ОДЕСЬКА НАЦІОНАЛЬНА АКАДЕМІЯ ЗВ’ЯЗКУ ім. О.С. ПОПОВАФакультет ІнфокомунікаційКафедра Вищої математики

Пояснювальна запискадо магістерської роботи

магістра

на тему ТЕНЗОРНИЙ МЕТОД ВИЗНАЧЕННЯ ХАРАКТЕРИСТИК ЯКОСТІ МЕРЕЖІ MPLS/VPN

Виконав: студент 6 курсу, групи ТЕ-6.1.01мспеціальності8.05090303 Технології та засоби телекомунікацій_____________ Смаглюк Г.Г.

Керівник _ Стрелковська І.В.

Рецензент Сукачов Е.О.

Одеса – 2013 року

Д О В І Д К А

кафедри ВМ про виконану магістерську роботу

студента 6 курсу факультету ІК групи ТЕ – 6.1.01м

Смаглюка Гліба Геннадійовича

на тему Тензорний метод визначення характеристик якості мережі MPLS/VPN

Висновок нормоконтролера ___________________________________________________ ____________________________________________________________________________

Нормоконтролер _викладач _(науковий ступінь, вчене звання)

__________(підпис, дата)

О.С. Білозьоров(і. б. прізвище)

Висновок консультанта з техніко-економічного обґрунтування ________________________ _______________________________________________________________________________

Консультант _ д.т.н., професор (науковий ступінь, вчене звання)

__________(підпис, дата)

І.В. Стрелковська(і. б. прізвище)

Висновок консультанта із заходів охорони праці _____________________________________ _______________________________________________________________________________

Консультант _ д.т.н., професор(науковий ступінь, вчене звання)

__________(підпис, дата)

І.В. Стрелковська (і. б. прізвище)

Попередня експертиза (захист) ____________магістерської роботи____________(дипломного проекту, дипломної чи магістерської роботи)

студ. __________Смаглюка Г.Г____________ проведена “11”_січня_ 2013 р.  (прізвище і.б.)

Висновки _________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________

Члени комісії ____________________ _д.т.н., проф. Стрелковська І.В.________(підпис, дата) (науковий ступінь, вчене звання, прізвище і.б. )

________________ _к.т.н., доц. Дмитрієва І.Ю___________(підпис, дата) (науковий ступінь, вчене звання, прізвище і.б.)

________________ _д.т.н., проф. Сукачов Е.О___________(підпис, дата) (науковий ступінь, вчене звання, прізвище і.б.)

________________ _ст. викл Паскаленко В.М. ___________(підпис, дата) (науковий ступінь, вчене звання, прізвище і.б.)

________________ доц. Соловська І.М.__________________(підпис, дата) (науковий ступінь, вчене звання, прізвище і.б.)

ОДЕСЬКА НАЦІОНАЛЬНА АКАДЕМІЯ ЗВ’ЯЗКУ ім. О.С. ПОПОВА

Факультет _________Інфокомунікацій___________________________________Кафедра ___________ Вищої математики ________________________________Освітньо-кваліфікаційний рівень_____Магістр ___________________________Спеціальність _____8.05090303 Технології та засоби телекомунікацій ________

ЗАТВЕРДЖУЮЗавідувач кафедри ВМ

доц.__________І.Ю. Дмитрієва

“ ____ ” ________ 20__ року

З А В Д А Н Н ЯНА МАГІСТЕРСЬКУ РОБОТУ СТУДЕНТУ

______________________ Смаглюку Глібу Геннадійовичу________________________

1. Тема роботи Тензорний метод визначення характеристик якості мережі MPLS/VPN___________________________________________________________

____________________________________________________________________керівник роботи_____Стрелковська Ірина Вікторівна, д.т.н., проф.__________

затверджені наказом вищого навчального закладу від “12” березня 2012 р. №01-08-982. Строк подання студентом роботи _____14 .0 1 .2013 ______________________3. Вихідні дані до роботи _____________________________________________1. Функціональна архітектура мережі MPLS згідно RFC 3031 2. Протоколи маршрутизації та сигналізації (OSPF, RSVP, BGP, LDP) регламентовані Y.1416, RFC 2328, RFC 1105, RFC 5036, RFC 22053. Архітектура мережі MPLS/VPN4. Основні положення концепції ТЕ згідно (RFC 2702)5. Основні характеристики якості, які визначають мережу MPLS/VPN згідно (RFC 2547) . ________________________________________________________________________________________________________________________4. Зміст розрахунково-пояснювальної записки (перелік питань, які потрібно розробити)___________________________________________________________ 1.Сучасний стан та основні тенденції розвитку транспортних мереж MPLS в Україні2. Архітектура мережі MPLS______________________________________________ 3. Розробка тензорної моделі дослідження мережі MPLS______________________

