CN111402600A - Urban road network mechanism association planning method based on complex network sand heap model - Google Patents

Urban road network mechanism association planning method based on complex network sand heap model Download PDF

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CN111402600A
CN111402600A CN202010065089.5A CN202010065089A CN111402600A CN 111402600 A CN111402600 A CN 111402600A CN 202010065089 A CN202010065089 A CN 202010065089A CN 111402600 A CN111402600 A CN 111402600A
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congestion
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CN111402600B (en
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房新力
关永发
程开宇
富强
邬雪松
张振宇
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PowerChina Huadong Engineering Corp Ltd
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/065—Traffic control systems for road vehicles by counting the vehicles in a section of the road or in a parking area, i.e. comparing incoming count with outgoing count
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
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Abstract

The invention discloses an urban road network mechanism association planning method based on a complex network sand heap model. The method provides a sand pile avalanche model in a complex network theory, analyzes the congestion distribution condition of the urban traffic network, helps to know the congestion mechanism between traffic roads, and finds defects in the design and planning process of the urban roads. The method comprises the steps of firstly, establishing an urban road network mechanism association model, considering the traffic dispersion capacity of roads and dynamic factors having correlation effect on congestion, and reasonably considering the factors into the association model through operations such as normalization and the like; by system simulation, an evolution mechanism process of the urban road is simulated, and an evolution propagation process of congestion after the urban road is congested is presented by means of an analysis process of a sand heap model in a complex network theory, so that the rationality of design and planning of the whole urban road network is integrally known, and a scientific basis is provided for further optimization of urban road planning.

Description

Urban road network mechanism association planning method based on complex network sand heap model
Technical Field
The invention relates to the field of traffic planning and design, in particular to an urban road network mechanism association planning method based on a complex network sand heap model.
Background
With the rapid development of society and the acceleration of urbanization process, the scale of urban road networks becomes increasingly large and complex, and the problem of traffic jam becomes more and more serious. Many cities try to solve the problem of traffic congestion by means of new construction, reconstruction, road widening, traffic guidance increase and the like, but the effect is not obvious, and the reason for this is that the design of the urban roads is unreasonable and the planning is lack of scientificity. Therefore, accurate future traffic state prediction has important significance and application value for urban traffic planning and design, and has important scientific significance for improving the overall throughput of a road network and relieving traffic jam degree by designing an efficient and stable dynamic route planning method. The structural characteristics of the road network have important influence on the traffic flow transmission process, so that the deep cognition of the structure of the road network and the disclosure of the internal operation and congestion mechanism of the traffic flow have important theoretical and practical significance for the efficient and reliable traffic guidance strategy in the future.
Disclosure of Invention
The invention aims to analyze the congestion distribution condition of an urban traffic network by combining a sand pile avalanche model in a complex network theory, help to know the congestion action mechanism among traffic roads, and further help to effectively discover the defects in road design in the design and planning process of the urban roads, thereby finally optimizing an efficient urban planning road network or modifying the defects in the existing roads and improving the running efficiency of the urban roads. The technical scheme adopted by the invention is as follows:
the urban road network mechanism association planning method based on the complex network sand heap model is characterized by comprising the following steps of:
step (1): establishing a unidirectional directed network set of an urban road network, wherein the urban road network is abstracted into the unidirectional directed network set:
Figure BDA0002375736340000021
v is a network node set, and the network node represents a traffic intersection set;
step (2): determining the self bearing capacity of each road section in the city according to the actual situation
Figure BDA0002375736340000022
Figure BDA0002375736340000023
Figure BDA0002375736340000024
Figure BDA0002375736340000025
Figure BDA0002375736340000026
Figure BDA0002375736340000027
The factor of influence of the road section i assumed to be congested in the formulas (1) and (2) on the road section connected to the rear side is
Figure BDA0002375736340000028
The influence factor on the left turn and the right turn is
Figure BDA0002375736340000029
And
Figure BDA00023757363400000210
the factor affecting the road section ahead is
Figure BDA00023757363400000211
ni_front,ni_left,ni_right,ni_back∈R+Indicating the front of a congested road i linkNumber of roads into which rows, left rows, right rows and rear converge, R+The system is a positive integer set, and k _ back, k _ left, k _ right and k _ front represent that k _ back roads and k _ left, k _ right and k _ front roads converge in a congested road section i;
in the formula (3), the load-bearing capacity of each road section is ηiThe length of the road i is liThe number of the one-way lanes is piThe number of the roads which are connected with the road i and move forward, left and right is n respectivelyi_front,ni_left,ni_right. The number of roads merging from the rear is ni_backThe duration of the traffic light is
Figure BDA0002375736340000031
In the formulae (4) and (5), lmax,tmax,pmax,
Figure BDA0002375736340000032
The method is characterized by comprising the following steps of representing the longest road length, the longest traffic light duration, the largest one-way lane number and the largest number of roads which are connected in the planned urban road network and are in forward, backward, left and right movement.
