1

Abstract — The growing demand for services generated by the

massive speed of Internet, motivated Angolans network operators

have invested in building their own transport network

infrastructure with modern technology to meet market demands.

However, the continued growth in demand for services by users

associated with the technological advancement, highlighted the

continuous optimization problems of these networks.

This study is dedicated to the planning of OTN (Optical

Transport Network) transport networks, analysing possible

scenarios and solutions to solve the problem of optimization of

Angolans networks operators. Begins the approach to the

definition and creation of a physical topology of reference

transport network to Angola from existing networks of national

operators and the traffic matrix that describe a realistic scenario

and that constitutes a unique transport network solution to be

shared by all national network operators in order to reduce

operating and maintenance costs.

It is still studied the traffic routing algorithms using the traffic

matrix as reference in this study and makes a comparison of these

to determine the routing method for presenting results more

balanced in traffic distribution on network links.

For the wavelengths assignment some formulations and

heuristics are studied in order to minimizing the number of

wavelengths used in the network. In particular, and for large

networks, the graph colouring is implemented technique, which is

extensively studied and implements the algorithm that solves the

problem of wavelengths assignment.

On the other hand, the equipment dimensioning is carried out

according to the technological development of manufacturers

market.

Finally, it is studied survival mechanisms to be used in the

studied network and associated algorithms to creation of

alternative disjoint paths. In this particular analyses the impact of

the implementation of these algorithms in traffic routing, in the

wavelengths assignment and in the network dimensioning.

Index Terms—Traffic matrix, OTN, Shortest path, Graph

colouring.

I. INTRODUCTION

HE main objective of this thesis is planning of OTN

(Optical Transport Networks), starting from obtaining a

reference topology that aid to calculate the traffic matrix. The

determination of this matrix took into account different aspects

such as population and the number of Internet users with a view

to analysis for a period of time of 10 years. Also study up

several routing strategies, wavelengths assignment and analyze

their resilience.

Thus showing the impact that different formulations can be

in the planning of network resources and routing management

and selection of the wavelengths for comparison heuristic

algorithms for traffic balancing, to ensure a better utilization of

the links.

Section II is dedicated to the study of the physical topology

of a proposed transport network from various networks of

different existing network operators in Angola, in order to

propose a transport network infrastructure that meets the

capacity requirements and availability likely to be shared by

network operators and reduce investment costs (CAPEX) and

operating and maintenance costs (OPEX) thereof. Additionally

an estimate is made and also the analysis of traffic in the

network growth.

In Section III are made studies based on applying methods

and formulations for traffic routing and wavelengths

assignment.

The performance of the different heuristic algorithms for

routing are compared to the wavelengths assignment (with

highlighting to the graph colouring heuristic) and also analyzed

the results of survival technique used in various application

scenarios. Finally, some results are presented in Section IV for

essentially the previous sections.

II. ASPECTS OF TRANSPORTE NETWORKS

The growing need for services caused by the increase in the

number of Internet service users and implementation based on

multimedia services, have contributed to the growth in traffic in

telecommunications networks which require investments in the

implementation of these networks to meet the requirements of

this demand.

A. Network representation

A network can be represented as a graph𝐺 = (𝑉, 𝐸), where

𝑉 = (𝑣1, 𝑣2, … , 𝑣𝑁) is a finite number of vertices or nodes and

𝐸 = (𝑒1, 𝑒2, … , 𝑒𝐿 , ) is the set of links.

A link form node i to node j is represented by the notation

(𝑖, 𝑗). When the links are ordered, traffic can be transported only

in the direction of orientation and the graph is called oriented or

digraph. When there is no ordering of the links, traffic can be

transported in both directions and the graph is called non-

oriented.

As can be seen in Figure 1 is a generic graph of a network

with 18 vertices and respective links. In the connections there

is the illustrative indication of some physical distances, in

kilometers, between the vertices.

Planning and optimization of OTN network with

survival

Duano L. Silva, João J. O. Pires

T

2

Figure 1. Representation of a network graph.

A way to represent a network other than the use of a graph is

using the adjacency matrix (A), which is a 𝑁𝑋𝑁 matrix

dimension, where N represents the number of nodes in the

network. The element 𝑎𝑖𝑗 = 1 if there is a connection between

i and j. Otherwise the element is zero.

Another feature is the node's analysis of the degree

representing the number of connections that converge on a

given node and can be calculated from the adjacency matrix [1]

𝛿𝑖 = ∑ 𝑎𝑖𝑗

𝑁

𝑗=1

(1)

B. OTN technologies

Traffic growth has forced the evolution of particular

transport networks, to increase their ability to transmit large

volumes of information. One of the ways chosen to achieve this

purpose was the development of multiplexing technologies of

signals, whether in the form of the creation of the data

transmission capacity (Payload) as the rationalization of the

fiber optic as the transmission medium.

This approach led to the development of WDM allowing

exploit more efficiently the capabilities offered by fiber optics,

allowing multiple signals/optical channels sharing the same

fiber.

WDM technology is classified according to the wavelengths

multiplexed spacing in Coarse WDM (CWDM) and Dense

WDM (DWDM). CWDM system has a channel spacing of 20

nm that occupies the entire optical band in which it operates

(ITU standard G.694.2) while the DWDM channels have

constant spacing (fixed grid) and typically 50 GHz (0.4 nm),

standardized by ITU-T G 694.1 with reference ITU-T

(International Telecommunication Union – Telecommunication

Standardization Sector) [2] [3].

Networks with fixed grids (called fixed grid networks) have

allowed accommodate growth in traffic either by increasing the

torque output of the transponder on each channel or traffic

moving to a denser grid spacing (25GHz and 12.5GHz spacing

between channels) . This approach causes the transponder to

increase its data rate by 2.5Gbps to 100Gbps channel with

improvements in technology that allows them to remain within

a 50GHz channel.

