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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.
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