Figure 4.3 shows the experimental results of the LU Decomposition graph of about 150 tasks. Figure 4.3(a) shows the average schedule lengths in the 45 different DHC system types when the number of heterogeneous machines is equal to 4, 8, or 16. The pair wise comparison of the algorithms is presented in Tables 4.1(a)~4.1(c). The performance ranking of these algorithms is {SBCT > ESBCT >
DLS > HEFT}. Figure 4.3(b) shows the average schedule lengths when the CCR
value is equal to 0.1. The pair wise comparison of the algorithms is presented in Tables 4.1(d)~4.1(f). The performance ranking of these algorithms is {ESBCT >
DLS > SBCT > HEFT}. Figure 4.3(c) shows the average schedule lengths when the CCR value is equal to 0.5. The pair wise comparison of the algorithms is presented in Tables 4.1(g)~4.1(i). The performance ranking of these algorithms is {ESBCT >
DLS > SBCT > HEFT}. Figure 4.3(d) shows the average schedule lengths when the CCR value is equal to 1. The pair wise comparison of the algorithms is presented in Tables 4.1(j)~4.1(l). The performance ranking of these algorithms is {ESBCT >
SBCT > DLS > HEFT}. Figure 4.3(e) shows the average schedule lengths when the CCR value is equal to 5. The pair wise comparison of the algorithms is presented in Tables 4.1(m)~4.1(o). The performance ranking of these algorithms is {ESBCT >
SBCT > HEFT > DLS}. Figure 4.3(f) shows the average schedule lengths when the CCR value is equal to 10. The pair wise comparison of the algorithms is presented in Tables 4.1(p)~4.1(r). The performance ranking of these algorithms is {ESBCT >
SBCT > HEFT > DLS}. Obviously, the ESBCT algorithm is suitable for all kinds of the CCR values, but the SBCT algorithm outperforms the others just when the CCR value is larger.
In Figures 4.3(b)~(d), because the sizes of available idle time slots are smaller, they could make these algorithms employed the insertion strategy harder to insert new incoming tasks into these available idle time slots. In other words, in every scheduling round, these algorithms could have the similar result in estimating the possible earliest start times of candidate tasks. These possible earliest start times probably are the useful information to decide which candidate task is urgent or which processor is suitable to be scheduled. Therefore, the possible reason why ESBCT and DLS outperform HEFT and SBCT may be that ESBCT and DLS dynamically tune the priority values. Contrarily, in Figures 4.3(e)~(f), the sizes of available idle
time slots are getting larger. It could prevent DLS from obtaining the possible earliest start times of candidate tasks in every scheduling round. The penalty could make DLS not to correctly identify the urgent tasks.
In Figure 4.3(c), the average schedule length obtained by ESBCT is worse than that obtained by SBCT when the number of heterogeneous machines is equal to 16.
The possible reason for this anomaly is that although we employ the minimal sbct attribute as a part of the priority function, we do not guarantee the smaller minimal sbct values to have the smaller maximal sbct values. In other words, we could first select a task and machine pair with the relative larger minimal sbct value, but the task and machine pair has the smaller maximal sbct value. The phenomenon is named as max-min problem in parallel processing (Kruatrachue & Lewis, 1988) caused by a tradeoff between maximizing parallelism and minimizing inter-processor communication. The same anomaly can also be observed in Figures 4.3(d) when the number of heterogeneous machines is equal to 8.
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Figure 4.3 The experimental results of the LU Decomposition graph. (a) Average schedule length. (b) Average schedule length when the CCR value is equal to 0.1. (c) Average schedule length when the CCR value is equal to 0.5. (d) Average schedule length when the CCR value is equal to 1. (e) Average schedule length when the CCR value is equal to 5. (f) Average schedule length when the CCR value is equal to 10.
(Continue)
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Figure 4.3 The experimental results of the LU Decomposition graph. (a) Average schedule length. (b) Average schedule length when the CCR value is equal to 0.1. (c) Average schedule length when the CCR value is equal to 0.5. (d) Average schedule length when the CCR value is equal to 1. (e) Average schedule length when the CCR value is equal to 5. (f) Average schedule length when the CCR value is equal to 10.
