CN101799839B - Method for establishing public traffic network model with controllable network diameter based on random overlapping faction and public traffic network model - Google Patents
Method for establishing public traffic network model with controllable network diameter based on random overlapping faction and public traffic network model Download PDFInfo
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Abstract
The invention relates to a method for establishing a public traffic network model with a controllable network diameter based on random overlapping faction. The public traffic network is represented as the relationship between a site and a line (i.e., faction, the maximum complete subgraph in the network), and the network relationship diagram is represented by an adjacent matrix during representation of numerical values. The method comprises the following steps of: setting the network diameter to be N; the network is logically represented to be (N+1)-layer structure, wherein the faction of the (m-1)th layer is mapped to be a point in the layer m (m is no less than 1 and no more than N+1); the original network is formed by overlapped factions, wherein a faction is added in the original network and each layer of network is formed by the faction, wherein the network on the (N-1)th layer is a faction and the Nth layer of the network is a point so as to generate an ideal N-depth faction network. The invention reduces the maximum transferring time and the average transferring time of the public traffic network in case of nearly zero cost, thereby improving the service performance of the public traffic system.
Description
Technical field
The invention belongs to the network science and technology field, be specifically related to modeling method and public traffic network model based on the public traffic network model of the controllable network diameter of random overlapping factions.
Background technology
Urban public transport is the important foundation facility of living closely bound up with people, its basic task be for the passenger provide safety, convenient, rapidly, on schedule, comfortable condition by bus.Yet along with modernization process and development of urbanization, it is very crowded that urban transportation becomes, and urban public transport can not provide rapidly, the condition of riding on schedule, easily.The statistics that the Ministry of Construction provides shows; China's bus trip share rate only accounts for 10% to 25% of the total travel amount of city dweller; Compare with the trip proportion of developed country 40% to 60%; Differ also very big, the public transit system in city is not brought into play due advantage, is unfavorable for the progress of Chinese economic development and urban civilization.Therefore, China advocates energetically and first develops urban public transport, is to improve the traffic resource utilization ratio, alleviates the necessary means of traffic congestion, is the basic road of urban development.
At present, the application of complex network theory begins to cause people's research interest to the research of the research of city bus network characteristic and the network planning, has many scholars to utilize Complex Networks Theory that the city bus network is studied, and has obtained a large amount of achievements in research.Latora and Marchiopi (Latora V, Marchiori M.Is the Bostonsubway a small-world network [J] .Physica A, 2002,314 (1-4): 109-113) studied Bostonian subway network characteristic; Sienkiewicz (Sienkiewicz J; Holyst J A.Statistical analysis of 22public transport networks in Poland [J] .Phys.Rev.E; 2005; 72 (4): 046127) studied the public transit system in 22 cities of Poland, adopted two kinds of network models it is analyzed.(WuJ J such as Wu Jianjun, Gao Ziyou; Gao Z Y; Sun H J.Urban transit system as scale-free network [J] .Modern PhysicsLetters B; 2004,18 (19-20): 1043-1049.) analyzed " no scale " characteristic and " worldlet " characteristic of the public traffic network of Beijing, and studied the efficiency of public traffic network.(Yang XH such as Yang Xuhua, Wang Bo; Wang B; Wang W L; Et al.Research on some bus transport networks with randomoverlapping clique structure [J] .Communications in theoretical physics; 2008,50 (5): 1249-1254.) through research, propose that space P describes that public traffic network down is that height factions are overlapping, height factions cluster, have the worldlet network of exponential type degree distribution to the statistical property of actual bus-route network (Beijing, Shanghai and Hangzhou).
The design of public traffic network and optimization aspect; Many researchers is optimized public bus network from the local performance of network, proposes to increase the local performance that methods such as circuit and website are improved public traffic network, improves the network component efficiency; To shorten passenger's travel time, improve service quality.
