Complex Network Theoretical Analysis on Information Dissemination over Vehicular Networks

3 MB·

by  Jingjing Wang

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Complex Network Theoretical Analysis on
Information Dissemination over Vehicular
Networks
Jingjing Wang∗, Chunxiao Jiang∗, Longxiang Gao†, Shui Yu†, Zhu Han‡, and Yong Ren∗ ∗Department of
7 Electronic Engineering, Tsinghua University, Beijing, 100084, China
1 †School of Information Technology, Deakin University, Burwood, VIC 3125, Australia
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2 ‡Electrical and Computer Engineering Department, University of Houston, Houston, TX, USA
n E-mail: [email protected], {jchx, reny}@tsinghua.edu.cn, {longxiang.gao, syu}@deakin.edu.au, [email protected]
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J

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I Abstract
N
. How toenhance the communication efficiency and quality on vehicular networks is one critical important issue.
s
c While with the larger and larger scale of vehicular networks in dense cities, the real-world datasets show that the
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vehicular networks essentiallybelong tothecomplexnetwork model. Meanwhile, theextensive researchoncomplex
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v networks has shown that the complex network theory can both provide an accurate network illustration model and
0 further make great contributions to the network design, optimization and management. In this paper, we start with
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analyzingcharacteristicsofataxiGPSdatasetandthenestablishingthevehicular-to-infrastructure,vehicle-to-vehicle
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0 andthehybridcommunicationmodel,respectively.Moreover,weproposeaclusteringalgorithmforstationselection,
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a traffic allocation optimization model and an information source selection model based on the communication
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performances and complex network theory.
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: I. INTRODUCTION
v
i
X Due to the emerging of intelligent transport system, vehicular networks have received lots of attentions. Al-
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a though cellular networks enable convenientvoice communication and simple entertainment services to drivers and
passengers, they are not well-suited for certain direct vehicle-to-vehicle (V2V) or vehicle-to-infrastructure (V2I)
communications[1].Inparticular,howtoimprovetheperformancesofthecommunicationsystemhasalreadybeen
underdevelopment[2], where some key technologies[3], e.g., small cells, device-to-device(D2D) communication,
mobileclouds,flexiblespectrummanagement[4][5],etc.,canbeconsideredtobeemployedinvehicularnetworks.
In the literature of vehicular networks, many researches focused on improvement of the vehicle mobility mod-
els[6],communicationchannelmodelsandtheroutingstrategies[7][8][9][10],whilethenetworkpropertiesaswell
asthecomplexcharacteristicsofthevehicularnetworkshavenotbeenfullyinvestigated.Thevehicularnetworksare
associatedwithatremendousnetworksize.Moreover,diversehierarchicalstructuresandnodetypesgiverisetomore
complexinteractions.Furthermore,vehicularnetworkshave a complextime-spacerelationship.The mobilityof the
vehicleson the road lead to the dynamicevolutionarytopology.In terms of some hotcommunicationtechnologies,
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the ultra dense cellular deployment would lead to more than ever interactions among vehicle units (vehicles to
infrastructures and infrastructure to infrastructure) and the D2D based vehicular-to-vehicular communication also
lead to a more complex hybrid communication network. Therefore, it is necessary to view the vehicular networks
from the other dimension, i.e., using complex network theory to discover the complex characteristics of vehicular
networks, based on which the network performance can be improved.
Withthedevelopmentofrandomgraphmodel,thecomplexnetworktheoryemergedbasedonthe[11]and[12][13][14],
whichdiscoveredthesmall-wordpropertyandthepower-lawdistributionofthenodedegreeoftherealisticcomplex
networks. Based on the advantages of complex networks theory, this paper proposes a complex network theoretic
view on the vehicular networks with following original contributions. For one thing, this is the first work to
establish the vehicular network V2V and V2I models with complex network theory. Moreover, We use the node
degree,averagepathlength,clusteringcoefficientandbetweennesscentralityto analyzethetopologyofa vehicular
networkbasedonthetaxisGPSdatabaseofBeijing[15]andstudytherelationshipbetweenthenetworktopological
propertiesand communicationparameters.For anotherthing, we proposea clustering algorithm,a traffic allocation
model and an information source selection model depending on the communication impedance.
The rest of this paper is organizedas follows. Section II establishes a vehicularnetwork system model based on
the complexnetworktheory,andgivessome keyparametersandtheir characters.SectionIII describesthreetypical
vehicular communication models and three optimization algorithm models. Section IV gives the simulation results
for the proposed models. Concluding remarks and future work are given in Section V.
