Mathematical Challenges
in Telecommunication
a Tutorial

Comment

ZIB Telecom Team

ZIB Partners from Industry

Contents

Contents

What is the Telecom Problem?

What is the Telecom Problem?

Contents

Cell Phones and Mathematics

Chip Design

Design and Production of ICs and PCBs

Production and Mathematics: Examples

Drilling 2103 holes into a PCB

Siemens Problem

Siemens Problem

Mobile Phone Production Line

Contents

Network Components

Component „Cables“

Component „Antennas“

Component „Base Station“

Component
„Mobile Switching Center“:

Example of an MSC Plan

Contents

Network Design:  Tasks to be solved  Some Examples

Network Design:  Tasks to be solved  Some Examples (continued)

Connecting Mobiles: What´s up?

Connecting Computers or
other Devices

Contents

F
A
P

F
i
lm

Antennas & Interference

Interference

Separation

Frequency Planning Problem

Minimum Interference
Frequency Assignment Problem

A Glance at some Instances

Region Berlin - Dresden

Region Karlsruhe

The UMTS Radio Interface

Contents

G-WiN Data

G-WiN Problem

Potential node locations for the
3-Level Network of the G-WIN

Demand distribution

G-WiN Location Problem: Data

G-WiN Location/Clustering Problem

Solution: Hierarchy & Backbone

G-WiN Location Problem:
Solution Statistics

Contents

Re-Optimization of
Signaling Transfer Points

Signaling Transfer Point (STP)

STP – Problem description

STP – Mathematical model

STP – Mathematical model

STP – current (former) solution

STP – „Optimal solution“

STP – Practical difficulty

STP – Reformulated Model

STP – Alternative Model

STP – New Solutions

STP – Experimental results

STP - Conclusions

Contents

Network Optimization Film

Network Optimization

What needs to be planned?

The Network Design Problem

Capacities

Survivability

Model: Data & Variables

Model: Capacities

Model: Routings

Model: Survivability (one example)

Mathematical Model

LP-based Methods

Flow chart

Finding a Feasible Solution?

How much to save?

Contents

Comment

Summary

Summary

The Mathematical Challenges

Mathematical Challenges
in Telecommunication
The End