05M2 Lecture Telecommunication Network Design

Martin Grötschel Institut für Mathematik, Technische Universität Berlin (TUB)DFG-Forschungszentrum “Mathematik für Schlüsseltechnologien” (MATHEON)Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

[email protected] http://www.zib.de/groetschel

05M2 LectureTelecommunication

Network Design

Martin Grötschel Beijing Block Course

“Combinatorial Optimization at Work”September 25 – October 6, 2006

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CO atWork Contents

1. Telecommunication: The General Problem2. Newspaper Reports3. Survivability4. Integrated Topology, Capacity, and Routing

Optimization as well as Survivability Planning

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CO atWork Contents



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CO atWork What is the Telecom Problem?

Design excellent technical devicesand a robust network that survivesall kinds of failures and organizethe traffic such that high qualitytelecommunication betweenvery many individual units at many locations is feasibleat low cost!

SpeechData

VideoEtc.

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CO atWork What is the Telecom Problem?

Design excellent technical devicesand a robust network that survivesall kinds of failures and organizethe traffic such that high qualitytelecommunication betweenvery many individual units at many locations is feasibleat low cost!

ThisThis problemproblem is is tootoo generalgeneral

to to bebe solvedsolved in in oneone stepstep..

Approach in Practice:• Decompose whenever possible.• Look at a hierarchy of problems.• Address the individual problems one by one.• Recompose to find a good global solution.

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CO atWork Connecting Mobiles: What´s up?

BSC

MSC

BSC

BSC

BSC

BSC

BSC

BSC

MSC

MSCMSC

MSC

BTS

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CO atWork Contents



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CO atWork Clyde Monma

Cornell & Cayuga Lake 1987

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CO atWork USA 1987-1988

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CO atWork USA 1987-1988

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CO atWork Special Report by IEEE Spectrum

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Special Report

IEEE Spectrum

June1988

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CO atWork Berlin 1994 & Köln 1994

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High-TechTerrorism 1995

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CO atWork Berlin 1997 & Wien

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CO atWork Austria

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CO atWork Contents



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Network Design: Tasks to be solvedSome Examples

Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)

Assignment of frequencies to antennas

Cryptography and error correcting encoding for wirelesscommunication

Clustering BTSs

Locating base station controllers (BSCs)

Connecting BTSs to BSCs

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Network Design: Tasks to be solvedSome Examples (continued)

Locating Mobile Switching Centers (MSCs)

Clustering BSCs and Connecting BSCs to MSCs

Designing the BSC network (BSS) and theMSC network (NSS or core network)

Topology of the network

Capacity of the links and components

Routing of the demand

Survivability in failure situations

Most of these problems turn out to beCombinatorial Optimization or

Mixed Integer Programming Problems

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TheBellCorestudy

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CO atWork The Data

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CO atWork The IP Model

minimum cost spanning treeminimum cost Steiner treemin-cost k-edge or k-node-connected subgraph

Special cases:

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Nodetypes

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CO atWork b-matchings and r-covers

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CO atWork Generalizations of r-cover inequalities

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CO atWork Facets: one example

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Facets: anotherexample

≥

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CO atWork Data

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CO atWork Reduction

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CO atWork computational Results

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CO atWork LATA DL: optimum solution

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CO atWork The Ship Problem: higher connectivity

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CO atWork Contents



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CO atWork

Network Design: Tasks to be solvedSome Examples (continued)

Locating Mobile Switching Centers (MSCs)

Clustering BSCs and Connecting BSCs to MSCs

Designing the BSC network (BSS) and theMSC network (NSS or core network)

Topology of the network

Capacity of the links and components

Routing of the demand

Survivability in failure situations

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CO atWork Network Optimization

Networks

Capacities Requirements

Cost

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CO atWork What needs to be planned?

TopologyCapacitiesRoutingFailure Handling (Survivability)

IP RoutingNode Equipment PlanningOptimizing Optical Links and Switches

DISCNET: A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)

atesio ZIB Spin-Off

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CO atWork The Network Design Problem

200

65

258

134

30

42Düsseldorf

Frankfurt

Berlin

Hamburg

München

Communication Demands

Düsseldorf

Frankfurt

Berlin

Hamburg

MünchenPotential topology

&Capacities

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CO atWork Capacities

PDH

2 Mbit/s

34 Mbit/s

140 Mbit/s

SDH

155 Mbit/s

622 Mbit/s

2,4 Gbit/s

... WDM (n x STM-N)

Two capacity models : Discrete Finite CapacitiesDivisible Capacities

(P)SDH=(poly)synchronous digital hierarchy

WDM=Wavelength Division MultiplexerSTM-N=Synchronous Transport Modul with N STM-1 Frames