On the other hand, studies have been conducted on the

development of transponders bit rates of 200Gbps using

standard modulation formats, the positive results led

commercial use of this technology.

The need to ensure that the signal can be transported to

acceptable distances, highlighted in research an important

limitation, the difficulty of maintaining the spectral width

below 50GHz, that is, the grid with 50GHz spacing limits the

growth of traffic.

A first approach is based on increasing the grid spacing, i.e.,

moving traffic for a 100GHz grid. However, this adds to the

spectrum of services that use waste to transponder channels

with low bandwidth. An alternative possibility was studied

using a fixed frequency grid with slots of different sizes to

accommodate transponders with different bit rates, where the

advance knowledge of traffic growth.

These limitations led to the study of networks with flexible

grids (called Flexgrid networks) that allow a less rigid and fixed

approach in allocating wavelengths. These networks combine

the two concepts WDM layer: fine granularity of wavelengths

and the possibility to join adjacent slots wavelength to form a

channel with arbitrary size (from elemental frequency slots

12.5GHz), enabling systems accommodate channels 10, 40,

100, 400 and 1000Gbps.

C. Principals of optical transport network

ONT is structured as an OTH (Optical Transport Hierarchy),

which is composed of two domains, the optical and the

electrical.

As soon as the customer signal is received, it must be adapted

mapped and multiplexed to be contained in the Payload of

digital frames OPU (Optical Payload Unit). Then headers are

added (overheads) peculiar to the frames of the different sub-

layers to be transmitted to the client information (these headers

are so called "associated headers"). In terms of overhead OPU

frame contains information dedicated to the justification of the

frame and the type of customer conveys, after being mapped in

ODU (Optical Channel Data Unit). The ODU frames main

function is to allow monitoring the network and display

warning signs, that is, everything that is related to the most

critical procedures, such as aggregation, routing, protection, is

indicated by this plot, and the switching of the plots carried out

level of the same.

The next step comprises the conversion of ODU frame in the

OTU frame (Optical Channel Transport Unit) by adding the

header and FEC (Forward Error Correction). The transition to

the OTU layer and the need to make the frame alignment, is the

last step before entering the optical domain.

Each OTU will modulate an optical source and the optical

signal obtained together with a suitable header corresponds to

Och entity (Optical Channel), whose optical channel operating

on the network in terms of wavelength (based on the DWDM)

and are responsible for providing optical path to transport the

customer sign the OTN network.

With respect to the other optical layers, OMS layer (Optical

Multiplexing Section) is responsible for DWDM multiplexing

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and is demarcated by optical multiplexers / demultiplexers

which can be OADM (Optical Add/Drop Multiplexer) or, if

they are reconfigurable ROADM (reconfigurable OADM). The

OTS layer (Optical Transmission Section) relates to the optical

fiber section and is comprised between optical amplifying

points.

Finally, the OTM-n.m is the information structure used by

the optical interfaces of the OTN, wherein the index "n"

represents the number of transported wavelengths and index

"m" equals "k" of the electric field layers representing the

supported bit rate.

TABLE 1 shows the ODU-k channels, k = 0, 1, 2, 3, 4 and

corresponding bit rates used in OTN, and the OTU-k channels,

k = 1, 2, 3, 4 and corresponding standardized bit rates.

TABLE 1 – BIT RATES OF THE ODU AND OUT SIGNAL [4]

The process of mapping from OTN defines two

complementary concepts, the low-order ODU (described as

ODU-k (L), with k = 0, 1, 2, 3, 4) and higher-order ODU (ODU-

k (H), with k = 1, 2, 3, 4). The first refers to the structure that

comprises the payload which contains the client signal by the

OPU and the overhead of the ODU. The second is the ODU

signal lower order to which is added the overhead of OTU and

FEC code. In some situations, the lower-order ODUs map

directly in the higher-order ODU's.

It is to enhance the ODU-2e represents a pragmatic solution

to the 10GbE traffic transport over the OTN, which was

standardized to solve the problem of transport services with

data rates 10GbE (10.3125Gbps) which is higher than the

payload capacity of the ODU-2 (9.99528Gbps).

D. Features of the ROADMs

In the optical network equipment must be adapted to the

network in order to facilitate the delivery/receipt of traffic and

be accommodated in the respective wavelength. This allows

new services are deployed efficiently and quickly while

allowing legacy services can also be transported in the network.

These results are achieved by using reconfigurable optical

multiplexers add/drop (ROADM).

ROADMs may contain several switching levels associated

with the degrees of the nodes which are implemented, such as

the number of connections to these nodes have with other

adjacent nodes. These can range from the two degrees (which

means that the ROADM has two directions) and can amount to

nine degrees, which is already a reality today. The switching

levels are associated with the switching directions of

wavelengths and also the pairs of fiber they contain.

E. Client and Line Cards

The network nodes are basically composed of OTN/DWDM

equipment. These devices are constituted by physical and

mechanical structure for mounting, the frame having inner

spaces hardware fixation designated slots, power supplies, and

also cooling sources (usually, the latter two are redundant to

ensure the equipment protection and increase resilience),

Switch and control and management software.

The slots are installed with specific hardware configurations

depending on their use, such as the line cards are configured to

have lower capacity for transmitting data at full capacity node

transmission. The line card is composed of multiplexers /

demultiplexers OTN and by transponders/muxponders. Each

line card contains a number of doors with a certain transmission

capacity, a node occupying the slot. The slot capacity defines

the cost of the chassis and that your choice should be made

depending on their need to use (depending on the degree

expected node) [5].

