CN108897920A - A kind of subway network model building method - Google Patents
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Abstract
The present invention provides a kind of subway network model building method, belongs to network model constructing technology field.This method preferentially, when there is station identical with the website route degree that BA optimum selecting arrives in network, carries out second step station centre property preferentially to the station with same line degree first, in accordance with BA model.Finally, realizing newly-increased route random walk in the direction indicated.It is the preferentially mechanism being oriented to that the present invention, which is constructed with station centre's property, by the method for emulation experiment, has done comparative analysis to BA model, with the result that the Central model that station centre's property is guiding obtains.The results show that Central model obtains its scale factor, average least transfer number, cluster coefficients, maximum communication path characteristic value closer to original value, ratio highest of the optimum selecting to close intown website.Result of study can more really reflect subway network evolutionary process, be the scheme comparison of subway network design phase, and further network dynamics analysis provides basis.
Description
Technical field
The present invention relates to network model constructing technology fields, particularly relate to a kind of subway network model building method.
Background technique
Subway network model generates the simulation for being able to reflect real subway network feature by general theoretical model
Model.Subway network simulation model can be used in all kinds of power of Subway Network in China planning stage, design phase, operation stage
The assessment of knowledge topic and prediction, such as dissipation and absorbability assessment that subway network structure impacts emergency event extremely, Jin Ergui
It draws, Design and optimization subway network structure.
In network evolution model, key solves the problems, such as preferentially with growth by two.Subway network is a kind of typical physics rail
The public traffic network of road dependent form increases using physical track as basic unit.The physical track of newly-increased route passes through newly-built
Part creates station, and new line is added in network by reselection part used car station.In all used car stations how selected section
Website is attached, and is that preferential model will solve the problems, such as.Newly-increased station in new line should be how on two-dimensional space
It successively positions, i.e. the station from key station in direction of both ends, how successively to select spatial position, be that migration rule will solve
The problem of.
Subway network preferentially during, it is only few several sections of but since most of node all only has route to pass through
Point has several routes to pass through, and by the node degree of each node, (node degree here indicates the route number and node quilt that pass through node
Connection number) percentage markings of node degree summation are accounted on wheel disc, although the face that the big node of node degree occupies on wheel disc
Product is larger, and although area that the small node of node degree occupies is small, but since most of nodes are all the small nodes of node degree, because
This, this kind of node occupies very big area on wheel disc, when as roulette experiment, chooses the big node probability of node degree
Still very little.Illustrate this name of the game from the angle of mathematical analysis, i.e., when the denominator of analytic equation is very big, probability
Size will not depend on molecule, the node select probability of this and Angeloudis P and Fisk D (2006) catenet with
The unrelated discussion of node degree is consistent.In other words, why BA model can generate scales-free network, be because the model is drilled
The initial stage molecule of change is larger, so being connected to the high probability of node degree can be relatively high, with the progress of evolution, denominator gradually becomes
Greatly, the node being connected to starts to become to be randomized, so largely having selected mediocre node, here it is heavy-tailed effect the reason of institutes
?.In subway network, the ratio of mediocre node and rich node is much larger than other complex networks, and thus, BA model is preferentially
The probability of " affluence " node still very little is chosen, preferentially probabilistic model needs to improve.
Subway network is a kind of typical community network, is increased using physical circuit as basic unit.Correspondingly, from theory
The upper general evolutionary model of building should also fully consider this characteristic of subway system.Angeloudis and Fisk is earliest
Based on L spatial modeling, in tectonic network, the probability that had been friends in the past website is selected is identical, and independently of number of lines, emulates mould
Exponential distribution is obeyed in the quasi- subway network degree distribution generated；On this basis, Zhou Xizhao (2017) assumes every newly-increased route
Interstitial content obedience is just distributed very much, is modeled using P space law, analyze the ratio that newly-increased route includes old website take 0.1,0.6,
Analog network characteristic value variation in the case of 0.9 3 kinds.The Global-Coupling corporations of BA model are connected adjustment by Ding Yimin (2013)
For locally coupled corporations' link model, but newly-increased route selects old website with random chance P, the subway network ultimately generated it is different
Matter and probability P strong correlation.
