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Research ArticleImproved Road-Network-Flow Control Strategy Based onMacroscopic Fundamental Diagrams and Queuing Length inConnected-Vehicle Network

Xiaohui Lin,1 Jianmin Xu,2 Peiqun Lin,2 Chengtao Cao,1 and Jiahui Liu2

1 Institute of Rail Traffic, Guangdong Communication Polytechnic, Guangzhou, China2School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China

Correspondence should be addressed to Xiaohui Lin; [email protected]

Received 17 July 2017; Revised 7 October 2017; Accepted 16 October 2017; Published 12 November 2017

Academic Editor: Francesco Soldovieri

Copyright © 2017 Xiaohui Lin et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Connected-vehicles network provides opportunities and conditions for improving traffic signal control, and macroscopicfundamental diagrams (MFD) can control the road network at the macrolevel effectively. This paper integrated proposed real-timeaccess to the number of mobile vehicles and the maximum road queuing length in the Connected-vehicles network. Moreover,when implementing a simple control strategy to limit the boundary flow of a road network based onMFD, we determined whetherthemaximum queuing length of each boundary section exceeds the road-safety queuing length in real-time calculations and timelyadjusted the road-network influx rate to avoid the overflow phenomenon in the boundary section. We established a road-networkmicrotraffic simulation model in VISSIM software taking a district as the experimental area, determined MFD of the region basedon the number ofmobile vehicles, andweighted traffic volume of the road network.When the road network was tending to saturate,we implemented a simple control strategy and our algorithm limits the boundary flow. Finally, we compared the traffic signal controlindicators with three strategies: (1) no control strategy, (2) boundary control, and (3) boundary control with limiting queue strategy.The results show that our proposed algorithm is better than the other two.

1. Introduction

With the rapid development of the social economy, vehi-cle ownership has surged, causing urban traffic congestionproblems and bottlenecks in urban development. To reducevehicle-delay time and queuing length and ease traffic con-gestion, advanced traffic-control technologies are being used,and intelligent traffic signal control systems are implementedin largest cities [1–3]. However, as traffic volume continuesto increase, urban traffic appears oversaturated, and theeffectiveness of the original traffic-control system is reduced.

Daganzo et al. [4–9] researched many traffic-data reportsand found that there was objective regularity in the urbantraffic network. In other words, there is a connection betweenthe traffic condition of the road network and the number ofmobile vehicles, which is called themacroscopic fundamentaldiagrams (MFDs). He et al. [10] presented a figure-eighthysteresis pattern of MFDs for the 3rd ring urban freeway in

Beijing, China.The observation is unveiled to be the results ofthe counterclockwise loop in the figure-eight hysteresis pat-tern and the association between lower occupancy varianceand lower mean occupancy.

Some other scholars have proposed to control the trafficin oversaturated areas using MFD theory to improve thetraffic congestion in oversaturated areas. For example, Yanet al. [11] proposed a novel iterative learning control (ILC)strategy for traffic signals of urban road networks using therepeatability feature of traffic flow. Zhong et al. [12] exploreda new robust perimeter control framework for dynamic trafficnetworks with parameter uncertainty (on the MFD) andexogenous disturbance induced by travel demand. Ji et al. [13]proposed a feedback gating control policy which can be usedto mitigate network congestion by adjusting signal timingsof gating intersections based on MFD. Girault et al. [14]examined the impacts of signal coordination on an idealizedgrid network using the AIMSUN microsimulation software.

HindawiMathematical Problems in EngineeringVolume 2017, Article ID 8784067, 7 pageshttps://doi.org/10.1155/2017/8784067

https://doi.org/10.1155/2017/8784067

2 Mathematical Problems in Engineering

Han and Moutarde [15] pursued to describe the typicaltemporal patterns of the global traffic states and achievelong-term prediction of the large-scale traffic evolution ina unified data-mining framework. Geroliminis et al. [16]proposed an optimal perimeter control for two-region urbancities with the use of MFDs. Yi-Man et al. [17] proposeda new traffic management method that focuses on regionaltraffic volume dynamic control (based on macroscopic fun-damental diagram and gating measure) and supplementedby conventional optimization. An et al. [18] proposed four-step network partition approach to solve the problem ofheterogeneous network partitioning, which utilizes the con-cept of lambda-connectedness and the technique of regiongrowing. Lin [19, 20] also has proposed a simple controlstrategy to limit the boundary flow of a road network basedon MFD and verified its effectiveness. In our further study,strategies that limit the peripheral traffic flow on the roadnetwork should avoid the situation of upstream intersectioncongestion caused by overflow of vehicle queues at theintersection where peripheral flow is limited. In addition,we found that determining whether the boundary sectionoccurs the overflow phenomenon has become the key to theproblem.