It should be noted that the transponders and muxponders are

responsible for the major fraction of the cost of a network. This

cost is influenced by the different components that make up the

network. In particular, the costs stand out due to transponders

and also to muxponder, which are normalized to the cards

depending on the connections of different bit rates depending

on the optical range (called optical range). In the case of cards

with transponders with 10 Gbps speeds, it is achieved by an

optical range of 750 km with a unit cost. However, this cost

grows sharply higher speeds as in the case of 40 Gbps or 100

Gbps depending on the distance, which is the maximum

distance that can transmit signals without the use of

regenerators.

DWDM layer is traditionally composed of transponders

(with different line speeds such as 10/40/100 Gbps,

corresponding to OTU-k, with k = 2, 3, 4) and/or muxponders

(with line speeds 4X10/10x10 Gbps) to aggregate traffic from

different sites that are hundreds or thousands of kilometers

away [5].

An important aspect to consider choosing the cards is the cost

of regenerators. The transparent transmission does not need

regeneration in optical distances up to 2000/2500 km

(depending upon whether the output is 10/40/100 Gbps), which

contributes to reducing the number of regenerators and the

number of hops.

III. ROUTING AND WAVELENGTH ASSIGNMENT

An optical path (designated Lightpath) results from the

mapping of the logical topology physical topology. The

lightpaths optical links are implemented end to end, this a

source node to a destination node on a wavelength of each bond

without the conversion of signals to the electrical domain.

On the other hand, during this route the lightpath are

forwarded and a switched connection to another always in the

optical domain by network equipment. The various lightpaths

routed on the network may share common physical links which

allow some wavelengths may be reused in different parts of the

network.

The routing and wavelengths assignment (RWA) problem in

WDM networks is to route traffic the set of optical paths and

assign a wavelength to each of them, so that optical paths that

share some network connection using different wavelengths

Tipo de ODU Débito Binário [Gbps] Tipo de OTU Débito Binário [Gbps]

ODU0 1,244 OTU1 2,666

ODU1 2,498 OTU2 10,709

ODU2 10,037 OTU3 43,018

ODU2e 10,399 OTU4 111,809

ODU3 40,319

ODU4 104,794

4

[6].

Therefore, it is desirable to apply efficient RWA algorithms

to establish the links required with high network performance

indicators and analyze and solve at least the following issues:

Maximize the number of paths to be established;

Minimize the number of wavelengths used by the

network.

A. Routing Algorithms

1) Dijkstra Shortest Path Algorithms

It is a heuristic formulation consisting in determining the

shortest path between a source node and a destination node,

where the sum of the link weights is minimized. Being that,

typically, connection weights are proportional to their cost of

transmission, routing through the shortest path is the most

efficient resource saving wise.

Routing through the shortest path consists in routing

sequentially each element of the traffic matrix T to the shortest

path in the network defined by the graph G (V, E).

2) Yen k-Shortest Path Algorithms

This algorithm is implemented primarily for two purposes:

1) enumeration of the obtained shortest paths; 2) determination

of the first k-shortest paths from source to destination in

ascending order of value, in which the approach is made using

Yen algorithm.

This algorithm uses as a basis the principles of the Dijkstra

shortest path algorithm, determining the shortest path first (k =

1).

On the other hand, is constructed taking into account not

form paths with loops, that is, had in mind that in

telecommunication networks there is a concern to avoid

choosing paths containing two nodes repeated.

The algorithm which describes this process has as input the

matrix of distances and also the number of interactions

(alternative paths) that will be required to be analyzed by the

application Yen algorithm for determining the k-shortest paths

and enumerating respective shortest paths. As output is the list

of shortest paths, the matrix of weights and also the list of the

k-shortest paths.

B. Wavelength Algorithms

1) Graph colouring technique

The graph colouring technique is based on a heuristic

algorithm used for wavelengths assignment of a network.

The operation of graph colouring technique is to assign colours

to all nodes in a graph assuming that there are no adjacent nodes

of the graph that share the same colour. Namely, since the graph

of the network according to the physical topology, it creates an

equivalent graph, G (W, P) where W is the nodes of this new

graph representing the optical paths over physical links of the

initial graph and P are the links between nodes.

In practice the application of the algorithm has as an input

the network routing traffic matrix calculated from a routing

formulation (Dijkstra or Yen). This matrix is responsible for the

generation of adjacency matrix which is the equivalent network

of the G (W, P).

The basis for the study of graph theory remains valid, for

determining the parameters that characterize the network, such

as the node degree.

With this determination node degree and respective ordering,

following the nodes colouring that will help to define the

wavelengths assignment in each of the network nodes

represented by this new graph G (W, P).

The Algorithm 1 begins receiving as input the network

routing matrix obtained according to routing formulation

(Dijkstra or Yen). Following the determination of the adjacency

matrix represents the equivalent graph resulting of the

comparing between elements of the vector W, and this

adjacency matrix, each element is one if find any there is a

shared path between the paths compared and is zero in the

opposite case. This adjacency matrix is used also to calculate

the node degree, the basis for ordering and colouring of the

graph. As algorithm output have every node list of colours to be

used for the wavelengths assignment.

