Computational Intelligence - February 2015 - 41

Regarding the flowtime results, MaxPMinT is again the
Table 2 Mean ranks computed using the Friedman statistical test
best heuristic for the small instances, while MaxProfit is the
for the studied heuristics (profit results).
best for the largest workload dimensions. However, these
HeuriSTiC
OVerall
n = 50
n = 200
n = 400
n = 100
two heuristics are the worst ones in terms of profit, because
MaxPMinT
6.70
5.64
5.07
3.18
5.14
their low-quality planning forces the virtual broker to book
MinGAPMaxP
3.40
4.42
4.34
3.93
4.02
additional on-demand instances, as explained before. The
MinQTMaxP
2.59
2.85
2.79
4.01
3.06
good planning performed by MaxMaxProfit for the 400
MaxQTMaxP
2.81
2.78
3.57
3.31
3.12
workload dimension problem instances stands out, since it
MinTMaxP
2.36
1.64
1.69
2.19
3.06
provides the second-best result, while being the best heuris2.12
2.30
MinDMaxP
2.74
4.43
2.90
tic in terms of profit. This means that the solution of MaxMaxMaxProfit
2.68
2.43
1.71
0.57
1.85
MaxProfit is the best one according to the profit of the virMaxProfit
5.35
5.96
6.11
5.52
5.73
tual broker and the waiting time of users, which is a
2
443.69
342.26
309.29
238.33
985.89
|
desirable scenario.
asymptotic v
2.06
2.32
2.38
2.45
2.37
We proceed now to analyze the performance of the
p -value
110-3
110-3
110-3
110-3
110-3
heuristics according to the number of on-demand instances
used in the solutions. This is an important issue because, as it
We graphically compare the heuristics in terms of the numwas previously discussed, the virtual broker will need to book
ber of times they offered the solution requiring the lowest
on-demand resources to satisfy the requests deadlines and
number of on-demand instances in Fig. 4 (a more exhaustive
keeping high reputation. The use of on-demand VMs implies a
comparison of the heuristics regarding the use of on-demand
money loss that reduces the global profit, but it will positively
instances is given in Table 5 on the VMMP website). We can see
impact on the makespan and flowtime results.

90

Batch Dimension = 50

Batch Dimension = 100

80

Batch Dimension = 200

Batch Dimension = 400
66
63

70

58

#1

60

83
71

68
54

50
29

25

30
20
0

52

48

40

40

10

67

0

4 1 7

MaxPMinT

33

31

25

32
18

16

13
0

6

9

3

2

MinGAPMaxP MinQTMaxP MaxQTMaxP

MinTMaxP

MinDMaxP

0 0

6

MaxMaxProfit

MaxProfit

MinDMaxP MaxMaxProfit

MaxProfit

Heuristic

Use of On-Demand VM Instances

Figure 3 Number of times each heuristic is the best (summarized per each workload dimension).

Batch Dimension = 50
20%
15%

Batch Dimension = 100
Batch Dimension = 200
Batch Dimension = 400

10%
5%
0%

MaxPMinT MinGAPMaxP MinQTMaxP MaxQTMaxP

MinTMaxP

Heuristic
Figure 4 Number of on-demand VM instances used (summarized per each workload dimension).

february 2015 | Ieee ComputatIonal IntellIgenCe magazIne

41



Table of Contents for the Digital Edition of Computational Intelligence - February 2015

Computational Intelligence - February 2015 - Cover1
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