Recently, more and more developed and developingcountries have been vigorously promoting vehicle networktechnologies because of their great potentials in the intelligenttransportation systems. In the vehicle network, vehicle loca-tion, speed, and other information can be uploaded in real-time to the command centre through the vehicle terminal androadside unit to provide a reliable means to determine thenumber of vehicles and queuing length of the road networkand to provide opportunities and conditions for improvingthe traffic signal controllers.

In this new study, we proposed a control strategy to limitroad-network boundary traffic based on MFD and queuinglength that real-time accesses the number of vehicles inroad network and the maximum queuing length in the roadsection based on the MFD. Moreover, when implementingthe road traffic-control strategy in the road network, ourstrategy based on the MFD helps to determine whetherthe maximum queuing length of each boundary sectionexceeds the road safety queue length or not and timelyadjust the influx rate of road network to avoid the overflowphenomenon of the boundary section.

2. Methodology

2.1. Basic Assumptions. For the study, the following assump-tions are made:

(1) All the vehicles are equipped with GPS in connected-vehicle network, which can achieve the location,speed, and other information to the signal controldevice of the intersection.

(2) Thephase of the road boundary intersections used themode of individual release of each import.

(3) The traffic flow in the studied road network is over-saturated.

N0

qw

qwc

qwi

Ni Nc

(Ni, qwi )

Figure 1: Macroscopic fundamental diagrams, MFD.

(4) The studied road network with relatively uniformtraffic density (homogeneous network) has macro-scopic fundamental diagram.

2.2. Analysis of Microscopic Fundamental Diagrams. Accord-ing to MFD theory, the formula of relevant parameters is thefollowing:

𝑁 = ∑𝑖

𝑘𝑖𝑙𝑖,

𝑞𝑤 = ∑𝑖 𝑞𝑖𝑙𝑖∑𝑖 𝑙𝑖 ,𝑘𝑤 = ∑𝑖 𝑘𝑖𝑙𝑖∑𝑖 𝑙𝑖 ,𝑜𝑤 = 𝑘𝑤 ∙ 𝑠 = ∑𝑖 𝑜𝑖𝑙𝑖∑𝑖 𝑙𝑖 ,

(1)

where𝑁 represents road-network vehicles (pcu); 𝑞𝑤, 𝑘𝑤, and𝑜𝑤 represent weighted traffic flow (pcu/h), weighted density(pcu/km), and weighted time occupancy rate, respectively; 𝑖and 𝑙𝑖 represent section 𝑖 and the length of this section (km);𝑞𝑖, 𝑘𝑖, and 𝑜𝑖 represent the flow rate (pcu/h), density (pcu/km),and time occupancy of section 𝑖, respectively; and 𝑠 representsthe average of vehicle lengths.

According to the MFD theory, the relationship betweenthe weighted traffic (𝑞𝑤) and the number of vehicles (𝑁)in the urban road network can be established, as shown inFigure 1. When 𝑁 approaches 𝑁𝑐 (critical vehicle number),the road network begins to enter the congested state from thenoncongested state.

2.3. Real-Time Traffic Data ina Connected-Vehicles Environment

2.3.1. The Number of Mobile Vehicles and Traffic Volume inthe Road Network. In the connected-vehicles network, thevehicle is equipped with GPS (vehicle equipment), which cansend latitude, longitude, speed, and other information to the

Mathematical Problems in Engineering 3

roadside unit in real-time. Determining whether a mobilevehicle (vehicles with average speed greater than 5 km/h) fallswithin the network area is equivalent to determining whetherthe point falls within the polygon area. The ray method [21]can be used to determine whether the vehicle falls withinthe network area, which the ray method draws a line fromthe latitude and longitude point of the vehicle to be judgedin one direction and calculates the number of intersectionswithin the road-network boundary. If the number is evenor 0, then the point is outside the network area; if it isodd, then the point is inside the network area (ignore twospecial circumstanceswhen the line passes through the vertexof road-network boundary and when vehicle latitude andlongitude points are on the edge of road network). Based onthe above judgment, the number of vehicles falling withinthe road-network area is converted into the equivalent trafficvolume, and the number of vehicles 𝑁 and the flow rate ofeach road section qi of the road network (𝑖 represents the 𝑖thsection) can be determined.