4. Тензорний метод визначення характеристик якості мережі MPLS ____________ ____________________________________________________________5. Перелік графічного матеріалу (з точним зазначенням обов’язкових креслень)Аркуш 1 Узагальнена функціональна архітектура мережі MPLS Аркуш 2 Узагальнена функціональна архітектура мережі MPLS/VPN Аркуш 3 Структурна схема мережі MPLS-ТЕ/FRR у вигляді графу Аркуш 4 Результати розрахунку характеристик якості мережі MPLS-ТЕ/FRR Аркуш 5 Структурна схема мережі MPLS/VPN у вигляді графу Аркуш 6 Результати розрахунку характеристик якості мережі MPLS/VPN _______________________________________________________________________________

6. Дата видачі завдання______________01 . 0 9 . 201 1 _______________________КАЛЕНДАРНИЙ ПЛАН

№з/п

Назва етапів магістерськоїроботи

Строк виконання етапів роботи

Примітка

1 1.Сучасний стан та основні тенденції розвитку транспортних мереж MPLS в Україні

11.04.2012

2 2. Архітектура мережі MPLS 10.05.20123 3. Розробка тензорної моделі дослідження мережі MPLS 30.12.20124 4. Тензорний метод визначення характеристик якості

мережі MPLS22.11.2012

Студент _____________ ____Г.Г. Смаглюк____ ( підпис )

Керівник роботи _____________ ____І.В. Стрелковська_ ( підпис )

ВІДГУК КЕРІВНИКАна магістерську роботу студ. Смаглюка Г.Г.на тему Тензорний метод визначення характеристик якості мережі

MPLS/VPN

Магістерська робота студента Смаглюка Г.Г. присвячена розв’язанню задач визначення характеристик якості в мережі MPLS/VPN. У даній роботі розглянута можливість та продемонстрована доцільність використання тензорних методів на базі декомпозиції для вирішення задач оцінки характеристик якості в мережі MPLS/VPN

Під час написання магістерської роботи студ. Смаглюк Г.Г. відповідально і дисципліновано ставився до поставлених завдань, проявив працьовитість і цілеспрямованість при вивченні можливостей застосування математичного апарату тензорного аналізу, який є одним з основних методів дослідження в його роботі.

У магістерській роботі запропонована можливість використання вузлового тензорного методу, що дозволяє одночасно оцінювати структурні властивості та функціональні характеристики мережі. Розглядається задача знаходження характеристик якості мереж MPLS/VPN великої розмірності з застосуванням технології ефективного використання ресурсів TE-tunnel.

Науковою новизною роботи є практична реалізація методу декомпозиції для вирішення задач оцінки характеристик якості в мережі MPLS/VPN за допомогою тензорних методів. Застосування методу декомпозиції для мереж MPLS/VPN складної топологічної структури дозволяє розглянути топологічно більш прості підмережі, розрахунок характеристик якості яких є простішим, а отримані результати потім перенести на вихідну мережу.

Студент Смаглюк Г.Г. виступав з результатами роботи на двох науково-практичних конференціях за результатами яких видано збірники тез, брав участь у двох всеукраінських конкурсах студентських наукових робіт, має три публікації у фахових виданнях з тематики магістерської роботи.

В цілому магістерська робота студента Смаглюк Г.Г. заслуговує оцінки «відмінно», а її автор - присвоєння кваліфікації інженер зв’язку, науковий співробітник за заявленою спеціальністю 8.05090303 – Технології та засоби телекомунікацій.

 

Доктор технічних наук,професор каф. ВМ ОНАЗ ім. О. С. Попова І. В. Стрелковська

РЕЦЕНЗІЯна магістерську роботу студента Смаглюка Г.Г. з теми: Тензорний метод визначення характеристик якості мережі

MPLS/VPN

Магістерська робота студ. Смаглюка Г.Г. присвячена питанню розв’язання задач оцінки характеристик якості мереж MPLS. Тема роботи актуальна, бо присвячена сучасній проблемі визначення характеристик якості мережі.

У магістерській роботі проаналізовано існуючі математичні моделі, що використовуються для визначення характеристик якості обслуговування, показано, що у вузлових телекомунікаційних мережах, таких як MPLS-TE/FRR застосування тензорних методів дозволяє одночасно проаналізувати структурні та функціональні властивості мережі, а також знаходити оптимальні рішення для забезпечення мінімального часу затримки пакета. Продемонстровано, що використання методу декомпозиції для мереж MPLS/VPN, які володіють великою розмірністю та складною топологічною структурою, дозволяє отримати результати розрахунку характеристик якості окремо для кожної підмережі, а потім перенести отримані результати на вихідну мережу, тим самим зменшивши кількість розрахункових операцій..

Текстова частина випускної роботи викладена послідовно, чітко, технічно грамотно.

