CN105185107A - GPS-based traffic running tendency prediction method - Google Patents

Abstract

The invention provides a GPS-based traffic running tendency prediction method, which takes a GPS device as a technological base, and achieves the prediction of traffic running tendency through analyzing intermediate parameters of traffic running index variation. The GPS-based traffic running tendency prediction method comprises the steps of: calculating a period average speed of road sections by using GPS data; judging traffic congestion state of a single road section; calculating period road network traffic running indexes; calculating a series of intermediate parameters of traffic running index variation; determining a state of traffic running tendency; and predicting the traffic running tendency.

Description

A kind of traffic circulation trend estimation method based on GPS

Technical field

The present invention relates to gps data processing technology field, specifically a kind of traffic circulation trend estimation method based on GPS.

Background technology

Vehicle GPS device can obtain the real-time information such as vehicle instantaneous velocity, positional information (longitude and latitude), deflection, by map-matching method by be mounted with the vehicle of GPS device in computation period information distribution in city road network on corresponding section, obtain cycle road grid traffic by a series of Treatment Analysis and run index, by the change to traffic circulation index, infer the traffic circulation trend of road network.

The traffic circulation trend of road network can describe a road network traffic flow and to operate steadily state, is the major criterion weighing road network traffic flow change.Current urban road traffic congestion problem is very severe, how can infer that traffic circulation variation tendency is an emphasis difficult problem urgently to be resolved hurrily.Traffic In Beijing research centre once proposed the computing method of a similar traffic congestion index, but its critical parameter truck kilometer number is a constant, belong to expert method to determine, just determine according to the traffic characteristics of locality, Beijing, to a certain degree do not possessing applicability, the estimation method in addition for traffic circulation trend does not relate to.And the present invention mainly utilizes GPS device, obtain road grid traffic velocity information and traffic congestion index comprehensively, infer traffic circulation trend on this basis.

Summary of the invention

The object of the invention is to utilize gps data to analyze the defect of road grid traffic operation trend to solve in prior art to lack, providing a kind of method of GPS device supposition traffic circulation trend that utilizes to solve the problems referred to above.

To achieve these goals, technical scheme of the present invention is as follows, comprises the following steps:

(1) gps data is utilized to calculate the cycle average velocity in section;

(2) traffic congestion state in single section is judged;

(3) computation period road grid traffic runs index;

(4) traffic circulation index variation series intermediate parameters is calculated;

(5) state of traffic circulation trend is determined;

(6) traffic circulation trend is inferred.

The described gps data that utilizes calculates the cycle average velocity in section, first gps data in the sampling period is matched on each section of road network by longitude and latitude, each sample vehicle average velocity on the section in the cycle is taked to represent the bulk flow velocity in section, the traffic behavior in reaction section.

$\stackrel{\‾}{V}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{V}_i}{n}$

Vehicle fleet through section in the n--sampling period, unit:;

V _i--average velocity in the cycle of each sample car, unit: km/h;

--Road average-speed in the sampling period, unit km/h;

The traffic congestion state in the single section of described judgement adopts threshold method to carry out traffic state judging, road-section average travel speed and the threshold value preset is compared, and then judges whether it blocks up, and determine the traffic behavior of its correspondence.

Described computation period road grid traffic runs index and comprises the following steps:

(41) calculate section to block up mileage ratio RCR, calculate through street mileage ratio RCRf, trunk roads block up mileage ratio RCRm and the branch road of mileage ratio RCRa, secondary distributor road that block up that block up respectively and to block up mileage ratio RCRl, computing formula is as follows:

If during through street,

If during trunk roads,

If during secondary distributor road,

If during branch road,

RCR＝RCRf*ω ₁+RCRa*ω ₂+RCRm*ω ₃+RCRl*ω ₄；

Wherein,

L (i) is the length of section i, the length of section i of Lc (i) for getting congestion,

N _fthe total number in section ,-through street,

N _athe total number in-trunk roads section,

N _mthe total number in-secondary distributor road section,

N _lthe total number in-branch road section,

W ₁, w ₂, w ₃, w ₄represent the weight of each grade road respectively,

(42) calculate road grid traffic congestion index TCI, computing formula is as follows:

$\mathrm{TCI}=\left\{\begin{array}{c}\frac{a}{2}(0\&le;a\&le;4)\\ 2+\frac{a-4}{2}(4<a\&le;8)\\ 4+\frac{(a-8)\&times;2}{3}(8<a\&le;11)\\ 6+\frac{(a-11)\&times;2}{3}(11<a\&le;14)\\ 8+\frac{a-14}{5}(14<a\&le;24)\\ 10(a\&GreaterEqual;24)\end{array}\right.$

Wherein: a=RCR*100.