Summary of the invention
For the deficiency that optimization efficiency is lower, network performance is relatively poor that overcomes existing public traffic network; The present invention provides a kind of operational efficiency height, network performance optimized good and needn't increase the method for building up and the public traffic network model based on the public traffic network model of the controllable network diameter of random overlapping factions of cost, and this model can reduce passenger's in the network maximum and average number of transfer.
The technical scheme that the present invention is proposed for the above-mentioned technology of solution:
A kind of based on the controlled public traffic network method for establishing model of the network diameter of random overlapping factions; Public traffic network is expressed as the relation of website and circuit; When numerical value is explained, adopt adjacency matrix to represent cyberrelationship figure, said public traffic network method for establishing model may further comprise the steps:
Step 1: the setting network diameter is N, and N is a natural number; Network will be from showing as (N+1) layer structure in logic, and wherein the factions of (m-1) layer are mapped as a bit of m layer, and 1≤m≤N+1, m are natural number;
Step 2: each layer network of initialization: it is a c of factions that initial primitive network begins
0, c
0Constitute by m node, a public bus network with m website is promptly initially arranged; The 1st～N layer network is 1 node;
Step 3: newly-increased factions in primitive network, the c of factions that promptly to increase a size be m
i, c
iMiddle m
1Individual node is a picked at random from the existing node of primitive network, m
2Individual for increasing node newly, wherein, i=1,2,
Step 4: if the k layer has new factions to occur; Wherein, 0≤k≤N-2 will increase the node that factions are mapped to (k+1) layer newly; If this node and certain existing (k+1) layer factions constitute new maximum factions; Find out this factions, make them form new factions, at this moment factions' number of (k+1) layer is constant; Otherwise from the existing factions of (k+1) layer, find out a maximum complete subgraph that comprises this point, promptly comprise the maximum factions of this point, make they and this node constitute new factions of (k+1) layer, at this moment factions' number of (k+1) layer adds 1;
Step 5: network is carried out (N-1) inferior mapping,, promptly obtain desirable N degree of depth factions network if the N-1 layer of network is made up of factions;
Step 6: if the N-1 layer of network can not constitute factions, in primitive network, select corresponding factions that it is interconnected, guarantee that (N-1) layer network can become factions all the time according to interdenominational maximum similarity.
Step 7: repeating step 3～step 6, when all factions all join in the network, this network is a desirable N degree of depth factions network, then finishes.
Further, in said step 2 and the step 3, m～N (μ, σ
2), m
1～N (μ
1, σ
1 2), m
2～N (μ
1, σ
2 2), and μ=μ
1+ μ
2,
M=m
1+ m
2, wherein, m, m
1And m
2Be the random number of accord with normal distribution, the average of m and variance are respectively μ and σ
2, m
1Average and variance be respectively μ
1And σ
1 2, m
2Average and variance be respectively μ
2And σ
2 2
Further again, in the said step 4, the method for finding out new node place factions is, adopts bipartite graph to describe network, if all nodes of factions all link to each other with this new node, then these factions and new node constitute new factions.
Further, in the said step 6, interdenominational similarity is meant two interdenominational common node numbers, and the many more similarities of number are big more.
Further, in the said step 7, desirable N degree of depth factions network is from show as (N+1) layer structure in logic.Primitive network is made up of many overlapping factions, and the definition primitive network is 0 degree of depth factions network; Factions in the primitive network are mapped to node; If between the factions in the primitive network overlapping node is arranged; Think that then its corresponding mapping node has the limit of company, form a new network like this, be referred to as 1 degree of depth factions network; According to design of the present invention, 1 degree of depth factions network also will be made up of different factions connected to one another; Repeat above process, promptly (0≤m≤N-1) layer network generates (m+1) layer network, and (N-1) layer network will be factions, and the N layer of network is a point by m.We obtain a network of total (N+1) layer in logic like this.