До недоліків випускної роботи варто віднести:– доцільно було б для розробленої тензорної моделі використати розподіл

трафіку за класами обслуговування QoS;– розроблену модель застосовано та проаналізовано лише для однієї

топологічної мережі MPLS-TE;– розроблену модель застосовано та проаналізовано лише для однієї

топологічної мережі MPLS/VPN.В цілому магістерська робота студ. Смаглюка Г.Г. відповідає вимогам щодо

магістерської роботи за заявленою спеціальністю 8.05090303 - Технології та засоби телекомунікацій. Виконану роботу можна оцінити на «відмінно», а її автор заслуговує присвоєння кваліфікації - інженер зв’язку, науковий співробітник.

Доктор технічних наукпрофесор каф. ТЕД та СРЗОНАЗ ім. О. С. Попова Е.О. Сукачов

2013 р.

РЕФЕРАТ

Текстова частина магістерської роботи: 54 с., 9 рис., 8 таблиць, 23 джерела.

Об'єкт дослідження – транспортна мережа MPLS/VPN.

Мета проекту –дослідження можливостей використання тензорних методів

та методу декомпозиції при розв’язанні задач визначення характеристик якості

мережі MPLS/VPN з використанням технології TE/FRR.

Метод дослідження – тензорний метод аналізу, метод декомпозиції, метод

лінійної алгебри.

Розвиток сучасних телекомунікацій у напрямку до мереж нового покоління

NGN потребує якісно нового технологічного розвитку транспортної мережі на

базі технології MPLS, котра дозволить забезпечити обслуговування трафіку з

підтримкою параметрів QoS, при цьому забезпечивши можливості керування

трафіком за допомогою технології Traffic Engineering а також безпечний та

високошвидкісний доступ до віддалених мережевих ресурсів за технологією VPN.

У магістерській роботі розглянуто можливості розрахунку характеристик якості мережі MPLS, для чого запропоновано математичний апарат тензорного аналізу. На конкретному прикладі мережі MPLS-TE/FRR продемонстровано розв’язання задачі маршрутизації трафіка і отримано результати ефективного використання мережевих ресурсів за допомогою організації TE-tunnel швидкої пере маршрутизації FRR при гарантованому мінімальному часі доставки пакетів

Розглянуто можливості використання декомпозиції на базі тензорного

методу для розрахунку характеристик якості складної мережі на прикладі мережі

MPLS/VPN, для якої були отримані результати розрахунку характеристик якості

окремо для кожної підмережі та кожного об’єкта мережі.

ТЕХНОЛОГІЯ MPLS, ІНЖИНІРІНГ ТРАФІКА TRAFFIC ENGINEERING,

МЕРЕЖА VPN, МЕРЕЖА MPLS/VPN, ТЕНЗОР, ВУЗЛОВИЙ ТЕНЗОРНИЙ

МЕТОД, КЕРУВАННЯ МАРШРУТИЗАЦІЄЮ, ЯКІСТЬ ОБСЛУГОВУВАННЯ

QOS, ТЕХНОЛОГІЯ FRR, TE-tunnel, ДЕКОМПОЗИЦІЯ, МЕРЕЖА MPLS-TE/FRR

Умови одержання магістерської роботи: за дозволом проректора з навчальної роботи ОНАЗ ім. О.С. Попова.

ABSTRACT

 

Text part of the master's work: 54 pages, 9 figures, 8 tables, 23 sources.

Object of study - transport MPLS/VPN network.

Project aim – to study opportunities of tensor decomposition methods application

and dealing with problems of quality characteristics obtaining for MPLS/VPN network

using TE/FRR technology.

Research method - tensor analysis method, the method of decomposition method

of linear algebra.

The development of modern telecommunication towards Next Generation

Networks NGN require a qualitatively new technological development of the transport

network technology-based on MPLS, which will provide services to support parameters

of QoS, thus providing more control for traffic using technology Traffic Engineering as

well as safe and high-speed remote network resources by VPN technology.

In the master's project examined the possibility of calculating the quality

characteristics of MPLS network, for which proposed mathematical apparatus of tensor

analysis. In the concrete example of MPLS-TE/FRR network demonstrated problem of

traffic routing solving and results of effective use of network resources by organizing

TE-tunnel of instant rerouting FRR for guaranteed minimum time packet delivery

The possibilities of using tensor decomposition-based method for calculating the

characteristics of complex network as an example of MPLS/VPN network, for which

were obtained results of quality characteristics separately for each subnet and each

network object.

 

MPLS TECHNOLOGY, TRAFFIC ENGINEERING, VPN NETWORK,

MPLS/VPN NETWORK, NODAL TENSOR METHOD, QUALITY OF SERVICE

QoS, TECHNOLOGY FRR, TE-tunnel, DECOMPOSITION, NETWORK

MPLS-TE/FRR

 

Conditions for obtaining master's work: the permission of vice-rector of

educational work of ONAT by A.S. Popov.

