Davide Cherubini - PhD Thesis - UniCA Eprints

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6.4 LP models6.4.1.2 Node-arc FormulationThe node-arc formulation of the first model makes use of a different set of data andits MPLS flow variable is not anymore a path but a flow traversing a specific link.This formulation has been preferred during the tests phase because it presents abetter algebraic structure.DataN - Node setA - Edge setF - Commodity setc ij - Capacity associated with link (i, j)d fx f ij- Effective bit rate of flow f- Share of flow f carried by ISIS and traversing link (i, j)Variablesu maxis fMaximum utilization in the network - to be minimizedShare of flow f carried by ISISflow ij Share of flow f carried by MPLS and traversing link (i, j)The mathematical model for the GRP using the node-arc formulation, is for-55
6.4 LP modelsmalized as follows:z = min(u max ) (6.38)∑x f ij · isf + ∑ flow f ij ≤ u max · c ij ∀(i, j) ∈ A (6.39)f∈F f∈F⎧⎪⎨∑flow f ji −∑−d f + is f ∀i ∈ N : i = I(f)flow f ij = d⎪ f − is f ∀i ∈ N : i = E(f) (6.40)⎩j:(j,i)∈Aj:(i,j)∈A0 otherwiseflow f ij ≥ 0 ∀(i, j) ∈ A, ∀f ∈ F (6.41)is f ∈ [0, d f ] ∀f ∈ F (6.42)While the objective function 6.38 remains unaltered, the capacity constraints6.39 and the flow conservation equations 6.40 become different. While the formeris really close to 6.33 because it is defined for each arc and only the MPLS“variable” has changed, the latter assumes a brand new form, being defined foreach node.Commodity per source aggregationIn order to reduce the number of variables and to make the model easier to solve,the commodities have been grouped based on their source node as follows:flowij h =∑flow f ij (6.43)f:I(f)=hWhere I(f) identifies the ingress node for commodity f.Let us consider the example in figure 6.1 where the commodities A → B,A → C, and A → D are replaced by a single commodity “A” which is the sumof them.Considering F (h) as the set of commodities having as ingress the generic node h,56
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AcknowledgementsThis dissertation w
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AbstractThis dissertation investiga
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CONTENTS7.4 The Real ISP’s Italia
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LIST OF FIGURES7.3 Default metrics
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1.2 Objectives of the dissertation2
Page 15 and 16: Chapter 2Basic knowledgeThis chapte
Page 17 and 18: 2.1 Understanding IS-IS• A = sour
Page 19 and 20: 2.2 Understanding MPLS Technology2.
Page 21 and 22: 2.2 Understanding MPLS TechnologyTh
Page 23 and 24: 2.4 Restoration SchemesHowever, fai
Page 26 and 27: 3.1 Optimization of IS-IS/OSPF rout
Page 28: 3.3 Survivability problemhas been d
Page 31 and 32: 4.1 Heuristic Algorithmsmeta-heuris
Page 33 and 34: 4.1 Heuristic Algorithmsto keep a c
Page 35 and 36: 4.1 Heuristic Algorithmsprobability
Page 37 and 38: 4.3 Linear Programming ApproachExam
Page 39 and 40: 5.2 Traffic monitoring• 60% of th
Page 41 and 42: 5.2 Traffic monitoringExporting the
Page 43 and 44: 5.2 Traffic monitoringare included
Page 45 and 46: 5.2 Traffic monitoringthe Internet.
Page 47 and 48: 5.2 Traffic monitoring5.2.3 The net
Page 49 and 50: 5.2 Traffic monitoring5.2.4 Monitor
Page 51 and 52: 5.2 Traffic monitoringFigure 5.9: S
Page 53 and 54: Chapter 6LP Optimization ModelsThis
Page 55 and 56: 6.2 Graphs and Network Flowswith a
Page 57 and 58: 6.2 Graphs and Network FlowsWhere B
Page 59 and 60: 6.2 Graphs and Network Flows6.2.3 T
Page 61 and 62: 6.3 Multicommodity Flow Problemscom
Page 63 and 64: 6.4 LP modelsThe second layer intro
Page 65: 6.4 LP modelsEquation 6.32 is the o
Page 69 and 70: 6.4 LP models(a) Rerouting flow p
Page 71 and 72: 6.4 LP models(a) 1 st solution(b) 2
Page 73 and 74: 6.4 LP models∑f∈Fx f,lij⎛⎝i
Page 75 and 76: 6.4 LP modelsterm is the MPLS part
Page 77 and 78: 7.2 The highly meshed network7.2 Th
Page 79 and 80: 7.3 The IBCN European network7.3 Th
Page 81 and 82: 7.3 The IBCN European networkmaximu
Page 83 and 84: 7.3 The IBCN European networkSurviv
Page 85 and 86: 7.3 The IBCN European networkFigure
Page 87 and 88: 7.4 The Real ISP’s Italian Backbo
Page 93 and 94: 7.5 Conclusion and validation of re
Page 95 and 96: optimal configuration of network pa
Page 97 and 98: REFERENCES[14] Jones Lustig Format
Page 99 and 100: REFERENCES[40] A. V. Fiacco and G.
Page 101: REFERENCES[61] A. Nucci, B. Schroed
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Davide Cherubini - PhD Thesis - UniCA Eprints

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