INPUT:

E: Matrix of traffic paths

OUTPUT:

A: Adjacent matrix of graph G (W, P)

g: Grade of node cor: Number of colors

Initialization:

kk = 2 cont = 1

1: Create the vector of traffic paths

2: FOR each j 3: FOR each k

4: IF j = k

A (j, k) = 0

5: END IF

6: IF there is shared link

A (j, k) = 1 7: ELSE

A (j, k) = 0

8: END IF

9: END FOR

10: END FOR

11: Create an empty vector (n) with dimension equal to the A

12: Find the major degree of each node and its index and store in vector

first column of the vector n

13: Create a vector of colours (cores) and set the minimum number of colours equal to dimension to the column of A

14: Set all the colours of the nodes equal to zero (second column of the vector n)

15: Order the vector n in descending order of the node degree (nd)

16: WHILE there is a node without colour in the vector n DO 17: FOR each ii to length of A

18: IF nd (ii, 3) = 0

19: k = ii break

20: END IF

21: END FOR

22: nr = nd (k, 2)

23: line = A (nr, :)

24: END WHILE

25: FOR each jj to length of A

26: IF line (1, jj) = 0 or jj = nr

line (3, jj) = -1 (there is not interaction)

continue

27: END IF

line (2, jj) = n (jj, 3) (colors) line (3, jj) = n (jj, 1) (degree)

28: END FOR

29: FOR each kk to length of vector of colors (cores) 30: IF any line (2, :) = cores (kk)

continue

5

31: ELSE

n (nr, 3) = cores (kk)

nr (k, 3) = cores (kk)

break

32: END IF

33: END FOR

34: WHILE any line (1, :) = 1 DO

Search for major degree in a line Collects all the colors of the lines with interactions

Assigns the color on node 2

35: END WHILE

Algorithm 1 – Graph Colouring Algorithm

C. Protection planning

Any transport network (including optical) must ensure high

levels of resilience in case of network failures. Node failure due

to equipment failure or damage (of part or all of the equipment)

resulting from an event such as a fire or failure in the power

system, with the result that some or all of the communication

links that terminate on are node affected by this failure.

Software failures that may impact a large part of the network

and is generally difficult to identify and consequently to

recover.

Link failures due to accidental cutting of fiber optic cables.

In general, fiber cables that carry traffic from one node to

another run through the streets of the cities/towns, whether

buried in underground conduits or support poles (usually along

pedestrian walks). However, due to resulting heavy activities

constantly modernized society causes destruction occurs

frequently causing these infrastructures Link cuts. The attempt

to mitigate these effects requires further patrol and surveillance

efforts, with the consequent increase in maintenance costs.

It is essential to ensure mechanisms that create alternatives

to transport traffic between two nodes and / or equipment in the

transport network, using techniques of protection or restoration.

In OTN network protection/restoration can be done in the

electrical domain (at ODU layer), or in the optical domain. In

the optical domain protection switching can be done

individually for each optical channel (in terms of Och layer), or

it may take place in the OMS layer by switching all WDM

signals.

The protection/restoration of a network can be made at the

level of Och or ODU, or at the connection level (called link

protection, made at the OMS level). In turn, the path protection

can be shared or dedicated.

In the path protection, between the source and destination

nodes are established alternative paths (protection / backup). In

case of failure of the service path, this failure is only detected

in the termination of the path (the destination node), which then

initiates the traffic protection process.

The link protection, the path may consist of multiple

connections. Thus, if the level of required that is used to register

a fault an alternate path to route the traffic and thus avoid the

link with the failure.

Moreover, these protections can be dedicated and shared.

Protect the dedicated protection/backup resources are reserved

for each path, that is, for each working entity (path or link) there

is always an entity protection/backup. If the resources reserved

for the failing service traffic, it is guaranteed that there will be

resources available to recover from failures.

In the shared protection features protection/backup are

shared among the N paths that is the path (1: N). Typically this

scenario requires significantly less protective features than the

dedicated (typically 50% to 75% less) [2].

Nevertheless, as a technique to apply another must allow

traffic according to the preferred strategy. In particular, the

implementation of survival technique should take advantage of

the features of the sub-layers constituting the network and / or

their network elements, whether the sub-layers in the electrical

domain or in the optical domain. Typically the level of Och it

uses dedicated protection (1 + 1), i.e., sends the path Och the

service and a copy of this Och an alternative/protection

different path (usually disjoint service path). As a result of this

strategy, the terminal node is always receiving information

from these two paths and consequently there will be duplication

of resources on the network with the consequent increase in the

cost of the network. Similar approach is made at the level of the

ODU using dedicated protection between nodes.

1) Shortest Path pair calculating Algorithms

There are two algorithms for determining the pair of shortest

paths between the source and destination node:

1) Algorithm TE (Two-step approach Edge-disjoint

pair): for a given pair of nodes in the graph, one

begins by calculating a pair of paths by first finding

the Dijkstra shortest path algorithm and then find

the shortest path in the same graph, but with the

removal of the shortest path (links) given initially

[7].

2) Algorithm TV (Two-step approach Vertex-disjoint

pair): for a given pair of nodes, begins calculating

the Dijkstra shortest path and then find the shortest

path in the same graph, but with the link incident on

the shortest path before us (except extremes nodes)

removed. Removing these links ensures that the

second path between the nodes will be each other

disjoint.

Note that the paths may be disjoint in terms of nodes

(meaning that there will be a node duplication) or in terms of

the links (doubling the links between the source and destination

nodes).

One of the limitations that these algorithms have in practice

is that they can help generate pairs of paths (link disjoint and

disjoint node). That would be a significant concern if these

algorithms were implemented in the real network, as one of the

quality pf service requirements of the business customers is that

the paths are physically separated from a given source node and

destination in the network [7].

The way to work around this limitation is by applying the

Suurballe algorithm to find the pairs of shortest paths disjoint.

This algorithm performs a transformation graph of a modified

graph, thereby facilitating the use of the standard Dijkstra

algorithm. For disjunction node, each node (except the source

and destination nodes) in the shortest path of the original graph

is divided into a path of sub-nodes, causing the initial graph

modification.

6

IV. RESULTS ANALYSIS

Based on the physical network topology of the three network

operators described, it is made an analysis to choose a possible

physical topology for Angolan transport network.

A. Traffic matrix estimation

Figure 2 – Proposed Network Graph with distances [in km]

The analysis of the characteristics of the physical topology of

the network is done using the network graph shown in Figure 2.

Each node of the graph representing the provinces, are

numbered according to the alphabetical order of the names of

the respective provinces.

