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lower (about 9% over the previous calculation) than the c3.xlarge instance (20%
compared to the previous point).
The analysis of hardware features of such instances (ng"m1.large and c3.xlarge)
shows that they have: (i) two and four vCPUs respectively and (ii) the same RAM
memory (7.5 GBytes). Then it can be concluded that the decrease of processing
times could be due to the load balancing between processors and the access to
shared resources such as memory, buses, etc.
Figure 2b shows the empirical economic costs. Is noted that economic costs
are the same from 10 to 400 nodes. The cause of this behavior is because Amazon
set the pricing of instances per hour of use. Reason why, the pricing is the same
if the processing time is less or equal than one hour. Similarly, if processing time
is longer than one hour (for example 800 to 1000 nodes), it doubles the cost and
so on.
5.2 Perfomance Estimation Proposed Models
In this subsection we introduce the proposed models in order to estimate the
performance for each instance considered. These models were obtained through
polynomials up to second degree of the form:
t
=
ax
2
+
bx
+
c,
where,
x
is the number of sensor nodes processed and
t
is the estimated execution
time. The values of the coe
cients
a
,
b
and
c
for each scenario are detailed in
Table 2).
Tabl e 2 . Coe
cients of Each Scenario Theoretical Model
Amazon EC2 Instance
a
b
c
t1.micro
0
7
.
85
E −
01
−
1
.
44
m1.small
1
.
84
E −
06
1
.
78
E −
01
1
.
80
6
.
02
E −
06
6
.
50
E −
02
9
.
98
E −
01
m1.large
m1.xlarge
1
.
40
E −
05
8
.
24
E −
02
2
.
25
1
.
66
E −
05
6
.
73
E −
02
2
.
59
c3.xlarge
In order to evaluate the proposed models we calculate the execution time and
economic cost for each scenario. In addition, the execution of the application has
been conducted for more than 1000 nodes (up to 5000).
Finally, with the aim of determining the accuracy of the proposed models,
Figure 3 and Figure 4 show a comparison between the results of empirical ex-
periments and our performance models for each scenario.
Specifically, Figure 3 shows that execution times calculated through the pro-
posed model differ seconds or few minutes (depending on the instance) with
respect to those obtained through the execution of the frost prediction applica-
tion. Then the proposed models can predict the results with a reasonable good
accuracy.