And (3): determining dynamic congestion function y of each road sectioni(t)；
Figure BDA0002375736340000033
Figure BDA0002375736340000034
In the formula (6), t is the simulation time step length;
in the formula (7), the first and second groups,
Figure BDA0002375736340000035
the highest speed limit of the congested road i is the average running speed of the vehicles on the road i
Figure BDA0002375736340000036
Current time period Ti(t) compliance with
Figure BDA0002375736340000037
Axis of ordinate, Ti(t) is a normal distribution function of the abscissa axis.
And (4): judgment of yi(t) whether it is greater than a congestion function threshold
Figure BDA0002375736340000038
Setting congestion function thresholds
Figure BDA0002375736340000039
Namely when
Figure BDA00023757363400000310
Considering that the road i is congested;
total daily congestion times m of road ii＝mi+1。
And (5): and establishing a congestion time evaluation function of each road, and evaluating the reasonability of the design of the congestion time evaluation function.
Ti TotalTotal congestion time for road i in one day:
Ti Total＝mi×t(8)；
the congestion time evaluation function of each road is as follows:
Figure BDA00023757363400000311
the following preparation work is carried out before the simulation is carried out:
A) and setting parameters: simulating a time step t; average running speed of vehicle
Figure BDA0002375736340000041
With the current time period Ti(t) to determine expression (7);
B) generating the urban traffic network
Figure BDA0002375736340000042
C) Initializing the urban traffic network
Figure BDA0002375736340000043
The relevant parameters of (2): road length l of each section iiNumber p of unidirectional lanesiThe number n of the roads which are connected with the road i and move forward, left and righti_front,ni_left,ni_rightAnd the number n of roads merging behindi_backTime length of traffic lights
Figure BDA0002375736340000044
Highest speed limit of road i
Figure BDA0002375736340000045
Total daily congestion times m of road ii；
D) Determining influence factors of road sections with rear side connection on each road section i at the starting moment according to expressions (1) and (2)
Figure BDA0002375736340000046
Left-turn and right-turn influence factor
Figure BDA0002375736340000047
And
Figure BDA0002375736340000048
influence factor of road section ahead
Figure BDA0002375736340000049
E) Calculating the bearing capacity η of each road section at the starting moment according to the expression (3)iAnd normalizing the same into the same according to (4) and (5)
Figure BDA00023757363400000410
F) Calculating a congestion function y of each road i at the initial moment according to an expression (6)i(t)；
G) And determining
Figure BDA00023757363400000411
If yes, the road condition at the moment is congestion;
the simulation step circularly carries out the steps D) to G) according to the step length t);
calculating the total congestion times m of the road i in the whole day according to the judgment conditioniAnd calculating the total congestion time T of the road i in one day according to the expressions (8) and (9)i TotalAnd congestion time evaluation function
Figure BDA00023757363400000412
According to the total congestion time T of the road i in one dayi TotalAnd congestion time evaluation function
Figure BDA00023757363400000413
And calculating a result, and evaluating the total congestion condition of the urban road design.