2.3.2. The Maximum Queuing Length of Road Section. Wehave previously discussed calculating the distance betweeneach vehicle and the entrance stop line of each road sectionin the connected-vehicles network [15, 16], and the formula isas follows:

𝑑𝑖𝑗= √(𝐴𝑊𝑖𝑗 − 𝐵𝑊𝑖)2 × 115.7892 + (𝐴𝐽𝑖𝑗 − 𝐵𝐽𝑖)2 × 86.6672,

(2)

where 𝑑𝑖𝑗 represents the distance between the 𝑗th vehicle inthe 𝑖th section and the entrance stop line of this section;𝐴𝐽𝑖𝑗, and 𝐴𝑊𝑖𝑗 represent the latitude and longitude of the𝑗th vehicle in the 𝑖th section, respectively; and 𝐵𝐽𝑖, and 𝐵𝑊𝑖represent the latitude and longitude of the entrance stop linein the 𝑖th section, respectively.

Therefore, the distance set𝐷 of the vehicles arriving at thestop line in each section is expressed as follows:

𝐷 = {𝑑𝑖𝑗 | 𝑖 ∈ 𝐿, 𝑗 ∈ 𝑁} . (3)The instantaneous velocity set 𝑉 of the vehicles is

expressed as follows:

𝑉 = {V𝑖𝑗 | 𝑖 ∈ 𝐿, 𝑗 ∈ 𝑁} , (4)where V𝑖𝑗 represents the instantaneous speed of the 𝑗th vehiclein the 𝑖th section.

The vehicle with the instantaneous speed V ≤ 5 km/h isdefined as a queuing vehicle, so the queuing length set 𝑄𝐿 ofall the queuing vehicles in the road section can be obtained:

𝑄𝐿 = {𝑑𝑖𝑗, V𝑖𝑗 | 𝑖 ∈ 𝐿, 𝑗 ∈ 𝑁, V𝑖𝑗 ≤ 5} . (5)Therefore, the maximum queuing length of the vehicle in

the 𝑖th section can be expressed as follows:𝑞𝐿max(𝑖) = max (𝑄𝐿 𝑖) . (6)

Take 95% of the road section length 𝐿 𝑖 as the roadsafety queue length 𝐿 𝑠𝑖. If 𝑞𝐿max(𝑖) ≥ 𝐿 𝑠𝑖, it causes thevehicle to queue up to the upstream of upstream intersection,resulting in traffic congestion at the upstream intersections.Therefore, we should avoid upstream intersection congestionby implementing a strategy to limit road-network boundaryintersection flow.

2.4. Boundary Traffic Limitation Strategy. We previouslyproposed to determine the road network traffic status basedon the MFD. When the road network tends to be congested,we can apply a simple control strategy to limit the boundaryflow on the road network [12] as follows.

𝑞𝐺 (𝑡 + Δ𝑡) + 𝑁 (𝑡) − 𝑂 (𝑡) = 𝑁𝐶,𝑅in = 𝑞𝐺 (𝑡 + Δ𝑡)𝐼 (𝑡) ,

𝐼𝑖 (𝑡 + Δ𝑡) = 𝑅in ∙ 𝐼𝑖 (𝑡) ,(7)

where 𝑡 represents time (h); Δ𝑡 represents time step (h); 𝑞𝐺represents postcontrol road-network boundary traffic flowinflux volume (pcu/h); 𝐼 represents road-network traffic flowinflux volume at time 𝑡 (pcu/h); 𝐼𝑖(𝑡) represents the trafficinflux volume (pcu/h) at the 𝑖th entrance at time 𝑖; 𝐼(𝑡)=∑𝐼𝑖(𝑡);𝑂(𝑡) represents the road-network outflow volume ata time (pcu/h); and 𝑅in represents the influx rate (allowabletraffic flow influx rate).