ЗМІСТ

ВСТУП............................................................................................................... 91 СУЧАСНИЙ СТАН ТА ОСНОВНІ ТЕНДЕНЦІЇ РОЗВИТКУ ТРАНСПОРТНИХ МЕРЕЖ MPLS В УКРАЇНІ............................................ 102 АРХІТЕКТУРА МЕРЕЖІ MPLS.................................................................. 12

2.1 Функціональна архітектура мережі MPLS.................................... 122.2 Технологія керування маршрутизацією TE................................... 162.3 Принципи функціонування MPLS/VPN......................................... 17

3 РОЗРОБКА ТЕНЗОРНОЇ МОДЕЛІ ДОСЛІДЖЕННЯ МЕРЕЖІ.............. 19

3.1 Постановка задачі дослідження...................................................... 193.2 Переваги та можливості тензорного аналізу для дослідження

мереж MPLS..................................................................................................... 203.3 Основні поняття тензорного аналізу............................................. 213.4 Основні принципи розробки тензорної моделі............................. 243.5 Узагальнюючі постулати тензорного узагальнення..................... 26

4 ТЕНЗОРНИЙ МЕТОД ВИЗНАЧЕННЯ ХАРАКТЕРИСТИК ЯКОСТІ МЕРЕЖІ MPLS................................................................................................. 28

4.1 Дослідження характеристик якості мережі MPLS-TE/FRR......... 284.2 Дослідження характеристик якості мережі MPLS/VPN.............. 36

ВИСНОВКИ та ПРОПОЗИЦІЇ........................................................................ 49

ПЕРЕЛІК ПОСИЛАНЬ.................................................................................... 50

CONTENTS

 

INTRODUCTION 91 CURRENT STATE AND MAIN TRENDS OF MPLS TRANSPORT

NETWORK IN UKRAINE ............................................................................... 102 MPLS NETWORK ARCHITECTURE ......................................................... 12

2.1 Functional MPLS network architecture ............................................ 122.2 Traffic engineering technology ......................................................... 162.3 Principles of MPLS/VPN operation................................................... 17 

3 DEVELOPMENT OF TENSOR MODEL FOR NETWORK

INVESTIGATION.............................................................................................. 193.1 Formulation of research problem ...................................................... 193.2 Advantages and possibilities of tensor analysis in researching

MPLS networks……………………………………………………………….. 203.3 Basic concepts of tensor analysis ...................................................... 213.4 Basic design principles of tensor model ............................................ 243.5 Generalizing postulates of tensor analysis ........................................ 26 

4 TENSOR METHOD OF MPLS NETWORK QUALITY

CHARACTERISTICS OBTAINING…………………………………………. 284.1 Investigation of the quality characteristics of MPLS-TE/FRR

network............................................................................................................... 284.2 Investigation of the quality characteristics of MPLS/VPN network.. 36 

CONCLUSIONS AND PROPOSALS .............................................................. 49REFERENCES ................................................ ................................................. 50

INTRODUCTION

A characteristic feature of the development of modern telecommunication

networks is the introduction of NGN (Next Generation Network), which is convergent

and have heterogeneous properties, because simultaneously use many technologies and

protocols. Active implementation of multiservice access technology, packet switching

networks in NGN require a qualitatively new technological development of the

transport network. Application on the main level of Multiprotocol Label Switching

MPLS (MultiProtocol Label Switching) technology will ensure effective transfer of

traffic supporting parameters of QoS (Quality of Service), by means of technology

Traffic Engineering (TE) by selecting the optimal route, use and distribution of

reservation procedures for network load balancing and prevent congestion

mechanisms [1,2].

To ensure high scalability of MPLS network, wide possibilities of configuration

and integration with external networks, as well as the safe and high-speed access to

remote network resources used technology VPN (Virtual Private Network). Managing

routing networks MPLS/VPN is applied by using routing protocols (Open Shortest Path

First OSPF, Resource ReSerVation Protocol RSVP), providing optimal load and

supported on all network elements.

In the master’s work given the task of quality characteristics evaluation for MPLS

network, which requires taking into account the structural characteristics and functional

properties forecasting of the network state at a certain period of time, as well as network

protocols and interfaces. As mathematical tools used tensor analysis method, which

allows to consider complex topological and functional architecture networks MPLS, as

well as describing possible reconfiguration of traffic flow when changing network

topology. Evaluation of network quality characteristics for MPLS-TE/FRR is scheduled

to perform for configuring tunnels opportunities TE-tunnel, for values length packet

queues and delays in packet transmission paths. When analyzing MPLS/VPN network

high dimensionality and complex architecture will use the method of decomposition,

which will determine the length of packet queues and packet delay for subnets and

transfer the results to the original network.

.

10

1 CURRENT STATE AND MAIN TRENDS OF MPLS TRANSPORT

NETWORK IN UKRAINE

Implementation on telecommunication networks of Ukraine Next Generation

Networks is performed due to urgent market requirements and the need to expand the

range of new services - data, IP-telephony, video services and others [2].

