Transactions on Industrial Informatics

 
 
 

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1551-3203 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2016.2590302, IEEE
Transactions on Industrial Informatics
9 
Appendix: t-test results 
 
All fuzzy-logic based algorithms significantly outperform AdaptiveLight, as shown in Fig. 4 and Fig.5. 
So, the concern in this comment must be about the performance difference among fuzzy algorithms. 
Since the results under different traffic load levels are from different sampling spaces, we cannot test 
the results under different traffic level as one series. So, we can only test the results of different algorithms 
under the same traffic level individually.
The hypothesis:
H
0
: the results of FuzzyGroup/FuzzyGroupLearning are NOT statistically different from those of 
NoGroup. 
H
1
: the results of FuzzyGroup/FuzzyGroupLearning are statistically different from those of NoGroup. 
Significant level, 
α
= 0.05 
Number of samples, 
n
= 10 (we conducted simulations under each traffic level for ten times) 
We use the following 
t
-test to test our results: 
where 
S
is standard deviation, 
μ
0
 
is the result of NoGroup. 
 
t
α
/2,n-1
= 
t
0.05/2,9
= 2.26.
P
= 
TDIS
(
t,n-1,2
) 
If 
t
<
t
α
/2,n-1
, 
P
> 
α
, 
H
0
is acceptable, otherwise 
H
1
is acceptable. 
The following tables show the t-test results. The tables show that, under high traffic levels, 
H
1
is 
acceptable, while under low traffic levels, 
H
0
is acceptable. Therefore, our simulation results show 
statistical difference among different algorithms. Due to page limit, we do not include the 
t
-test results in 
our manuscript.
Average Waiting Time (Uniform traffic) 
t_fuzzyGroup 
0.39 2.09
0.91
1.45
21.91
6.32
2.81
t_fuzzyGroupLearning 
1.05 0.24
0.56
1.00
0.50
7.91
9.14
P_fuzzyGroup 
0.71 0.07
0.38
0.18
4.06E-09 
0.00014 
0.02 
P_fuzzyGroupLearning 
0.32 0.81
0.59
0.34
0.63 
2.43E-05 
7.52E-06 
Average Waiting Time (Backbone traffic) 
t_fuzzyGroup 
1.17
1.61
1.09
0.20
3.48
5.82
28.93
t_fuzzyGroupLearning 
1.19
2.68
0.98
0.18
7.39
9.55
9.46
P_fuzzyGroup 
0.27
0.14
0.31
0.84
0.007 
0.0003 
3.43E-10 
P_fuzzyGroupLearning 
0.27
0.03
0.35
0.86
4.13E-05 
5.24E-06 
5.67E-06 
Waiting Time Variance (Uniform traffic) 
t_fuzzyGroup 
0.30
2.92
2.13
3.28
4.96
14.35
2.93
t_fuzzyGroupLearning 
0.25
0.48
1.27
1.42
4.13
19.36
3.76
P_fuzzyGroup 
0.77
0.02
0.06
0.01 
0.0008 
1.66E-07 
0.017 
P_fuzzyGroupLearning 
0.81
0.64
0.24
0.19 
0.0026 
1.21E-08 
0.004 

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1551-3203 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2016.2590302, IEEE
Transactions on Industrial Informatics
10 
Waiting Time Variance (Backbone traffic) 
t_fuzzyGroup 
2.47
0.00
1.19
0.97
5.29
9.08
17.19
t_fuzzyGroupLearning 
1.22
2.14
1.21
1.55
7.53
9.52
8.92
P_fuzzyGroup 
0.04
1.00
0.26
0.36
0.0005 
7.97E-06 
3.43E-08 
P_fuzzyGroupLearning 
0.25
0.06
0.26
0.16
3.56E-05 
5.36E-06 
9.15E-06