According to the allowable influx flow rate 𝐼𝑖(𝑡 + Δ𝑡), theWebster timing method can be used to recalculate the bestsignal cycle of each boundary intersection after limiting theflow. The green light time 𝑔𝑖(𝑡 + Δ𝑡) of boundary entranceafter limiting the flow can be simplified as 𝑔𝑖(𝑡 + Δ𝑡) =𝑅in × 𝑔𝑖(𝑡), and in order to avoid the influence of the greentime of the opposite direction, it can be used in single phaserelease limiting direction, or, for the release of the symmetricphase, it can turn off the control signals (green time) ofentering direction ahead of time, and the green time for theexit direction remains unchanged.

After further study, we found that after implementing thesimple strategy to control boundary flow, because individualboundary intersections fail to provide enough space forthe vehicle queue, the queue overflows to the upstreamintersections. To avoid queue overflow, we should implementthe control strategy to limit boundary flow while consideringthe boundary section queuing space. Specific ideas are asfollows:

𝑞𝑚 (𝑡) = (1 − 𝑅in) ∙ ∑𝑆

𝐼𝑆 (𝑡) , (8)where 𝑆 is the numbering of entrance sections of boundaryintersections that are not suitable for limiting the flow.

If 𝑞𝑚(𝑡) = 0, the strategy to limit the peripheral flow isimplemented based on the 𝑅in influx rate; if 𝑞𝑚(𝑡) > 0, then𝑞𝑚(𝑡) is evenly transferred to other boundary intersections,readjusting the influx rate 𝑅in, and the formula derivationprocess is as follows:

Δ𝑞𝑚 = 𝑞𝑚 (𝑡)𝑛 − 𝑥 =(1 − 𝑅in) ∙ ∑𝑆 𝐼𝑆 (𝑡)𝑛 − 𝑥 , (9)


where 𝑛 is the total number of entrance sections at the road-network boundary intersections; 𝑥 is the total number ofentrance sections that are not suitable for limiting flow atthe road-network boundary intersections; 𝑛 − 𝑥 is the totalnumber of entrance sections suitable for limiting flow at theroad-network boundary intersections; andΔ𝑞𝑚 is the averageflow limit, which should be increased in other boundarysectionswhen there is an overflowphenomenon in individualboundary sections.

The entrance flow limit that is suitable for limiting theflow at the road-network boundary intersections is calculatedas follows:

𝑞𝑚𝑦 (𝑡 + Δ𝑡) = (1 − 𝑅in) ∙ 𝐼𝑦 (𝑡) + Δ𝑞𝑚, (10)where 𝑦 is the numbering of entrance sections suitable forlimiting flow at the road-network boundary intersection.

The new influx volume of each entrance suitable forlimiting flow at the road-network boundary intersections isexpressed as follows:

𝑞𝐺𝑦 (𝑡 + Δ𝑡) = 𝐼𝑦 (𝑡) − 𝑞𝑚𝑦 (𝑡 + Δ𝑡)= 𝐼𝑦 (𝑡) − [(1 − 𝑅in) ∙ 𝐼𝑦 (𝑡) + Δ𝑞𝑚]= 𝑅in ∙ 𝐼𝑦 (𝑡) − Δ𝑞𝑚.

(11)

The new influx volume of all the entrances suitable forlimiting flow at the road-network boundary intersections iscalculated as follows:

𝑞𝐺 (𝑡 + Δ𝑡) = ∑𝑦

𝑞𝐺𝑦 = 𝑅in ∙ ∑𝑦

𝐼𝑦 (𝑡) − (𝑛 − 𝑥) Δ𝑞𝑚= 𝑅in ∙ ∑

𝑦

𝐼𝑦 (𝑡) − 𝑞𝑚 (𝑡)

= 𝑅in ∙ [𝐼 (𝑡) −∑𝑆

𝐼𝑆 (𝑡)]− (1 − 𝑅in) ∙ ∑

𝑆

𝐼𝑆 (𝑡)= 𝑅in ∙ 𝐼 (𝑡) − ∑

𝑆

𝐼𝑆 (𝑡) .

