the cavitation traffic capacity a of description is gathered around with traffic in (application No. is 201811172485.7)
Plug rate B with respect to variation relation equations in space and time, as shown in formula (6),
(6)
In formula (6), B is traffic congestion rate, and a is the space-time flow by any cross section in the section, and s indicates cross section
The number of track-lines at place, p0Indicate there is no the probability of vehicle in queuing system.
Number of track-lines x1 value in formula (3) and cavitation traffic capacity a2 value are substituted into formula (6), the traffic that can obtain section is gathered around
Plug rate B.
Utilize formula (5) and formula (6), so that it may obtain the opposite variation of the cavitation traffic capacity and congestion ratio in section
Relationship realizes the relativity relationship analysis of road section traffic volume capacity and congestion ratio, and overcoming traditional Road Network Capacity theory cannot be right
The deficiency that road section traffic volume capacity and Congestion Level SPCC are analyzed.
Technical application
If the number of track-lines s in a unidirectional section is equal to 2, link length is 1 km, and transit time is unrestricted, and waits position
Long enough is set, using formula (1), can be obtained in a hour, the maximum climate resourcee C1 in the section, as shown in formula (7),
(7)
In the intensive traffic section, all it is used as M/M/s to wait queuing service system processed the cavitation queuing service system of any cross section
The Poisson process that parameter is λ, Mei Gejiao are obeyed in the arrival of system, average arrival rate λ, average service rate μ, and traffic unit
The service time of logical unit obeys the quantum condition entropy that parameter is μ.
If traffic flow passes through the cavitation capacity a occupied when inspection surface equal to 0.86 in the unit time, formula is utilized
(5), the practical climate resourcee C2 that section can be obtained, as shown in formula (8),
(8)
The number of track-lines of cavitation the capacity a and section that occupy when passing through inspection surface using traffic flow can be obtained 1 hour by formula (6)
It is interior, the traffic congestion rate B in section, as shown in formula (9),
(9)。
Detailed description of the invention
Fig. 1 is the European geometry three dimensional analysis figure in traffic road, and a section is placed on the three-dimensional of European geometry in figure and is sat
In mark system, x-axis, z-axis unit are port number, and y-axis unit is rice or km.Traffic road is longitudinally located on x/y plane, traffic road
Cross section is located in xz plane, particle P (x1, z1) indicate a width be x1 lane, be highly z1 lane traffic road
Cross section, particle Q (x1, y1, z1) indicate that a width is x1 lane, is highly z1 lane, the section that length is y1 meters.
Fig. 2 is the European geometry two-dimension analysis figure in traffic road, and when analyzing plane communications and transportation, z1 is fixed as shown in 1, Fig. 1
The 3 D stereo coordinate system of European geometry can be converted into two-dimensional plane coordinate system shown in Fig. 2, and channel cross-section is handed over to translate into
The traffic road transversal of x-axis direction, the longitudinal direction in traffic road are y-axis direction, and wherein x-axis unit is port number, and y-axis unit is length
Rice or km of the International System of Units etc..At this moment, particle P (x1) indicates that a width is x1 lane traffic road cross section, particle Q
(x1, y1) indicates that a width is x1 lane, length is y1 meters of sections.
Fig. 3 is the three-dimensional space-time analysis chart in traffic road, is to be placed on plane the intensive traffic section in theorem in Euclid space shown in Fig. 2
Gained in the three-dimensional system of coordinate of Min Shi space-time, the setting of Min Shi space-time coordinates is as follows, and x-axis, y-axis and time shaft t axis constitute
Three reference axis of Min Shi space-time, x-axis unit are port number, and y-axis unit is rice or km of the length International System of Units etc., t axis
Unit be the time International System of Units second, minute or hour etc., section particle Q (x1, y1, t) with time change world line
For straight line.
Fig. 4 is the space-time analysis figure that Road Network Capacity is calculated in traditional Time-Space Occupancy, uses Min Shi space-time shown in Fig. 3
Geometry describes climate resourcee calculating process in section in traditional Time-Space Occupancy, first calculates the effective of shadow representation road in figure
The mileage of transport in sevice (area), then multiplied by time span.The setting of Min Shi space-time coordinates is as follows, x-axis, y-axis and time shaft t axis group
At three reference axis of Min Shi space-time, x-axis unit is port number, and y-axis unit is rice or km of the length International System of Units etc.,
T axis unit is second, minute or the hour etc. of the time International System of Units.
Fig. 5 is the space-time analysis figure that novel road link speed calculates, and is described using Min Shi spacetime geometry shown in Fig. 3 new
The section climate resourcee calculating process of type first calculates the road cross section climate resourcee of shadow representation in figure, then multiplied by section
Length.The setting of Min Shi space-time coordinates is as follows, and x-axis, y-axis and time shaft t axis constitute three reference axis of Min Shi space-time, x
Axis unit is port number, and y-axis unit is rice or km of the length International System of Units etc., and t axis unit is the time International System of Units
Second, minute or hour etc..