The method is combined with a sand pile avalanche model in a complex network theory, analyzes the congestion distribution condition of the urban traffic network, helps to know the congestion action mechanism among the traffic roads, further helps to effectively discover the defects in the road design in the design and planning process of the urban roads, thereby finally optimizing an efficient urban planning road network or modifying the defects in the existing roads and improving the running efficiency of the urban roads.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides an urban road network mechanism association planning method based on a complex network sand pile model, and provides a method for analyzing the congestion distribution condition of an urban traffic network by combining a sand pile avalanche model in a complex network theory, helping to know the congestion action mechanism among traffic roads, finding lines which are easy to be congested and exist in the design and planning process of the urban roads, and further helping to effectively find defects in the road design in the design and planning process of the urban roads, so that an efficient urban planning road network is optimized finally or the defects in the existing roads are modified, and the operation efficiency of the urban roads is improved. The method comprises the steps of firstly, establishing an urban road network mechanism association model, reasonably considering the traffic dispersion capability of roads and dynamic factors which play a role in correlation to congestion of a certain road section in the process of congestion of urban roads, and reasonably considering the factors into the association model through operations such as normalization and the like; by system simulation, an evolution mechanism process of the urban road is simulated, and by means of an analysis process of a sand heap model in a complex network theory, the congestion evolution process and the congestion propagation process after the urban road is congested are presented, so that the rationality of the design and planning of the whole urban road network is integrally known, and a scientific basis is provided for further optimization of urban road planning. To illustrate the effects of the present invention, the following is a detailed description of the process of the present invention:
1. considering that the actual road lanes are usually bidirectional roads (there are also roads such as unidirectional lanes or tidal lanes), but congestion of a road in one direction usually does not affect the unobstructed condition of a road in another direction (special and few cases such as dotted line turning around are ignored), therefore, the urban road network can be abstracted into a unidirectional directional network set:
Figure BDA0002375736340000051
where V is the set of network nodes (representing traffic ports).
2. Suppose that the road section i with congestion is influenced by the road section connected at the rear side by the factor of
Figure BDA0002375736340000052
The influence factor on the left turn and the right turn is
Figure BDA0002375736340000053
And
Figure BDA0002375736340000054
the influence factor on the road section ahead is
Figure BDA0002375736340000055
The factor indicates the number of vehicles in the rear side vehicles driving into the road section and the number of vehicles in the road section, and the number of vehicles in the rear side vehicles passing through the front intersection makes forward movement, left turn and right turn, so that the vehicles are converged into the connected road. Wherein:
Figure BDA0002375736340000061
Figure BDA0002375736340000062
wherein n isi_front,ni_left,ni_right,ni_back∈R+Indicating the number of roads joining the front, left, right and rear of the congested road i+Is a positive integer set;
3. the bearing capacity of each road section is ηiLength l of the road iiNumber p of unidirectional lanesiAnd the number of the roads (n) connected with the road i, which are going forward, left and righti_front,ni_left,ni_right) And the number n of roads merging behindi_backTime length of traffic lights
Figure BDA0002375736340000063
The condition factors are related to:
Figure BDA0002375736340000064
4. taking into account the length l of the road iiNumber p of unidirectional lanesiAnd the number of the roads (n) connected with the road i, which are going forward, left and righti_front,ni_left,ni_right) And merging at the rearNumber of roads ni_backDuration of traffic lights
Figure BDA0002375736340000065
The isogenic dimensions are different, so the normalization processing is carried out as follows:
Figure BDA0002375736340000066
wherein: lmax,tmax,pmax,
Figure BDA0002375736340000067
The method is characterized by comprising the following steps of representing the longest road length, the longest traffic light duration, the largest one-way lane number and the largest number of roads which are connected in the planned urban road network and are in forward, backward, left and right movement. The load-bearing capacity of each road section can be further expressed as
Figure BDA0002375736340000068
Figure BDA0002375736340000071
5. Dynamic congestion function y of each road sectioni(t) of (d). The function and the self-bearing capacity of the road
Figure BDA0002375736340000072
Average running speed of vehicle
Figure BDA0002375736340000073
Current time period Ti(t), rear road congestion function
Figure BDA0002375736340000074
And forward and left-right steering road congestion function
Figure BDA0002375736340000075
And its influence factor
Figure BDA0002375736340000076
It is related. Then y isi(t) can be expressed as:
Figure BDA0002375736340000077
wherein t is a simulation time step length; n isi_front,ni_left,ni_right,ni_back∈R+Indicating the number of roads into which the front, left, right and rear of the congested road i are connected, R+Is a positive integer set;
Figure BDA0002375736340000078
wherein:
Figure BDA0002375736340000079
is the highest speed limit of the congested road i. Average running speed of vehicle
Figure BDA00023757363400000710
Current time period Ti(t) compliance with
Figure BDA00023757363400000711
Axis of ordinate, Ti(t) is a normal distribution function of the abscissa axis.