(12)

The actual influx volume 𝐼(𝑡) of road-network boundaryintersections suitable for limiting flow is calculated as follows:

𝐼 (𝑡) = 𝐼 (𝑡) −∑𝑆

𝐼𝑆 (𝑡) . (13)The new influx rate 𝑅in after readjustment is calculated as

follows:

𝑅in = 𝑞𝐺 (𝑡 + Δ𝑡)𝐼 (𝑡) =

𝑅in ∙ 𝐼 (𝑡) − ∑𝑆 𝐼𝑆 (𝑡)𝐼 (𝑡) − ∑𝑆 𝐼𝑆 (𝑡)= (1 − 𝑅in) ∙ 𝑅in ∙ 𝐼 (𝑡) − 𝑞𝑚(1 − 𝑅in) ∙ 𝐼 (𝑡) − 𝑞𝑚 .

(14)

Thedetails of above control process are shown in Figure 2.

Exited flow No

Yes

No

Yes

Yes

No

Yes

According to the the in�ux rate,implemented the boundary currentlimiting control strategy

No

No

Yes

Set i = i + 1

qm(t) > 0?

qm(t) = qm(t) + (1 − Rin) ∗ Ii(t)

qLmax(i)(t) ≥ Lsi?

N(t) ≥ Nc?

Under the vehiclenetworking, calculate thenumber of mobile vehiclesN(t), qm(t) = 0

Δt = 0?

Readjusted the in�ux rate:

RＣＨ =(1 − RＣＨ)RＣＨI (t) − qm(1 − RＣＨ) I (t) − qm

Under the vehicle networking, calculatethe maximum queue length of the number i ofthe boundary road, qLmax(i)(t)

RＣＨ =NC − N(t) + O(t)

I(t)

Set the in�ux rateas Rin

i ≤ n

Figure 2: Flow chart of a control strategy to limit the boundary flowthat takes queuing space into account.

3. Simulation Experiments

In this paper, we also chose to study the Guangzhou TianheDistrict Sports Center business district, as we did in aprevious report [15, 16] and as shown in Figure 3, of whichTianhe North Road, Tianhe Road, and Tianhe East Road arethe main roads of the region.

3.1. Determine MFD. In the VISSIM traffic simulation soft-ware, we established the simulation model for the road-network traffic, which can effectively simulate the connected-vehicles network, as shown in Figure 4. In the road-networksimulationmodel, we started to simulate the traffic flow fromthe lowest value and increased drive-in traffic volume ineach road section of road-network boundary by 100 pcu/hevery 900 s until reaching the peak of oversaturated state.The total-simulation time was 27000 s and the data wascollected once every 120 s for a total of 225 data points; finally,statistics were performed on the number of road-network


AB

C E

D

F

G

H

IJ

K

L

M

N

O

P

R

LＨＩ. = 10

402 m

446 m

LＨＩ. = 10

256 m

LＨＩ. = 10

285 m

LＨＩ. = 10

682 m

LＨＩ. = 10

963 m

LＨＩ. = 10

627 m

LＨＩ. = 10

695 m

LＨＩ. = 4

LＨＩ. = 4

870 m

LＨＩ. = 6

185 mLＨＩ. = 4

180 m

LＨＩ. = 10

208 mLＨＩ. = 6

331 m

LＨＩ. = 4

367 m

LＨＩ. = 8

448 m

LＨＩ. = 4

800 m

Note: LＨＩ._thenumber lanes of

the two ways of

the road

Figure 3: Tianhe District Sports Center business district diagram.

Figure 4: Tianhe business district road-network simulation model.

mobile vehicles (obtained by calculating road section density𝑘𝑖 ∗ road section length 𝐿 𝑖), traffic influx volume at bound-ary intersections, traffic outflow volume, and road sectiontraffic volume for further processing to obtain the road-network benchmark MFD, as shown in Figure 4.

From the fitting curve of Figure 5, themaximumweightedflow 𝑞𝑤𝑐 = 15978 pcu/h and the critical vehicle number 𝑁𝑐 =1090 pcu of the region were calculated. Figure 5 shows thatwhen the number of vehicles𝑁 > 1090 pcu, the road networkis in an oversaturated congestion state.