The TABLE 3 describe the information on telecommunications

indicators of the Angolan market, where contains general data

of the population (according to the census conducted in 2014

[8]) and also the total statistics data of all Angolan telecom

operators Angolan, whether in the voice and also the Internet

area.

In networks are used 64kbps for voice channels

(bidirectional) each in frames formatted in 2 Mbps or 30 voice

channels, in both cases, for the sake of simplicity in reconciling

the various networks of various operators. In mobile networks

the Short Message Services (SMS) are also considered on 64

kbps channels.

For the0utilization time period is assumed equal to 12 hours,

whereas for the average use, becomes the value of 8 minutes.

It is still considered a compensation factor of 5 to safeguard

the increased traffic in the busiest hour, motivated by the high

prevalence of the number of mobile users in all the users and in

that there is also high volume local traffic (that does not use the

transmission system).

To estimate the traffic in the Internet application area, fixed

network operators offer the broadband service based (generally

over ADSL and FTTH/GPON technologies) in flat rate tariffs,

without limiting consumption. The accesses bandwidths these

networks are for operators in any way the plans bandwidths

(asymmetric) access is between 2-20 Mbps upwards. The

commercial approach contractually establishes the monthly

rational consumption, for access, 2GB (in both directions).

In mobile networks, in general, there is no bandwidth control

approach due to network radio access limitations that they use

(3G/4G networks). Their tariffs are based on accounting

download each user volume, usually in prepayment mode.

TABLE 2 – FEATURES OF THE PROVINCES COVERED IN 201414 [8] [9]

Even so, these operators also contractually safeguard the

limitation of rational use of identical consumption used by fixed

operators, exactly the 2 GB although in practice does not make

any sense. Since there are not many local content (although

there is an IXP - Internet Exchange Point - this just changes the

interconnection traffic of the various operators and service

providers) there is no separation between national international

traffic. Thus, the rational use of the networks does not make this

distinction and is considered to be for both directions.

These assumptions are summarized in TABLE 3 below and will

be used to estimate total traffic in 2014 for the whole territory.

TABLE 3 – BASIC PARAMETERS FOR TRAFFIC ESTIMATION, IN 2014

Long distance traffic model (transmission) for the three areas

of application related users traffic with their geographical

distance and also requests for each traffic, i.e., the total traffic

to the application areas ( voice, Internet and transaction data)

are given by expression [10] [11]:

𝑉𝑜𝑖𝑐𝑒 𝑡𝑟𝑎𝑓𝑓𝑖𝑐(𝑖, 𝑗) = 𝐾𝑉

𝑃𝑖 ∗ 𝑃𝑗

𝐷𝑖𝑗

(2)

𝑇𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑑𝑎𝑡𝑎 𝑡𝑟𝑎𝑓𝑓𝑖𝑐(𝑖, 𝑗) = 𝐾𝑇

𝐸𝑖 ∗ 𝐸𝑗

√𝐷𝑖𝑗

(3)

𝐼𝑃 𝑡𝑟𝑎𝑓𝑓𝑖𝑐(𝑖, 𝑗) = 𝐾𝐼 ∗ 𝐻𝑖 ∗ 𝐻𝑗 (4)

In previous expressions:

Core da Rede

Luanda

(11)Malange

(14)

Cunene (8)

Huila (10)

Huambo

(9)

Benguela

(2)

Cuanza Sul

(7)

Cuanza Norte

(6)

Bengo (1)

Zaire

(18)

Cabinda

(4)

Bié (3)

Rede

Ccomplementar

Namibe

(16)Cuando Cubango

(5)

Uige (17)

Lunda Norte

(12)

Lunda Sul

(13)

Moxico

(15)

518

1060

135

660

265

398

718

342

386

415

560

225

426

257

481

165

407

341

402

208

492

295

248175

365

357

409

67

# Node location Population

Fixed voice

customers

Mobile voce

customers

Fixed Internet

customers

Mobile Internet

customers

1 Bengo 351.579 2.309 24.430 383 2.520

2 Benguela 2.036.662 19.006 198.109 7.729 18.441

3 Bié 1.338.923 5.238 53.850 1.004 3.721

4 Cabinda 688.285 8.656 448.515 2.006 27.892

5 Cuando Cubango 510.369 1.513 6.259 42 636

6 Cuanza Norte 427.971 3.495 43.464 442 3.801

7 Cuanza Sul 1.793.787 4.234 72.247 863 7.060

8 Cunene 965.288 2.430 6.767 639 630

9 Huambo 1.896.147 4.213 89.807 1.338 9.018

10 Huíla 2.354.398 8.845 75.641 2.099 10.690

11 Luanda 6.542.944 196.891 12.848.582 71.106 3.527.319

12 Lunda Norte 799.950 2.068 25.064 201 2.466

13 Lunda Sul 516.077 1.715 11.546 130 1.172

14 Malanje 968.135 5.904 50.819 1.056 5.263

15 Moxico 727.594 2.954 4.535 79 435

16 Namibe 471.613 3.517 22.215 820 3.103

17 Uíge 1.426.354 3.195 36.042 1.279 4.637

18 Zaire 567.225 5.144 34.666 392 3.587

Total 24.383.301 281.327 14.052.558 91.608 3.632.391

Unit Voice traffic Internet traffic

Number of users per 2 Mbps line # 30

Utsage (average per line per day) munutes 8

Time frame of usage (per day) hours 12 12

Total number of usars Users 14.333.885 3.723.999

Segurity factor for rush hour # 5

Average consume per user (per month) GB 2

Annual traffic growth rate % 10,0 30,0

User annual growth rate % 3,0 21,5

7

𝑃𝑖: is the population at node 𝑖 (identical analysis for

𝑃𝑗);