The described public traffic network model of setting up based on the controlled public traffic network method for establishing model of the network diameter of random overlapping factions of a kind of usefulness, said public traffic network model is:
(1) original state: existing c of factions at random that length is m
0
(2) random overlapping factions increase: increase a c of factions that size is m
i, c
iMiddle m
1Individual node is a picked at random in the existing node from primitive network, m
2Individual for increasing node newly;
(3) desirable N degree of depth factions network mapping: carry out subideal N degree of depth factions network struction,,, regulate the newly-increased c of factions according to interdenominational similarity if can not become desirable N degree of depth factions network
iConnection, make primitive network can become desirable N degree of depth factions network.
Further, m～N (μ, σ
2), m
1～N (μ
1, σ
1 2), m
2～N (μ
2, σ
2 2) and μ=μ
1+ μ
2, m=m
1+ m
2, wherein, m, m
1And m
2Be the random number of accord with normal distribution, the average of m and variance are respectively μ and σ
2, m
1Average and variance be respectively μ
1And σ
1 2, m
2Average and variance be respectively μ
2And σ
2 2
Further again, interdenominational similarity is meant the number of two overlapping nodes between the factions.
Technical conceive of the present invention is: based on the Complex Networks Theory of factions, consider from topology of networks and overall network performance, propose to improve the model or the method for public traffic network, promote the integrity service performance of public traffic network.According to the statistics to bus passenger trip psychological research, secondly the primary factor of considering when the minimum passenger of being of number of transfer goes on a journey is operating range, time, expense etc.Number of transfer is regarded as the important indicator of public traffic network performance.Thus, designing a kind of public transit system that better network performance is arranged, have lower maximum and average number of transfer, is the necessary means and the method for present city bus development and optimization.
Based on the Complex Networks Theory of random overlapping factions, the public traffic network model of controllable network diameter has been proposed, to reduce network diameter and average shortest path length; Thereby maximum number of transfer in the reduction public traffic network and average number of transfer; Promote the integrity service performance of public traffic network, make public transit system can share more trip rate, reach and improve the city road network operational efficiency; Alleviate the urban traffic pressure, and play the effect of energy-saving and emission-reduction.
The public traffic network model of the controllable network diameter based on random overlapping factions of the present invention; Be that desirable N degree of depth factions' network establishing method and a kind of public traffic network evolutionary model based on the weighting Complex Networks Theory are combined, the public traffic network evolutionary model that increases based on random overlapping factions of a kind of network diameter of foundation controlled (network diameter can be assumed to be N in advance).
According to the method for Space P, in the public traffic network model, the bus station is mapped to the point in the public traffic network, if having a public bus network process at least between certain two website, think that then these two points have the limit of company.Factions in the network are defined as in the network maximum subgraph that is coupled fully, and promptly all nodes in the factions are to link to each other in twos.Adopt the describing method of Space P; As far as any public bus network, the limit of company is all arranged between wherein any two bus stations, and in whole public traffic network; There is not a point outside this public bus network; The limit of company can all be arranged with all websites of this public bus network, and this is explanation just: every public bus network is a maximum complete subgraph in the public traffic network, and promptly arbitrary public bus network can be regarded factions as.
The distance definition of two nodes is the limit number on the shortest path that connects these two nodes in the network; Network diameter is defined as in the network maximal value of distance between any two nodes, and average shortest path length is defined as the mean value of the distance between any two nodes in the network.For public traffic network, maximum number of transfer is that network diameter subtracts 1, and average number of transfer is that average shortest path length subtracts 1.The network diameter of the public traffic network of China big and medium-sized cities is bigger than normal, and number of transfer is more, and for example, the network diameter in Beijing, Shanghai and Hangzhou is respectively 6,6 and 5.The present invention is the public traffic network model that designs with regard to being based on the purpose that reduces network diameter and number of transfer, and the present invention has realized that network diameter is 3 public traffic network model.