Table 4.1(a) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.1(b) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.1(c) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.1(d) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.1(e) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.1(f) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.1(g) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.1(h) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.1(i) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.1(j) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.1(k) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.1(l) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.1(m) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.1(n) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.1(o) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.1(p) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.1(q) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.1(r) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Figure 4.4 shows the experimental results of the GE graph of about 150 tasks.
Figure 4.4(a) shows the average schedule lengths in the 45 different DHC system types when the number of heterogeneous machines is equal to 4, 8, or 16. The pair wise comparison of the algorithms is presented in Tables 4.2(a)~4.2(c). The performance ranking of these algorithms is {ESBCT > HEFT > SBCT > DLS}.
Figure 4.4(b) shows the average schedule lengths when the CCR value is equal to 0.1.
The pair wise comparison of the algorithms is presented in Tables 4.2(d)~4.2(f).
The performance ranking of these algorithms is {ESBCT > DLS > HEFT > SBCT}.
Figure 4.4(c) shows the average schedule lengths when the CCR value is equal to 0.5.
The pair wise comparison of the algorithms is presented in Tables 4.2(g)~4.2(i). The performance ranking of these algorithms is {ESBCT > HEFT > DLS > SBCT}.
Figure 4.4(d) shows the average schedule lengths when the CCR value is equal to 1.
The pair wise comparison of the algorithms is presented in Tables 4.2(j)~4.2(l). The performance ranking of these algorithms is {DLS > ESBCT > SBCT > HEFT}.
Figure 4.4(e) shows the average schedule lengths when the CCR value is equal to 5.
The pair wise comparison of the algorithms is presented in Tables 4.2(m)~4.2(o).
The performance ranking of these algorithms is {ESBCT > HEFT > SBCT > DLS}.
Figure 4.4(f) shows the average schedule lengths when the CCR value is equal to 10.
The pair wise comparison of the algorithms is presented in Tables 4.2(p)~4.2(r).
The performance ranking of these algorithms is {ESBCT > SBCT > HEFT > DLS}.
Obviously, the ESBCT algorithm is suitable for all kinds of the CCR values, but the SBCT algorithm does not perform well.
In Figure 4.4(d), the average schedule length obtained by ESBCT is worse than that obtained by SBCT when the number of heterogeneous machines is equal to 4 or 16. The possible reason for this anomaly has been explained above.
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Figure 4.4 The experimental results of the GE graph. (a) Average schedule length. (b) Average schedule length when the CCR value is equal to 0.1. (c) Average schedule length when the CCR value is equal to 0.5. (d) Average schedule length when the CCR value is equal to 1. (e) Average schedule length when the CCR value is equal to 5. (f) Average schedule length when the CCR value is equal to 10. (Continue)
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Figure 4.4 The experimental results of the GE graph. (a) Average schedule length. (b) Average schedule length when the CCR value is equal to 0.1. (c) Average schedule length when the CCR value is equal to 0.5. (d) Average schedule length when the CCR value is equal to 1. (e) Average schedule length when the CCR value is equal to 5. (f) Average schedule length when the CCR value is equal to 10.
Table 4.2(a) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.2(b) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.2(c) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.2(d) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.2(e) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.2(f) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.2(g) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.2(h) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.2(i) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.2(j) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.2(k) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.2(l) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.2(m) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.2(n) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.2(o) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.2(p) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.2(q) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.2(r) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Figure 4.5 shows the experimental results of the FFT graph of about 190 tasks.
Figure 4.5(a) shows the average schedule lengths in the 45 different DHC system types when the number of heterogeneous machines is equal to 4, 8, or 16. The pair wise comparison of the algorithms is presented in Tables 4.3(a)~4.3(c). The performance ranking of these algorithms is {ESBCT > SBCT = HEFT > DLS}.