It will be to increase unit to be improved to route with node although the unit that the above scholar increases network is improved
To increase unit, but model does not all account in subway network transfer station to the attraction of new line and station centre's property (such as
Old website near transport hub, business activity center, political activity center, tourist attractions) attraction of new line is asked
Topic.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of subway network model building methods, choose subway station conduct
Node in network, the company side between node are exactly the physical track between station.Subway network passes through increasing in forming process
New line is added to carry out extended network.From the convenient angle of passenger's trip, new line preferentially selects transfer station or is located at downtown
Access point as new line of transport hub, business activity center, political activity center, the station near tourist attractions, newly
Website random walk on planning traffic corridor on route, this phenomenon meet existing positive research achievement.Based on these realities
Border situation, proposed by the present invention take station centre's property as the central model of guiding, while considering transfer station to new line
Attraction with attraction of station centre's property to new line.Further comparative analysis BA is preferentially selected with central proposed by the present invention
The order of accuarcy that excellent evolutionary model simulates subway network.
The construction method first step according to BA model preferentially, but in subway network, the ratio of mediocre node and rich node
Value is much larger than other complex networks, thus, the probability of BA model optimum selecting to " affluence " node still very little, preferentially probability
Model needs to improve.Therefore, when there is the identical vehicle of website route degree (Wang Zhiru, 2012) that arrives with BA optimum selecting in network
When standing, second step station centre property is carried out preferentially to the station with same line degree.Meaning is：One newly-increased route with
Through existing station be connected probability P, not only (first step is preferentially) directly proportional to the route degree at station, and with locating for station
Position is also related (second step is preferentially).
The construction method specifically includes that steps are as follows：
(1) BA model is preferentially：
Provide the probability π (k whether some website i in initial network is increased newly route L connectioni), and with this probability π
(ki) as whether the foundation of next step is entered, if providing the collection for possessing all websites of this probability into next step
Close Ω={ 1,2,3......m }；
(2) the Central model based on space center's property preference is preferentially：
There is equal probabilities π (k what step (1) providedi) Website Hosting in Ω={ 1,2,3......m }, utilize sky
Between the Central model of centrality preference further the website in set is carried out preferably, finally to provide newly-increased route L access net
The first access point n of network, subsequently into the route migration model of next step；
(3) route random walk in the direction indicated is increased newly：
The connection for newly accessing new road L and current subway network is completed, by specified migration rule, so that current subway
The route number of network becomes m+1 item by m item.
Wherein, in step (1) BA model preferentially in, BA model is a route degree k according to website iiIt carries out preferred
Probability Choice Model.Its process is as follows, traverses the website i of current network and calculates the probability π (k of the connection of website ii), such as
Possess in the set of other websites of the current subway network of fruit other than website i and is greater than 1 with the website number of website i equal probabilities
When, set omega={ 1,2,3......m } for possessing all websites of this probability is provided, so that kn(n∈Ω)=ki, and enter one
The preferred steps of step.Otherwise, if possessed and website i in the set of current other websites of the subway network other than website i
When the website number of equal probabilities is equal to 0, after website i is chosen by random chance, website i is exactly the first access of newly-increased route L
Website.Probability π (the k that BA model preferentially connectsi) be calculated as follows：
In formula, i indicates the i-th each site identity traversed, kiIndicate the metro operation for passing through website i in current procedures
The sum of route, j identify the mark of website in network in current procedures, ∑ kjAll websites passes through route number in expression network
Summation.