The construction method of desirable N degree of depth factions network, at first given N value, according to this construction method, desirable N degree of depth factions network will be from showing as (N+1) layer structure in logic.Primitive network is made up of many overlapping factions, and the definition primitive network is 0 degree of depth factions network; Factions in the primitive network are mapped to node; If between the factions in the primitive network overlapping node is arranged; Think that then its corresponding mapping node has the limit of company, form a new network like this, be referred to as 1 degree of depth factions network; According to design of the present invention, 1 degree of depth factions network also will be made up of different factions connected to one another; Repeat above process, promptly (0≤m≤N-1) layer network generates (m+1) layer network, and (N-1) layer network will be factions, and the N layer of network is a point by m.We obtain a network of total (N+1) layer in logic like this.
Concerning every layer, if having a few all in certain factions, and this layer interconnects by several factions and forms, and then is referred to as desirable N degree of depth factions network.The characteristics of desirable N degree of depth factions network do, and each degree of depth network all is that factions constitute, and for the network of certain one deck [be assumed to be k (degree of depth of 1≤k≤N)]; Group node in all corresponding primitive network of any node of network; Our called after k degree of depth corporations of this group node, according to the model that we invented, its network diameter of k degree of depth corporations is k; Therefore, the primitive network diameter in the desirable N degree of depth factions network is N.Be that we can be according to pre-set network diameter, tectonic network.As shown in Figure 1, be the building process of an ideal 3 degree of depth factions networks.
Beneficial effect of the present invention is:
(1) according to the public traffic network of this modelling, not only the public traffic network with reality has very approximate network characteristic, but also the characteristic that performance makes new advances.Under the situation that satisfies the public transport coverage rate, this model has been realized network diameter controlled (littler) and littler average shortest path length, realizes in public traffic network that promptly littler the and average number of transfer of maximum number of transfer is littler.This model generates has more excellent network performance and the public traffic network of service quality, can make public transport can bear more trip share rate, finally reaches and improves the city road network operational efficiency, plays the effect of alleviation urban traffic pressure.
(2) this model can directly apply to actual public traffic network, and it is optimized.Only need a spot of public bus network of adjustment and website; Rather than increase circuit and website; The maximum number of transfer that under the situation of zero cost almost, just reduces public traffic network with reduce average number of transfer, reach the effect of improving whole transportation network performance, improve the service quality of public transit system.
Description of drawings
Fig. 1 is the building process synoptic diagram of desirable 3 degree of depth factions networks.
Fig. 2 is the processing synoptic diagram of singular point in the desirable N degree of depth factions network mapping process.
Embodiment
Below in conjunction with accompanying drawing the present invention is done and to further describe.
Embodiment 1
See figures.1.and.2; A kind of method for building up of public traffic network model of the controllable network diameter based on random overlapping factions; Adopt bipartite graph to represent public traffic network, be about to the relation that public traffic network is expressed as website and circuit, when numerical value is explained, adopt adjacency matrix to represent cyberrelationship figure.Concrete modeling procedure is following:
Step 1: the setting network diameter is N, and N is a natural number; (can be assumed to be 3 to public traffic network): network will be from showing as (N+1) layer structure in logic, and wherein the factions of (m-1) layer are mapped as a bit of m layer, and 1≤m≤N+1, m are natural number;
Step 2: each layer network of initialization.It is a c of factions that primitive network begins
0, c
0Be to constitute, a public bus network with m website is promptly initially arranged by m node.The the 1st～(N-1) degree of depth network is 1 node.
Step 3: newly-increased factions (public bus network) in primitive network, the c of factions that promptly to increase a size be m
i, c
iMiddle m
1Individual node is a picked at random from the existing node of primitive network, m
2Individual for increasing node newly.(i＝1，2，…)
Step 4: if (0≤k≤N-2) layer has new factions to occur to k; To increase the node that factions are mapped to (k+1) layer newly; If this node can constitute new maximum factions with certain existing (k+1) layer factions; Find out this factions, make them form new factions, at this moment factions' number of (k+1) layer is constant; If there are not such factions; Then from the existing factions of (k+1) layer, find out a maximum complete subgraph that comprises this point; The maximum factions that promptly comprise this point make they and this node constitute new factions of (k+1) layer, and at this moment factions' number of (k+1) layer adds 1.