6. Setting congestion function thresholds
Figure BDA00023757363400000712
Namely when
Figure BDA00023757363400000713
It is assumed that the road i is congested. At the moment, the total daily congestion times m of the road ii＝mi+1；
7、Ti TotalTotal congestion time for road i in one day: t isi Total＝mi×t(8)
8. The congestion time evaluation function of each road is as follows:
Figure BDA00023757363400000714
the method is combined with a sand pile avalanche model in a complex network theory, analyzes the congestion distribution condition of the urban traffic network, helps to know the congestion action mechanism among the traffic roads, further helps to effectively discover the defects in the road design in the design and planning process of the urban roads, thereby finally optimizing an efficient urban planning road network or modifying the defects in the existing roads and improving the running efficiency of the urban roads.
Before the specific simulation steps are carried out, the following preparation work can be carried out:
1. setting simulation program starting parameters: the simulation time step length t can be selected according to 10 minutes; average running speed of vehicle
Figure BDA0002375736340000081
With the current time period Ti(t) determining an expression (7) as a normal distribution function;
2. generating urban traffic networks
Figure BDA0002375736340000082
Establishing a unidirectional directed network set of an urban road network, wherein the urban road network is abstracted into the unidirectional directed network set:
Figure BDA0002375736340000083
wherein V is a network node set, the network node representing a traffic intersection set;
3. initializing an urban traffic network
Figure BDA0002375736340000084
The relevant parameters of (2): road length l of each section iiNumber of unidirectional lanes piAnd the number of the roads (n) connected with the road i, which are going forward, left and righti_front,ni_left,ni_right) And the number n of roads converged at the reari_backTime length of traffic lights
Figure BDA0002375736340000085
Highest speed limit of road i
Figure BDA0002375736340000086
Total daily congestion times m of road iiEtc.;
4. determining the influence factor of each road section i by the road section connected at the rear side according to the expressions (1) and (2)
Figure BDA0002375736340000087
The influence factor on the left turn and the right turn is
Figure BDA0002375736340000088
And
Figure BDA0002375736340000089
the influence factor on the road section ahead is
Figure BDA00023757363400000810
An equal factor ratio;
5. calculating the bearing capacity η of each road section according to expression (3)iAnd normalizing the same into the same according to (4) and (5)
Figure BDA00023757363400000811
6. The simulation step is carried out according to the step length t in a circulating way: calculating the congestion function y of each road i according to the expression (6) in each circulationi(t) of (d). Because general urban roads are distributed in a network shape, and each road section is a forward road or a rear road of other roads, the congestion condition of any road section is influenced by the traffic condition of the rear road of the road section through the expression (6), and meanwhile, the road condition of the road section can influence other road conditions; by analogy, when a certain road is congested, the congestion can be propagated downwards like 'sand pile avalanche', and further, the reasonability of the planning and design of the road network of the whole city can be reflected under the 'sand pile avalanche' condition.