Described calculating traffic circulation index variation series intermediate parameters, formula is as follows:

$\stackrel{\&OverBar;}{\mathrm{TCI}}=\frac{{\mathrm{TCI}}_{j-2}+{\mathrm{TCI}}_{j-1}+{\mathrm{TCI}}_j}{3};$

$\mathrm{\&sigma;}=\sqrt{\frac{1}{3}\underset{i=j-2}{\overset{j}{\mathrm{\&Sigma;}}}{({\mathrm{TCI}}_i-\stackrel{\&OverBar;}{\mathrm{TCI}})}^2};$

k ₁＝TCI _j-TCI _j-1,k ₂＝TCI _j-1-TCI _j-2；

$W=\frac{\mathrm{\&sigma;}}{\mathrm{TCI}}.$

Wherein:

TCI _jthe traffic circulation index of-current period;

TCI _j-1the traffic circulation index in-previous cycle;

TCI _j-2the traffic circulation index in-the first two cycle;

traffic circulation index and two cycle traffic in the past of-current period run the mean value of index;

Traffic circulation index and two cycle traffic in the past of σ-current period run the standard variance of index;

K ₁, k ₂traffic circulation index and two cycle traffic in the past of-current period run the first order difference of index;

Traffic circulation index and two cycle traffic in the past of W-current period run the standard variance average ratio of index.

The state of described determination traffic circulation trend, comprising: stability rises, sharpness rises; Stability declines, sharpness declines; Stability fluctuation, sharpness fluctuation.

The described supposition traffic circulation sharpness downtrending specific rules that becomes is as follows:

(71) if k ₁> 0, k ₂> 0, then development trend is for rising:

If (71A) W≤W ₁, then development trend is that stability rises;

If (71B) W > W ₁, then development trend is that sharpness rises;

(72) if k ₁< 0, k ₂< 0, then development trend is for rising:

If (72A) W≤W ₂, then development trend is that stability declines;

If (72B) W > W ₂, then development trend is that sharpness declines;

(73) if k ₁* k ₂≤ 0, then development trend is fluctuation:

If (73A) W≤W ₃, then development trend is stability fluctuation;

If (73B) W > W ₃, then development trend is sharpness fluctuation;

Wherein parameter W ₁, W ₂, W ₃determine according to concrete data.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 road section traffic volume Operation class divides figure.(illustrate: according to traffic engineering correlation theory, distribution frequency statistics is carried out to different brackets road vehicle travel speed, determine according to 85%, 50%, 30% and 15% speed of a motor vehicle respectively.)

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is speed-saturation degree corresponding relation figure.

Embodiment

Based on a traffic circulation trend estimation method of GPS, comprise the following steps:

S1, gps data is utilized to calculate the cycle average velocity in section.First match on each section of road network by gps data in the sampling period by longitude and latitude, on the section in the fetch cycle, each sample vehicle average velocity represents the bulk flow velocity in section, the traffic behavior in reaction section.

$\stackrel{\&OverBar;}{V}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i}{n}$

Wherein, the vehicle fleet through section in the n--sampling period, unit:;

V _i--average velocity in the cycle of each sample car, unit: km/h;

--Road average-speed in the sampling period, unit km/h;

S2, judge the traffic congestion state in single section.Adopt threshold method to carry out traffic state judging, road-section average travel speed and the threshold value preset are compared, and then judges whether it blocks up, and determine the traffic behavior of its correspondence.

Threshold value is in table 1.Table 1 is originated: Guangzhou Local technical standard---urban highway traffic postitallation evaluation index system.