Currently most of the transport network of operators in Ukraine are based on

various media and transmission systems. Typically, this is fiber-optic systems of type

DWDM (Dense Wavelength-division Multiplexing), which enables the transmission

and reception of different traffic types - from SDH containers to IP-packets on one pair

of optical fibers. This technology allows a single optical fiber to transmit information at

speeds up to 10 Gbit/s on each of the 32 optical subcarriers, which generally is

320 Gbit/s per direction.

The basic technology of the transport network of fixed, mobile and data

communications technology is IP/MPLS. For example, the transport network of the

company "MTS Ukraine" is based on the backbone DWDM-network consists of 42

transport hubs and unites the cities of Kyiv, Odessa, Lvov and Chop. The hardware and

software platform network is an optical transport platform ONS 15454 Cisco Systems,

divided into segments. IP-based backbone MPLS technology combines seven cities of

Ukraine: Kyiv, Kharkiv, Donetsk, Dnipropetrovsk, Simferopol, Odessa and Lviv that

contain powerful routers LSR (Label Switching Router). Backbone network provides

WAN traffic at 1 Gbit/s. In order to increase reliability of the system at each point of

presence (Point of Present) installed two routers LSR and two boundary LER (Label

Edge Router). Cross-connection data devices ensures redundancy in case of equipment

failure or a communications channel, and switching time less than 50 ms.

Similarly organized transport networks of other operators in Ukraine:

"Ukrtelecom" the equipment Cisco ONS 15454 MSTP with bandwidth of 80 Gbit/s,

"Ukrainian Radio Systems" based on DWDM equipment Huawei Technologies,

"Kyivstar" on the equipment Cisco IP Solutions Center 4.0.

A characteristic feature of the construction of transport infrastructure of most

corporate networks Ukraine is their geographically distributed architecture, giving rise

to the task of uniting the distributed enterprise branch offices and remote workstations

employees in a network. Using MPLS technology for building virtual private networks

VPN, allowing you to create secure virtual private networks of any size in a single

infrastructure. For example, today the VPN from MTS using about a hundred large

11

Ukrainian companies, "Raiffаisen Bank Aval", "Alfa-Bank", "Kievpastrans", and

others.

Thus, the main direction of development of telecommunications companies in

Ukraine is the further technological extension of transport networks, the phased

implementation of DWDM technology with the development of their network based on

IP/MPLS. These technologies provide efficient transfer of high-traffic parameters

support QoS (Quality of Service), which is implemented through mechanisms of traffic

engineering, reservation procedures, load distribution and balancing the network traffic

with mechanisms to prevent overload.

12

2 MPLS NETWORK ARCHITECTURE

2.1 Functional architecture of MPLS network

Technology MPLS (MultiProtocol Label Switching) is a multiprotocol switching

on labels, respectively to recommendation RFC 3031. It combines the functionality of

traffic management inherent link layer technologies and protocols flexibility that is

characteristic of the network layer and provides the main requirements for the

technology of backbone, namely, high bandwidth, nominal packet delay and

scalability [1].

MPLS network architecture based on the following hardware and

software (Figure 2.2) [1,2]:

LSR - a network router that is designed to perform tasks of routing and switching

on labels;

LER - end network router that is designed to perform tasks of routing and

switching with the use of labels, and without them.

The main feature of the functioning of technologies MPLS - is the process of

switching without the traditional analysis of signal information in the packet header,

which can significantly increase the speed of packet switching. Using protocols

supporting QoS allows for MPLS network traffic operation prioritization, selection of

the optimal route of traffic TE-tunnel considering QoS criteria and performance

optimization procedures of queues to control bandwidth [2].

According to the technology of MPLS network devices assigne to each point of

entry to the routing table special label and report this label to neighboring devices. The

label serves as a fixed-length identifier that specifies Forwarding Equivalence Class

(FEC) and has local significance. Place of the label in the package depends on the link

layer technology used. The presence of such tags allowing routers enabled for MPLS,

determine the next step in the route package without the procedure, search for an

address. As a protocol independent label can be used to encapsulate packets of any

protocol network layer. It can be a label identifiers of virtual channel and virtual path

identifier or channel layer connection label [2,3].

13

Figure 2.1 – Label format

Size of label is 4 bytes. ID of the tag is the first 20 bits. Information about the

level of quality of service in MPLS network is transmitted to the field CoS, which

occupies the next three bits in the box label. This field is necessary to provide

differentiated services in the MPLS. For pass-through support services IP QoS MPLS-

border network, you can copy the box IP-precedence field CoS. The last bit of the third

byte is used to indicate the end of a stack of labels. Fourth byte fields label format is

parameter TTL (Time to Live), which indicates the time during which the file must exist

in the network, providing some level of protection from network loops and restricts the

distribution package. A characteristic feature of labels is their uniqueness. The

uniqueness of labels is as follows: Router LSR has the right to bind label to FEC only if

it can uniquely determine the stack labels router which it relates. The sequence of

devices in MPLS domain through which passed a package labeled with a fixed amount

of stack labels, called Label Switch Path (LSP) [1,2].