7. Judgment of
Figure BDA00023757363400000812
8. Calculating the total daily congestion times m of the road i according to the judgment conditioniAnd calculating the total congestion time T of the road i in one day according to the expressions (8) and (9)i TotalAnd congestion time evaluation function
Figure BDA0002375736340000091
According to the total congestion time T of the road i in one dayi TotalAnd congestion time evaluation function
Figure BDA0002375736340000092
And evaluating the total congestion condition of the urban road design according to the calculation result, and performing targeted adjustment (for example, by simulating to find out the total congestion time T of a certain road i)i TotalAnd congestion time evaluation function
Figure BDA0002375736340000093
If the road is larger, the number of lanes, the number of left and right forward connecting roads, the number of rear merging roads and the like of the road section can be planned again, and the bearing capacity is improved ηiAnd further, the improvement of the traffic level of the road section best explains how to adjust), effectively avoids the occurrence of the phenomenon, and further optimizes the parameters implemented in the simulation as the guiding basis for urban road planning design and traffic management.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. The urban road network mechanism association planning method based on the complex network sand heap model is characterized by comprising the following steps of:
step (1): establishing one-way directed network of urban road networkIn aggregate, urban road networks are abstracted into unidirectional directed network sets:
Figure FDA0002375736330000011
wherein V is a network node set, and the network node represents a traffic intersection set;
step (2): determining the self bearing capacity of each road section in the city according to the actual situation
Figure FDA0002375736330000012
And (3): determining dynamic congestion function y of each road sectioni(t)；
And (4): judgment of yi(t) whether it is greater than a congestion function threshold
Figure FDA0002375736330000013
And (5): and establishing a congestion time evaluation function of each road, and evaluating the reasonability of the design of the congestion time evaluation function.
2. The method of claim 1, wherein in step (2)' each road segment has its own load-bearing capacity
Figure FDA0002375736330000014
"described using the following mathematical model:
Figure FDA0002375736330000015
Figure FDA0002375736330000016
Figure FDA0002375736330000017
Figure FDA0002375736330000018
Figure FDA0002375736330000021
wherein, the influence factor of the road section i assumed to be congested in the formulas (1) and (2) by the road section connected at the rear side is
Figure FDA0002375736330000022
The influence factor on the left turn and the right turn is
Figure FDA0002375736330000023
And
Figure FDA0002375736330000024
the influence factor on the road section ahead is
Figure FDA0002375736330000025
ni_front,ni_left,ni_right,ni_back∈R+Indicating the number of roads joining the front, left, right and rear of the congested road i+Is a positive integer set;
in the formula (3), the load-bearing capacity of each road section is ηiThe length of the road i is liThe number of the one-way lanes is piThe number of the roads which are connected with the road i and move forward, left and right is n respectivelyi_front,ni_left,ni_right(ii) a (ii) a (ii) a The number of roads merging from the rear is ni_backThe duration of the traffic light is
Figure FDA0002375736330000026
In the formulae (4) and (5), lmax,tmax,pmax,
Figure FDA0002375736330000027
Indicating the longest road length, longest red in the planned urban road networkThe length of the green light, the maximum number of one-way lanes and the maximum number of roads which are connected in each road and are forward, backward, left and right.
3. The method as claimed in claim 1, wherein in the step (3), "the dynamic congestion function y of each road segmenti(t) "is described using the following mathematical model:
Figure FDA0002375736330000028
Figure FDA0002375736330000029
in the formula (6), t is the simulation time step length;
in the formula (7), the first and second groups,
Figure FDA00023757363300000210
the highest speed limit of the congested road i is the average running speed of the vehicles on the road i
Figure FDA00023757363300000211
Current time period Ti(t) compliance with
Figure FDA00023757363300000212
Axis of ordinate, Ti(t) is a normal distribution function of the abscissa axis.
