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Journal of Uncertainty Analysis and Applications

Table 6 Average o.f. values for simulation of the static and the dynamic routing model

From: Stochastic hierarchical multiobjective routing model in MPLS networks with two service classes: an experimental study on imprecision and uncertainty issues

α

O.f.

Initial

Analytical

Static routing

Dynamic routing model results

  

solution

results

model results

τ=10 m

τ=20 m

τ=30 m

 

W Q

20,636.78

21,596.83 a

21,587.85 ± 34.78

21,605.44 ± 37.10

21,617.39 ± 38.95

21,617.09 ± 35.60

 

B M m|Q

0.138

0.0220

0.0238 ± 0.00130

0.0245 ± 0.00202

0.0224 ± 0.00148

0.0219 ± 0.00140

 

B m 1|Q

0.138

0.0220

0.0238 ± 0.00130

0.0245 ± 0.00202

0.0224 ± 0.00148

0.0219 ± 0.00140

 

B m 2|Q

0.0872

0.00655

0.00779 ± 0.000317

0.00507 ± 0.000480

0.00432 ± 0.000205

0.00457 ± 0.000923

0.0

B m 3|Q

0.00394

0.000390

0.000399 ± 0.0000138

0.000423 ± 2.79·10−5

0.000375 ± 2.00·10−5

0.000365 ± 2.32·10−5

 

B M 1|Q

0.410

0.130

0.137 ± 0.0156

0.165 ± 0.0250

0.156 ± 0.0195

0.138 ± 0.0122

 

B M 2|Q

0.268

0.0920

0.0952 ± 0.0105

0.0162 ± 0.00137

0.0209 ± 0.00379

0.0303 ± 0.0225

 

B M 3|Q

0.0127

0.00312

0.00296 ± 0.000193

0.00377 ± 0.000302

0.00336 ± 0.000281

0.00325 ± 0.000220

 

W B

6,606.51

6,940.64

6,954.27 ± 7.20

7,114.88 ± 25.83

7,053.08 ± 14.05

7,046.89 ± 43.31

 

W Q

17,599.15

17,685.84 b

17,683.50 ± 15.54

17,683.45 ± 15.52

17,683.54 ± 15.54

17,683.51 ± 15.54

 

B M m|Q

0.0194

3.22 ·10−5

2.23 ·10−5 ± 5.46 ·10−5

6.35 ·10−5 ± 7.22 ·10−5

5.02 ·10−7 ± 3.66·10−7

2.16 ·10−5 ± 5.45 ·10−5

 

B m 1|Q

0.0194

3.22 ·10−5

2.14 ·10−5 ± 5.50 ·10−5

6.32 ·10−5 ± 7.26 ·10−5

0

2.13 ·10−5 ± 5.47 ·10−5

 

B m 2|Q

0.0107

1.47 ·10−8

0

0

0

0

0.5

B m 3|Q

0.000419

2.50 ·10−6

1.09 ·10−6 ± 7.54·10−7

7.08 ·10−7 ± 2.97 ·10−7

5.02 ·10−7 ± 3.66·10−7

4.08 ·10−7 ± 2.13 ·10−7

 

B M 1|Q

0.0911

0.000701

0.00235 ± 0.00603

0.00277 ± 0.00335

0

0.00347 ± 0.00892

 

B M 2|Q

0.0534

6.05 ·10−8

0

0

0

0

 

B M 3|Q

0.00215

1.31 ·10−5

2.17 ·10−5 ± 1.81 ·10−5

3.35 ·10−5 ± 2.18 ·10−5

1.60 ·10−5 ± 1.08·10−5

1.74 ·10−5 ± 6.86·10−6

 

W B

5,239.94

5,296.26

5,297.08 ± 12.94

5,297.31 ± 12.77

5,297.23 ± 12.72

5,297.24 ± 12.86

 

W Q

16,027.90

16,028.14 c

16,077.61 ± 15.03

16,077.61 ± 15.03

16,077.61 ± 15.03

16,077.61 ± 15.03

 

B M m|Q

5.04 ·10−5

9 ·10−10

0

0

0

0

 

B m 1|Q

5.04 ·10−5

9 ·10−10

0

0

0

0

 

B m 2|Q

3.75 ·10−5

<1·10−10

0

0

0

0

1.0

B m 3|Q

1.21 ·10−6

<1·10−10

0

0

0

0

 

B M 1|Q

0.000400

8.7 ·10−10

0

0

0

0

 

B M 2|Q

0.000209

<1·10−10

0

0

0

0

 

B M 3|Q

7.17 ·10−6

<1·10−10

0

0

0

0

 

W B

3,355.75

3,355.88

3,350.97 ± 24.92

3,350.97 ± 24.92

3,350.97 ± 24.92

3,350.97 ± 24.92

  1. Average o.f. values, and 95% confidence intervals, for simulation of the static (with a warm-up time of 8 h) and the dynamic routing model (with t0 = t1 = 4 h, update period τ and b = 0.3), a total simulation time of 48 h on the test networkE, for different values of α, when the HMOR-S2 is used to update the routing plan. a99.47%; b100%; c99.75% of the approximate ideal values for the QoS flows revenue, W Q ideal, from the data in [25].
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