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CO atWork Survivability

H B

D

FM

120H B

D

FM

3030

60Diversification„route node-disjoint“

Path restoration„reroute affected demands“(or p% of all affected demands)

6060

H B

D

FM

H B

D

FM

H B

D

FM

60

60

Reservation„reroute all demands“(or p% of all demands)

120

H B

D

FM

H B

D

FM

H B

D

FM

60

60

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CO atWork Model: Capacities

Capacity variables : e ∈ E, t = 1, ..., Te

{0,1}tex ∈

Cost function :

1

mineT

t te e

e E t

k x∈ =∑ ∑

Capacity constraints : e ∈ E0 11 0eTe e ex x x= ≥ ≥ ≥ ≥

0

eTt t

e e et

y c x=

= ∑

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CO atWork Model: Routings

Path variables :

Capacity constraints :

Demand constraints :

, , ss uvs S uv D P∈ ∈ ∈ Ρ

( ) 0suvf P ≥

0

0

:

( )uv

e uvuv D P e P

y f P∈ ∈Ρ ∈

≥ ∑ ∑e E∈

0

0 ( )uv

uv uvP

d f P∈Ρ

= ∑uv D∈

Path length restriction

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CO atWork Model: Survivability (one example)

Path restoration „reroute affected demands“

H B

D

F

M

120

60

60

H B

D

F

M

0

0

s suv uv uv

suv uv uv uv

P Ρ Ρ P Ρ :e P

f (P) f (P) dσ∈ ∩ ∈ ∈

+ ≥∑ ∑for all s∈S, uv∈Ds

0

0(s ss uv uv uv

suv uv e

uv D P Ρ Ρ :e P P Ρ :e P

f (P) f (P) ) y∈ ∈ ∩ ∈ ∈ ∈

+ ≤∑ ∑ ∑for all s∈S, e∈Es

60

60

H B

D

F

M

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CO atWork Mathematical Model

topology decisison

capacity decisions

normal operation routing

component failure routing

suvs PDuvSs Ρ∈∈∈ ,,0)( ≥Pf suv

)(:

0

0

PfyDuv PeP

uveuv

∑ ∑∈ ∈Ρ∈

≥ Ee∈

∑Ρ∈

=0

)(0

uvPuvuv Pfd Duv ∈

∈ =∑ ∑

1

m ineT

t te e

e E t

k x

, 1, , ee E t T∈ = …

∈ = …, 1, , ee E t T∈ {0,1}tex

1t te ex x− ≥

0

eTt t

e e et

y c x=

= ∑ e E∈0

0

s suv uv uv

suv uv uv uv

P Ρ Ρ P Ρ :e P

f (P) f (P) dσ∈ ∩ ∈ ∈

+ ≥∑ ∑

0

0

s ss uv uv uv

suv uv e

uv D P Ρ Ρ :e P P Ρ :e P

( f (P) f (P)) y∈ ∈ ∩ ∈ ∈ ∈

+ ≤∑ ∑ ∑ sEeSs ∈∈ ,

sDuvSs ∈∈ ,

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CO atWork Flow chart

No

Yes

Separationalgorithms

Optimalsolution

InitializeLP-relaxation

Runheuristics

SolveLP-relaxation

Separationalgorithms

AugmentLP-relaxation

Solve feasibilityproblem

Inequalities?

x variablesinteger?

Yes

No

Feasibleroutings?

Yes

No

Polyhedral combinatoricsValid inequalities (facets)Separation algorithmsHeuristicsFeasibility of a capacity vector

LP-based approach:

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CO atWork Finding a Feasible Solution?

HeuristicsLocal search

Simulated Annealing

Genetic algorithms

...

Nodes Edges Demands Routing-Paths

15 46 78 > 150 x 10e6

36 107 79 > 500 x 10e9

36 123 123 > 2 x 10e12

Manipulation ofRoutingsTopologyCapacities

Problem Sizes

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CO atWork How much to save?

Real scenario• 163 nodes• 227 edges• 561 demands

34% potential savings!==

> hundred million dollars

PhD Thesis: http://www.zib.de/wessaely

[email protected]

Martin Grötschel Institut für Mathematik, Technische Universität Berlin (TUB)DFG-Forschungszentrum “Mathematik für Schlüsseltechnologien” (MATHEON)Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

[email protected] http://www.zib.de/groetschel

05M2 LectureTelecommunication

Network Design

Martin Grötschel Beijing Block Course

“Combinatorial Optimization at Work”September 25 – October 6, 2006The End

05M2 Lecture Telecommunication Network Design

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