Claims (3)
1. a kind of space-time analysis method for the traffic capacity variation opposite with congestion ratio for studying section, referenced patent application " grind by one kind
Study carefully the space-time analysis method of traffic congestion qualitative change opposite with the traffic capacity " the research side of (application No. is 201811172485.7)
Method is studied, characterized in that includes:
Step 1: spatial analysis is carried out to section, obtains its space characteristics；
Using theorem in Euclid space method of geometry, one section of road is analyzed, the 3D shape and Simplified two-dimension shape of road are obtained,
In the three-dimensional system of coordinate of theorem in Euclid space geometry, the space hold situation in section is described with a particle Q (x1, y1, z1),
Two reference axis length units of xz plane where middle cross section indicate that road longitudinal direction y-axis is with common international with port number
Length unit indicates (such as rice and km, etc.), as shown in Fig. 1；If it is in planes such as road traffic, water surface transports
In communications and transportation, the z1 coordinate value of road is generally fixed for 1, the 3 D stereo coordinate system of European geometry shown in attached drawing 1, Ke Yizhuan
The mode for turning to two-dimensional plane coordinate system carries out Simplified analysis, and the space hold feelings in section are described with a particle Q (x1, y1)
Condition, as shown in Fig. 2；
Step 2: carrying out space-time analysis to section, obtains its maximum climate resourcee；
Using Min Shi spacetime geometry method, the climate resourcee in section on the above theorem in Euclid space x/y plane is analyzed, with one
Particle Q (x1, y1, t) describes the space-time occupancy situation in section, wherein the length unit of the x-axis of road transverse direction is with port number table
Show, the y-axis of road longitudinal direction is indicated (such as rice and km, etc.) with common meter, time t axis with it is common when
Between unit indicate, as shown in Fig. 3, due to the particle Q in section be it is stationary, particle Q with the time variation world line
It is straight line, in unit time t1, the maximum climate resourcee in section, equal to solid line, dotted line and 3 reference axis in attached drawing 3
The volume size of the cuboid constituted, as shown in formula (1),
(1)；
Step 3: the practical climate resourcee equation in section is found；
It is assumed that section apart from long enough, with the increase of section Congestion Level SPCC, section provide practical climate resourcee C2 be become
Change, as shown in formula (2),
(2)
Wherein, k is road link speed coefficient undetermined, and dimensionless, numerical value is greater than 0, and is less than or equal to 1, when k is equal to 1, road
The climate resourcee C2 of section is equal to maximum value C1,
Then once again, it is assumed that as shown in formula (3),
(3)
In formula (3), since k is nondimensional coefficient, for numerical value between 0 to 1, the unit of k*x1*t1 is the space * time,
Therefore a2 is just represented by the space-time flow by cross section any in the section,
When t1 is small equal to 1, formula (3) carries out being converted into following formula, as shown in formula (4),
(4)
In formula (4), a2 is the space-time flow by any cross section in the section, and x1 is the width of cross section, and unit is vehicle
Road number, a kind of referenced patent application " space-time analysis method for studying traffic congestion qualitative change opposite with the traffic capacity " (patent Shen
Please be number for 201811172485.7), at this moment, k is equivalent to the space-time density p on road cross section；
Formula (3) are substituted into formula (2), then shown in the practical climate resourcee C2 in section such as formula (5),
(5)
Formula (5) illustrates that the calculating of the intensive traffic section climate resourcee can be converted into the cavitation traffic capacity in road cross section and road
Long product calculates, and indicates analytic process using Min Shi space-time diagram shown in Fig. 3, as shown in figure 5, i.e. formula (5) is on analysis road
When section climate resourcee, the cavitation traffic capacity in shadow representation road cross section in figure is first calculated, then multiplied by the longitudinal direction of road
Length；
Step 4: the congestion ratio in section is calculated；
Assuming that the cavitation queuing service system of any cross section is all that M/M/s waits queuing service system processed in the intensive traffic section,
Average arrival rate is λ, average service rate μ, and the Poisson process that parameter is λ, each traffic list are obeyed in the arrival of traffic unit
Member service time obey parameter be μ quantum condition entropy, then traffic unit need wait probability (also known as time delays rate,
Or congestion ratio) and the traffic capacity between opposite changing rule, patent application " a kind of research traffic congestion and traffic capacity phase
To the space-time analysis method of qualitative change " the cavitation traffic capacity a of description is gathered around with traffic in (application No. is 201811172485.7)
Plug rate B with respect to variation relation equations in space and time, as shown in formula (6),
(6)
In formula (6), B is traffic congestion rate, and a is the space-time flow by any cross section in the section, and s indicates cross section
The number of track-lines at place, p0Indicate there is no the probability of vehicle in queuing system,
Number of track-lines x1 value in formula (3) and cavitation traffic capacity a2 value are substituted into formula (6), the traffic congestion rate in section can be obtained
B。
2. analysis method according to claim 1, the accounting equation of the practical climate resourcee in the section of acquisition, characterized in that
In the accounting equation for the practical climate resourcee in section that step 3 obtains, as shown in formula (2), wherein k indicates road link speed coefficient,
Dimensionless, numerical value is greater than 0, and is less than or equal to 1, and the space-time density p being equivalent in section on cross section, formula (2) illustrates, hands over
The practical climate resourcee of forehearth section, equal to the space-time density on cross section in section multiplied by the maximum climate resourcee in the section.
3. analysis method according to claim 1, the accounting equation of the practical climate resourcee in the section of acquisition, characterized in that
In the accounting equation for the practical climate resourcee in section that step 3 obtains, as shown in formula (5), wherein a2 is indicated by the section
The space-time flow of any cross section, y1 are the longitudinal length in section, and formula (5) illustrates, the practical climate resourcee of the intensive traffic section,
Equal to the cavitation traffic capacity in road cross section multiplied by the longitudinal length in section.
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