𝐷𝑖𝑗: is the distance between two interconnected nodes

(node i to node j); (node i to node j);

𝐸𝑖: the number of employees of companies in the node

𝑖 (applied also to the case of pair 𝐸𝑗);

𝐻𝑖: is the number of Internet users (Host) at node 𝑖. The constant traffic, 𝐾𝑦 (y = V, T, I) are calculated by the

following expressions:

𝐾𝑉 =𝑇𝑡𝑜𝑡𝑎𝑙

𝑣𝑜𝑖𝑐𝑒

∑𝑃𝑘 ∗ 𝑃𝑙

𝐷𝑘𝑙𝑘,𝑙

𝑘≠𝑙

(5)

𝐾𝑇 =𝑇𝑡𝑜𝑡𝑎𝑙

𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑑𝑎𝑡𝑎

∑𝐸𝑘 ∗ 𝐸𝑙

√𝐷𝑘𝑙

𝑘,𝑙𝑘≠𝑙

(6)

𝐾𝐼 =𝑇𝑡𝑜𝑡𝑎𝑙

𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡

∑ 𝐻𝑘 ∗ 𝐻𝑙𝑘,𝑙𝑘≠𝑙

(7)

Where:

𝐾𝑉: is the traffic constant to voice area; 𝐾𝑇: is the traffic constant to transactional data area; 𝐾𝐼: is the traffic constant to Internet área;

𝑇𝑡𝑜𝑡𝑎𝑙𝑦

: is the total traffic volume in application areas

for voice (𝑦 = 𝑣𝑜𝑖𝑐𝑒), transactional data (𝑦 =𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑑𝑎𝑡𝑎) and Internet (𝑦 = 𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡), respectively.

Thus, for calculating the constants for the traffic of voice and

Internet application area are used the equations traffic matrix,

the results are as follows:

𝐾𝑉 = 5.6184𝑒 − 11[𝐺𝑏𝑝𝑠 ∗ 𝑘𝑚]; 𝐾𝑇 = 0; 𝐾𝐼

= 1.5033𝑒 − 9[𝐺𝑏𝑝𝑠 (8)

To estimate the growth of traffic from various application

areas, for 5 and 10 years, it is essential to analyze the growth of

the individual components of the model estimates that the

annual growth of the population will be 3,24% [8].

For voice application area, it is estimated that the annual

growth of users is 3% [9]. However, the growth of voice traffic

will be about10%, a value very much influenced by growth in

the mobile network users. For the case of Internet application

area, it is estimated that in Africa traffic growth varies between

30 – 50% until 2018 [1] [12].

The TABLE 4 summarizing these values or for population

growth according to [8] and also the number of host growth as

well as growth factors for 5 to 10 years in each of the

application areas calculated from the annual growth figures.

TABLE 4 – ESTIMATION OF TRAFFIC GROWTH RATES TO 5 AND 10 YEARS

B. Network planning

For the design of the proposed transmission system, as has

been assumed to know the total network traffic matrix for 10

years and it is assumed that traffic is static, as Figure 3.

Figure 3 – Total traffic matrix in 2024 [in ODU-0]

C. Network routing analysis

Application of Dijkstra’s algorithm will be made for the

shortest path, where the distances between the source and the

destination nodes are used. For this case, will have as input the

matrix of distances (Figure 5) and will output the routing matrix

representing the set of traffic shortest path.

Figure 4 – Matrix of distances for the shortest path [in km]

The traffic routing using Dijkstra’s algorithm for the shortest

path between the source and destination nodes.

Similarly determines the routing of traffic using the Yen

algorithm for k- shortest paths. This particular value is assumed

for k = 2 (note that for k = 1 is the Dijkstra shortest path) and

for comparison between the two algorithms is based on

individual routing of each of the algorithm and the capacity of

the link calculated using the traffic matrix in ODU-0's (Figure

3).

The results of this process are shown in Figure 5, whether it

be for the shortest path as the k-shortest path.

Comparatively, the shortest path algorithm reaches the

minimum in link 12 -> 17 (with a capacity of 0 ODU-0) and the

maximum in link 7 -> 11 (capacity 4,617 ODU-0). In the k-

shortest paths algorithm (assuming k = 2), the minimum is

Growth factor Voice traffic Internet traffic

Annual P @ 3,24% H @ 21,5%

5 years 1,61 3,71

10 years 2,59 13,79

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 0 2 1 2 1 1 1 1 1 1 222 1 1 1 1 1 1 1

2 2 0 4 17 1 3 7 2 8 10 1955 2 1 4 1 3 4 3

3 1 4 0 4 1 1 2 1 4 2 355 1 1 2 1 1 2 1

4 2 17 4 0 1 3 6 1 7 9 2232 2 1 5 1 3 5 3

5 1 1 1 1 0 1 1 1 1 1 52 1 1 1 1 1 1 1

6 1 3 1 3 1 0 2 1 2 2 319 1 1 1 1 1 1 1

7 1 7 2 6 1 2 0 1 4 4 595 1 1 2 1 1 2 1

8 1 2 1 1 1 1 1 0 1 2 96 1 1 1 1 1 1 1

9 1 8 4 7 1 2 4 1 0 5 776 1 1 2 1 2 2 2

10 1 10 2 9 1 2 4 2 5 0 957 1 1 3 1 2 3 2

11 222 1955 355 2232 52 319 595 96 776 957 0 200 98 474 39 293 446 299

12 1 2 1 2 1 1 1 1 1 1 200 0 1 1 1 1 1 1

13 1 1 1 1 1 1 1 1 1 1 98 1 0 1 1 1 1 1

14 1 4 2 5 1 1 2 1 2 3 474 1 1 0 1 1 2 1

15 1 1 1 1 1 1 1 1 1 1 39 1 1 1 0 1 1 1

16 1 3 1 3 1 1 1 1 2 2 293 1 1 1 1 0 1 1

17 1 4 2 5 1 1 2 1 2 3 446 1 1 2 1 1 0 1

18 1 3 1 3 1 1 1 1 2 2 299 1 1 1 1 1 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 0 767 916 813 1258 315 559 1644 916 1323 67 1285 1150 490 1314 1169 295 548

