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