II. DATA-DRIVENCOMPLEX NETWORK MODEL
A. Dataset Analysis
In vehicular networks, vehicles can communicate with each other (V2V), and can also establish communication
withtheroadsideinfrastructures(V2I).Inthissubsection,weconstructthecomplexnetworkmodelforthevehicular
networks based on a real-world dataset, which contains the taxi GPS data of Beijing (longitude from 116.25 to
116.55, and latitude from 39.8 to 40.05) obtained from the Microsoft Research Asia [15].
Based ontheaforementionedGPSdataset,weplotthe vehiclespositiondistributionin theFig.1 atonemoment.
The vehicles position distribution clearly reflects the shape planning structure of Beijing and distinguishes its
downtown and suburban areas. In the following subsection, we will construct a weighted and undirected graph
model based on some key communication parameters for vehicular networks.
B. Weighted and Undirected Graph Models for Vehicular Networks
In accordance with the analyses above, we build the vehicular network model as a weighed and undirected
complexnetworkinwhichthenodesrepresentthevehiclesintheroadsegmentsandtheundirectededgesrepresent
the interaction between the nodes. The interaction in this paper means the communication between each two
vehicles. The edgesweightsmeasure the communicationperformanceson the vehicularnetworkswhich dependon
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40.05
40
Beijing39.95
The latitude of 39.9
39.85
Taxi GPS
39.8
116.25 116.3 116.35 116.4 116.45 116.5 116.55
The longitude of Beijing
Fig.1. Thetaxis GPSdistribution inBeijing (longitude from116.25to116.55andlatitude from39.8to40.05).
thedistancebetweenthecommunicationpairs,communicationchannelfading,theenvironmentdisturbanceandthe
cellular radius.
To simplify modeling and calculation, we assume that the communication ability of each vehicle is identical
and communicationchannel meets the COST 231-Bertoni-Ikegamimodel [16]. In addition, we neglect the cellular
gapsand the cellular shapes, which are notaffected by terrain. Accordingly,the weighted and undirectedvehicular
network is noted as a graph G=(V,E,R), where V is the set of vertices representing vehicles and E is the set
of edges representing the interaction among the vertices. Weights R reflect the communicationperformanceon the
vehicular network. R reflects the communication performance in the vehicular ad hoc network, where the specific
definition of the communication impedance R is based on the following key communication technologies:
Channel Model: Because of the city dotted with tall buildings and luxuriant trees, signals from sources may be
attenuatedseverelytodestinations.ThispaperusetheCOST231-Bertoni-IkegamiModeltoanalyzethetransmission
path loss. We assume that there exists a line-of-sight transmission path between each two communication-capable
vehicles. Therefore, the relatively accurate path loss in the urban area, L can be calculated as:
u
L =42.6+26logd+20logf dB, (1)
u c
where d is the transmission distance and f represents the signal carrier frequency.
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Ultra Dense Cellular Handover: Communicationsystem tends to construct a multi-layer heterogeneousnetwork
covering base stations and low power micro-stations. In order to improve spectrum efficiency and the transmission
capacity, we have made unremitting endeavor on the enhancement of the modulation and encoding methods,
while the decrease of cell radius can also result in a sharp increase of system capacity. Therefore, an appropriate
communicationcellradiusimprovesspatialmultiplexratioandreducesthesystempowerconsumption.Nonetheless,
an ultra dense cellular handover means a frequency conversion, more shared-spectrum interferences and more
difficulties in multi-point coordination. Spontaneously, the time-delay and handoff dropping probability are both
increased due to the ultra dense cellular handover, which increases the impedance of communication of each
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communicationlink. We make a statistical calculation of the number of cellular switching on each communication
link, noted as n . Based on the communication channel model and ultra dense cellular handover mentioned above
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andconsideringthenodedegreesandbetweennesscentralitiesinthecomplexnetworktheory,we definetheweight
of the edge connecting node i and node j, marked as R , which is named as link communication impedance:
ij
α(k B +k B )υ+βL ψ−µ(ϑ/d )ξ+ζn , d ≤r
 i i j j u ij s ij
R = (2)
ij 
∞, d ≤r
ij

where k represents the degree of the node i and B notes the betweenness centrality of vehicle i. ϑ shows the
i i
energy noise ratio, α,β,µ are characterized parameters varying with diffident network topology, and υ,ψ,ξ and
ζ are nonlinear control parameters. Based on the above definition, the communication impedance depends on
the node degree, link distance, frequency of communication, average signal energy noise ratio and the cellular
switching times. First, a vehicle with a large degree or high betweenness centrality means it participating in
quantitiesofcommunicationmissions,whichleadstoarelativelylongstore-and-forwarddelayandhighprobability
of blocking. Second, long communication distance conduces high path loss and consumes much more signal
power. What is more, a small cellular radius leads to more cell handovers n , which also increases the time delay
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and deteriorates the communication performance. In these two aspects, the communication impedance should be
positivelycorrelatedwith k, B and n . Third,a high averagesignalenergynoise ratio per unitdistance contributes
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a robust communication, naturally being negatively correlated to the impedance. In this way, we have completely
established a complex network graph model for the vehicular network communication.
