## Comm.utoronto.ca

Mobility-based Clustering in VANETs using
Affinity Propagation
Christine Shea, Behnam Hassanabadi and Shahrokh Valaee
Department of Electrical and Computer Engineering
University of Toronto
Toronto, ON, M5S 2E4,

*Abstract*—The recent research in cluster-based MAC and rout-
There has been much research on cluster-based VANETs in
ing schemes for Vehicle Ad Hoc Networks (VANETs) motivates
the recent literature, which has been focused on developing
the necessity for a stable VANET clustering algorithm. Due to the
cluster-based MAC protocols, as in [3 – 9]. and cluster-based
highly mobile nature of VANETs, mobility must play an integralrole in cluster formation. We present a novel, mobility-based
routing protocols, as in [10] and [11]. In [4] and [9], the cluster
clustering scheme for Vehicle Ad hoc Networks, which utilizes
head (CH) takes on a managerial role and facilitates intra-
the Affinity Propagation algorithm in a distributed manner.

cluster communication by providing a TDMA schedule to its
The proposed algorithm considers typical vehicular mobility
cluster members. In [9], adjacent clusters are assigned different
during cluster formation to garner clusters with high stability.

CDMA codes to avoid interference between clusters. The work
Simulation results confirm the superior performance of theproposed algorithm, when compared to other accepted mobility-
in [9] shows a substantial reduction in probability of message
based clustering techniques, in terms of average cluster head
delivery failure, when compared to traditional 802.11 MAC.

duration, average cluster member duration, and average rate of
The recent research discussing cluster-based MACs and
cluster head change.

routing schemes for VANETs, present many similar low-
maintenance clustering algorithms. In these schemes nodes
are required to transmit periodic HELLO beacons to indicate
Research in vehicular communications, specifically Vehic-
their present state of either Undecided, Cluster Head or Cluster
ular Ad Hoc Networks (VANETs), is playing a vital role
Member. An undecided node will join the first CH that it hears
in the future safety and ease of our roads. VANETs will
a HELLO beacon from, and if the node does not hear from a
enhance driver safety and reduce traffic deaths and injuries
CH within a given time period, it will become a CH itself. In
by implementing collision avoidance and warning systems. In
these schemes, the first node to declare CH status wins.

addition, VANETs can relieve traffic congestion by providing a
Node mobility should play an integral part in cluster cre-
driver with live routes that avoid road hazards and bottleneck
ation in order to achieve stability. In [4], mobility is addressed
areas. The vast sensor network that VANETs will create, is
during cluster collision; when two cluster heads come within
inciting countless other applications, and making VANETs a
range, the winning CH will be the one with both lower relative
hot topic in ad hoc networking today.

mobility and closer proximity to its members. Alternatively,
The VANET scenario has various difficult challenges for
[8] addresses mobility by first classifying nodes into speed
communication, many of which can be addressed by a clus-
groups, such that nodes will only join a CH of similar velocity.

tered network. VANETs have a highly-mobile environment
The above clustering techniques are lacking in cluster stability,
with a rapidly changing network topology. By clustering the
because they do not attempt to select a stable CH during initial
vehicles into groups of similar mobility, the relative mobility
cluster head election.

between communicating neighbor nodes can be reduced. Both
Although there is not a VANET clustering scheme focused
delay-intolerant (e.g. safety messages) and delay-tolerant (e.g.

on cluster stability, there are many mobility-based clustering
road/weather information) data will need to be transmitted, ne-
techniques for ad hoc networks. A well-known mobility-based
cessitating Quality-of-Service (QoS) requirements. Clustering
clustering technique is MOBIC [12], which is an extension
has been shown to effectively reduce data congestion [1], and
of the Lowest-ID algorithm [13]. In Lowest-ID, each node is
can support QoS requirements [2]. In addition, traffic jams and
assigned a unique ID, and the node with the lowest ID in
high node density in urban areas will be inevitable. This leads
its two-hop neighborhood is elected to be the cluster head.