S3, computation period road grid traffic run index.Comprise the following steps:

S31, calculate section and to block up mileage ratio RCR, calculate through street mileage ratio RCRf, trunk roads block up mileage ratio RCRm and the branch road of mileage ratio RCRa, secondary distributor road that block up that block up respectively and to block up mileage ratio RCRl, computing formula is as follows:

If during through street,

If during trunk roads,

If during secondary distributor road,

If during branch road,

RCR＝RCRf*ω ₁+RCRa*ω ₂+RCRm*ω ₃+RCRl*ω ₄；

Wherein,

L (i) is the length of section i, the length of section i of Lc (i) for getting congestion,

N _f: the total number in section, through street,

N _a: the total number in trunk roads section,

N _m: the total number in secondary distributor road section,

N _l: the total number in branch road section,

W _f, w _a, w _m, w _lrepresent the weight of each grade road respectively, its computing formula is as follows:

$w_f=\frac{L_f}{L_f+L_a+L_m+L_l}$

$w_a=\frac{L_a}{L_f+L_a+L_m+L_l}$

$w_m=\frac{L_m}{L_f+L_a+L_m+L_l}$

$w_l=\frac{L_l}{L_f+L_a+L_m+L_l}$

Wherein:

L _fit is the total length of through street in Regional Road Network;

L _ait is the total length of trunk roads in Regional Road Network;

L _mit is the total length of secondary distributor road in Regional Road Network;

L _lit is the total length of branch road in Regional Road Network.

S32, calculating road grid traffic congestion index TCI, computing formula is as follows:

$\mathrm{TCI}=\left\{\begin{array}{c}\frac{a}{2}(0\&le;a\&le;4)\\ 2+\frac{a-4}{2}(4<a\&le;8)\\ 4+\frac{(a-8)\&times;2}{3}(8<a\&le;11)\\ 6+\frac{(a-11)\&times;2}{3}(11<a\&le;14)\\ 8+\frac{a-14}{5}(14<a\&le;24)\\ 10(a\&GreaterEqual;24)\end{array}\right.$

Wherein: a=RCR*100.

S4, calculating traffic circulation index variation series intermediate parameters

$\stackrel{\&OverBar;}{\mathrm{TCI}}=\frac{{\mathrm{TCI}}_{j-2}+{\mathrm{TCI}}_{j-1}+{\mathrm{TCI}}_j}{3};$

$\mathrm{\&sigma;}=\sqrt{\frac{1}{3}\underset{i=j-2}{\overset{j}{\mathrm{\&Sigma;}}}{({\mathrm{TCI}}_i-\stackrel{\&OverBar;}{\mathrm{TCI}})}^2};$

k ₁＝TCI _j-TCI _j-1,k ₂＝TCI _j-1-TCI _j-2；

$W=\frac{\mathrm{\&sigma;}}{\mathrm{TCI}}.$

Wherein:

TCI _jthe traffic circulation index of-current period;

TCI _j-1the traffic circulation index in-previous cycle;

TCI _j-2the traffic circulation index in-the first two cycle;

traffic circulation index and two cycle traffic in the past of-current period run the mean value of index;

Traffic circulation index and two cycle traffic in the past of σ-current period run the standard variance of index;

K ₁, k ₂traffic circulation index and two cycle traffic in the past of-current period run the first order difference of index;

Traffic circulation index and two cycle traffic in the past of W-current period run the standard variance average ratio of index.

S5, determine the state of traffic circulation trend

1. stability rising, 2. sharpness are risen;

3. stability decline, 4. sharpness decline;

5. stability fluctuation, 6. sharpness fluctuation.

S6, supposition traffic circulation trend

1) if k ₁> 0, k ₂> 0, then development trend is for rising:

(1) if W≤W ₁, then 1. development trend is;

(2) if W > is W ₁, then 2. development trend is;

2) if k ₁< 0, k ₂< 0, then development trend is for rising:

(1) if W≤W ₂, then 3. development trend is;

(2) if W > is W ₂, then 4. development trend is;

3) if k ₁* k ₂≤ 0, then development trend is fluctuation:

(1) if W≤W ₃, then 5. development trend is;

(2) if W > is W ₃, then 6. development trend is;

Wherein parameter W ₁, W ₂, W ₃determine according to concrete data.

