Skip to main content

Table 5 Average o.f. values for the 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

54,803.69

64,905.26 a

64,774.12 ± 68.28

64,776.24 ± 76.03

64,774.68 ± 68.46

64,750.27 ± 61.42

 

B M m|Q

0.413

0.0752

0.0773 ± 0.00356

0.0774 ± 0.00363

0.0771 ± 0.00333

0.0793 ± 0.00302

 

B m 1|Q

0.413

0.0752

0.0773 ± 0.00356

0.0774 ± 0.00363

0.0771 ± 0.00333

0.0793 ± 0.00302

 

B m 2|Q

0.314

0.0184

0.0236 ± 0.000576

0.0235 ± 0.000655

0.0237 ± 0.000601

0.0238 ± 0.000696

0.0

B m 3|Q

0.0198

0.00184

0.00200 ± 0.0000499

0.00200 ± 0.0000445

0.00200 ± 0.0000567

0.00204 ± 0.0000592

 

B M 1|Q

0.912

0.708

0.706 ± 0.00912

0.702 ± 0.0145

0.704 ± 0.0115

0.682 ± 0.0198

 

B M 2|Q

0.766

0.103

0.110 ± 0.00600

0.108 ± 0.0154

0.111 ± 0.00488

0.0916 ± 0.00800

 

B M 3|Q

0.0585

0.0301

0.0303 ± 0.000146

0.0300 ± 0.000287

0.0303 ± 0.000384

0.0292 ± 0.000978

 

W B

15,106.57

17,039.20

17,017.10 ± 39.32

17,030.28 ± 57.28

17,015.51 ± 39.62

17,059.73 ± 42.35

 

W Q

51,785.21

60,739.76 b

60,676.12 ± 61.43

60,659.89 ± 53.91

60,675.17 ± 66.08

60,287.27 ± 57.93

 

B M m|Q

0.413

0.0278

0.0306 ± 0.00145

0.0317 ± 0.00146

0.0308 ± 0.00149

0.0533 ± 0.00158

 

B m 1|Q

0.413

0.0278

0.0306 ± 0.00145

0.0317 ± 0.00146

0.0308 ± 0.00149

0.0533 ± 0.00158

 

B m 2|Q

0.296

0.00230

0.00463 ± 0.000355

0.00511 ± 0.000556

0.00460 ± 0.000674

0.0163 ± 0.000714

0.5

B m 3|Q

0.0174

0.000857

0.000922 ± 0.0000167

0.000904 ± 0.0000179

0.000912 ± 0.0000156

0.00105 ± 0.0000369

 

B M 1|Q

0.882

0.629

0.626 ± 0.0196

0.622 ± 0.0243

0.628 ± 0.0207

0.481 ± 0.0280

 

B M 2|Q

0.722

0.00959

0.0158 ± 0.00216

0.0166 ± 0.00142

0.0155 ± 0.00130

0.0552 ± 0.00348

 

B M 3|Q

0.0517

0.0244

0.0245 ± 0.000261

0.0239 ± 0.000315

0.0244 ± 0.000236

0.0171 ± 0.000325

 

W B

13,787.49

16,685.60

16,696.08 ± 40.87

16,757.72 ± 80.12

16,702.89 ± 72.29

17,562.04 ± 41.26

 

W Q

49,010.41

56,106.51 c

56,036.04 ± 45.53

56,044.88 ± 66.47

56,036.66 ± 49.07

55,895.41 ± 61.80

 

B M m|Q

0.405

0.0256

0.0274 ± 0.00174

0.0271 ± 0.00319

0.0273 ± 0.00121

0.0375 ± 0.00219

 

B m 1|Q

0.405

0.0256

0.0274 ± 0.00174

0.0271 ± 0.00319

0.0273 ± 0.00121

0.0375 ± 0.00219

 

B m 2|Q

0.275

0.00499

0.00805 ± 0.000619

0.00772 ± 0.00123

0.00803 ± 0.000747

0.0131 ± 0.00110

1.0

B m 3|Q

0.0150

0.000567

0.000643 ± 0.0000157

0.000590 ± 0.0000498

0.000640 ± 0.0000154

0.000686 ± 0.0000270

 

B M 1|Q

0.841

0.556

0.552 ± 0.0304

0.495 ± 0.0826

0.555 ± 0.0262

0.354 ± 0.0517

 

B M 2|Q

0.667

0.0186

0.0310 ± 0.00318

0.0298 ± 0.00504

0.0310 ± 0.00446

0.0492 ± 0.00497

 

B M 3|Q

0.0446

0.0200

0.0201 ± 0.000295

0.0168 ± 0.00444

0.0202 ± 0.000248

0.0110 ± 0.000972

 

W B

12,445.64

16,465.58

16,436.45 ± 17.45

16,443.61 ± 81.71

16,438.56 ± 16.88

16,690.18 ± 50.64

  1. Average o.f. values, and 95% confidence intervals, for the 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 network, for different values of α, when the HMOR-S2 is used to update the routing plan. a99.62%; b99.85%; c99.59% of the upper bounds W Q max for the optimal value of the QoS traffic revenue W Q in [24].