to contention and the hidden terminal problem, which are the
In MOBIC, an aggregate local mobility metric is the basis
performance limiting factors in a dense network and can be
for cluster formation instead of node ID. The node with
effectively alleviated by a clustered topology.

the smallest variance of relative mobility to its neighbors is
This work was supported in part by AUTO21 NCE and MARK IV
elected as the cluster head. The relative mobility for a certain
Industries - IVHS Division
node is estimated by comparing the received power of two
consecutive messages from each neighboring node. Cluster
all the data points are initialized with the same constant self-
head re-election only occurs when two cluster heads move
similarity, then all data points are equally likely to become
within range of one another for a certain contention interval.

exemplars. By increasing and decreasing this common self-
When a cluster member moves out of range of its cluster head,
similarity input, the number of clusters produced is increased
it joins any current cluster head in its neighborhood, or forms
and decreased respectively.

a new cluster.

There are two types of messages passed in this technique.

The previous cluster-based VANET research motivates the
The

*responsibility*,

*r*(

*i, j*), is sent from

*i *to candidate exemplar
need for a stable VANET clustering scheme. In this paper,

*j *and indicates how well suited

*j *is to be

*i*'s exemplar, taking
we propose a distributed mobility-based clustering algorithm
into account competing potential exemplars. The

*availability*,
focused on cluster stability, where stability is defined by

*a*(

*i, j*), is sent from candidate exemplar

*j *back to

*i*, and
long cluster head duration, long cluster member duration,
indicates

*j*'s desire to be an exemplar for

*i *based on supporting
and low rate of cluster head change. We achieve this al-
feedback from other data points. The

*self-responsibility*,

*r*(

*i, i*)
gorithm by utilizing a new data clustering technique called
and

*self-availability*,

*a*(

*i, i*), both reflect accumulated evidence
Affinity Propagation (AP) [14]. Our clustering scheme will
that

*i *is an exemplar.

form clusters with both minimum distance and minimum
The update formulas for responsibility and availability are
relative velocity between each cluster head and its members.

We assume position information is provided by the vehiclesGPS. We validate our proposed algorithm by comparing it
to the mobility-based ad-hoc clustering scheme, MOBIC [12].

*r*(

*i, j*)

*← s*(

*i, j*)

*−*
*a*(

*i, j *) +

*s*(

*i, j *)

*j0 s.t.j0 6*=

*j*
MOBIC is well-established and stability driven, thus providinga good benchmark for our algorithm's success.

The rest of this paper is organized as follows. Section
II presents the Affinity Propagation algorithm. Section III

*a*(

*i, j*)

*← *min
0

*, r*(

*j, j*) +
max 0

*, r*(

*i , j*)
proposes our distributed, mobility-based, VANET clustering
algorithm. Section IV presents our simulation results, andfinally this paper concludes with Section V.

*a*(

*j, j*)

*←*
max 0

*, r*(

*i , j*)
II. AFFINITY PROPAGATION

*i0 s.t.i0 6*=

*j*
Thus far, we have discussed clustering from an ad hoc
Responsibility and availability message updates must be
networking perspective, however clustering is also used in
damped to avoid numerical oscillations that will prevent the
scientific data analysis, where it aims to process and detect
algorithm from converging. This is done by updating new
patterns in data. Data clustering is a static, one-shot process
messages as follows:

*mnew *=

*λmold *+ (1

*− λ*)

*mnew*, where
that searches data for a set of centers, or

*exemplars*, which best

*λ *is a weighting factor between 0 and 1. In AP, the clustering
describe the data. In this context, clustering aims to minimize
is complete when the messages converge. Another feature
the distance between each data point and its assigned exemplar,
of the algorithm is the ability to determine when a specific
where distance could be Euclidian distance, or any other
data point has converged to cluster head status in its given
application-specific function. A revolutionary new technique
cluster. When a point's self-responsibility plus self-availability
for data clustering is the Affinity Propagation (AP) algorithm
becomes positive, that point has become the cluster head.