2 767 0 506 1546 848 617 208 962 341 627 700 1304 1169 792 904 402 1049 1181

3 916 506 0 1201 342 601 522 728 165 572 849 798 663 426 398 797 683 1330

4 813 1546 1201 0 1543 950 1338 1929 1366 1773 846 1570 1435 775 1599 1948 518 365

5 1258 848 342 1543 0 943 864 386 507 801 1191 1118 983 768 718 946 1025 1672

6 315 617 601 950 943 0 409 1329 766 1173 248 970 835 175 999 1019 432 729

7 559 208 522 1338 864 409 0 1170 357 764 492 1320 1185 584 920 610 841 973

8 1644 962 728 1929 386 1329 1170 0 822 415 1577 1504 1369 1154 1104 560 1411 2058

9 916 341 165 1366 507 766 357 822 0 407 849 963 828 591 563 632 848 1330

10 1323 627 572 1773 801 1173 764 415 407 0 1256 1370 1235 998 970 225 1255 1737

11 67 700 849 846 1191 248 492 1577 849 1256 0 1218 1083 423 1247 1102 362 481

12 1285 1304 798 1570 1118 970 1320 1504 963 1370 1218 0 135 795 400 1595 1052 1699

13 1150 1169 663 1435 983 835 1185 1369 828 1235 1083 135 0 660 265 1460 917 1564

14 490 792 426 775 768 175 584 1154 591 998 423 795 660 0 824 1194 257 904

15 1314 904 398 1599 718 999 920 1104 563 970 1247 400 265 824 0 1195 1081 1728

16 1169 402 797 1948 946 1019 610 560 632 225 1102 1595 1460 1194 1195 0 1451 1583

17 295 1049 683 518 1025 432 841 1411 848 1255 362 1052 917 257 1081 1451 0 843

18 548 1181 1330 365 1672 729 973 2058 1330 1737 481 1699 1564 904 1728 1583 843 0

8

reached in the link 5 -> 15 and the maximum in 6 -> 11, with

capacity 4 ODU-0 and 4,368 ODU-0 respectively.

Figure 5 – Links capacity shortest path vs. k-shortest paths

Compared the differences between the extremes both

formulations, we have 4,617 ODU-0 and 4,364 ODU-0, i.e.,

Yen formulation is more balanced distribution of capacities of

the links, as compared to the formulation of Dijkstra.

Figure 6 – Distribution of logical links by Yen [in km]

Moreover, the application of Yen formulation has as

consequence the worsening of the logical links of distances.

Figure 6 shows the distribution of logical links by applying the

formulation ordering of k-shortest paths Yen seconds (for k =

2). Repairs to that in figure should be noted links with greater

distances to 2,000 kilometers that. Beyond the optical range of

the transponders (for signals at 100 Gbps this range is equal to

2000 km), which result in a significant increase in investment

in the placement of regenerators.

D. Wavelength assignment

The wavelength assignment is made by using of graph

colouring technique based on Algorithm 1 assuming as input

the routing matrix calculated by the Dijkstra algorithm.

The step of this application are:

1st. Start felling the vector W with the set of traffic paths

of the routing matrix above to main diagonal.

2nd. Compare the traffic path each other starting by the

first element of the W and comparing to the all of the

remaining elements of W. this capering determine

the elements of the first line of the adjacency matrix.

3rd. If two elements share the physical link the element

of the adjacency matrix is one, otherwise is zero.

4th. Go to the 2nd step to complete the all the elements of

the line until the end of W.

The resulted adjacency matrix representing the graph G (W,

P) for this network dimension is 153X153 calculated by the

dimension of the vector W.

TABLE 5 – WAVELENGTH ASSIGNMENT TO THE G (W, P) GRAPH USING GRAPH

COLOURING TECHNIQUE

The next step is the allocation of the colors to the graph

starting from the major degree:

0 03

19

24

30

38

15 14

64

0

5

10

15

20

25

30

35

40

[0 -200]

[200 -400]

[400 -600]

[600 -800]

[800 -1000]

[1000 -1200]

[1200 -1400]

[1400 -1600]

[1600 -1800]

[1800 -2000]

[2000 -2200]

Nú

mer

o d

e Links

lógi

cos

Comprimento dos Links [km]

9

Take as reference the node with major degree in the

studied network, corresponding to the node with traffic

path “5 14” with degree 35, according to the adjacency

matrix and then assign the color to this node.

In the next, take the adjacent node with greater degree

and assign the next color (different form the first one).

Continuing on this node as reference and search for (in

decreasing ordering of the degree of the node) sharing

or not another adjacent node and also the adjacent node

form the initial, there is adjacency each other.

If so, assign a new color to this node, otherwise reuse

one of the previous color.

This process is repeated until assign colors to all the

node of the graph.

The result of the graph colouring assign is in fact the

wavelength assignment of the network in the real network

conditions. That means the traffic per link must be take into

consideration to the wavelength assignment.

Assuming the traffic matrix to take the traffic for each traffic

path and using the graph colouring it is possible to define the

optical channels according to the fixed grid of the DWDM

system.

E. Node dimensioning

To the dimensioning of the network node is essential to

consider the architecture of the node, either by knowledge of

the degree of each node whose formulation is defined by

expression (1) as their line and customers cards. To emphasize

that the line cards (transponders or muxponders) operating at

100Gbps (OUT-4) and client cards, which interconnect the

IP/MPLS routers, can operate at 1/10/100 GbE.