Central model of the step (2) based on space center's property preference preferentially in, the Central of space center's property preference
Model is a cluster coefficients c according to website iiSize judge website in the model of the center degree in subway network space, ci
Value is bigger, then website i is more in the center in subway network space.When the cluster coefficients at stations all in Website Hosting Ω are both less than
Equal to the station i of BA model optimum selecting, then station i is as the access point for increasing route L newly；Otherwise to set omega=1,2,
3......m cluster coefficients are greater than c in the website in }iWebsite in the maximum website n of cluster coefficients again according to cluster coefficients
Probability π (cn) carry out probability it is preferred：
The wherein cluster coefficients c of website iiIt is calculated by document Wang Zhi such as (2016).Based on space center's property preference
Central model preferentially in step (1) with same line degree station set according to cluster coefficients preferential attachment probability into
It goes for the second time preferentially：
In formula, ciFor the cluster coefficients of subway station i, cnFor the cluster coefficients of website n in subway network, n ∈ Ω, set
Ω={ 1,2,3......m } is the Website Hosting to be selected that previous step provides, π (ci) it is website i according to cluster coefficients ciIt is selected
Probability, as π (ciWhen)=1, website i must be selected；
Probability π (cn) calculated as the following formula：
In formula, cmFor the cluster coefficients at station any in set omega={ 1,2,3......m }, set omega=1,2,
3......m in }, station cluster coefficients maximum value is cn, π (cn) it is website n according to cluster coefficients cnSelected probability.
The migration rule specified in step (3) includes the random walk of orthogonal type direction, radial pattern random walk and toroid
Road migration.Wherein orthogonal type random walk refers to that new line attachment L is when subway network is grid type network with access station
Point o is two sides migration of the starting point respectively to the vertical direction of the old route by website o.During route migration if with
Original old route has intersection in network, then generates new site k.If not having intersection point with old route, work as route
When the arbitrary width t that migration is set to subway network, new website f is generated.Until the z default websites of new line attachment L
Number is all generated and is finished.
Wherein radial pattern random walk refers to that new line attachment L is when subway network is grid type network with access point
O is two sides migration of the starting point respectively to the non-vertical direction of the old route by website o.During route migration if with
Original old route has intersection in network, then generates new site k.If not having intersection point with old route, work as route
When the arbitrary width t that migration is set to subway network, new website f is generated.Until the z default websites of new line attachment L
Number is all generated and is finished.
Wherein ring-like route migration is referred to when subway network has loop line, the first access website of new line attachment L
When o and network center distance d is greater than network center's radius r, new line attachment L is with network center using access point o as starting point
The center of circle, using distance d as radius migration clockwise or counter-clockwise, during route migration if with original old in network
Route has intersection, then generates new site k.If not having intersection point with old route, when route migration is set to subway network
When fixed website average headway, new website f is generated.Until website o is returned in new line attachment L migration, then route L is generated
It finishes.
The advance of above scheme is：
Firstly, new line select old website as the preferentially mechanism of access point in terms of, in subway network, from initial stage
Start, the ratio of mediocre node and rich node is much larger than other complex networks, cause BA model preferentially mechanism in subway network
The problem of randomization of middle change, preferentially by two steps point two layers, i.e., the first step according to route degree preferentially, if existing in network same
The station of route degree, then carry out second step with station centre's property for guiding preferentially, can reach time in choose, use up new line
Amount can select nearly intown station as access point, meet practical subway construction situation.
Secondly, how the newly-increased station in new line should successively position on two-dimensional space, i.e., from key station to two
How station on extreme direction successively selects spatial position, is that migration rule will solve the problems, such as.Pass through the reality of inventor's early period
Card analysis finds that the route degree of subway network obeys drift power law distribution, not only there is random exponential distribution, but also exist preferentially
Scale-free degree distribution, therefore, on the basis of selecting new line access point according to above-mentioned preferentially mechanism, further according to city road
Circuit planning, the main center in city and sub-center plan the network structure form for determining subway network, then according to subway network structure
Form, the migration direction of given line control route migration direction by the corner dimension of control new line and old route, are pressing from both sides
New site is generated at random within the scope of certain step pitch in angular region.
Above-mentioned technical proposal of the invention has the beneficial effect that：
In above scheme, Central model choose it is larger compared with the probability at nearly (within 5 stations) apart from downtown, in network
Transfer station appears in that a possibility that position closer apart from downtown is bigger, which is able to reflect used car station in city
Geographical location attribute in space is consistent with Research Hypothesis to the attraction feature of new line.Also, pass through Central preferentially mould
The subway network that type generates, scale factor, average least transfer number, cluster coefficients, maximum communication path characteristic value more connect
Nearly original value.Illustrate that the preferentially rule based on space preference is more in line with the dynamic evolution mechanism of real subway network, research knot
Fruit can be the scheme comparison of subway network design phase, and further network dynamics analysis provides basis.