Each router contains a label MPLS LIB (Label Information Base), through which

the packets and routes are linked together. For labels in a LIB contains accurate record

of the corresponding output label and interface information encapsulation link layer

required for promotion package. Based on information obtained from the database LIB,

LSR replaces it received input on the original label and forwards the packet to the

output interface. This operation is repeated while passing each LSR router. Base LIB

simplifies the process of moving packets and increase network scalability by comparing

several labels are one and the same unit of information on the original label, thereby

realized a new type of routing. When LIB several LSR collects information related to

the same destination, creating so-called "switched by labels tract", which is a sequence

of labels in the nodes in the path of flow from source to destination. For such paths in

the MPLS network realized data transfer. Packets belonging to the same FEC, are

transmitted by one LSP. LSP path between the two routers is unidirectional [2,3].

14

In MPLS network to provide QoS parameters of different types of traffic to

different parts of the network are used different technologies and protocols for routing

and signaling:

1) RSVP (Resource ReSerVation Protocol) - a protocol of reserving resources,

defining nodes that require a certain class service and ensures the necessary capacity to

service the network traffic in MPLS.

2) OSPF (Open Shortest Path First) - dynamic routing protocol, designed to

determine the network topology and table routing.

3) LDP (Label Distribution Protocol) - protocol of label distribution among

routers needed to build routing tables based on the paths LSP.

4) BGP (Border Gateway Protocol) - routing protocol that distributes routes in

backbone network only to preconfigured neighboring LSR. Also use MP-BGP -

multiprotocol extension protocol BGP, which has additional options for configuring

networks specifically for MPLS.

5) IntServ (Integrated Services) - technology of integrated interaction of network

routers to provide the required quality of service along the LSP path between devices.

6) DiffServ (Differentiated Services) - technology to ensure the necessary quality

of service parameters that determines the differentiated service traffic at border routers

LER static resource reservation.

Thus the total work of routing protocols and signaling provides independence

from the link layer technology, optimum loading and resource reservation

15

Fig

ure

2.2

–MP

LS

net

wor

k ar

chit

ectu

re

16

2.2 Traffic engineering technology

The main mechanism for traffic management in MPLS networks is the Traffic

Engineering (TE), shown in Figure 2.3, which provides the basic methods and

mechanisms to achieve load balancing of essential resources through rationa choice of

traffic route through the network, load balancing procedure, selecting the optimal route

of traffic, using of reservation procedures, distribution of load balancing traffic and

avoid overloading mechanisms [2].

TE mechanism is based on the structural characteristics of the network, which is

the source data for selection by routing traffic. Traffic Engineering provides a set of

search paths, in which there is found to be the optimal solution that takes into account

the length of the shortest TE-tunnel and selected QoS criteria - meaning delays packets

on the network. There are following types of routing in the tunnel TE-tunnel: static

routing, policy routing and auto-routing [2].

In order to optimize the parameters of reliability and providing the required

criteria for network QoS MPLS-TE technology instantly realized rerouting FRR (Fast

ReRout), which minimizes packet loss in case of failure of the resource to be protected,

by selecting alternate tunnel backup tunnel on the section of the path LSP, given the fact

that the choice of alternate tunnel is pre-configured and can maintain the required

throughput considering the characteristics of the network.

Figure 2.3 –MPLS-TE/FRR operation principles

Reserve tunnel is configured for the given criteria, such as minimum transmission

delay of packet or throughput or the minimum number of network devices in the TE-

17

tunnel. Given the configuration of spare tunnels (backup tunnel), using the criterion of

time delay, and the main is sufficient amount of time switching tFRR time (about 50ms in

the area between routers and less 100ms on the router) [2].

Implementing technology FastReRoute can be done to protect different types of

network objects: channel (Link protection), node (Node protection), route (Path

protection) [2].

2.3 Principles of MPLS/VPN operation

Modern trends in network architectures pay special attention to the

implementation of virtual private networks VPN (Virtual Private Network), which

provide the needs of users in a secure and high-speed access to remote network

resources [1,2]. Building a VPN networks based on MPLS technology provides

opportunities of configuration, scalability and transfer traffic with guaranteed

parameters of QoS.

The network architecture MPLS/VPN, according to recommendations RFC

2547bis, based on the MPLS core network and connected to it, isolated geographically

distributed virtual networks VPN [1,2]. The network architecture MPLS/VPN is shown

in Fig. 2.3.

MPLS core network based on the internal P (Provider router) and boundary

routers PE (Provider Edge router) [3,4]. Internal routers support the functioning of the

core network are responsible for routing packets in the IP/MPLS network and provide

interaction with virtual networks, so do not contain routing information of VPN.