[14], which has been shown to produce clusters in much less
Upon convergence, each node

*i*'s cluster head is:
time, and with much less error than traditional techniques(such as K-means clustering [15]). Here, clustering error refers

*CHi *= arg max

*{a*(

*i, j*) +

*r*(

*i, j*)

*}*
to the application-specific distance between each data pointand its assigned exemplar. In Affinity Propagation, data points
III. PROPOSED VANET CLUSTERING SCHEME
pass messages to one another, which describe the current
The proposed clustering technique uses the fundamental
affinity that one data point has for choosing another data point
idea of Affinity Propagation from a communications per-
as its exemplar.

spective and in a distributed manner. We call this algorithm,
This algorithm takes an input function of similarities,

*s*(

*i, j*),
Affinity PROpagation for VEhiclar networks, (APROVE). In
where

*s*(

*i, j*) reflects how well suited data point

*j *is to be
our algorithm, each node in the network transmits the respon-
the exemplar of data point

*i*. Affinity Propagation aims to
sibility and availability messages to its neighbors, and then
maximize the similarity

*s*(

*i, j*) for every data point

*i *and
makes a decision on clustering independently. This results, in
its chosen exemplar

*j*, therefore an application requiring a
a distributed algorithm, where every node is only clustering
minimization (e.g. Euclidean distance) should have a negative
with those in its one-hop neighborhood.

similarity function. Each node

*i *also has a self-similarity,
We design a similarity function for our algorithm with the

*s*(

*i, i*), which influences the number of exemplars that are
goal of creating stable clusters, and tailored to the VANET
identified. Individual data points that are initialized with a
environment. Our similarity function, shown below in (5), is a
larger self-similarity are more likely to become exemplars. If
combination of the negative Euclidean distance between node
positions now and the negative Euclidean distance between
The broadcast period for availability and responsibility
node positions in the future. This is a simple way to consider
messages is defined as

*TM *, which we set to 1

*s *in our
both node position and node mobility in cluster creation.

simulations. Each node

*i *will calculate its responsibility with
each neighbor

*j *using (1). This value is damped with the

*s*(

*i, j*) =

*− k*xi

*− *xj

*k *+

*k*x

*0*i

*− *x

*0*j

*k*
previous transmitted responsibility (where

*λ *= 0

*.*5), and stored
as

*r*(

*i, j*). Node

*i *then accumulates

*r*(

*i, j*) for each neighbor

*i *+

*vx,iτf*
*j *in the responsibility array, R
i, and broadcasts the array in

*yi *+

*vy,iτf*
the RESP packet. Each node

*i *will calculate the availability
where xi is a vector of node

*i*'s current position, and x

*0 *is
with each neighbor

*j *using the update equation (2). Node

*i*
a vector of node

*i*'s predicted future position. The function
will store

*j*'s damped availability in

*a*(

*j, i*) and accumulates
predicts each node

*i*'s future position in

*τf *seconds from now,
all

*a*(

*j, i*)'s in the availability array, Ai. This array is broadcast
based on node

*i*'s current velocity

*vx,i *in the x direction and
in the AVAIL packet.

velocity

*v*
The AVAIL packet also includes the flag

*CH*
*y,i *in the y direction. The Time Future parameter,

*cnvg *. Due to
the nature of the AP algorithm, a node's self-responsibility

*f *, can be tuned for different types of mobility.

The self-similarities were initialized to the same value
plus self-availability will become positive when it has con-
and was set such that the number of clusters produced was
verged to cluster head status. For every iteration of the
minimized. We gave equal preference to each node, however
algorithm, each node

*i *checks for this condition, and then
it is possible to assign certain vehicles (such as large trucks)
sets the

*CHcnvg *flag accordingly. This flag indicates to

*i*'s
a higher preference, making them more likely to become the
neighbor nodes whether or not they should consider

*i *as
cluster head.

a potential cluster head. The responsibility and availabilitybroadcast procedure is outlined in Procedure 2.

