[PPT] - Resilient Networks 3.1 Resilient Network Design - Intro Prepared PowerPoint Presentation

SLIDE 1

1

Resilient Networks

3.1 Resilient Network Design - Intro

Prepared along: Michal Pioro and Deepankar Medhi - Routing, Flow, and Capacity Design in Communication and Computer Networks, The Morgan Kaufmann Series in Networking, 800 pages, 2004

Mathias Fischer

SLIDE 2

2

Outline

Motivation
Introduction to Network Design Problems

– Traffic and Demand – Network Design and Routing – Multi-layer Networks – Network Management

Notations and mathematical formulation

– Link-Path Formulation – Link-Demand-Path-Identifier-based Notation

Some basic design problems

– Minimizing costs of network links – Capacitated design problems – Shortest path routing

Summary

SLIDE 3

3

A Network Analogy

Frankfurt Moscow Peking Kuala Lumpur Sydney San Francisco NY Sao Paolo Johannesburg

New links are expensive
Economies of scale
Store and forward concept
Hop-by-Hop routing

SLIDE 4

4

Network Basics

Communication network carries traffic
Network has different links of different capacity (bandwidth)

– Economies of scale principle applies

Traffic may be routed via different paths to destination

– According to store-and-forward principle – Hop-by-hop

We need to have enough bandwidth to carry all data
We might want to reduce the average packet traversal delay

SLIDE 5

5

Network Design Questions

Can we find better routes?
Where should we add more bandwidth?
Where and when should we add new nodes (and links) in the network?
How does the inherent property of a network technology or protocol can affect our

decision making?

What level of abstraction is appropriate for a particular network for modeling

purpose so that meaningful results can be obtained How to design cost-effective, resilient core/backbone networks taking into consideration properties of the network? - How to do network design?

SLIDE 6

6

Routing in the Internet – Autonomous Systems

Internet consists out of connected Autonomous Systems (AS)

– Stub AS: small organization (one connection to the Internet) – Multi-homed AS: large organization (several connections, no transit traffic) – Transit AS: Provider (several connections , transit traffic)

The Internet today consists out of 44.000 AS

– Of different size – AS Exchange data packets as

Peers
Provider AS and Customer AS
Each AS has a unique ID (number)
Each AS needs to know at least
ne route to any other AS

Bildquelle: caida.org

SLIDE 7

7

Communication Networks and Network Providers (1) Packet sending in the Internet

Involves series of different AS networks
Each network with own switches or routers
Packet routing depends completely on the specific network
Network design problems are confined within

each network or administrative domain

AS 3 AS 2 AS 1

SLIDE 8

8

Communication Networks and Network Providers (2) Layered (or Hierarchy of) Networks

Private networks of large companies and corporations
Telecommunication network providers that
perate transport or transmission networks
Different ISPs may use the same transport network
Multi-layer network environment

AS 1 AS 2 AS 3 Transport Provider 1 AS 5 AS 4 Transport Provider 2

SLIDE 9

9

Autonomous Systems in Germany

Bildquelle: Institut für Internet-Sicherheit, Fachhochschule Gelsenkirchen

SLIDE 10

10

Communication Networks and Network Providers (3) Network providers

Design and manage their networks
Need to know

– traffic demands in their networks – Considering all network nodes, they need to know traffic volume between any two such nodes

Traffic volume matrix or demand volume matrix as input to network design required

SLIDE 11

11

Traffic and Demand (1)

Task of a network

– Route packets from one end to another, – without considering the reliability of delivery

Reasons for lost packets

– Physical transmission errors – Traffic congestion and routers running out of buffer space

Task of network designer (our task)

– Keep delay low – Design networks to prevent or at least limit congestion at routers

SLIDE 12

12

Traffic and Demand (2) What do we need for this?

Prediction of traffic demand, e.g., via statistical approaches
Estimating traffic volume by capturing statistics about traffic arrival

distribution

We need this information in between different network points
Necessary Measurements

– Average arrival rate of packets – Average size of packets – Both influence delay

SLIDE 13

13

Traffic and Demand (3)

Example: M/M/1 queuing system

Packet arrival follows Poisson process
Packet size is exponentially distributed

D average delay in seconds λp average packet arrival in seconds μp average link service rate C link capacity per second Kp average packet size

Average delay increases drastically when average arrival rate is closer to average service rate of the link

SLIDE 14

14

Traffic and Demand (4)

What is the acceptable delay users would like to tolerate?