Figure 4.5(b) shows the average schedule lengths when the CCR value is equal to 0.1.
The pair wise comparison of the algorithms is presented in Tables 4.3(d)~4.3(f).
The performance ranking of these algorithms is {ESBCT = DLS > HEFT = SBCT}.
Figure 4.5(c) shows the average schedule lengths when the CCR value is equal to 0.5.
The pair wise comparison of the algorithms is presented in Tables 4.3(g)~4.3(i). The performance ranking of these algorithms is {ESBCT > HEFT = SBCT > DLS}.
Figure 4.5(d) shows the average schedule lengths when the CCR value is equal to 1.
The pair wise comparison of the algorithms is presented in Tables 4.3(j)~4.3(l). The performance ranking of these algorithms is {ESBCT = SBCT = HEFT > DLS}.
Figure 4.5(e) shows the average schedule lengths when the CCR value is equal to 5.
The pair wise comparison of the algorithms is presented in Tables 4.3(m)~4.3(o).
The performance ranking of these algorithms is {ESBCT > HEFT = SBCT > DLS}.
Figure 4.5(f) shows the average schedule lengths when the CCR value is equal to 10.
The pair wise comparison of the algorithms is presented in Tables 4.3(p)~4.3(r).
The performance ranking of these algorithms is {ESBCT > HEFT = SBCT > DLS}.
Obviously, the ESBCT algorithm is suitable for all kinds of the CCR values, but the SBCT and HEFT algorithms give very similar results.
In Figure 4.5(d), the average schedule length obtained by ESBCT is worse than that obtained by SBCT when the number of heterogeneous machines is equal to 8.
The possible reason for this anomaly has been explained above.
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Figure 4.5 The experimental results of the FFT graph. (a) Average schedule length. (b) Average schedule length when the CCR value is equal to 0.1. (c) Average schedule length when the CCR value is equal to 0.5. (d) Average schedule length when the CCR value is equal to 1. (e) Average schedule length when the CCR value is equal to 5. (f) Average schedule length when the CCR value is equal to 10. (Continue)
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Figure 4.5 The experimental results of the FFT graph. (a) Average schedule length. (b) Average schedule length when the CCR value is equal to 0.1. (c) Average schedule length when the CCR value is equal to 0.5. (d) Average schedule length when the CCR value is equal to 1. (e) Average schedule length when the CCR value is equal to 5. (f) Average schedule length when the CCR value is equal to 10.
Table 4.3(a) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.3(b) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.3(c) The pair wise comparison of the algorithms when the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.3(d) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.3(e) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.3(f) The pair wise comparison of the algorithms when the CCR value is equal to 0.1 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.3(g) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.3(h) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.3(i) The pair wise comparison of the algorithms when the CCR value is equal to 0.5 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.3(j) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.3(k) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.3(l) The pair wise comparison of the algorithms when the CCR value is equal to 1 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.3(m) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.3(n) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.3(o) The pair wise comparison of the algorithms when the CCR value is equal to 5 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Table 4.3(p) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 4.
SBCT ESBCT HEFT DLS
Table 4.3(q) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 8.
SBCT ESBCT HEFT DLS
Table 4.3(r) The pair wise comparison of the algorithms when the CCR value is equal to 10 and the number of heterogeneous machines is equal to 16.
SBCT ESBCT HEFT DLS
Figure 4.6 show the experimental results of the 100 randomly generated graphs when the number of heterogeneous machines is equal to 8. The pair wise comparison of the algorithms is presented in Tables 4.4 when the CCR value is equal to 0.1, 0.5, 1, 5, or 10. The performance ranking of these algorithms is {ESBCT >
DLS > SBCT = HEFT} when the CCR value is equal to 0.1. The performance ranking of these algorithms is {ESBCT > DLS > SBCT > HEFT} when the CCR
DLS > SBCT = HEFT} when the CCR value is equal to 0.1. The performance ranking of these algorithms is {ESBCT > DLS > SBCT > HEFT} when the CCR