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Journal of Uncertainty Analysis and Applications

Table 8 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

20,358.90

21,616.01 a

21,597.91 ± 30.13

21,606.57 ± 44.40

21,616.80 ± 35.49

21,610.35 ± 34.71

 

B M m|Q

0.169

0.0224

0.0245 ± 0.00175

0.0245 ± 0.00173

0.0216 ± 0.00141

0.0225 ± 0.00146

 

B m 1|Q

0.169

0.0224

0.0245 ± 0.00175

0.0245 ± 0.00173

0.0216 ± 0.00141

0.0225 ± 0.00146

 

B m 2|Q

0.111

0.00341

0.00580 ± 0.000523

0.00492 ± 0.000528

0.00456 ± 0.000432

0.00506 ± 0.000633

0.0

B m 3|Q

0.00536

0.000596

0.000601 ± 4.99·10−5

0.000417 ± 6.38·10−5

0.000461 ± 7.60·10−5

0.000491 ± 9.88·10−5

 

B M 1|Q

0.711

0.146

0.157 ± 0.0231

0.161 ± 0.0326

0.148 ± 0.0176

0.151 ± 0.0277

 

B M 2|Q

0.518

0.0145

0.0215 ± 0.00229

0.0192 ± 0.00232

0.0203 ± 0.00429

0.0183 ± 0.00445

 

B M 3|Q

0.0293

0.00362

0.00376 ± 0.000476

0.00339 ± 0.000239

0.00299 ± 0.000433

0.00315 ± 0.000510

 

W B

6,434.17

6,927.67

6,935.83 ± 10.55

7,027.38 ± 34.64

6,991.64 ± 8.57

6,971.23 ± 20.73

 

W Q

17,419.40

17,685.82 b

17,683.45 ± 15.55

17,683.50 ± 15.56

17,683.50 ± 15.55

17,683.49 ± 15.55

 

B M m|Q

0.0558

4.86 ·10−5

4.55 ·10−5 ± 0.000109

2.23 ·10−5 ± 5.38·10−5

2.23 ·10−5 ± 5.46·10−5

2.27 ·10−5 ± 5.44·10−5

 

B m 1|Q

0.0558

4.86 ·10−5

4.28 ·10−5 ± 0.000110

2.12 ·10−5 ± 5.44·10−5

2.14 ·10−5 ± 5.50·10−5

2.14 ·10−5 ± 5.50·10−5

 

B m 2|Q

0.0335

1.78 ·10−7

0

0

0

0

0.5

B m 3|Q

0.00143

2.27 ·10−6

3.28 ·10−6 ± 1.41·10−6

1.27 ·10−6 ± 7.82·10−7

1.21 ·10−6 ± 8.71·10−7

1.66 ·10−6 ± 5.64·10−7

 

B M 1|Q

0.327

0.000910

0.00273 ± 0.00702

0.000850 ± 0.00219

0.00179 ± 0.00461

0.00179 ± 0.00461

 

B M 2|Q

0.205

9.58 ·10−7

0

0

0

0

 

B M 3|Q

0.00906

1.61 ·10−5

3.56 ·10−5 ± 9.78·10−6

4.35 ·10−5 ± 1.69·10−5

2.93 ·10−5 ± 1.54·10−5

2.94 ·10−5 ± 1.61·10−5

 

W B

5,119.13

5,295.76

5,296.16 ± 13.30

5,297.13 ± 12.82

5,296.73 ± 12.83

5,296.48 ± 13.08

 

W Q

15,998.35

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

0.00678

1.78 ·10−8

0

0

0

0

 

B m 1|Q

0.00678

1.78 ·10−8

0

0

0

0

 

B m 2|Q

0.00416

<1·10−10

0

0

0

0

1.0

B m 3|Q

0.000153

1.6 ·10−9

0

0

0

0

 

B M 1|Q

0.0530

4.76 ·10−7

0

0

0

0

 

B M 2|Q

0.0298

<1·10−10

0

0

0

0

 

B M 3|Q

0.00113

1.10 ·10−8

0

0

0

0

 

W B

3,341.90

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 networkℋ, for different values of α, when the HMOR-S2 is used to update the routing plan. a99.56%; 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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