Speeding Up the Evaluation of a Mathematical Model for VANETs Using OpenMP - Simulation and Modeling Methodologies, Technologies and Application - page 29

Ta b l e 4 . Execution times in minutes and speedup for each program using 4 processors

0% 10% 20% 30% 40% 50%

Time SU Time SU Time SU Time SU Time SU Time SU

P1 0 . 002 1 . 00 0 . 308 1 . 00 7 . 838 1 . 00 62 . 653 1 . 00 203 . 757 1 . 00 297 . 930 1 . 00

P2 0 . 001 2 . 00 0 . 199 1 . 55 5 . 053 1 . 55 30 . 676 2 . 04 94 . 173 2 . 16 135 . 907 2 . 19

P3 0 . 001 2 . 00 0 . 098 3 . 14 2 . 473 3 . 17 19 . 488 3 . 21 59 . 724 3 . 41 95 . 360 3 . 12

P4 0 . 004 0 . 50 0 . 078 3 . 95 1 . 998 3 . 92 16 . 072 3 . 90 51 . 830 3 . 93 86 . 175 3 . 45

P5 0 . 002 1 . 00 0 . 101 3 . 05 2 . 494 3 . 14 19 . 933 3 . 14 63 . 464 3 . 21 95 . 158 3 . 13

P6 0 . 005 0 . 40 0 . 091 3 . 38 2 . 251 3 . 48 18 . 013 3 . 48 59 . 810 3 . 40 89 . 064 3 . 34

P7 0 . 004 0 . 50 0 . 089 3 . 46 2 . 232 3 . 51 17 . 754 3 . 53 57 . 699 3 . 53 85 . 988 3 . 46

P8 0 . 003 0 . 67 0 . 090 3 . 42 2 . 245 3 . 49 17 . 926 3 . 49 59 . 453 3 . 43 88 . 422 3 . 37

mentioning that Program 7 is built by a combination of the parallelized tasks B and
C, parallelizing the for loops that cover the range of average inter-vehicle distances and
the number of combinations resulting from the technology penetration rate respectively.
We obtain thus:

- Sequential time (P 1 ): 297 . 975 minutes.
- Parallel time (P 7 ): 156 . 433 minutes.

The achieved speedup (P 1 /P 7 )is 1 . 9 , which implies an improvement of around 47 . 5%
referred to the execution time.

6.2 Execution with 4 Processors

The computation times resulting from the execution of the eight programs with the
selected penetration rates of CCA technology using 4 processors are presented in Table
4 and depicted in Figure 4.
When the CCA penetration rate equals the 50% we reach the highest computational
load. So we also analyze the results with this penetration rate using 4 processors, focus-
ing on the best and worst execution times achieved. The reference is still the sequential
Program 1 with a duration of 297 . 93 minutes (around 5 hours). If we make a compar-
ison among the parallelized programs we conclude that the best result is given again
by the Program 7 with a calculation time of 85 . 988 minutes (around 1 . 43 hours). We
obtain thus:

- Sequential time (P 1 ): 297 . 93 minutes.
- Parallel time (P 7 ): 85 . 988 minutes.

The achieved speedup is 3 . 46 , which implies an improvement of around 71 . 1% referred
to the execution time.

6.3 Execution with 8 Processors

The computation times resulting from the execution of the eight programs with the
selected penetration rates of CCA technology using 8 processors are gathered in

Table 5 and illustrated in Figure 5.