*A. Message Passing and the Neighbor List*
Every node

*i *will maintain a neighbor list, N
Procedure 2 Broadcast of RESP and AVAIL messages
a neighbor list entry, Nj, for every neighbor

*j*. Each neighbor
Every

*TM *, each node

*i *will:
list entry, Nj contains the following fields:
1) Calculate responsibility,

*r*(

*i, j*) for each neighbor

*j*
2) Update with damping factor:
(

*x, y*)

*j*:
position vector of node

*j*
*r*(

*i, j*) = (1

*− λ*)

*r*(

*i, j*)

*new *+

*λr*(

*i, j*)

*old*
(

*vx, vy*)

*j*:
velocity vector of node

*j*
3) Store responsibilities,

*r*(

*i, j*), in array: Ri

*s*(

*i, j*):
similarity for

*i *and

*j*
4) Calculate availability,

*a*(

*j, i*) for each neighbor

*j*
*a*(

*i, j*):
last availability received from

*j*
5) Update with damping factor:

*a*(

*j, i*):
last availability transmitted to

*j*
*a*(

*j, i*) = (1

*− λ*)

*a*(

*j, i*)

*new *+

*λa*(

*j, i*)

*old*
*r*(

*j, i*):
last responsibility received from

*j*
6) Store availabilities,

*a*(

*j, i*), in array: Ai

*r*(

*i, j*):
last responsibility transmitted to

*j*
7) Determine if converged to CH status:
cluster head converge flag for node

*j*
if

*r*(

*i, i*) +

*a*(

*i, i*)

*> *0, then set

*CHcnvg*
Index of

*j*'s current cluster head
8) Broadcast the RESP packet:

*h*Ri

*i*
Time that node

*j *expires
9) Broadcast the AVAIL packet:

*h*Ai

*, CHcnvgi*
Each node

*j *will periodically broadcast a HELLO beacon
containing its ID, position, velocity and current cluster head.

When node

*i *receives a RESP or AVAIL packet from

*j*,
The hello broadcast period is defined as

*TH*, where we have
it will search for its id in the Rj or Aj array, and if found,
used

*TH *= 1

*s *in our simulations. Upon reception of a
it reads off its specific responsibility or availability message.

HELLO beacon from node

*j*, node

*i *will calculate its current
These message are stored in the received message fields,

*r*(

*j, i*)
similarity with

*j*,

*s*(

*i, j*), using (5) and update its neighbor list
or

*a*(

*i, j*) of

*j*'s neighbor list entry, Nj. If the received packet
with the new information. A node only considers neighbors
is of AVAIL type, node

*i *will also update the

*CHcnvg,j *field
moving in the same direction, and ignores broadcasts from
for

*j *according to the

*CHcnvg *flag received. This routine is
traffic in the opposite direction. This procedure is outlined in
summarized in Procedure 3.

Procedure 1.

Procedure 3 Reception of RESP and AVAIL messages
Procedure 1 Broadcast and Reception of Hello Beacons
Upon reception of a RESP or AVAIL packet from node

*j*,
1) Every

*T*
node

*i *will:

*H *, each node

*j *broadcasts HELLO beacon:

*hj, *(

*x, y*)

*j, *(

*vx, vy*)

*j, CHji*
1) Search for its id,

*i *in the Rj or Aj array.

2) Each receiving neighbor,

*i*, checks if

*j *is traveling in
2) If a message addressed to

*i *is found, update the

*r*(

*j, i*)
the same direction
or

*a*(

*i, j*) field in the neighbor list entry, Nji
3) If true,

*i *calculates similarity with

*j*,

*s*(

*i, j*)
3) Check if

*CHcnvg *flag is set, and update

*CHcnvg,j *field
4) Node

*i *adds/updates

*j*'s neighbor list entry, Nj's:
in

*j*'s neighbor list entry, Nji

*hj, *(

*x, y*)

*j, *(

*vx, vy*)

*j, s*(

*i, j*)

*, texpire, CHji*
*B. Cluster Formation and Maintenance*
Highway scenarios were created using the VanetMobiSim
Clustering decisions are made periodically with a period of
traffic simulator [16], which generates realistic mobility pat-

