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ation, vehicles cannot change lane or perform evasive
maneuvers.
We have developed a first approach mathemati-
cal model to calculate the average percentage of ac-
cidents in the platoon, varying the number of consid-
ered vehicles, their average speed, the average inter-
vehicle spacing and the penetration ratio of the CCA
technology. Specifically when the CCA penetration
ratio is taken into account, the growth in the num-
ber of operations of the analytical model is such that
the sequential computation of a numerical solution is
no longer feasible. Consequently, we resort to the
use of parallelization techniques such as OpenMP for
solving those computational cases considered as un-
approachable by means of sequential procedures.
Additionally, we execute our programs in the Ben-
Arabi Supercomputingenvironment(FPCMur, 2011),
taking the advantage of utilizing the fourth fastest Su-
percomputer in Spain.
In the current work we show how the paralleliza-
tion techniques coordinated with supercomputing re-
sources make the simulation process a more suitable
and efficient one, therefore we succeed to evaluate the
CCA application thoroughly.
The remainder of this paper is organized as fol-
lows. In Section 2 we briefly review the related work.
In Section 3 the OpenMP environment is briefly re-
viewed and the Ben-Arabi Supercomputer architec-
ture introduced. A description of the mathematical
model, its implementation and parallelization are pro-
vided in Sections 4 and 5. Finally, some results are
shown and discussed in Section 6 to illustrate the per-
formance of the resulting parallel algorithm. Conclu-
sions and future work are remarked in Section 7.
2 RELATED WORK
So far, most typical high performance computing
(HPC) problems focused either on those fields related
with the Grand Challenges defined as fundamental
problems in science and engineering or directed to-
ward Web search databases (Barney, 2010). That is
the reason why we consider our VANET mathemati-
cal model approximationas a non-classical issue to be
solved under HPC conditions, contributing to extend
the use of supercomputing to other fields of interest.
In the implementation of our mathematical model
we parallelize a sparse matrix-vector multiplication.
This operation is considered as a relevant compu-
tational kernel in scientific applications, which per-
forms not optimally on modern processors because of
the lack of compromise between memory and com-
puting power and irregular memory access patterns
(Liu et al., 2009). In general, we find quite a lot of
done work in the field of sparse matrix-vector mul-
tiplications using parallelization techniques (Kotake-
mori et al., 2008; Goumas et al., 2009; Williams et al.,
2009). These papers study in depth the optimal per-
formance of this operation, but in this paper, we show
that even using a simpler parallelization routine, the
computation time is noticeably shortened.
Several mathematical models have been devel-
oped to study different aspects of VANETs. Most
of them are related with the vehicle routing optimiza-
tion (Ning et al., 2009; Wisitpongphan et al., 2007),
the broadcasting methods (Du et al., 2009; Fasolo
et al., 2006; Li et al., 2010), the mobility of vehicles
(Harri et al., 2009; Djenouri et al., 2008) and the com-
munication delay time (Abboud and Zhuang, 2009;
Fukuyama, 2009; Prasanth et al., 2009). Other re-
lated VANET issues have been studied as well, like
network connectivity (Khabazian and Mehmet Ali,
2008), or survivability (Xie and Xiao, 2008). In this
paper we focus on collision models for a chain of ve-
hicles, particularly those based on physical parame-
ters to assess the collision process itself (Glimm and
Fenton, 1980; Touran and Brackstone, 1999; Kim and
Jeong, 2010).
However in an attempt of searching related work
we find that few work has been done specifically re-
garding to the parallelization of these VANET math-
ematical models, strictly speaking. Moreover, to the
best of our knowledge, only the vehicle routing prob-
lem has been approached using parallelization tech-
niques (Cook and Rich, 1999; Ghiani and Guerriero,
2003; Bouthillier and Crainic, 2005).
Therefore and summing up, in this paper we de-
scribe a preliminary model (although computation-
ally expensive) for a CCA application to compute the
number of chain collisions and to address the bene-
fits of using parallelization techniques in the VANET
arena.
3 SUPPORTING TOOLS
3.1 The OpenMP Technique
OpenMP is a well-known open standard for providing
parallelization mechanisms to multiprocessors with
shared memory (Chandra et al., 2001). OpenMP
API supports shared memory programming, multi-
platform techniques for the programming languages
like Fortran, C and C++, and for every architecture
including Unix and Windows platforms. OpenMP is
a scalable and portable model developed for hardware
and software distributors which provides shared me-
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