CN116523345A - Urban road topology network connectivity evaluation method - Google Patents
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Abstract
The invention discloses an urban road topology network connectivity evaluation method, which comprises the following steps: s1: abstracting the urban road network into a directed graph G; s2: computing node v i And v j The number of communication paths between the nodes and the reachability a between any nodes are determined ij The method comprises the steps of carrying out a first treatment on the surface of the S3: according to the reachability a in step S2 ij Constructing a reachability matrix A of the directed graph G; s4: calculating two nodes v i And v j The total length of each communication path between the two paths is introduced with a steering coefficient q ikj To describe the steering condition of the intersection, and to determine two cases when the steering of the intersection is limitedShortest path l between nodes ij The method comprises the steps of carrying out a first treatment on the surface of the S5: according to the number of the road sections passing by the shortest path, calculating a node v i And v j Shortest distance d between ij The method comprises the steps of carrying out a first treatment on the surface of the S6: through the accessibility a among all nodes ij And shortest distance d ij Computing node v i Degree of connectivity k i The method comprises the steps of carrying out a first treatment on the surface of the S7: through the connectivity k to each node i Accumulating to calculate the connectivity Con of the urban road network A . The method is suitable for evaluating the lane-level connectivity of the road networks in different forms, and reflects the actual reachable degree of the urban road network more in a fitting way.
Description
Technical Field
The invention relates to the technical field of urban traffic management and control, in particular to an urban road topology network connectivity evaluation method.
Background
Along with the acceleration of the urban process in China, the cities are continuously expanded, the urban road network becomes larger and more complex, the problem of urban traffic jam is also more serious, and the problem of traffic jam is more prominent in large-scale cities in China. Traffic jam characteristics vary from city to city, but one of the important reasons is that the road network connectivity is inadequate. The phenomena of 'dislocation intersection', 'right in and right out intersection', 'forbidden left turn and right turn', and the like cause the reduction of the connectivity of a road network, so that the traffic problems of 'concentrated traffic of a few trunk roads, insufficient utilization of other roads', and the like are highlighted, and the traffic jam of main trunk roads and nodes is aggravated.
The road network connectivity is used for evaluating the connection strength between road sections, and the road network connectivity is used as a road network operation evaluation index, so that the connection condition of the road network can be intuitively reflected, and the operation current situation of the whole road network can be evaluated. At present, related researches on urban road network connectivity in China are few, and the related researches are generally reflected by a connectivity index, namely the ratio of the sum of the line segments connected by each network node to the number of the whole network node. Although the connectivity index may reflect the connectivity of the urban road network to some extent, lane-level road network connectivity cannot be described, such as road left-hand prohibition, head-drop prohibition, etc. The road network connectivity is evaluated by establishing road network connectivity indexes, which mainly can be classified into alpha indexes, beta indexes, gamma indexes and the like, but the indexes describe the road network connectivity from the connection number of nodes and road sections, only the condition that four entrance roads of a road network intersection are fully communicated can be evaluated, and the road network connectivity condition when the lane direction in the intersection is limited (such as the left turn and right turn of a road is forbidden) can not be described. At present, more methods for evaluating the connectivity of the road network exist, but the connectivity of the road network is basically evaluated from the condition of full connectivity of an intersection, and the condition of the road network connectivity when the lane direction is limited is not considered.