Suggestion W ₁, W ₂, W ₃∈ [0.08,0.1].

More than show and describe ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; the just principle of the present invention described in above-described embodiment and instructions; the present invention also has various changes and modifications without departing from the spirit and scope of the present invention, and these changes and improvements all fall in claimed scope of the present invention.The protection domain of application claims is defined by appending claims and equivalent thereof.

Embodiment

Based on intersection traffic congestion index computing method for Floating Car, comprise the following steps:

(1) Floating Car gps data is utilized to calculate section bicycle sample speed;

(2) road-section average travel speed is extracted;

(3) saturation degree of each entrance driveway of crossing is calculated;

(4) saturation degree of crossing is calculated;

(5) congestion index of crossing is calculated;

(6) crossing operation service horizontal estimated.

S1, to utilize floating car data to calculate section bicycle sample speed be bicycle sample mean travelling speed in calculating measurement period.Obtain sample vehicle j the routing information { P of adjacent 2 of front and back of process _i, i=1, after 2, L, n}, obtains the Average Travel Speed in this path by path and mistiming when approach section number only have one (not crossing over crossing) or time kilometer/hour (unimpeded state), will be assigned to section P ₁; Otherwise, by following principle, in conjunction with the instantaneous velocity v of starting point ₁with the instantaneous velocity v of terminal ₂, point four kinds of traffic behaviors are to each section speed of approach assignment respectively:

1. deceleration regime (meets ) time

Initial section velocity amplitude is composed other section velocity amplitude calculates according to the travel time principle of correspondence, namely uses total travel time Δ t _jdeduct the travel time in initial section, then obtain speed by distance divided by this time.

2. acceleration mode (meets ) time

Stopping section velocity amplitude tax is other section velocity amplitude calculates according to the travel time principle of correspondence.

3. first slow down when accelerating afterwards

Initial section velocity amplitude is composed as v ₁, stop section velocity amplitude and compose as v ₂, middle section (if existence) velocity amplitude calculates according to the travel time principle of correspondence.

When 4. first accelerating to slow down afterwards

Vehicle is in the state of loitering, and approach section velocity amplitude is composed and is

S2, extraction road-section average travel speed are the many cars sample mean travel speeds according to section in a measurement period.Computing formula is as follows:

$\left\{\begin{array}{ccc}{V}_i=\frac{l_i}{t_i}=\frac{l_i}{\left(\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{l_i}{v_j}\right)/n}=\frac{n}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{v_j}},& \mathrm{if}& n_i\&NotEqual;0\\ V_i={\stackrel{\&OverBar;}{V}}_i,& \mathrm{if}& n_i=0\end{array}\right.$

V in formula _ifor segmental arc P _iaverage velocity, l _ifor segmental arc P _ilength, t _ijfor jth car segmental arc P in the paths _ion travel time, n _ifor segmental arc P _ithe upper number of vehicles participating in calculating.Here, n is worked as _iequal 0, when namely this section not having data cover, we supplement by the historical average speeds of one week different time sections of historical accumulation; Work as n _iwhen being not equal to 0, section travelling speed is the harmonic average speed of multiple sample.

S3, single entrance driveway section saturation computation, step is as follows:

S31, using road-section average travel speed as module, determine that entrance driveway section traffic behavior divides threshold criteria.Entrance driveway section traffic behavior is divided into 5 grades: freely flow, unimpeded, jogging, crowded, block up, corresponding threshold criteria interval be (s0, s1], (s1, s2], (s2, s3], (s3, s4], (s4, s5].

