Davide Cherubini - PhD Thesis - UniCA Eprints

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6.4 LP models6.4.1.1 Arc-path FormulationNotationDataN - Node setA - Edge setF - Commodity setc ij - Capacity associated with link (i, j)P(h) - Set of edges which belong to path hP(f) - Set of paths for commodity fd fx f ij- Effective bit rate of flow f- Share of flow f carried by IS-IS and traversing link (i, j)Variablesu maxis fp hMaximum utilization in the network - to be minimizedShare of flow f carried by ISISShare of flow f which uses path h with MPLS technologyThe General Routing Problem can be specified as follows:z = min(u max ) (6.32)∑is f · x f ij +∑p h ≤ u max · c ij ∀(i, j) ∈ A (6.33)f∈F∑h∈P(f)h:(i,j)∈P(h)p h = d f − is f ∀f ∈ F (6.34)p h ≥ 0 ∀h ∈ P(f) (6.35)is f ∈ [0, d f ] ∀f ∈ F (6.36)53
6.4 LP modelsEquation 6.32 is the objective function to be minimized, while the left handside (LHS) of capacity constraints in equation 6.33, specifies the total amount oftraffic traversing link (i, j) and it is composed by the traffic routed by IS-IS (firstsum) and by the LSP-carried traffic. Obviously, for each link (i, j) this value hasto be smaller than variable umax times the link capacity c ij .Equation 6.34 determines the amount of traffic carried by MPLS and representsa sort of flow conservation defined for each commodity instead of node.It is important to pay attention to constraint 6.36 because it states thatvariable is f is a real variable making the model entirely linear and, as shown inthe previous sections and subsections, a (pure) linear program is “easy” to solve.In fact, changing the definition of variable is f , for example considering a “binary”variable {0, d f } by specifying that every commodity f is carried only byIS-IS or only by MPLS, the problem becomes a Mixed Integer Program (MIP) becauseit integrates linear constraints and linear objective function with an integerconstraint. MIPs are known to be harder to solve with respect to LPs.The solution of GRP gives the optimal distribution of LSPs that minimizesthe maximum bandwidth occupation and this is also an important result becauseit represents a lower bound during the optimization process of IS-IS metrics [43],in normal working conditions.Survivability ConstraintsThe survivability constraints introduced in the model are formalized as follows:⎛ ⎞∑is f · x f,lij + ∑p h + x l ⎝ ∑ij p h⎠ ≤ u max · c ij ∀(i, j), l ∈ Af∈Fh:(i,j)∈P(h)h:l∈P(h)(6.37)Where the constant x l ij specifies the share of MPLS traffic, flowing along linkl that, in case of failure of such link, is rerouted by IS-IS along link (i, j), whilex f,lijl fails.is the share of flow f carried by IS-IS and traversing link (i, j), when the linkNote that, if x f,lij is less than x l ij the constraint specified by equation 6.33 isredundant.54
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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
Page 13 and 14: 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: 6.4 LP modelsThe second layer intro
Page 67 and 68: 6.4 LP modelsmalized as follows:z =
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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