Disclosure of Invention
Aiming at the defects of the prior art, the technical problem to be solved by the application is how to provide an urban road topology network connectivity evaluation method which is applicable to various crossing conditions and is fit with the actual road conditions of the city.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for evaluating the connectivity of an urban road topology network comprises the following steps: s1: abstracting the urban road network into a directed graph G; s2: calculating v of any two intersections as nodes i And v j Degree of accessibility a between ij The method comprises the steps of carrying out a first treatment on the surface of the S3: according to the reachability a in step S2 ij Constructing a reachability matrix A; s4: calculating two nodes v i And v j The total length of each path between them, introducing steering coefficient q ikj Describing the steering condition of the intersection, and obtaining the shortest path l between two nodes when the steering of the intersection is limited ij The method comprises the steps of carrying out a first treatment on the surface of the S5: according to the number of the road sections passing by the shortest path, calculating a node v i And v j Shortest distance d between ij The method comprises the steps of carrying out a first treatment on the surface of the S6: computing node v i Degree of connectivity k i : through the accessibility a among all nodes ij Shortest distance d between nodes ij Constructing single node connectivity k i Is calculated according to the formula; s7: the connectivity of each node is calculated through the steps, and the connectivity of each node is accumulated, so that the connectivity Con of the urban road network is calculated A 。
As an optimization, when the urban road network is abstracted into the directed graph in step S1, the intersections in the urban road network are regarded as nodes, and the road segments are regarded as edges, the urban road network can be abstracted into a simplified network graph, and the network graph is composed of a limited set of "nodes" V and a set of "edges" E, denoted by G, i.e. the network can be denoted as G (V, E)) The method comprises the steps of carrying out a first treatment on the surface of the In the network, the intersection is regarded as a node, v= { V 1 ,v 2 ,v 3 ,v 4 ,...,v n -is a set of intersection nodes; the road sections between adjacent intersections in the road network are edges connecting all nodes. E= { E 1 ,e 2 ,e 3 ,...,e n And is a collection of edges.
As an optimization, in step S2, the reachability a between nodes ij Representing node v i And v j The degree of connectivity, i.e., the number of paths connecting between two nodes; node v is considered to be a network node when there is at least 1 path connection between two nodes i To node v j Is communicated with, wherein the number of the communicating paths is a ij ，a ij 1 or more; if there is no path connection between two nodes, node v i To node v j Is not communicated with, a ij ＝0。
As an optimization, when the reachability matrix a is constructed in step S3, the method includes the following steps:
a1: the reachability adjacency matrix comprises reachability among all nodes of the whole road network;
a2: reachability adjacency matrix a is an n x n two-dimensional matrix. In the matrix, a ij Is an element of row i and column j in the matrix, representing node v i To node v j Is the degree of reachability of (a);
as optimization, in step S4, a distance weight coefficient Z is introduced into the initial road network directed graphTo express the length of the edge between two adjacent nodes, then G (V, E) to G (V, E, Z); when z ij ＝z ji > 0, then the edge is clearState, representing node v i And node v j Communicating; when z ij ＞0,z ji = infinity, representing a slave node v i Leading to node v j But not from node v j Leading to node v i The method comprises the steps of carrying out a first treatment on the surface of the When z ji ＞0,z ij = infinity, representing a slave node v j Leading to node v i Cannot be from node v i Leading to node v j The method comprises the steps of carrying out a first treatment on the surface of the When z ij ＝z ji = infinity, representing node v i To node v j Edges not directly connected;
as an optimization, the steering coefficient q is in step S4 ikj To describe steering behaviour between intersections, to describe the direction of travel v i →v k →v j Is a steering lane condition; q ik ＝q kj =1 to describe the steering of the first two nodes and the last two nodes; when q ikj =1, then the lane direction can pass normally; when q ikj And = ≡, the traffic is prohibited for that direction lane.
As an optimization, in step S4, l ij Is node v i To node v j The operation process of the shortest path of the path is as follows: at node v i To node v j And (3) respectively adding the lengths of edges between adjacent nodes communicated in each path, comparing the total length of each path between two nodes, and selecting the path with the shortest total length as the shortest path. Calculation of l ij Is calculated by the following formula:
wherein l ij For node v i To node v j Is the shortest path in (a); q ikj For node v i Through node v k Reach node v j Steering coefficient of (2); z ikj For node v i And node v j The length of the edges, i.e. node v i Through node v k Reach node v j The length of the edge.
