D EFINICIÓN DE LOS CASOS DE USO DEL S ISTEMA

In Chapter 4, the run-time overhead introduced by the ES-AS approach for the RTSC and RTMC problems is formally analyzed. However, this theo-retical analysis gave only an asymptotic result, i.e., how fast the overhead will increase in terms of input size. There is no information about the con-stants, which could influence the real overhead as well. Therefore, the main objective of this subsection is to study the actual run-time overhead. Since

1 1,02 1,04 1,06 1,08 1,1 1,12

5 6 7 8 9

normalized power consumption

size of task sets

Optimal HSA0.1 HSA0.05 HSA0.01 NoDVS

Figure 8.22: Estimation accuracy in terms of task number (ARM Cortex-A8 processor based platform)

the evaluation is made by simulation, the overhead of the ES-AS approach is compared with the scheduling overhead caused by the traditional EDF strat-egy, which is originally implemented in the abstract RTOS simulation frame-work. More specifically, two metrics to evaluate the run-time overhead are defined in (8.3) and (8.4).

ρ₁= ES-AS overhead at each hyper period boundary

EDF overhead at each scheduling point (8.3)

ρ2= ES-AS overhead at each scheduling point

EDF overhead at each scheduling point (8.4) Basically, ρ1, also referred to as HP-overhead, reflects the ratio between the overhead coming from the ES-AS approach at each hyper period bound-ary and the EDF overhead. Note that at each boundbound-ary one iteration of the HSASC or HSAMC algorithm is executed. Thus the overhead is measured as how long one iteration will take in average. ρ₂, also referred to as SC-overhead, gives the ratio between the total overhead of the ES-AS approach at each scheduling point and the EDF overhead. In what follows, the over-head for the RTSC problem is first evaluated and afterward the overover-head for the RTMC problem is investigated.

Figure 8.23 and 8.24 illustrate the HP- and SC-overhead (y-axis) in terms of task number (x-axis) on Intel and ARM processor based platforms, respec-tively. One can observe that the HP-overhead is generally higher than the SC-overhead. The main reason is due to Theorem 6.3.2, which shows that the overhead introduced by the ES-AS approach at each hyper period bound-ary is O(n) being higher than the overhead at each scheduling point, which

0

Figure 8.23: ES-AS run-time overhead in terms of task number (Intel XScale processor based platform)

is O(m · c)⁸. More interestingly, hereby the HP-overhead increases slightly while the SC-overhead decreases slightly, as the task number increases. This is accounted to the fact that the HP- and SC-overhead are defined as ratios between the actual overhead and the EDF overhead. The actual HP-overhead has a complexity of O(n) and SC-overhead of O(m · c)⁸while the time com-plexity of EDF is O(log n). In total, it is reasonable to conclude that the actual run-time overhead caused by the ES-AS approach is in the same order of magnitude as the EDF scheduling algorithm.

In case of multi-core processor platforms, the experiments are conducted for the following platforms: I2, (I1)², I4, (I2)²and (I1)⁴. Figure 8.25 shows the HP- and SC-overhead on the I2 and (I1)² platforms in terms of task number. The x-axis shows the number of tasks in a generated task set and the y-axis shows the run-time overhead. In general, the overhead is compa-rable to the case on single-core platforms, which indicates that the overhead introduced by the ES-AS approach for RTMC is in the same order of magni-tude as the EDF scheduling overhead as well. Furthermore, the HP-overhead increases as the number of tasks increases. This is due to the fact that the ac-tual overhead at each hyper period boundary is O(n) and the EDF overhead is O(log n). Moreover, since the ES-AS overhead for multi-core processor plat-forms at each scheduling point is O(log n + c)⁹ according to Theorem 6.4.1, the SC-overhead keeps constant as the number of tasks increases.

In addition, if one looks at Figure 8.25 and focuses on the results obtained for task sets with the same size, it is clear that both the HP- and SC-overhead decrease as the number of clusters increases, i.e., the cluster size decreases.

8The overhead hereby is O(m · c) according to Theorem 6.3.2. Since the number of devices m and the number of supported low power states c are relatively small and constant, the overhead can be considered as O(1) in practice.

9If the number of low power states c is considered as a constant, this overhead becomes O(log n).

0 0,5 1 1,5 2 2,5 3 3,5

5 6 7 8 9 10 11 12

ES-AS run-time overhead

size of task sets HP-overhead SC-overhead

Figure 8.24: ES-AS run-time overhead in terms of task number (ARM Cortex-A8 processor based platform)

For instance, in case of task sets with 7 or 8 tasks, the HP- and SC-Overhead on I2 are higher than them on (I1)², respectively. Through inspection of the simulation results, the main reason is due to the fact that the EDF overhead decreases as the cluster size increases while the actual HP- and SC-overhead remains. The main reason in turn for the EDF overhead decrease is that a processor with larger cluster size incurs more scheduling points. A processor core O_i may need to change its operating speed, if a scheduling point on another core O_jin the same cluster occurs, even though there is no task event on O_i. In such case the EDF scheduling overhead on O_iis rather low, because there is no need to change the running task but only the speed. Since the final result is a mean value over all the scheduling points, a multi-core processor with larger cluster size yields a lower overhead in average.

Moreover, Figure 8.26 shows the simulation results on multi-core processors with 4 cores. As shown in the x-axis, hereby the range of considered task number is different to them for dual-core processors (cf. Table 8.4). Gener-ally, the same trend as described previously can be observed as well.