Detailed description of the invention
Fig. 1 is test number of repetition and subway network station number Mean curve figure in the embodiment of the present invention, wherein (a)
It (b) is BA model test number of repetition for central model test number of repetition and subway network station number Mean curve figure
With subway network station number Mean curve figure；
Fig. 2 is test number of repetition and subway network linking number Mean curve figure in the embodiment of the present invention, wherein (a)
It (b) is BA model test number of repetition for central model test number of repetition and subway network linking number Mean curve figure
With subway network linking number Mean curve figure；
Fig. 3 is test number of repetition and subway network transfer station number Mean curve figure in the embodiment of the present invention, wherein
(a) it is central model test number of repetition and subway network transfer station number Mean curve figure, (b) is BA model test
Number of repetition and subway network transfer station number Mean curve figure；
Fig. 4 is example subway network in the embodiment of the present invention；
Fig. 5 is test number of repetition and access point select probability curve graph in the embodiment of the present invention, wherein (a) is
Central model test number of repetition and access point select probability curve graph (b) are BA model test number of repetition and access point
Select probability curve graph.
Specific embodiment
To keep the technical problem to be solved in the present invention, technical solution and advantage clearer, below in conjunction with attached drawing and tool
Body embodiment is described in detail.
The present invention provides a kind of subway network model building method.
Substantially steps are as follows for this method：
(1) BA model is preferentially：
The preferential attachment probability for the number of lines that newly-increased route passes through according to existing station is selected；
In formula, kiIndicate the subway line number of i of passing through a station, kjIndicate the subway line number of j of passing through a station；
Judge with the presence or absence of station identical with the route degree of station i is chosen in network, if there is no Website Hosting Ω
={ 1,2,3......m }, so that kn(n∈Ω)=ki, then the access point of station i that BA model selects as newly-increased route is executed；It is no
Then execute below step；
(2) based on the Central model of space center's property preference：
Station set in step (1) with same line degree is carried out second according to cluster coefficients preferential attachment probability
Preferentially：
In formula, ciFor the cluster coefficients of subway station i, cnFor the cluster coefficients of subway station n, n ∈ Ω, set omega=1,
2,3......m } the route degree k at any station inn(n∈Ω)=ki；
It is equal to the station i of BA model optimum selecting when the cluster coefficients at stations all in Website Hosting Ω are both less than, then vehicle
I stand as the access point for increasing route newly；Otherwise to the station in set omega={ 1,2,3......m } again according to being able to reflect
The station cluster coefficients of station centre's property carry out preferentially：
In formula, cmFor the cluster coefficients at any station in set omega={ 1,2,3......m }；
(3) route random walk in the direction indicated is increased newly：
If it is grid type network, two intersection routes are positive intersection road subway network, i.e., the website on newly-increased route
Need the migration on the orthogonal direction of line attachment；If it is radial pattern network, increase newly the website on route need with access
Route non-vertical direction migration；Ring-like route needs to guarantee that first and last node is overlapped in the last one time step.
In the specific implementation process, method is as follows：
In order to which preferentially the regular evolution for being more applicable for subway network, the present invention choose the stronger space preference that illustrates
The Moscow subway network of typical radial pattern network structure type carries out quantization comparative analysis, and it is excellent to compare traditional node degree
Modeling type selects the rule of old node, the subway network topological structure obtained by two kinds of models as newly-increased line access network
Scale factor, average least transfer number, cluster coefficients, maximum communication path characteristic value comparison, it was demonstrated that it is proposed by the present invention
The validity of algorithm.
The first step generates network.