As an optimization, the stepsS5, determining a node v i To node v j After the shortest path of (2), calculating the number of the sections passed by the shortest path to obtain a node v i To node v j D of the shortest distance of (2) ij . When l ij Not equal to infinity, d ij 1 or more, representing the shortest path l ij Distance d of (2) ij 。
As an optimization, in step S6, the connectivity k i For node v i Reachability a with other nodes ij And node v i Shortest distance d to other nodes ij The index can reflect the self connectivity condition of each node in the road network; is calculated by the following calculation formula:
as an optimization, in step S7, the road network connectivity Con A Calculating the independent connectivity of each node in the road network, and accumulating the connectivity of each node in the road network to obtain the connectivity of the road network; the calculation formula is as follows:
in summary, the invention has the beneficial effects of being applicable to various intersection conditions and fitting with the actual road conditions of cities.
Drawings
Fig. 1 is a flow chart of a method for evaluating the connectivity of an urban road topology network according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings. In the description of the present invention, it should be understood that the azimuth or positional relationship indicated by the azimuth words such as "upper, lower" and "top, bottom", etc. are generally based on the azimuth or positional relationship shown in the drawings, and are merely for convenience of description and simplification of the description, and these azimuth words do not indicate or imply that the apparatus or element to be referred to must have a specific azimuth or be constructed and operated in a specific azimuth, without limiting the scope of protection of the present invention; the orientation word "inner and outer" refers to inner and outer relative to the contour of the respective component itself.
As shown in fig. 1, a method for evaluating the connectivity of an urban road topology network comprises the following steps: s1: abstracting the urban road network into a directed graph G; s2: calculating v of any two intersections as nodes i And v j Degree of accessibility a between ij The method comprises the steps of carrying out a first treatment on the surface of the S3: according to the reachability a in step S2 ij Constructing a reachability matrix A; s4: calculating two nodes v i And v j The total length of each path between them, introducing steering coefficient q ikj Describing the steering condition of the intersection, and obtaining the shortest path l between two nodes when the steering of the intersection is limited ij The method comprises the steps of carrying out a first treatment on the surface of the S5: according to the number of the road sections passing by the shortest path, calculating a node v i And v j Shortest distance d between ij The method comprises the steps of carrying out a first treatment on the surface of the S6: computing node v i Degree of connectivity k i : through the accessibility a among all nodes ij Shortest distance d between nodes ij Constructing single node connectivity k i Is calculated according to the formula; s7: the connectivity of each node is calculated through the steps, and the connectivity of each node is accumulated, so that the connectivity Con of the urban road network is calculated A 。
In this embodiment, when the urban road network is abstracted into the directed graph in step S1, the intersections in the urban road network are regarded as nodes, and the road segments are regarded as edges, so that the urban road network can be abstracted into a simplified network graph, and the network graph is composed of a limited set V of "nodes" and a set E of "edges", denoted by G, i.e., the network can be denoted as G (V, E); in the network, the intersection is regarded as a node, v= { V 1 ,v 2 ,v 3 ,v 4 ,...,v n -is a set of intersection nodes; the road sections between adjacent intersections in the road network are edges connecting all nodes. E= { E 1 ,e 2 ,e 3 ,...,e n And is a collection of edges.
In the embodiment, in step S2, the nodeReachability a between points ij Representing node v i And v j The degree of connectivity, i.e., the number of paths connecting between two nodes; node v is considered to be a network node when there is at least 1 path connection between two nodes i To node v j Is communicated with, wherein the number of the communicating paths is a ij ，a ij 1 or more; if there is no path connection between two nodes, node v i To node v j Is not communicated with, a ij ＝0。
In this embodiment, when the reachability matrix a is constructed in step S3, the method includes the following steps:
a1: the reachability adjacency matrix comprises reachability among all nodes of the whole road network;
a2: reachability adjacency matrix a is an n x n two-dimensional matrix. In the matrix, a ij Is an element of row i and column j in the matrix, representing node v i To node v j Is the degree of reachability of (a);
in this embodiment, in step S4, a distance weight coefficient Z is introduced into the initial road network directed graphTo express the length of the edge between two adjacent nodes, then G (V, E) to G (V, E, Z); when z ij ＝z ji If > 0, the edge is in a clear state and represents node v i And node v j Communicating; when z ij ＞0,z ji = infinity, representing a slave node v i Leading to node v j But not from node v j Leading to node v i The method comprises the steps of carrying out a first treatment on the surface of the When z ji ＞0,z ij = infinity, representing a slave node v j Leading to node v i Cannot be from node v i Leading to node v j The method comprises the steps of carrying out a first treatment on the surface of the When z ij ＝z ji = infinity, representing node v i To node v j Edges not directly connected;
in this embodiment, the steering coefficient q is in step S4 ikj To describe steering behaviour between intersections, to describe the direction of travel v i →v k →v j Is a steering lane condition; q ik ＝q kj =1 to describe the steering of the first two nodes and the last two nodes; when q ikj =1, then the lane direction can pass normally; when q ikj And = ≡, the traffic is prohibited for that direction lane.