In contrast, the functionally more complex boundary routers PE perform routing

to geographically distributed VPN by using tables VRF (VPN routing and forwarding).

VRF route table stores information about all possible routes to a particular VPN, and

sets the principles of service packet traffic associated with the choice of route -

incoming or outgoing import policy export policy [4].

Isolated subnet VPN routers are based on LSR, which are connected to routers

CE (Customer Edge router). Boundary routers CE, set on the border virtual network

used for communication of geographically distributed VPN with a core network and

provide traffic services directly necessary between the core network and VPN. Thus, the

network MPLS/VPN use different routing principles, which are defined separately for

the core and virtual networks VPN [3,4].

18

Figure 2.4 - MPLS/VPN architecture

Performance of routing in the network is carried out by different protocols,

depending on the segment:

- In the backbone network IP/MPLS definition route traffic occurs by means of

protocol LDP, which selects the shortest route of traffic regardless of the set parameters

QoS, or the protocol RSVP, which maintains the required quality of service and

mechanisms of regulation of network resources.

- In virtual networks VPN routing traffic is running by a dynamic routing

protocol intranet IGP, which also operates on the principle of choosing the shortest path.

- The section joints PE-CE links routing management is carried out by dynamic

routing protocols OSPF, which uses data bandwidth in order to choose the shortest

path [1,4].

The most significant in terms of the use of network resources with a given quality

of service in networks MPLS/VPN connection is part of PE-CE, for which the

capacities of the dynamic routing protocol OSFP should be provided with guaranteed

delay value packages, value bandwidth and probability of loss packages in terms of

efficient use of network resources.

19

3 DEVELOPMENT OF TENSOR MODEL FOR NETWORK

INVESTIGATION

3.1 Formulation of research problem

Introduction of modern technological means of traffic management to ensure

sustainable use of MPLS network resources that supports QoS, implemented by means

of technology Traffic Engineering (TE). This technology uses mechanisms balanced

load resources, choosing the optimal route traffic, using reservation procedures,

balancing traffic and mechanisms to prevent overloading.

Using technologies to support QoS (IntServ/RSVP, DiffServ/RSVP +, DiffServ-

TE) can provide a variety of classes of transmission service by determining the

sequence of routers passing traffic queues optimization and control bandwidth [1,2]. At

the same time solving techniques routing problems seeking one and thus the only way

to deliver packages between a given pair of sender-receiver, which is a significant

limitation. The only one way, chosen under some criteria, provides loads of only part of

network resources [5].

The use of MPLS-TE/FRR technology allows by the simultaneous use of multiple

ways to deliver packages to provide the necessary bandwidth. However, this

complicates the process of monitoring quality of service (QoS), and challenges to the

definition of packet delay, jitter, packet delivery probability under the existing

theoretical models [1].

Therefore, the actual problem is rather theoretical basis, research and development

of models of traffic management, which may be considered for solving routing

networks MPLS-TE/FRR.

Networks MPLS/VPN analysis process quality characteristics and receipt of

analytical solutions is extremely difficult because of the need to take into account the

complexity of the topology, large dimension and functional properties of network

objects. Using the solutions obtained for topologically simpler networks

MPLS-TE/FRR, using decomposition will calculate the results of quality characteristics

separately for each subnet and the object of the [6,7].

20

3.2 Advantages and possibilities of tensor analysis in researching MPLS

networks

Technological improvement of existing telecommunications networks, usually

accompanied by a constant complication principles of their structural and functional

building that is especially true for protocol solutions transport layer in layered

architecture of next generation NGN. In this regard, the analysis and synthesis of

geographically-distributed network, as a complex organizational and technical systems,

tools of systems research presented mathematical formalism of tensor analysis [8].

To select a suitable mathematical apparatus consider methods of teletraffic theory,

graph theory and tensor analysis [8-10].

Using analytical methods of teletraffic theory allows to solve a wide class of

problems calculating the characteristics of a given node, not providing consideration the

structural organization of the network [9]. The mathematical apparatus of the theory of

graphs and network analysis allows to solve network problems, such as finding shortest

paths, network planning, resource allocation network and others. [10].

Solving simultaneous estimation of structural features and functional properties

forecasting of the network at a certain period of time based on the network topology and

protocols and interfaces used allows the use of a tensor method [11]. Therefore, for the

solution of this problem we use the unit tensor analysis, which will take into account the

complex topological and functional architecture networks MPLS., As well as the

possibility of describing reconfiguration of traffic flow by changing the topology of the

network [8].

The possibility of joint research structure telecommunications systems and

processes that take place in it, is the main advantage tensor research methodology [12].

Tensor analysis of networks laid by its abilities, is a logical means for describing

real objects in their multiplicity and contradictions. Tensor representation has maximum

integrity, allowing the focus to concentrate on the same system, regardless of possible

coordinate systems consideration [13].