Moscow subway network is generated using Central model and BA modeling respectively.Parameter setting l=12, wherein
1, ring-like route, 8 radial mode routes, 3 branching type routes, every route contain 17 websites, and the present invention is made using mean value
Standard is calculated for test number (TN), the station number of the subway network model of number of repetition and generation is tested, linking number, changes vehicle into
Number of standing Mean curve figure is shown in Fig. 1, Fig. 2 and Fig. 3.
Second step, model Validity are examined.
To Central model and BA model, preferentially mechanism repeats test 100 times, the characteristic value of the subway network of generation respectively
Average value, standard deviation, root-mean-square error are shown in Table 1.
Table 1 repeats 100 results of test and compares
By table 1, it can be seen that, the station number of the subway network based on the generation of Central preferential model, is changed linking number
Standard deviation at station number is 5.20,4.24,4.41, is all slightly less than the standard deviation 5.76,4.62,4.79 of BA preferential model,
Thus the stability of Central preferential model is relatively high, and the dispersion degree of test result is relatively small；Although being based on
Station number, the linking number root-mean-square error 6.18,10.58 for the subway network that Central preferential model generates are slightly larger than base
In the root-mean-square error 5.89,10.23 for the subway network that BA preferential model generates, but the root-mean-square error of transfer station number
4.48 are much smaller than the root-mean-square error 5.1 of BA preferential model transfer station number.In subway network, the number of transfer station is
Network heterogeneity, the most important characteristic quantity of connectivity are influenced, and increases or decreases 1 non-transfer station, to the dynamics of network
Characteristic influences not significant.Therefore, in terms of the stability of model and validity two, it is based on Central preferential model
Mechanism of Evolution be better than BA model.
Third step, interpretation of result
Basic assumption：The midpoint of one radial course is the center of route region in city, new line access point
It is closer apart from midpoint station, closer to downtown range, more meet Subway Network in China planning design principle of disposal wires.Illustratively with Fig. 4
For iron net network, subway line 1,2,3 is successively loaded into network, and the midpoint of route 1,2,3 is respectively station 4,2,10.Route
Station 2 on 2 selection routes 1 is linked into subway network, 2, station access point, which includes two companies apart from station 4
It connects, therefore access point and intown distance are 2 stations；Route 3 selects the station 10 on route 2 as access point, the access point away from
The distance of 2 key station 2 of offline road is 1 station.The induced effect that is formed to reflect subway gauze to city subsidiary-centers and right
The effect of discongesting of core space traffic pressure takes when defining a station while having a plurality of route to pass through apart from intown distance
Minimum value.
Based on condition assumed above, analyzing Central model and BA model respectively first, preferentially mechanism repeats test 100 times
The fluctuation situation of the curve of access point.Fig. 5 horizontal axis x indicates access point apart from intown distance, and longitudinal axis y indicates that access point is certain
The probability value of one distance, z-axis indicate experiment number.By Fig. 5, it can be seen that, when experiment number is less than 40 times, access point is certain
The fluctuation of the probability of one distance is larger, and when test number (TN) reaches 80 times, access point is that the fluctuation of the probability of a certain distance becomes smaller, and tries
It is almost the same to test 80,90,100 trend, therefore, it is credible to repeat to test 100 access points select probability that is averaged.
Comparing Central model and BA model, preferentially mechanism repeats test 100 times, and the average select probability of access point is shown in
Table 2.Preferentially by Central model, selecting the probability of key station is 8.84%, is higher than BA model optimum selecting downtown vehicle
The probability 6.81% stood；And probability of the Central model optimum selecting apart from 0~3 station of downtown is gradually increased, and is selected apart from city
The probability at 4 station of center reaches peak value 15.58%, selects the access point for being greater than 4 stations apart from downtown, and select probability is sequentially reduced,
Apart from downtown, most far the select probability at 8 stations is 2.91%；The access point of BA model selection and the position at station are not shown
Apparent correlation, randomness is larger, at 2 station of downtown and 5 stations occur two minor peaks, selection apart from 1 station of downtown,
The probability at 2 stations is greater than Central model, but the probability apart from 3~5 station of downtown is less than Central model；BA model selection away from
Probability from the farthest station in downtown is 3.70%, greater than the 2.91% of Central model.