*CI *called the Clustering Interval. Note that the

*T*
terns, including lane changing. The highway was generated
period must be small enough to allow the algorithm to con-
in a looped formation with a 3km, 3-lane highway moving
verge within a

*CI *period. Preliminary simulations show that a
in each direction. The vehicles reach their maximum speed
neighborhood of 40 nodes can converge in under 10 iterations.

during the main highway pass, and then slow significantly at
the turns, creating a realistic pattern with both low and high

*M *of 1

*s*, requires a minimum

*CI *of 10s)
density traffic. The highways moving in either direction were
Every

*CI*, node

*i *finds its cluster head using (4). However,
separated by more than the 250m broadcast range, so that clus-
node

*i *only considers its neighbors with the

*CHcnvg,j *flag
tering could not occur across them. Our proposed algorithm
set, which confirms node

*j *will become a cluster head. In the
will not cluster vehicles moving in opposite directions, but
event that none of the neighbors have set their

*CHcnvg,j *flag,
MOBIC will, which degrades cluster stability. This step was
node

*i *becomes its own cluster head.

taken to provide a fair comparison of MOBIC and APROVE.

In between clustering iterations of

*CI*, we perform cluster
maintenance. Every

*TCM *(the period of cluster maintenance),

*A. Clustering Performance Metrics*
node

*i *purges its neighbor list of old entries by checking the
To evaluate the cluster stability and overall performance of

*texpire *fields. After purging, node

*i *checks if its cluster head
our algorithm, we use the following metrics:
is still in its neighbor list. If the CH has been lost, node

*i*
*1) Average Cluster Head Duration: *Long cluster head
searches through its neighbors for current CHs to join, by
duration is important for MAC schemes where the cluster head
finding neighbors with

*CHj *=

*j*. The

*CHcnvg,j *flag is not
is the central controller and scheduler.

used here because it indicates the potential cluster heads for

*2) Average Cluster Member Duration: *This metric judges
the next round, not the current cluster heads. If multiple CHs
the overall stability of the initial clustering.

are found in the neighbor list, node

*i *uses (4) to select the best

*3) Average Rate of Cluster Head Change: *This metric is
one. If node

*i *can not find another neighbor that is currently
useful since it takes into account both cluster head duration
a CH, it becomes its own cluster head.

and the number of clusters formed.

There are some important notes regarding the passing of

*4) Average Number of Clusters: *To effectively decrease
availability and responsibility messages. Firstly, the messages
network contention, fewer clusters is desirable.

are not reset between clustering iterations, which gives mem-ory to the algorithm and provides preference to previous

*B. Performance Analysis*
cluster heads. This feedback results in less frequent cluster
In the first set of simulations, the maximum velocity of the
changes. Secondly, our algorithm does not assume synchro-
vehicles was 40m/s (144km/h). The Cluster Interval,

*CI*, was
nization, and each vehicle can run it independently of one
swept from 10s to 150s and Time Future,

*τ*
another. In the asynchronous case, the received availability

*f *, was swept from
0s to 120s. Figure 1 plots the effect of

*CI *and

*τ*
and responsibility messages will be at most one period old.

Since these messages are averaged over time and a vehicle's
It can be seen from Figures 1a, 1b, and 1c that APROVE's
movement over one time period is small, the algorithm's
cluster stability far exceeds that of MOBIC. Figure 1d in-
performance will not be effected. In the case of a lossy
dicates that MOBIC performs better in terms of number
channel, messages can be older than one time period, which
of formed clusters. However, the cluster change rate, which
may cause the algorithm's performance to degrade. In this
involves the joint effect of CH duration and the number
case, a more reliable MAC (such as [7]) can be used to increase
of clusters, proves that APROVE's overall performance is
the message reception probability.

superior. Notice that average cluster change rate is proportionalto the number of clusters formed, and inversely proportional
IV. SIMULATION RESULTS
to the CH duration. From Figure 1c we can see that there is
We have implemented the proposed algorithm in NS2,
an optimal

*τf *setting for each setting of

*CI*. Based on this
which has been highly validated by the networking research
plot, a