– If acceptable delay is 15 ms, then the acceptable average utilization can be no more than 64,5% on the link

Good News

– At least for purpose of network design maximum link utilization can be used as alternative criterion to the delay

However, traffic arrival does not follow Poisson process

– Realistic delay is worse than the calculated one – In reality average utilization has to be kept lower, e.g., at 50% to achieve the 15 ms

SLIDE 15

15

Traffic and Demand (5)

We need to know whether observed utilization is higher than acceptable threshold for a particular link type

In single-link networks

– Measurement is easy – Bandwidth can be easily added

In multi-link networks

– Utilization is further impacted by routing of traffic flows – Adding bandwidth becomes complex network design problem

Lesson learned / What we need to solve network design problems

– Average arrival rate in between different nodes in the network – Traffic demand volume as input for all network design problems

SLIDE 16

16

Network Design and Routing (1)

In reality we have many source-destination (egress-ingress) traffic demands

between various points in the network Traffic-demand matrix required as input to network design

Goal: Determine a network with enough capacity and connectivity to route

traffic, so that acceptable service guarantees can be provided

– In single-link networks it is sufficient to determine link utilization threshold for given traffic demand – However, this is not the case in multi-link networks anymore

SLIDE 17

17

Network Design and Routing (2) Role of network design

Distinction between (usually continuous) Demand Volume Units (DVU) and

(usually discrete) Link Capacity Units (LCU)

Three node network with traffic demand
f 300Kbps between each node

– QoS goal: utilization threshold below 60% – Three T1 links (LCU: each 1.54 Mbps) 300 Kbps/1.54Mbps ≈ 19,5% – Two T1 links (2-1, 1-3) (300 +300)Kbps / 1.54 Mbps ≈ 39%

Network design also depends on

routing capabilities

1 2 3

300 Kbps 300 Kbps 300 Kbps

1 2 3

300 Kbps 300 Kbps 300 Kbps

SLIDE 18

18

Network Design and Routing (3)

Some Definitions

Candidate path list: All possible paths between two points
Route: Particular path chosen as valid path by network design
Flow: The amount of traffic associated with a route

SLIDE 19

19

Multi-layer Networks (1)

End- system Layer 5 Layer 4 Layer 3

Application Layer Transport Layer Network Layer

Layer 2 Layer 1

Data Link Layer Physical Layer

IP

OpenFlow / MPLS / …

End- system Layer 5 Layer 4 Layer 3

Application Layer Transport Layer Network Layer

Layer 2 Layer 1

Data Link Layer Physical Layer

Optical Networks

UDP / TCP SMTP/ POP3 / IMAP/ HTTP / …

Traffic networks

Aka service level
Traffic arrival

stochastic in nature

Has switching / routing

capabilities

Transport networks

service level traffic as

demand input

High-data rate services that

are required to be set up at permanent or semi- permanent basis

Traffic deterministic or

precise in nature over time Ethernet / GMPLS OC-1 / OC-3 / OC-48 / T-1 / …

SLIDE 20

20

Multi-layer Networks (2) The architecture of communication networks

A network (or layer) on top another
A network may look logically diverse, but

may not be diverse in another layer Implications in protection and restoration design (network resilience) due to inter-relation between layers

Multi-layer network design as

important problem to consider

SLIDE 21

21

Multi-layer Networks (3) - Traffic and Demand Traffic, Demand, and layered Networks

Output bandwidth requirement for each Internet, telephone, and private-

line service from service networks, is input demand to layer beneath

Capacity requirement of one network becomes

traffic demand volume for network below

SLIDE 22

22

Network Management Cycle (1)

Network management is the entire process from planning a network, to deploying it, and to operate it on a day-to-day basis.