S32, basis " HCM " and " urban road intersection planning and design specification " relevant regulations, determine the corresponding relation of each entrance driveway traffic behavior, speed and saturation degree.See the following form:

The mapping table of table entrance driveway traffic behavior, speed and saturation degree

Traffic behavior rank	Traffic behavior describes	Speed class	Saturation degree V/C
				1	Freely flow	(s0，s1]	(r0，r1]
2	Unimpeded	(s1，s2]	(r1，r2]
				3	Jogging	(s2，s3]	(r2，r3]
4	Crowded	(s3，s4]	(r3，r4]
				5	Block up	(s4，s5]	(r4，r5]

S33, single entrance driveway section saturation computation

Corresponding certain the entrance driveway saturation degree (R in crossing _i) computing formula is as follows:

$R_i=r_n-\frac{s-s_n}{s_{n-1}-s_n}(r_n-r_{n-1})$

Wherein:

S: the value of road-section average travel speed;

N: corresponding traffic behavior rank, the value of n is 1,2,3,4,5;

S _n: the threshold speed upper limit that traffic behavior n rank is corresponding;

S _n-1: the threshold speed lower limit that traffic behavior n rank is corresponding;

R _n: the saturation degree upper threshold that traffic behavior n rank is corresponding;

R _n-1: the saturation degree bottom threshold that traffic behavior n rank is corresponding.

S4, intersection saturation degree ISV calculate, and intersection saturation degree is the weighted sum of all importers upwards saturation degree.Step is as follows:

S41, intersection saturation degree calculate, and formula is as follows:

ISV＝R ₁*ω ₁+R ₂*ω ₂+...+R _j*ω _j

Wherein:

ω _i(i=1 ..., n): i-th importer to weighting coefficient intersection saturation degree be the weighted sum of all importers upwards saturation degree.

R _i(i=1 ..., n): i-th importer to saturation degree.

S42, weighing computation method

The weighting coefficient in crossing inlet direction is relevant with category of roads.In table 2:

Table 2 category of roads and weighted value mapping table

Category of roads	Through street	Trunk roads	Secondary distributor road	Branch road
					Weighted value	w' 1	w' 2	w' 3	w' 4

Four weighted values meet

Then the some importers in crossing to weighted value computing formula as follows:

$w_j=\frac{{w^{\&prime;}}_j}{\underset{1}{\overset{n}{\mathrm{\&Sigma;}}}{w^{\&prime;}}_j}$

Wherein:

W' _jcalculate importer to weighted value corresponding to category of roads;

that each importer of this crossing is to category of roads respective weights value sum.

S5, crossing congestion index ICI calculate, and formula is as follows:

$\mathrm{ICI}=\left\{\begin{array}{cc}10*\mathrm{ISV}& \mathrm{ISV}<1\\ 10& \mathrm{ISV}\&GreaterEqual;1\end{array}\right.$

S6, crossing operation service horizontal estimated are based on the congestion index of crossing, estimate crossing congestion level.In Table.

Show the crossing congestion level analytical table based on crossing congestion index

Congestion index	[0,3)	[3,6)	[6,7.5)	[7.5,9)	[9,10]
						Crossing congestion level	Very unimpeded	Unimpeded	Slightly block up	Moderate is blocked up	Heavy congestion

At present, Beijing provincial standard is blocked up in evaluation criterion exposure draft and the application such as Guo Jifu relevant, just simple concept and the computing method proposing road network congestion index, and mainly to block up mileage according to section in the method computation process, crossing congestion index is not proposed.Due to crossing singularity, section of comparing is comparatively complicated, therefore does not embody.In addition, if the information spinner that prior art obtains intersection saturation degree relies on the fixed detecting devices such as traditional coil checker, video detector, these detector device costs are high, Maintenance Difficulty, therefore propose and calculate intersection saturation degree based on floating car technology.

The method has two major features, and one is that the speed obtained according to floating car technology calculates intersection saturation degree; Two is crossing congestion index computing method.The proposition of the method makes up the disappearance of domestic crossing congestion index computing method, utilize the Road average-speed that floating car technology obtains, by the calculating of intersection stomatodeum saturation degree, realize the calculating to crossing congestion index, achieve the operation service horizontal estimated to crossing, can meet the demands such as signal control, intersection channelizing, intersections planning, cost is low and effect is high.

More than show and describe ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; the just principle of the present invention described in above-described embodiment and instructions; the present invention also has various changes and modifications without departing from the spirit and scope of the present invention, and these changes and improvements all fall in claimed scope of the present invention.The protection domain of application claims is defined by appending claims and equivalent thereof.