Step 5:, network is carried out (N-1) inferior mapping according to step 4.If (N-1) of network layer constitutes factions, promptly can be mapped to desirable N degree of depth factions network, get into step 5, if can not, get into step 6.
Step 6: if (N-1) of network layer can not become factions; Black real point in as shown in Figure 2; Then in primitive network, select corresponding factions that it is interconnected, guarantee that (N-1) layer network can become factions all the time according to interdenominational maximum similarity.
Step 7: return step 3, if all factions all join in the network, and this network is a desirable N degree of depth factions network, then finishes.
In the above-mentioned steps 2 and 3, m～N (μ, σ
2), m
1～N (μ
1, σ
1 2), m
2～N (μ
2, σ
2 2) and μ=μ
1+ μ
2, m=m
1+ m
2, wherein, m, m
1And m
2Be the random number of accord with normal distribution, the average of m and variance are respectively μ and σ
2, m
1Average and variance be respectively μ
1And σ
1 2, m
2Average and variance be respectively μ
2And σ
2 2
In the above-mentioned steps 4, the method for finding out new node place factions is, adopting bipartite graph to describe under the situation of network, if all nodes of factions all link to each other with this new node, then these factions can constitute new factions with new node.
In the above-mentioned steps 6, interdenominational similarity is meant two interdenominational common node numbers, and the many more similarities of number are big more.When actual public traffic network was operated, the distance between the considered website can use longitude and latitude to calculate.
In the said step 7, desirable N degree of depth factions network is from show as (N+1) layer structure in logic, and primitive network is made up of many overlapping factions, and the definition primitive network is 0 degree of depth factions network; Factions in the primitive network are mapped to node; If between the factions in the primitive network overlapping node is arranged, think that then its corresponding mapping node has the limit of company, forms a new network; Be referred to as 1 degree of depth factions network, 1 degree of depth factions network also will be made up of different factions connected to one another; Repeat above process, promptly generate (m+1) layer network by the m layer network, 0≤m≤N-1, (N-1) layer network will be factions, and the N layer of network is a point, obtains a network of total (N+1) layer in logic.
Embodiment 2
See figures.1.and.2, the public traffic network model is:
(1) original state: existing c of factions that length is m
0
(2) random overlapping factions increase: increase a c of factions that length is m
i, c
iMiddle m
1Individual node is a picked at random from existing node, m
2Individual for increasing node newly;
(3) desirable N degree of depth factions network mapping: carry out subideal N degree of depth factions network struction,,, regulate the newly-increased c of factions according to interdenominational similarity if can not become desirable N degree of depth factions network
iConnection, make primitive network can become desirable N degree of depth factions network.
M～N (μ, σ
2), m
1～N (μ
1, σ
1 2), m
2～N (μ
2, σ
2 2) and μ=μ
1+ μ
2, wherein, m, m
1And m
2Be the random number of accord with normal distribution, the average of m and variance are respectively μ and σ
2, m
1Average and variance be respectively μ
1And σ
1 2, m
2Average and variance be respectively μ
2And σ
2 2Interdenominational similarity is meant the number of two overlapping nodes between the factions.When in to actual public traffic network, operating, also will consider the distance between the website, available longitude and latitude calculates.