Requires network management systems and protocols
Different management tasks run at different time granularity

SLIDE 23

23

Network Management Cycle (2)

Packet Discarding, Buffer Management, Packet Routing TCP Feedback control Call Routing, Call Setup, Call Admission Control, Call Rerouting, Routing, Information Update Traffic Engineering OSPF weight updates Trunk Rearrangement Periodic Traffic Estimation Traffic Network Capacity Expansion SONET / SDH ring restoration Mesh Transport Network Restoration Transport Network Routing/Loading Transport Network Capacity Planning / Expansion

Micro-secs Mili-secs Secs Minutes Hours Days Weeks Months Year(s)

Traffic Network Transport Network

SLIDE 24

24

Network Management Cycle (3) – Traffic Networks

Traffic Network (IP)

Real-Time Traffic Management Capacity Management Traffic Engineering Network Planning

various controls secs-mins days-weeks months-years routing update capacity change Traffic data Forecast adjustment Marketing input

Network Management

SLIDE 25

25

Network Management Cycle (3) – Transport Networks

Transport Network

Near Real-Time Management Capacity Management Traffic Engineering Network Planning

restoration mins-hours days-weeks months-years route loading Capacity expansion/ protection Network fill factor, loading New Transport Demand, Marketing Input

Network Management

SLIDE 26

26

Notation for Network Design Problems Network Design Problems

Can be formally specified using mathematical notations
Representation of specific design problems in compact way
Eventually helps to understand the problem at hand
Eventually helps to solve the problem

Notations for Network Design Problems

Link-Path Formulation
Link-Demand-Path-Identifier-based Formulation

SLIDE 27

27

Link-Path Formulation (1)

Three node network example

– Demand volume hij in between nodes i and j – Example demand

Each demand volume between two

nodes can be routed over two paths

3 2 1 2 1 3 1 3 2 1 3 2 1 3 2 3 2 1 Path 1-2 Path 1-3 Path 1-3-2 Path 1-2-3 Path 2-1-3 Path 2-3

SLIDE 28

28

Link-Path Formulation (2)

Demand between nodes 1 and 2 can be routed via direct link 1-2 and via

alternate route 1-3-2

– Demand path flows 𝑦^ are non-negative, i.e., 𝑦^ > 0 for all paths

Link capacities 𝑑12

^ , 𝑑13 ^ , 𝑑13 ^

– Assumption, capacity of first two links is 10 and the third is 15

3 2 1

SLIDE 29

29

Link-Path Formulation (3)

System of linear equations and inequalities (constraints)
ො

𝑦 are unknowns for all three considered demands

System has multiple solutions and defines set of feasible solutions

But which solution is

f interest?

SLIDE 30

30

Link-Path Formulation (4)

Different goals/objectives possible

– Minimizing total routing costs – Minimizing congestion of most congested link – ...

In mathematical way, goals are expressed as objective functions that needs

to be either minimized or maximized

Example: Minimizing total routing costs

– cost of routing one unit of flow on every link along a path is simply 1 – Resulting objective function F: 3 2 1

SLIDE 31

31

Link-Path Formulation (5)

Routing minimization problem

Capacity Constraints Demand Volume Constraints Objective Function

SLIDE 32

32

Link-Path Formulation (6) – Routing Minimization Routing minimization problem

Multi-Commodity Flow Problem

– Multiple demands (or commodities) – Need to be routed in a network simultaneously – Compete for resources

Optimization Context: Linear Programming Problem

– All constraints are linear – The objective function is linear

SLIDE 33

33

Link-Path Formulation (7) – Routing Minimization

Optimal solution for demand

Required: feasible solution for decision variables (ො

𝑦) that minimize F

Common sense solution

– Route everything on direct (cheapest) path, other x-variables are zero

Total optimal cost F*=20

3 2 1

SLIDE 34

34

Link-Path Formulation (8) – Routing Minimization

However

Optimal solution may not be unique
Not in all cases a solution is that simple to obtain
Constraints

– Need to be satisfied by optimal solution – Especially link capacity constraints need not be violated 3 2 1

SLIDE 35

35

Link-Path Formulation (9) – Routing Minimization Let‘s change the objective function

From
To
For demand
Solution not that easy anymore

– Cheapest path routing violates capacity constraints of link 1-3 – We are happy to announce a solution with total cost F*=25 3 2 1

SLIDE 36

36

Link-Path Formulation (10) – Routing Minimization

Lessons learned from Routing Minimization Problem

Changing objective function affects

– optimal solution to a problem – and the way of finding it

Carefully selection of right objective function (or goal)

for particular network required,

– Otherwise obtained solution might not be meaningful

SLIDE 37

37

Link-Path Formulation (11) – Pros and Cons

All demands and paths easy to follow from node-reference point of view
Works well for three-node example but not in general case
Drawbacks