4. The method of claim 1, wherein y is judged in the step (4)i(t) whether it is greater than a congestion function threshold
Figure FDA0002375736330000031
The specific method of the algorithm is as follows:
setting congestion function thresholds
Figure FDA0002375736330000032
Namely when
Figure FDA0002375736330000033
Considering that the road i is congested;
total daily congestion times m of road ii＝mi+1。
5. The method as claimed in claim 1, wherein the step (5) of establishing the congestion time evaluation function of each road is described by using the following mathematical model: :
Ti Totaltotal congestion time for road i in one day:
Ti Total＝mi×t (8)；
the congestion time evaluation function of each road is as follows:
Figure FDA0002375736330000034
6. the method of claim 1, wherein the traffic conditions of the urban road network are described using a mathematical model described by the following expression:
Figure FDA0002375736330000035
Figure FDA0002375736330000036
Figure FDA0002375736330000037
Figure FDA0002375736330000038
Figure FDA0002375736330000041
Figure FDA0002375736330000042
Figure FDA0002375736330000043
Ti Total＝mi×t (8)
congestion time evaluation function of each road
Figure FDA0002375736330000044
Wherein, the influence factor of the road section i assumed to be congested in the formulas (1) and (2) by the road section connected at the rear side is
Figure FDA0002375736330000045
The influence factor on the left turn and the right turn is
Figure FDA0002375736330000046
And
Figure FDA0002375736330000047
the influence factor on the road section ahead is
Figure FDA0002375736330000048
ni_front,ni_left,ni_right,ni_back∈R+Indicating the number of roads joining the front, left, right and rear of the congested road i+Is a positive integer set;
in the formula (3), the load-bearing capacity of each road section is ηiThe length of the road i is liThe number of the one-way lanes is piThe number of the roads which are connected with the road i and move forward, left and right is n respectivelyi_front,ni_left,ni_right(ii) a The number of roads merging behind isni_backThe duration of the traffic light is
Figure FDA0002375736330000049
In the formulae (4) and (5), lmax,tmax,pmax,
Figure FDA00023757363300000410
Representing the longest road length, the longest traffic light duration, the largest number of one-way lanes and the maximum number of roads which are connected in each road and are used for forward running, backward entering, left running and right running in the planned urban road network;
in the formula (6), t is the simulation time step length;
in the formula (7), the first and second groups,
Figure FDA00023757363300000411
the highest speed limit of the congested road i is the average running speed of the vehicles on the road i
Figure FDA00023757363300000412
Current time period Ti(t) compliance with
Figure FDA00023757363300000413
Axis of ordinate, Ti(t) is a normal distribution function of the abscissa axis;
in the formula (8), Ti TotalThe total congestion time of the road i in one day;
the parameters in the model are optimized through the simulation of the mathematical model of the expressions (1) to (9);
the following preparation work is carried out before the simulation is carried out:
A) and setting parameters: simulating a time step t; average running speed of vehicle
Figure FDA0002375736330000051
With the current time period Ti(t) to determine expression (7);
B) and generate cityCity traffic network
Figure FDA0002375736330000052
C) Initializing the urban traffic network
Figure FDA0002375736330000053
The relevant parameters of (2): road length l of each section iiNumber p of unidirectional lanesiThe number n of the roads which are connected with the road i and move forward, left and righti_front,ni_left,ni_rightAnd the number n of roads merging behindi_backTime length of traffic lights
Figure FDA0002375736330000054
Highest speed limit of road i
Figure FDA0002375736330000055
Total daily congestion times m of road ii；
D) Determining influence factors of road sections with rear side connection on each road section i at the starting moment according to expressions (1) and (2)
Figure FDA0002375736330000056
Left-turn and right-turn influence factor
Figure FDA0002375736330000057
And
Figure FDA0002375736330000058
influence factor of road section ahead
Figure FDA0002375736330000059
E) Calculating the bearing capacity η of each road section at the starting moment according to the expression (3)iAnd normalizing the same into the same according to (4) and (5)
Figure FDA00023757363300000510
F) Calculating a congestion function y of each road i at the initial moment according to an expression (6)i(t)；
G) And determining
Figure FDA00023757363300000511
If yes, the road condition at the moment is congestion;
the simulation step circularly carries out the steps D) to G) according to the step length t);
calculating the total congestion times m of the road i in the whole day according to the judgment conditioniAnd calculating the total congestion time T of the road i in one day according to the expressions (8) and (9)i TotalAnd congestion time evaluation function
Figure FDA00023757363300000512
According to the total congestion time T of the road i in one dayi TotalAnd congestion time evaluation function
Figure FDA00023757363300000513
And (5) calculating a result and evaluating the total congestion condition of the urban road design.
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