C. Complex Network Verification
In this section, we quantitatively analyze and verify the small-world property and scaling-free property of the
vehicular networks. In the first place, we propose some key parameters depending on the complex network theory.
Node Degree Distribution: The node degree of a vehicle i in the vehicular network, marked as k , is defined as
i
the number of the vehicles it can communicate with. Moreover, p(k) is the probability that a randomized node’s
degree is k. And the distribution of p(k) is defined as the node degree distribution.
Clustering Coefficients: The characteristic that neighbors can also communicated with each other is called the
clusteringcharacteristic,whichmeasuresthetightnessofthenetwork.Thevehiclei’sclusteringcoefficientisdefined
as the following:
E
i
C = , (3)
i
k (k −1)/2
i i
where k represents the node degree of vehicle i and E is the number of communication links among neighbors.
i i
Further more, the general clustering coefficient of the entire network is the average of C .
i
Betweenness Centrality: The normalized betweenness centrality B, and therefore, is defined to measure the
importance of the node from another dimension, i.e.,
2 ni
B = st, (4)
i (N −1)(N −2) X g
st
s6=i6=t
5
60 1
Node degree Clustering coefficient
0.9
50
0.8
Node degree k234000 Clustering coefficient00..67
0.5
10
0.4
0
0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450
Node index n Node index n
(a)NodeDegree (b)Clustering Coefficient
0.7 0.25
2−neighbor clustering coefficient Betweeness centrality
0.6
0.2
2−neighbor Clustering coefficient0000....2345 Betweeness centrality00..001.551
0.1
0 0
0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450
Node index n Node index n
(c)2-neighbor Clustering Coefficient (d)Betweenness Centrality
Fig.2. TheComplexNetworkParameters Verification.
where g is the number of the shortest path from s to t, and ni notes the number of the shortest path via i from
st st
s to t.
A data-driven numerical simulation is conducted for the vehicular network and we verify the complex network
properties based on the Taxi GPS dataset. Fig. 2 demonstrates the parameters mentioned above of the proposed
network with communicationdistance r =500.Moreover,we calculated the average network clustering coefficient
C =0.7225 and the average path length l=6.73374.
The simulation results conform to the small world property (a high degree of clustering and a short average
path length) and a scaling free distribution in node degree and betweenness centrality. In consequence, we can
quantitatively treat the vehicular network as a complex network and the complex network theory bring us a new
perspective in network design, optimization and management for the communication on vehicular networks. Next
section, we will propose three optimization models under different communication models.
III. COMMUNICATION ON THEVEHICULARNETWORKS
In Section II, we have discussed the network topology of vehicular networks. Based on the analysis above,
we establish the V2I (Section III-A), V2V (Section III-B) and the hybrid communication model (Section III-C),
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respectively,withthecommunicationimpedance.Moreover,weproposeaclusteringalgorithmforstationselection,
a traffic allocation optimization model and an information source selection model.
A. Clustering Algorithm of the V2I Model
In the following, we will focus on the V2I communication model. Similarly, the vehicle impedance in the V2I
modelisdefinedbasedontheMassiveMIMOinvehicularcommunicationsystem,whichisatechnologytoenhance
the overall networks performance.With a large excess of service antennas over terminals and time-division duplex
operation, the extra antennas focuses energy into ever smaller regions of space and bring huge improvements in
communicationthroughputand energy efficiency. In [17], the authors proposed the throughputR (achievable rate
k
f
of the uplink transmission from user k to measure the behavior of massive MIMO systems):
R ,(1−τ −ς)E[log(1+γ )], (5)
k k
f
whereγ showsthethesignal-to-interference-plus-noise-ratio(SINR)whichisafunctioncontainingchannelmodel
k
parameters and antennas parameters. τ is the channel estimation (CE) time, and ς is the wireless energy transfer
(WET) time. In our model, we only consider the value of R instead of its impact factors. We assume that the
k
f
base stations directly communicate with vehicles within its control range, which means that the distance from a
vehicleto a basestationis lessthanthecellularradiusinthe V2IModel.Inthisway,wedefinethecommunication
impendence of vehicle i as follows:
R =α(k B )υ+βR ψ,i=1,2,...,N. (6)
i i i k
f
Similarly,k representsthedegreeofthenodei andB notesthe betweennesscentralityofthevehiclei. R shows
i i k
f
the throughput of a certain vehicle-to-station communication link. Besides, α and β are characterized parameters
varying with diffident network topologies, while υ and ψ are nonlinear control parameters. A clustering algorithm
based on the generalized distance D is presented.