Claims (7)

1., based on a traffic circulation trend estimation method of GPS, it is characterized in that comprising the following steps:

(1) gps data is utilized to calculate the cycle average velocity in section;

(2) traffic congestion state in single section is judged;

(3) computation period road grid traffic runs index;

(4) traffic circulation index variation series intermediate parameters is calculated;

(5) state of traffic circulation trend is determined;

(6) traffic circulation trend is inferred.

2. a kind of method utilizing GPS device to infer traffic circulation trend according to claim 1, it is characterized in that, first gps data in sampling period matches on each section of road network by longitude and latitude by the described cycle average velocity utilizing gps data to calculate section, get and take each sample vehicle average velocity on the section in the cycle to represent the bulk flow velocity in section, the traffic behavior in reaction section.

Vehicle fleet through section in the n--sampling period, unit:;

V _i--average velocity in the cycle of each sample car, unit: km/h;

--Road average-speed in the sampling period, unit km/h.

3. a kind of method utilizing GPS device to infer traffic circulation trend according to claim 1, it is characterized in that, judge that the traffic congestion state in single section adopts threshold method to carry out traffic state judging, road-section average travel speed and the threshold value preset are compared, and then judge whether it blocks up, and determine the traffic behavior of its correspondence.

4. a kind of method utilizing GPS device to infer traffic circulation trend according to claim 1, it is characterized in that, described computation period road grid traffic runs index and comprises the following steps:

(41) calculate section to block up mileage ratio RCR, calculate through street mileage ratio RCRf, trunk roads block up mileage ratio RCRm and the branch road of mileage ratio RCRa, secondary distributor road that block up that block up respectively and to block up mileage ratio RCRl, computing formula is as follows:

If through street,

If trunk roads,

If secondary distributor road,

If branch road,

RCR＝RCRf*ω ₁+RCRa*ω ₂+RCRm*ω ₃+RCRl*ω ₄；

Wherein,

L (i) is the length of section i, the length of section i of Lc (i) for getting congestion,

N _fthe total number in section ,-through street,

N _athe total number in-trunk roads section,

N _mthe total number in-secondary distributor road section,

N _lthe total number in-branch road section,

W ₁, w ₂, w ₃, w ₄represent the weight of each grade road respectively,

(42) calculate road grid traffic congestion index TCI, computing formula is as follows:

Wherein: a=RCR*100.

5. a kind of method utilizing GPS device to infer traffic circulation trend according to claim 1, is characterized in that, described calculating traffic circulation index variation series intermediate parameters, and formula is as follows:

k ₁＝TCI _j-TCI _j-1,k ₂＝TCI _j-1-TCI _j-2

Wherein:

TCI _jthe traffic circulation index of-current period;

TCI _j-1the traffic circulation index in-previous cycle;

TCI _j-2the traffic circulation index in-the first two cycle;

traffic circulation index and two cycle traffic in the past of-current period run the mean value of index;

Traffic circulation index and two cycle traffic in the past of σ-current period run the standard variance of index;

K ₁, k ₂traffic circulation index and two cycle traffic in the past of-current period run the first order difference of index;

Traffic circulation index and two cycle traffic in the past of W-current period run the standard variance average ratio of index.

6. a kind of method utilizing GPS device to infer traffic circulation trend according to claim 1, it is characterized in that, the state of described determination traffic circulation trend, comprising: stability rises, sharpness rises; Stability declines, sharpness declines; Stability fluctuation, sharpness fluctuation.

7. a kind of method utilizing GPS device to infer traffic circulation trend according to claim 1, is characterized in that, the described supposition traffic circulation sharpness decline gesture specific rules that becomes is as follows:

(71) if k ₁> 0, k ₂> 0, then development trend is for rising:

If (71A) W≤W ₁, then development trend is that stability rises;

If (71B) W > W ₁, then development trend is that sharpness rises;

(72) if k ₁< 0, k ₂< 0, then development trend is for rising:

If (72A) W≤W ₂, then development trend is that stability declines;

If (72B) W > W ₂, then development trend is that sharpness declines;

(73) if k ₁* k ₂≤ 0, then development trend is fluctuation:

If (73A) W≤W ₃, then development trend is stability fluctuation;

If (73B) W > W ₃, then development trend is sharpness fluctuation;

Wherein parameter W ₁, W ₂, W ₃determine according to concrete data.