– Paths may contain many intermediate nodes – Flow variables have indices of different length – Some node pairs might not have any demand – Not all nodes directly connected

Link-Path Formulation insufficient for Multi-Commodity-Flow Problems

SLIDE 38

38

Link-Path Formulation (12) – Pros and Cons

Link-Demand-Path-Identifier-based Notation (1)

Compact, allows to list only necessary objects
Non-zero demand pairs with indices from 1 to their total number
Total number of demands D, index d (D=3, d=1,2,3)
Links are assigned labels from 1 to total number of links
Total number of links E, index e

(E=3, e=1,2,3)

3 2 1

SLIDE 40

40

Link-Demand-Path-Identifier-based Notation (2)

Mapping for demand volumes h and link capacities c
Path identifiers (path-flow variables) 𝑦𝑒𝑞

– Demand-pair identifier d used as first subscript – Path label p for demand pair as second subscript

Candidate paths for demand pair numbered from 1 to total number
Total number of candidate paths for demand 𝑒 will be denoted 𝑄𝑒
Paths are labeled with index 𝑞

SLIDE 41

41

Link-Demand-Path-Identifier-based Notation (3) Example

Demand between nodes 1 and 2 identified by label d = 1 (first subscript)

has two candidate paths (𝑄

1 = 2)

Paths 1-2 and 1-3-2 are labeled with p=1,2 (second subscript)
Paths are identified as (1,1) and (1,2)
Path-flow variables

3 2 1

SLIDE 42

42

Link-Demand-Path-Identifier-based Notation (4)

Mapping of path identifiers and paths from:

node-identifier-based notation to link-demand-path-identifier-based notation Node-identifier-based Link-demand-path-identifier-b. Path identifier Path Path identifier Path 132 1-3-2 12 {2,3} 213 2-1-3 32 {1,2} 23 2-3 31 {3}

SLIDE 43

43

Link-Demand-Path-Identifier-based Notation (5)

Routing Minimization Problem in Link-Demand-Path-Identifier-based Notation

SLIDE 44

44

Link-Demand-Path-Identifier-based Notation (6) Comparison

Link-path formulation Link-demand-path-identifier-based

SLIDE 45

45

Link-Demand-Path-Identifier-based Notation (7)

Notation Summary

SLIDE 46

46

DP: Minimizing Costs of Network Links (1) Minimizing costs of networks links

Minimizing total link capacity cost

required to carry given demand

Assuming not a fixed, but

variable capacity 𝑧𝑓 of links

Dimensioning Problem (DP):

Determine

– required demand flows – and link capacities – to carry given demand volumes 4 3 1 2 2 3 1 Demand Network

SLIDE 47

47

DP: Minimizing Costs of Network Links (2) 4-node example network

Four nodes with routable demands
Node 4 is only transit node
𝜊𝑓 as costs for sending one unit via link e
Demands:

– d=1, only one path P11={2,4} allowed – d=2, paths P21={5}, P22={3,4} – d=3, paths P31={1}, P32={2,3}

Demand constraints

4 3 1 2 2 3 1 Demand Network

SLIDE 48

48

DP: Minimizing Costs of Network Links (3)

Demand constrains in general form

– Vector of flows assigned to demand d:

Hence, we can write
In summation notation
Flow allocation vector x

SLIDE 49

49

DP: Minimizing Costs of Network Links (4)

Capacity constraints

– Assures that for each link e its capacity ce (or ye, if capacity is a variable) is not exceeded by the flows using the link Sum on left side are link loads ye (total flow through that link)

SLIDE 50

50

DP: Minimizing Costs of Network Links (5)

To write down link loads in compact manner we need

to know relationships between links and paths

Formally defined via link-path incidence coefficients
In more compact manner via coefficient δ𝑓𝑒𝑞:

e\ Pdp P11={2,4} P21={5} P22={3,4} P31={1} P32={2,3}

1 1 2 1 1 3 1 1 4 1 1 5 1

4 3 1 2 2 3 1

SLIDE 51

51

DP: Minimizing Costs of Network Links (6)

Link load ye on link e in compact manner
Summation over all paths
appearing in routing lists
f all demands, over all

combinations (d,p)

SLIDE 52

52

DP: Minimizing Costs of Network Links (7)

Minimizing capacity costs, objective function

– 𝜊𝑓 as costs for sending one unit via link e

SLIDE 53

53

DP: Minimizing Costs of Network Links (8)