The average select probability of 2 access point of table
It is available by the above test result, the Central model of building choose apart from downtown it is relatively close (5 stations with
It is interior) probability it is larger, i.e., a possibility that transfer station appears in position closer apart from downtown, is bigger, which can
Reflect that geographical location attribute of the used car station in city space to the attraction feature of new line, is more in line with real subway network
Dynamic evolution mechanism.
For the validity for further examining Central preferential model to simulate subway network, the present invention is from subway network
Three the scale factor characteristic quantity of uncalibrated visual servo characteristic, the least transfer number of small world, cluster coefficients characteristic quantities, it is right
The average value of 100 test results of Central preferential model and BA model is compared, and is shown in Table 3.
100 assay features value average values of 3 Central preferential model of table and BA model
As can be seen from Table 3, the subway network generated by Central preferential model, scale factor, average minimum are changed
Multiply number, cluster coefficients, maximum communication path characteristic value closer to original value.This illustrates that Central preferential model more can be true
Subway network mechanism of Evolution on the spot.
The above is a preferred embodiment of the present invention, it is noted that for those skilled in the art
For, without departing from the principles of the present invention, several improvements and modifications can also be made, these improvements and modifications
It should be regarded as protection scope of the present invention.
Claims (4)
1. a kind of subway network model building method, it is characterised in that：Including steps are as follows：
(1) BA model is preferentially：
Provide the probability π (k whether some website i in initial network is increased newly route L connectioni), and with this probability π (ki) make
Whether to enter the foundation of next step, if entered in next step, provide possess the set omegas of all websites of this probability=
{ 1,2,3......m }；
(2) the Central model based on space center's property preference is preferentially：
There is equal probabilities π (k what step (1) providedi) Website Hosting in Ω={ 1,2,3......m }, using in space
The Central model of disposition preference further carries out the website in set preferably, finally to provide newly-increased route L access network
First access point n, subsequently into the route migration model of next step；
(3) route random walk in the direction indicated is increased newly：
The connection for newly accessing new road L and current subway network is completed, by specified migration rule, so that current subway network
Route number m+1 item is become by m item.
2. subway network model building method according to claim 1, it is characterised in that：BA model in the step (1)
Probability π (the k preferentially connectedi) be calculated as follows：
In formula, i indicates the i-th each site identity traversed, kiIndicate the metro operation route for passing through website i in current procedures
Sum, j identifies the mark of website in network in current procedures, Σ kjIndicate network in all websites by the total of route number
With.
3. subway network model building method according to claim 1, it is characterised in that：Based on sky in the step (2)
Between centrality preference Central model preferentially in step (1) with same line degree station gather according to cluster coefficients
Preferential attachment probability carries out for the second time preferentially：
In formula, ciFor the cluster coefficients of subway station i, cnFor the cluster coefficients of website n in subway network, n ∈ Ω, set omega=
{ 1,2,3......m } Website Hosting to be selected provided for previous step, π (ci) it is website i according to cluster coefficients ciSelected is general
Rate, as π (ciWhen)=1, website i must be selected；
Probability π (cn) calculated as the following formula：
In formula, cmFor the cluster coefficients at station any in set omega={ 1,2,3......m }, set omega={ 1,2,3......m }
In, station cluster coefficients maximum value is cn, π (cn) it is website n according to cluster coefficients cnSelected probability.
4. subway network model building method according to claim 1, it is characterised in that：It is specified in the step (3)
Migration rule includes the random walk of orthogonal type direction, radial pattern random walk and loop line migration.
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| CN101799839B (en) * | 2010-01-19 | 2012-05-23 | 浙江工业大学 | Method for establishing public traffic network model with controllable network diameter based on random overlapping faction and public traffic network model |
| CN103034753B (en) * | 2012-11-29 | 2015-03-04 | 浙江工业大学 | Method for modeling public transport network based on oriented random walk |
| CN107766969A (en) * | 2017-09-28 | 2018-03-06 | 东南大学 | A kind of major station cable release distribution method based on the identification of subway service ability bottleneck section |
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