Claims (4)
1. one kind based on the controlled public traffic network method for establishing model of the network diameter of random overlapping factions; It is characterized in that: the relation that public traffic network is expressed as website and circuit; When numerical value is explained, adopt adjacency matrix to represent cyberrelationship figure, said public traffic network method for establishing model may further comprise the steps:
Step 1: the setting network diameter is N, and N is a natural number; Network will be from showing as (N+1) layer structure in logic, and wherein the factions of (h-1) layer are mapped as a bit of h layer, and 1≤h≤N+1, h are natural number;
Step 2: each layer network of initialization: initial primitive network is a c of factions
0, said primitive network is the 0th layer network, c
0Constitute by m node, a public bus network with m website is promptly initially arranged; The 1st～N layer network is 1 node;
Step 3: newly-increased factions in primitive network, the c of factions that promptly to increase a size be m
i, c
iMiddle m1 node is picked at random from the existing node of primitive network, m
2Individual for increasing node newly, wherein, i=1,2 ...;
Step 4: if the k layer has new factions to occur; Wherein, 0≤k≤N-2 will increase the node that factions are mapped to (k+1) layer newly; If this node and certain existing (k+1) layer factions constitute new maximum factions; Find out this factions, make them form new factions, at this moment factions' number of (k+1) layer is constant; Otherwise from the existing factions of (k+1) layer, find out a maximum complete subgraph that comprises this node, promptly comprise the maximum factions of this node, make they and this node constitute new factions of (k+1) layer, at this moment factions' number of (k+1) layer adds 1;
Step 5: network is carried out (N-1) inferior mapping,, promptly obtain desirable N degree of depth factions network if the N-1 layer of network constitutes factions;
Step 6: if (N-1) of network layer can not constitute factions, in primitive network, select corresponding factions that it is interconnected, guarantee that (N-1) layer network can become factions all the time according to interdenominational maximum similarity;
Step 7: repeating step 3～step 6, when all factions all join in the network, this network is a desirable N degree of depth factions network, then finishes;
In said step 2 and the step 3, m～N (μ, σ
2),
And μ=μ
1+ μ
2,
M=m
1+ m
2, wherein, m, m
1And m
2Be the random number of accord with normal distribution, the average of m and variance are respectively μ and σ
2, m
1Average and variance be respectively μ
1And σ
1 2, m
2Average and variance be respectively μ
2And σ
2 2
2. as claimed in claim 1 based on the controlled public traffic network method for establishing model of the network diameter of random overlapping factions; It is characterized in that: in the said step 4; The method of finding out new node place factions is; Adopt bipartite graph to describe network, if all nodes of factions all link to each other with this new node, then these factions and new node constitute new factions.
3. as claimed in claim 1 based on the controlled public traffic network method for establishing model of the network diameter of random overlapping factions, it is characterized in that: in the said step 6, interdenominational similarity is meant two interdenominational common node numbers, and the many more similarities of number are big more.
4. as claimed in claim 1 based on the controlled public traffic network method for establishing model of the network diameter of random overlapping factions; It is characterized in that: in the said step 7; Ideal N degree of depth factions network is from show as (N+1) layer structure in logic; Primitive network is made up of many overlapping factions, and the definition primitive network is 0 degree of depth factions network; Factions in the primitive network are mapped to node; If between the factions in the primitive network overlapping node is arranged, think that then its corresponding mapping node has the limit of company, forms a new network; Be referred to as 1 degree of depth factions network, 1 degree of depth factions network also will be made up of different factions connected to one another; Repeat above process, promptly generate (m+1) layer network by the m layer network, 0≤m≤N-1, (N-1) layer network will be factions, and the N layer of network is a point, obtains a network of total (N+1) layer in logic.
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| CN102122434B (en) * | 2011-01-24 | 2013-07-24 | 浙江工业大学 | Urban public transport network optimization method capable of improving overall transfer performance |
| CN102331919B (en) * | 2011-09-09 | 2013-11-20 | 西安电子科技大学 | Maximum complete subgraph-based embedded system register allocation method |
| CN102982395B (en) * | 2012-11-28 | 2015-10-28 | 浙江工业大学 | A kind of bus rapid transit transfer method based on space nodes clustering method |
| CN104239965B (en) * | 2014-08-27 | 2017-06-30 | 浙江工业大学 | A kind of extensive road network bilayer method for routing divided based on overlap corporations |
| CN111915884B (en) * | 2020-06-18 | 2021-09-28 | 北京航空航天大学 | Traffic network behavior description method and device, electronic equipment and storage medium |
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| CN108897920A (en) * | 2018-06-06 | 2018-11-27 | 北京科技大学 | A kind of subway network model building method |
| CN108897920B (en) * | 2018-06-06 | 2021-03-05 | 北京科技大学 | Subway network model construction method |
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