In this embodiment, the shortest path l in step S4 ij The operation process of (1) is as follows: at node v i To node v j And (3) respectively adding the lengths of edges between adjacent nodes communicated in each path, comparing the total length of each path between two nodes, and selecting the path with the shortest total length as the shortest path. The shortest path calculation formula is as follows:
wherein l ij For node v i To node v j Is the shortest path of (a); q ikj For node v i Through node v k Reach node v j Steering coefficient of (2); z ikj For node v i And node v j The length of the edges, i.e. node v i Through node v k Reaching the length of the node edge.
In this example, in step S5, node v is determined i To node v j Is the shortest path l of (1) ij Calculating the number of road segments passing through the shortest path to obtain a node v i To node v j D of the shortest distance of (2) ij . When l ij Not equal to infinity, d ij 1 or more, representing the shortest path l ij Distance d of (2) ij 。
In this embodiment, in step S6, the connectivity k i For node v i With other nodesDegree of accessibility a between ij And node v i Shortest distance d to other nodes ij The index can reflect the self connectivity condition of each node in the road network; is calculated by the following calculation formula:
in the embodiment, in step S7, the road network connectivity Con A Calculating the independent connectivity of each node in the road network, and accumulating the connectivity of each node in the road network to obtain the connectivity of the road network; the calculation formula is as follows:
the beneficial effects are that:
the road network connectivity is one of important indexes for evaluating whether an urban road network is reasonable, the existing urban connectivity index describes whether road segments are connected or not, the influence of intersection steering limitation on road network connectivity cannot be reflected, and the road network connectivity is influenced by the steering limitation (left turning prohibition, right turning prohibition and the like) of different lanes of an urban intersection.
Finally, it should be noted that: various modifications and alterations of this invention may be made by those skilled in the art without departing from the spirit and scope of this invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (10)
1. A method for evaluating the connectivity of an urban road topology network comprises the following steps:
s1: abstracting the urban road network into a directed graph G;
s2: calculating v of any two intersections as nodes i And v j Degree of accessibility a between ij ；
S3: according to the reachability a in step S2 ij Constructing a reachability matrix A;
s4: find node v i And v j Shortest path between the two ij : comparison node v i And v j The total length of all the communication paths between the two paths is selected as the shortest path l ij ；
S5: computing node v i And v j Shortest distance d between ij : calculating the shortest distance by calculating the number of road sections passed by the shortest path;
s6: computing node v i Degree of connectivity k i : through the accessibility a among all nodes ij Shortest distance d between nodes ij Constructing single node connectivity k i Is calculated according to the formula;
s7: the connectivity of each node is calculated through the steps, and the connectivity of each node is accumulated, so that the connectivity Con of the urban road network is calculated A 。
2. The method for evaluating the network connectivity of the urban road topology according to claim 1, wherein when the urban road network is abstracted into a directed graph in the step S1, intersections in the urban road network are regarded as nodes, road sections are regarded as edges, the urban road network can be abstracted into a simplified network graph, and the network graph is composed of a limited set of nodes V and a set of edges E, denoted by G, i.e., the network can be denoted by G (V, E); in the network, the intersection is regarded as a node, v= { V 1 ,v 2 ,v 3 ,v 4 ,...,v n -is a set of intersection nodes; road section between adjacent intersections in road networkI.e. the edges connecting the nodes.