DP: Minimizing capacity costs

4 3 1 2 2 3 1 Demand Network

SLIDE 54

54

DP: Minimizing Costs of Network Links (10)

Optimal solution for DP

Feasible solution (x,y) with y1(x)=y1=5, y2(x)=y2=20, y3(x)=y3=10,y4(x)=y4=20, y5(x)=y5=15, and

thus y = (y1, y2, y3, y4, y5) = (5,20,10,20,15) has

total cost F=115
However, solution not optimal,

because of usage of P22 with costs ζ22= ξ3 +ξ4 = 1 + 3 = 4

Other possible path P21 has

costs ζ21= ξ5= 1

Cost of path Pdp is given by:

4 3 1 2 2 3 1 Demand Network

SLIDE 55

55

DP: Minimizing Costs of Network Links (11)

Optimal solution to DP

In example we need to move all the flow for demand d=2

from path P22 to path P21, which gives savings of (ζ22- ζ21) = 3 per flow unit, in our case the total savings are x22(ζ22- ζ21) = 15

d=1: x*

11= 15

d=2: x*

21= 20, x* 22= 0

d=3: x*

31= a, x* 32= 10-a, for

any 0 ≤ a ≤ 10

y*

1 = 10 –a, y* 2 = 15 + a,

y*

3 = a, y* 4 = 15, y* 5 = 20

F*=100

4 3 1 2 2 3 1 Demand Network

SLIDE 56

56

DP: Minimizing Costs of Network Links (12)

Shortest Path allocation rule:

For each demand allocate entire demand volume to its shortest path

(w.r.t. to link unit costs and candidate paths)

If there is more than one shortest path for a demand then

demand volume can be split among shortest paths arbitrarily

Works well for dimensioning problems, but no general solution approach for
ther multi-commodity flow problems, e.g.,

– Restriction to non-bifurcated flows – Modular design problems: in real networks capacities can be installed only in modular units (e.g., T1, E1, OC-3)

SLIDE 57

57

DP: Minimizing Costs of Network Links (13)

The observed DP is an uncapacitated design problem
Another type of problem are capacitated design problems

– Link capacities ce given instead of variable ye – Find a feasible flow allocation that satisfies demand and capacity constraints with ce appearing on the right-hand sides – In such scenario there might not be an objective function, except flow routing cost minimization is required – Capacitated problem in compact form

SLIDE 58

58

Capacitated Design Problems (1)

4-Node Network Example

Capacity vector 𝒅 = 𝑑1, 𝑑2, 𝑑3, 𝑑4, 𝑑5 = (5,10,10,5,30)
Additional path for d=1: P13 = {1,3,4}
All solutions are necessarily bifurcated
Possible solution:
Note that d=1 also uses path 𝑄

13,

its longest path

When non-bifurcated solutions are

required, additional constraints necessary to force single-path solution

4 3 1 2 2 3 1 Demand Network

𝑄

11

𝑄22 𝑄21 𝑄32 𝑄31 𝑄

13

SLIDE 59

59

Shortest Path Routing (1)

Shortest path routing, e.g., OSPF routing in IP networks
Shortest paths are

– essential for network design, – pre-requisite for resilient network design

For each d all volume ℎ𝑒 realized on shortest path w.r.t. to

– given link weight system 𝑥 = 𝑥1, 𝑥2, … , 𝑥𝐹 – and link weight cost we for link e

Path selection based on additive calculation of link weights
Flow allocation vector x(w), thus flow allocation dictated by link weights w
Shortest-path routing and term shortest-path allocation are not the same!

SLIDE 60

60

Shortest Path Routing (2)

Modified 4-Node Network Example

Capacity vector

– 𝒅 = 𝑑1, 𝑑2, 𝑑3, 𝑑4, 𝑑5 = (5,10,10,5,30)

Additional paths for d=1:

– P12 = {1,5} – P13 = {1,3,4} 4 3 1 2 2 3 1 Demand Network

𝑄

11

𝑄22 𝑄21 𝑄32 𝑄31 𝑄

12

𝑄

13

SLIDE 61

61

Shortest Path Routing (3) 4-Node Network Example

Link weight system 𝒙 = (1,3,1,2,4)
Solution
Rest of flow variables are 0
Shortest paths are unique for each

demand pair → flow allocation vector 𝒚(𝑥) is also unique 4 3 1 2 2 3 1

Demand Network

𝑥4 = 2 𝑥2 = 3 𝑥3 = 1 𝑥1 = 1 𝑥5 = 4

SLIDE 62

62

Shortest Path Routing (4) 4-Node Network Example

However, flow allocation not feasible for capacity vector 𝒅=(5,10,10,5,30)
Link loads resulting from allocation vector 𝒚(𝒙) would be

y(w) = (y1,y2,y3,y4,y5) = (25,0,35,35,0)

Solution violates capacity constraints!
Changing link capacity so that c = y(w): shortest path allocation w.r.t. to w

becomes (trivially) feasible again

SLIDE 63

63

Shortest Path Routing (5)

Single shortest-path allocation problem

For given link capacities c and demand volumes h, find a link weight system w such that the resulting shortest paths are unique and the resulting flow allocation vector 𝒚(𝒙) is feasible, i.e., such that 𝒚(𝒙) satisfies

Three reasons for complexity of the problem

A non-bifurcated (single-path) feasible flow allocation may not exist,

while bifurcated feasible flow allocations may exist

Even if single-path solution exists, in most cases it can be hard to determine
Even if we find single-path flow solution, the weight system to induce it may not

exist

SLIDE 64

64

Shortest Path Routing (6)

Infeasible unique shortest path case

Two demands

– d=1 between nodes 1 and 7 – d=2 between nodes 2 and 6 – ℎ1 = ℎ2 = 1, ce ≡ 1(∀𝑓 ∈ 𝐹)

Two paths per demand

– d=1: 𝑄

11:1-3-5-7, 𝑄 12: 1-3-4-5-7

– d=2: 𝑄21:2-3-4-5-6, 𝑄22: 2-3-5-6

Allocating flows d=1: 𝑦11=1, d=2: 𝑦21=1
No link weight system that induces single shortest path solution!

1 3 5 7 6 4 2

SLIDE 65

65

Shortest Path Routing (7) 4-Node Example

Considering weight system w=(1,1,1,1,1), which

is shortest path routing w.r.t. hop count

d=1: there are two shortest paths

– 𝑄

11 = 2,4 , 𝑄 12 = {1,5}

Which path has to be used for traffic?

– In OSPF: Equal Cost MultiPath (ECMP) rule – Split all outgoing demands at a node among its outgoing links that are on shortest paths to destination 4 3 1 2 2 3 1

Demand Network

𝑥4 =1 𝑥2 =1 𝑥3 = 1 𝑥1 = 1 𝑥5 =1

𝑄

11

𝑄

12

SLIDE 66

66

Shortest Path Routing (8)

Infeasible unique shortest path case
Two demands: d=1, d=2, ℎ1 = ℎ2 = 1, ce ≡ 1(∀𝑓 ∈ 𝐹)
Paths:

𝑄

11:1-3-5-7,

𝑄

12: 1-3-4-5-7 ,

𝑄21:2-3-4-5-6, 𝑄22: 2-3-5-6

Solution: assign link weight 2 to all links except

to links 2-3 and 4-5 that obtain weight 1

Result is feasible solution under ECMP rule

1 3 5 7 6 4 2

w=2 w=2 w=2 w=2 w=2 w=1 w=1

SLIDE 67

67

Additional Network Design Problems

Fair Networks

– Demand is elastic and can consume any bandwidth assigned to its path, e.g., within certain predefined bounds (lower and upper bound for demand) – Capacity constraints should not be violated – Network needs to carry more than lower bound for each demand volume to maintain fairness, e.g., Max-Min-Fairness or Proportional Fairness criterion

Topological Design

– Cost function takes into account not only capacity-dependent costs of links 𝜊𝑓, but also link installation costs 𝜆𝑓 – Additional binary variable 𝑣𝑓 that indicates if link is installed or not – Problem similar to uncapacitated design problem with modular links

SLIDE 68

68

Summary

Network design as generic problem in multitude of areas
Traffic and demand as input to network design
Networks have multiple layers
Network management based on multitude of different systems and

protocols

Right notation makes a lot of problems way easier

– Even when it seems to be more complicated on first sight – Even when you do not believe me yet ;)

Network design problems covered

– Capacitated vs. uncapacitated problems

Minimizing costs of networks links