*τf *of 30s was chosen for future simulations, as it gave
community. All simulations were performed with 100 vehicles
the best performance for this mobility scenario.

on a highway. Each simulation ran for 500s, however only the
By sweeping over different velocities, we compare the clus-
last 200s were used for performance metric calculations. This
tering performance of APROVE and MOBIC. Using VanetMo-
was to ensure that the algorithm had reached a steady state
biSim, highway scenarios were generated with approximate
before measuring its performance. All of the simulation results
maximum velocities of 15, 25, 35, 40, and 50m/s. The perfor-
were averaged over 10 different mobility scenarios, and used
mance results are displayed in Figure 2. Figure 2d shows that
the following timing parameters:

*TH *=

*TM *=

*TCM *= 1

*s*.

MOBIC generates a smaller number of clusters, however, it
The 802.11 MAC and the 914MHz Lucent WaveLAN DSSS
can be observed from Figures 2a, 2b, and 2c, that APROVE's
network card with a radio range of 250m, have been used
stability performance far exceeds that of MOBIC. Figure 2c
in the NS2 simulations. The MOBIC code was taken from a
allows us to judge overall clustering performance, and when
legacy version of NS2 provided by [12].

comparing APROVE and MOBIC at a typical highway speed
Fig. 1. The impact of

*τf *on cluster performance for different

*CI *settings. Simulations run with 100 nodes and maximum velocity = 40m/s.

*τf *= 0, 10, 30,
50, 70, 90, and 120s, and

*CI *= 10, 30, 60, 90, 120, and 150s. MOBIC's performance is also plotted. (a) The average cluster head duration. (b) The averagecluster member duration. (c) The average rate of cluster head change. (d) The average number of clusters
of 40m/s, APROVE shows 300% improvement in average rate
of cluster head change. It is also evident that while MOBIC's
Motivated by the ample research in cluster-based MACs
performance degrades at higher mobility, APROVE's perfor-
and routing schemes for VANETs, we have proposed a novel
mance degrades at lower mobility. A possible explanation
and stable mobility-based clustering algorithm. Our algorithm
for this trend is that parameter optimization was done for
elects cluster heads periodically, by using affinity propagation
40m/s, thus the timing parameters have been tuned to higher
from a communications perspective, and in a distributed man-
ner. The algorithm finds clusters that minimize both relative
MOBICs lesser stability performance could be caused by
mobility and distance from each cluster head to its cluster
error in the mobility metric and cluster member suitability.

members. The clusters created are stable and exhibit long
The use of received power in the mobility metric can lead
average cluster member duration, long average cluster head du-
to inaccuracies in the relative mobility calculation due to
ration, and low average rate of cluster head change. APROVE's
channel fluctuations. In addition, the MOBIC algorithm does
high stability makes it a suitable candidate for clustering in a
not consider cluster member suitability when forming clusters.

mobile and dynamic environment, such as VANETs.

Although the CH will initially have the lowest relative mobility
in its neighborhood, a cluster member with high relative
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ocho razones por las que la juventud norteamericana Cómo se ha aplastado la resistencia juvenil en Estados Unidos Cuadernos de reflexión: La juventud y la rebeldía Nota de presentación: Dr. Bruce E. Levine es un psicólogo estadounidense, especializado en psicología clínica, muy crítico de la corriente principal de su profesión. Escribe habitualmente en diversos medios, AlterNet,

The Right To Refuse Hail Abdullah In recent years pharmacy counters have become a new front in the bitter battle over abortion. The refusal of some pharmacists to dispense emergency contraceptives (ECs) or abortaficient drugs all around the nation have been increasing. In Missouri, a pharmacist, citing personal moral grounds, refused to dispense an EC.1 In Texas, a pharmacist refused to dispense such a drug to a rape victim, and in Ohio, a pharmacist was fired from Kmart for obstructing access to emergency contraceptives and other birth control drugs.2,3 This has sparked a controversy of whether or not pharmacists should have the right to refuse to dispense ECs or abortive drugs based on their moral and religious beliefs.