3.2. Simulation Boundary Traffic Flow Limitation Strategy.We used the C# programming language to perform sec-ondary development on the com programming interfaceprovided by VISSIM and implemented the control strategyto limit the boundary flow while considering the boundarysection queuing space. To obtain the maximum boundarysection queuing length, a queuing detector was established inthe road safety queuing position.When the road networkwassimulated to 133 cycles (simulation time was about 15960 s),the road network entered the congestion state. Accordingto the control strategy to limit boundary flow, the initialroad-network influx rate was 92% and 8% of the traffic rateneeded to be limited. Therefore, to simplify the calculation,we reduced 8%of the green light time in the drive-in direction

R2 = 0.915

y = −0.013x2 + 28.34x + 532.82

02,0004,0006,0008,000

10,00012,00014,00016,00018,000

Wei

ghte

d tr

affic (

qw

)

500 1,000 1,500 2,0000Number of vehicles (N)

Figure 5: MFD graph of the simulated road network.

of boundary section for resimulation analysis. After runningabout 156 cycles, due to the limited queuing space of roadsections CR, ED, and FG (as shown in Figure 3), queuingspace become insufficient, and the queue overflowed toupstream intersections.Thus, we needed to readjust the road-network outflow rate. Based on the boundary flow controlalgorithm that considers queuing space, we recalculated theoutflow rate as 90%. In other words, we did not limit the flowon the road sections CR, ED, and FG, and we implemented90% of influx rate limit on other boundary sections and redidthe simulation analysis.

We analyzed simulation data of oversaturated roadnetwork (15960–27000 s were simulation time period foroversaturation) with three control strategies: (1) no controlstrategy which was not implemented the strategy to limitperipheral flow; (2) boundary control which implementedthe simple strategy to limit the peripheral flow; and (3)boundary control with limiting queue strategy which imple-mented the control strategy to limit the boundary flow whileconsidering queuing space and obtaining the traffic signalcontrol indicators of the oversaturated road network, asshown in Figures 6–8.

Table 1 shows that the average delay time of boundarycontrol and boundary control with limiting queue strat-egy were 12.6% and 17.1%, lower than no control strategy,respectively. The average stop times of boundary control andboundary control with limiting queue strategy were 6.7% and4.2%, lower than no control strategy, respectively.The averagequeuing lengths of boundary control and boundary controlwith limiting queue strategy were 17.7% and 18.6%, lower thanno control strategy. Respectively, the service indicators ofboundary control and boundary control with limiting queuestrategy are better than no control strategy, and boundarycontrol with limiting queue strategy is slightly better thanboundary control.

4. Conclusion

The connected-vehicles network andMFD present new ideasfor studying traffic signal control methods. We implementedthe control strategy to limit the boundary while consideringboundary section queuing space on the road network at


Table 1: Comparison of traffic signal control indicators for oversaturated road networks with three strategies.

No control strategy Boundary control Boundary control with limiting queue strategyAverage delay time (s) 19.9 17.4 16.5Average number of stops (times) 0.45 0.42 0.39Average queuing length (m) 23.1 19.0 18.8

No control strategyBoundary controlBoundary control with limiting queue strategy

L J G D R BNThe no. of the intersection

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

The a

vera

ge o

f the

que

ue le

ngth

(m)

Figure 6: Average queuing lengths at each intersection in oversatu-rated road network.

No control strategyBoundary controlBoundary control with limiting queue strategy

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

The a

vera

ge o

f he d

elay

tim

e (s)

L J G D R BNThe no. of the intersection

Figure 7: Average delay time at each intersection in oversaturatedroad network.

No current limitingThe simple boundary current limitingThe algorithm of this paper

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

The a

vera

ge o

f the

stop

s (tim

es)

L J G D R BNThe number of the intersection

Figure 8: Average stop times at each intersection in oversaturatedroad network.

the macrolevel in this paper by using the MFD theory inthe connected-vehicles network environment. However, theroad-network boundary mentioned in this paper is prede-fined, and we will continue to study the dynamic divisionmethod of road-network boundaries based on MFD in thenext stage.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This paper is jointly funded by Guangdong Province Scienceand Technology Development Special Funds (2016 Basic andApplied Basic Research, 2016A030313786) and GuangdongProvince Higher Education Outstanding Young TeachersTraining Program in 2015 (YQ2015184).

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