D =ǫ(R +R )+(1−ǫ)d , (7)
ij i j ij
where R representsthe vehicle impendence,d representsthe realistic distance of two vehicles and ǫ denotes the
i ij
weighting coefficient.
Clustering algorithm based on generalized distance.
Step1: Select one sample point as the clustering center c .
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Step2: Calculate the generalized distances to the center, and select the i with max D as center c .
i ic1 2
Step3: Calculate all the generalized distances to the two centers, and select the j with max{min{D ,D }} as
jc1 jc2
center c , the rest can be done in the same manner.
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Step4: Based on the nearest neighbouring rule classifying other samples.
7
1000
6 10
900 14 18 23
m) 800 2 12
xis y ( 700 3 21 25
ng vertical a 456000000 4 7 8 9 16 17 20
Clusteri 230000 1 11 19 24
5 15
100 13 22
0
0 200 400 600 800 1000
Clustering horizontal axis x (m)
Fig.3. Aclustering example basedonthegeneralized distances (different colordotsdistinguishing thecategories).
Fig.3 shows a clustering example based on the generalized distance, which provides a constructive suggestion
on the base station selection and cellular division.
B. Traffic Allocation on the V2V Model
Intermsofthecomplexcommunicationmissionsinvehicularnetworks,a varietyofserviceslike real-timevoice
services, high definition video services and Internet access services should be supported whenever and wherever.
However, how to allocate the communication traffic in an optimal fashion is worth discussing in details. For
simplification,we assumethatthereare certainquantitiesof communicationtaskstransmittingfromn vehiclesto a
destinationvehicle.ThetotalcommunicationdemandquantityismarkedasQ.Letv bethevehiclenodesetandthe
starting vehicle set is denoted by S =s ,s ,...,s and X =x ,x ,...,x represents the allocated communication
1 2 n 1 2 n
traffic allocation set, where x is the actualcommunicationtask quantity on the ith communicationlink. We define
i
the cost function C(x) as:
n
C(x)=XXxiRuiv, (8)
i=1 u,v
whereRi isthecommunicationimpedancefromvehicleutovehiclev ontheDijkstrapathundertheconditionof
uv
transferringthe communicationtraffic x . Let c be the communicationcapacity of each communicationlink, which
i
denotes the maximum number of communication tasks and let m represents the total communication tasks on
uv
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the communication link between vehicle u and v, m ≤c. We have the following optimization problem:
uv
n
min C(x)= x Ri
XX i uv
i=1 u,v
s.t. x ≥0,∀i=1,2,...,n,
i
n (9)
x ≥Q,
X i
i=1
n
m = x ai ≤c,∀u,v ∈V,
uv X i uv
i=1
where x = [x ,x ,...,x ]T and ai = 1, when the traffic x goes through the link connecting the vehicle u and
1 2 n uv i
v, otherwise ai =0. The network traffic allocation optimization problem can be casted as a convex optimization
uv
problem in (11) by the definition of traffic-edge incidence matrix A∈RE×n, and
1, traffic j passing the edge i

A = (10)
ij 
0, otherwise

where E is the total number of probable links, x=[x ,x ,...,x ]T, and 1=[1,1,...,1] T. Then, we have
1 2 n
min C(x)
s.t. x≥0,
(11)
xT1≥Q,
Ax≤c1.
Furthermore, we can add a eigenfunction to this linear programming problem and rewrite it as follows:
n+E+1
1
min xTR + − log(−f (x))
w X t i
i=1
s.t. f (x)=−x ,i=1,2,...,n,
i i (12)
f (x)=Q−xT1,i=n+1,
i
f (x)=A x−c,i=n+2,n+3,...,n+E+1.
i i
where A represents the row vector of matrix A and auxiliary variable t>0 controls the computational accuracy.
i
R is the sum of the communication impendence of each the allocation routing.
w
The solution of the problem (12) is marked as x∗(t), which satisfies the condition:
1 1 1
tR − + ·1+AT =0, (13)
w x Q−xT1 c1−Ax
where let 1 =[ 1 , 1 ,..., 1 ]T, ∀x∈Rn. And we can prove that the deviation between x∗(t) and the optimal
x x1 x2 xn
solution of primal problem is not more than (n+E+1)/t. Many computer simulation algorithms can solve the
above optimization problem.
