EL736 Communications Networks II: Design and Algorithms

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EL736 Communications Networks II: Design and

Algorithms

Class4: Network Design Modeling (II)

Yong Liu10/03/2007

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Outline

Routing Restriction

Non-linear Link Dimensioning, Cost and Delay Functions

Budget Constraint, Incremental NDP

Extensions

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Introducing Routing Restriction

enforce the resulting routes w./w.o. certain properties path diversity vs. limited split equal splitting vs. arbitrary splitting

modular flows vs. unmodular flows

extend the basic formulation by introducing additional routing constraints.

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Path Diversity “never put all eggs in one basket”

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Lower Bounds on Non-Zero Flows

the flow volume on a path greater than B if any.

implicitly limit number of paths

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Limited Demand Split

only split among k paths

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Node-Link Formulation

Single Path

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Node-Link Formulation equally split among k link-disjoint paths

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Integral Flows

allocate demand volumes in demand modules

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Nonlinear Link Cost

Linear Link Cost link capacity = link rate linear cost: $/bps

Nonlinear Link Cost modular link capacities different link modules

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Dimensioning with Modular Links

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Dimensioning with Multiple Modules

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Convex Cost Functions

Convex Function non-negative second order derivative local minimum-> global minimum

good approx. for link delay

split demand if possible how to split?

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Minimal Delay Routing

link delay, network delay, avg. user delay

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Piecewise Linear Approximation of Convex

Function

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Piecewise Linear Approximation of Convex

Function

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From CXP to LP

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Concave Link Dimensioning Functions

Concave Function non-positive second derivative, unique maximum

Erlang B-Loss Formula (extend to real domain)

Implications merge resources if possible conflict?

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Piecewise Linear Approximation of Concave

Function

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Concave Link Dimensioning

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Budget Constraint

given budget constraint, maximize the realized ratio for all demands.

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Incremental NDPs design from scratch vs. improve existing network; sub-optimal solution

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Extensions: nodes

constraints on nodes node cost: input/output ports, link termination, switching fabric, installation, …

reliability: node disjoint virtual graph

two copies for a node: receiving/sending directed link from receiving copy to sending copy

incorporating node constraints node cost represented by link cost on its virtual link

node-disjoint in real graph <=> link-disjoint in virtual graph

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Extensions: nodes

link-path formulation

load on a node:

reliability against node failures: no node carries more than certain share for a demand link-path formulation node-link formulation