The steps for dimensioning of nodes spend the analyses of the

terminal traffic (referring to all the traffic with source from any

network node to the dimensioned node) and also the traffic

express (the one that makes transit to the node).

Figure 7 – ROADM structure of the network node 17

Assuming that each ODU-4 corresponds to Och (optical

channel), they need to 8 Gbps transponder of 100Gbps in the

ROADM structure, as shown in Figure 7.

The link between the node 1 and the node 17 are 6 Och. These

optical channels 1 Och contains express traffic at node 17,

whose corresponding ODU-0 should be switched to the node 4.

The same should happen with the express traffic from the

node 4 and the destination node 14.

The solution to switch traffic is using of the ODU Switch that

will be responsible for this switching.

For the case of express traffic, the switching of ODU-0 is

made to the ODU Switch level without this necessary

conversion to the electrical domain.

However, the terminal traffic will be switched to the electric

level in ODU Switch and finish in client cards, as shown in

Figure 8.

Figure 8 ROADM + ODU Switch structure of the network node 17

Thus, a possible configuration of the cards to the node 17 is

presented in Table 6, the chassis have 5 client cards of 100GbE

each, 8 cards of 10 GbE and also two cards of 1 GbE (all as part

of the ODU Switch). You will also have 8 transponders of 100

Gbps to accommodate traffic from the adjacent nodes.

TABLE 6 – CARDS DIMENSIONING OF THE NODE 17

F. Network survival

This approach assumes that the traffic routing strategy in case

of failure due to the unavailability of the path from the source

node to the destination node, in a different oath from the path

used for traffic service path.

To this end it uses to the Dijkstra algorithm to calculate the

shortest path disjoint between the nodes of origin and

destination.

Figure 9 – Distance of the links for the shortest path disjoint [in km]

10

It is assumed that there are already the shortest path according

to Dijkstra, explained previously. To find the disjoint path, the

shortest path between the source node and the destination is

removed, followed by applying the same algorithm to the graph

however obtained with this removal.

In Figure 9 is shown the distribution of network links

applying the Dijkstra formulation for the shortest path disjoint.

This result is obtained using the traffic routing matrix calculated

by shortest path disjoint algorithm.

The result of the application of this algorithm, there is the

expected worsening of the distances and the consequent

influence of these in the choice of the transponders.

Figure 10 – Links capacity shortest path vs. k-shortest paths

In Figure 10 shows the graph of the distribution of links

capacity of the network, whether for service connections and

for protection connections. In the overall traffic behavior on the

links is balanced. However, there are some links whose traffic

increases significantly when used protective connections.

V. CONCLUSIONS

The physical topology of the proposed network to Angola

serves as a reference network models of studies based on the

optimization of network operation and maintenance.

In a perspective of traffic analysis the application area of

Internet has huge influence on the network from the application

area of voice. This is due in large part by the large population

of users of Internet services and the inclusion of traffic from the

application area of the transactional data. For a 10 year period,

an estimated network traffic grow to 3 times the application area

of voice and over 10 times for the Internet application area. This

growth has an impact on the construction of the traffic matrix

and consequently on planning the architecture of us.

Many of the planning studies are based on routing

assumption dynamic traffic over the network using heuristics

and ILP formulations, with particular attention to minimizing

network congestion. This study has a slightly different

approach, because it makes the network analysis using the

traffic matrix for the purpose of sizing nodes to minimize the

load of links. In this case they are used heuristics formulations

Dijkstra and Yen (for k = 2) and in that comparison, it is

concluded that from the point of view of load distribution of the

links, Yen formulation has slightly more balanced results that

the formulation Dijkstra. However, the situation is reversed

when the perspective has is the comparative analysis of

distances, essential for determining the optical range of links,

where the formulation of Dijkstra presents more balanced

results in that it minimizes the cost of regeneration.

It is the wavelengths assignment where this study stands out

in that is based on graph colouring technique. This study was

done differently the application has so far been made in other

studies, it is built the equivalent graph G (W, P) using the theory

of graphs based on adjacency matrix and node degree. The

assignment of colors to the nodes is made depending on the

staining technique and still associate up the traffic behavior of

each node of the graph G (W, P). The results are particularly

interesting for a network dimensioning of the network under

study, in which the number of allocated wavelengths is about

64 fixed grid of wavelengths for DWDM systems.

The design of the nodes is also analyzed and the conclusions

are in line with the architecture of the nodes based on ROADM

equipment with ODU Switch included.

Survival was also taken into account. The study strategy is

based on the most likely occurrences of the transport network.

In particular we analyzed the network assuming that the

protection is dedicated linear path. The consequences of this

assumption is the increase in traffic on the links. However, the

application of a formulation for determining the Dijkstra

shortest path disjoint minimize this increase as the results

obtained.

REFERENCES

[1] J. Pires, Redes de Telecomunicações e Fibras Ópticas,

Apontamentos, Lisboa: IST Lisboa, Setembro 2014..

[2] J. Pires, "Redes de Telecomunicações e Fibras Ópticas,

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[3] J. Pires, Redes de Telecomunicações, Apontamentos,

Lisboa: IST Lisboa, 2014, pp. 238 - 272.

[4] ITU-T Telecommunication Stardardization Sector,

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TRANSMISSION SYSTEMS AND MEDIA,DIGITAL

SYSTEMS AND NETWORKS, pp. 12 - 69, 13 02 2002.

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[7] R. Bhandari, Survivable Network: Algorithms for

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11

habitação de Angola 2014, Relatório,” INE, Angola,

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[9] MTTI - Ministério das Telecomunicações e Tecnologias

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[10] A. Dwivedi and R. E. Wagner, "Traffic Model for USA

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[11] S. De Maesschalck, D. Colle, I. Lievens, M. Pickavet

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