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C. Information Source Selection on the Hybrid Model
The criterionfor selecting the informationsource location is to make the network capacity maximize.In another
word,the informationbroadcastingfacilitiesshouldbelocatednear thesourcevehiclesassociatedwith information
replicas. In this subsection, we focus on the hybrid communication model, where we study the optimal source
vehicles selection strategy. Let q(i) indicate the probability of any packet to pass node i, and ni and g are
st st
defined identically as (4):
ni
q(i)= p(s,t) st, (14)
X X g
st
s(s6=i)t(t6=i)
where p(s,t) is the probability of a packet to choose source vehicle s and vehicle t as its destination. Instead of
uniform distribution, the source vehicles obey the probability p(s), while we assume that the destination vehicles
of packets are uniformly distributed and are independently selected. We have:
p(s)
p(s,t)=p(s)p(t)= . (15)
N −1
Then, the probability of any packet to pass vehicle i can be calculated as follows:
1 ni
q(i)= p(s) st. (16)
N −1XX g
st
s6=i t6=i
Define the p(i|s) measuring the conditional probability of the situation where packet starts from vehicle s to pass
vehicle i,
1 ni
p(i|s)= st. (17)
N −1 X g
st
t(t6=s,t6=i)
Then, R can be estimated as:
c
C
R = , (18)
c
max {R p(s)p(i|s)}
i i s
P
where R indicates the upper bound packets generated per time step to maintain in a flow state, and serves
c
as a measure of the overall capacity of the network system, which is a function of betweenness centrality and
communication impendence R .
i
The base station selection model, therefore, reduces to a a min-max problem:
min max {R p(s)p(i|s)}
i iXs
s.t. 0≤p(s)≤1, (19)
p(s)=1.
X
s
After introducing an auxiliary variable Λ:
Λ=max {R p(s)p(i|s)}(i=1,2,...,N), (20)
i iXs
10
12 45 9 0.09
The average communication impedance R11016789 rrrr====0001...k258mkkkmmm Cellular switching times ns112233405050505 rrrrr=====00011...k.2585mkkkkmmmm Vehicle communiation impedance12345678 Vehicle communiation impedance Optimal source selection probability p(s)00000000........0000000012345678 Selection probability
150 00 Ca1r5ri0e0r frequency in 52G00 c0ommunication2 (5M0H0z) r=1.5km3000 00. 02 0.03 0.04 0C.0e5llular r0a.d0i6us rc (0k.m07) 0.08 0.09 0.1 00 50 100 150Ve2h0i0cle ind2e5x0 n 300 350 400 450 00 50 100 150 Ve2h0i0cle Ind2e5x0 n 300 350 400 450
(a) The impact of carrier fre- (b) Cellularswitchingtimeswith (c) Communication impedance (d) Optimal source selection
quency on the impendence with different communication ranges. of each vehicle in the descend probability p(s)distribution.
different communication ranges. order.
Fig.4. Communication impedances analysis andoptimalinformation sourceselection onthehybridmodel.
the optimization problem can be casted as a linear programming problem as follows:
min Λ
s.t. RAp−Λ1≤0,
(21)
pT1=1,
p≥0,
where A=[p(i|s)], p=[p(s),s=1,2,...,N]T and 1=[1,1,...,1]. R is defined in (22)
 R1 0 ··· 0 
.
.
R= ...0 R2 ... 0. . (22)
 
 
 0 ··· 0 RN 
Thus, we can easily find the minimal Λ by linear programming algorithms and get the numerical solution with
the help of calculating computer.
IV. SIMULATIONRESULTS
Inthissection,weconductsimulationontheextensivestudiesaboutthenetworktopologyandthecommunication
performancesbased on our models. First of all, we analyze the influence of the maximum communicationdistance
r and other key communication parameters on the network topology.
Section III-B proposed a vehicular network V2V communication model based on the complex network theory,
relyingonwhichweelaboratedsomecomplexityparameterstoanalyzetheperformanceofthenetworkintherespect
of topology structure. In the following, we analyze the effect of communicationparameters on the communication
impedance.Onthisscore,weonlyconcentrateonthetopologypropertiesofthevehicularnetworkbasedontheTaxis
GPS in Beijing for the time beingand give constructivesuggestionson the traffic managementand communication
design.
The carrier frequency mainly determines the transmission path loss L . We obtain five curves with different
u
maximum communication distances, as in Fig. 4 subgraph (a). The vertical coordinates represents the average
communicationimpedanceforeachoflinksandinthissituationweneglecttheeffectofnodeimportancebyletting