E＝{e 1 ,e 2 ,e 3 ,...,e n And is a collection of edges.
3. The method for evaluating network connectivity of urban road topology according to claim 2, wherein in step S2, the reachability a between nodes is determined ij Representing node v i And v j The degree of connectivity, i.e., the number of paths connecting between two nodes; node v is considered to be a network node when there is at least 1 path connection between two nodes i To node v j Is communicated with, wherein the number of the communicating paths is a ij ，a ij 1 or more; if there is no path connection between two nodes, node v i To node v j Is not communicated with, a ij ＝0。
4. The method for evaluating the connectivity of an urban road topology network according to claim 3, wherein the step S3 of constructing the reachability matrix a comprises the steps of:
a1: the reachability adjacency matrix comprises reachability among all nodes of the whole road network;
a2: reachability adjacency matrix a is an n x n two-dimensional matrix. In the matrix, a ij Is an element of row i and column j in the matrix, representing node v i To node v j Is the degree of reachability of (a);
5. the method for evaluating network connectivity of urban road topology according to claim 4, wherein in step S4, a distance weight coefficient Z is introduced to the initial road network directed graphTo express the length of the edge between two adjacent nodes, then G (V, E) to G (V, E, Z); when z ij ＝z ji If > 0, the edge is in a clear state and represents node v i And node v j Communicating; when z ij ＞0,z ji = infinity, representing a slave node v i Leading to node v j But not from node v j Leading to node v i The method comprises the steps of carrying out a first treatment on the surface of the When z ji ＞0,z ij = infinity, representing a slave node v j Leading to node v i Cannot be from node v i Leading to node v j The method comprises the steps of carrying out a first treatment on the surface of the When z ij ＝z ji = infinity, representing node v i To node v j There are no directly connected edges.
6. The method for evaluating the connectivity of an urban road topology network according to claim 5, wherein the steering coefficient q is in step S4 ikj To describe steering behaviour between intersections, to describe the direction of travel v i →v k →v j Is a steering lane condition; q ik ＝q kj =1 to describe the steering of the first two nodes and the last two nodes; when q ikj =1, then the lane direction can pass normally; when q ikj And = ≡, the traffic is prohibited for that direction lane.
7. The method for evaluating network connectivity of urban road topology according to claim 6, wherein in step S4, l ij Is node v i To node v j The operation process of the shortest path of the (a) is as follows: at node v i To node v j And (3) respectively adding the lengths of edges between adjacent nodes communicated in each path, comparing the total length of each path between two nodes, and selecting the path with the shortest total length as the shortest path. The formula is as follows:
wherein l ij For node v i To node v j Is the shortest path in (a); q ikj For node v i Through node v k Reach node v j Steering coefficient of (2); z ikj For node v i And node v j The length of the edges, i.e. node v i Through node v k Reach node v j The length of the edge.
8. The method for evaluating network connectivity of urban road topology according to claim 7, wherein in step S5, d ij For node v i To node v j The shortest distance is calculated by the number of the road sections passed by the shortest path. When l ij Not equal to infinity, d ij 1 or more, representing the shortest path l ij Distance d of (2) ij 。
9. The method for evaluating network connectivity of urban road topology according to claim 8, wherein in step S6, connectivity k is determined i For node v i Reachability a with other nodes ij And node v i Shortest distance d to other nodes ij The index can reflect the self connectivity condition of each node in the road network; is calculated by the following calculation formula:
10. the method for evaluating the connectivity of an urban road topology network according to claim 9, wherein in step S7, the connectivity of the road network Con A Calculating the independent connectivity of each node in the road network, and accumulating the connectivity of each node in the road network to obtain the connectivity of the road network; the calculation formula is as follows:
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