Simultaneous study of network structure and processes occurring in it, is the main

advantage of the tensor research methodology based on the integration capabilities of

differential geometry with the possibilities of combinatorial topology. That is, the

analysis of the system along with the functional behavior of the equations can be used

as a topological description of what constitutes an additional source of information for

the effective preparation and solve these equations [13].

21

3.3 Basic concepts of tensor analysis

Tensor is a geometric object, the value of which is given at each point in space

with their own (many) components for each axis, the main feature of which is a linear

transformation of its components by changing the coordinate system. Assume that the

matrix in r-dimensional space given the transformation of the old base

coordinate system to new basis with coordinates and the old base

into a new by formula [15]:

(3.1)

Then each of the tensor components is important for each axes at a given point and

a change of coordinate system is transformed by the matrix (covariant component), or

by using the inverse (contravariant component).

In general, the tensor in mathematics - a geometric object in the space of r-

measure, which asked each point (n+m) - function parameters, with r-component

projections for each axes [14]:

(3.2)

And the n components are transformed as covariant, i.e. the matrix , and m as

contrvariant - inverse .

Tensor has the second valence r2 component. There are three types of tensors of

second valence: twice covariant tensor, the total component which can be written as ,

twice contravariant tensor, the total component which can be written as , mixed - once

covariant once contrvariant - total component which can be written as . Components

of the second valence tensor can be represented as a square matrix [14]:

(3.3)

22

Arbitrary component of general covariant tensor with n indices m contrvariant in

some coordinate system can be represented in the form by expression (3.4). Sum

n+m=p – tensor valance that has rp components. Expression (3.4) defines an index entry

of tensor q [13].

(3.4)

where і hi – respectively covariant tensor and contrvariant valence one,

(i,j= ).

Law of conversion covariant quantities during the transition from one coordinate

system (CS) to another coincides with the law of transformation of basis vectors (ei=

), and transformation of contrvariant values occurs by inverse law [12].

During the transition from non-hatched CS submission to the hatched tensor

components it becomes subject of a linear law [13,14]:

(3.5)

(3.6)

despite the fact that .

The main requirement for the coordinate transformation (3.5) and (3.6) is zero

determinant matrix inequality. Then there is fair equality [13, 14]

(3.7)

where

Important role in tensor analysis plays notion metric and metric tensor that in each

partial coordinate systems becomes a fundamental (basic) matrix [13,14]:

(3.8)

Using the metric tensor is juggling operation (raising and lowering) indices. That

is, if needed covariant tensor , then using the metric tensor can be obtained

contravariant tensor hi and vice versa [13,14]:

23

(3.9)

Then tensors і hi are called associates. And juggling operation extends to tensors

of arbitrary type valence.

Sum (or difference) of two tensors with the same number of covariant and

contrvariant indices are tensor of the same type and valence as defined tensors. Any

linear combination of tensors of the same type and valence is also a tensor of the same

type and valence [13,14].

For example: if the tensors and are tensors of the same region of

space, their sum is the tensor of this region [12,13]:

(3.10)

Direct product of tensors and is such tensor [12,13]

(3.11)

which is covariant of valency (m + r) and contrvariant of valence (p + s). Thus, the

tensor reflects invariant geometric object whose coordinates by transforming the

coordinate system vary linearly.

3.4 Basic design principles of tensor model

For research necessary to develop a tensor model study. Methodology tensor

approach to the analysis of networks as a complex system is to perform basic steps [13]:

Step 1. Geometrization of a system: introducing the concepts of space, coordinate

systems and their transformation rules.

The space consists of nodes and branches connected beloved way. Twigs and

branches form a sequence in the space ways in which information flows can spread.

In tensor analysis network topological description of the system modeled, produced

by the district networks that meet simplical submission of appropriate dimension.

When describing the structure of the system within the apparatus of tensor analysis

network depending on how the impact may be interpreted as contour, nodular or

orthogonal. In contour networks starting point of the analysis is the path to node - a pair

24

of nodes in a network of orthogonal concepts contour and node pairs used together,

complementing each other. A distinctive feature of contour and nodal networks is

mandatory uniformity impacts on network elements. For orthogonal networks influence

can carry a combined character. Use during topological description of a particular type

of network depends largely on the nature of the problem being solved and in turn,

defines fully functional as a way to describe a system and method for calculating the

unknown parameters [13]. Consider formulas of vectors conversion from one coordinate

system to another [14]. We shall consider r – dimensional space. Considering

– unit vectors of the old coordinate system, and – unit vectors of the new

system. If we denote by projection of the unit vector Em onto the unit vector ek,

obtained in designing parallel plane formed by all the other axes of the old system, we

obtain r equations that can be written in abbreviated form:

, (3.12)

Equation (3.12) give us a new unit vectors Em as a function of the old unit vectors

ek. Having considered the inverse case we obtain:

, (3.13)

Vector, that is transformed while transformation of the coordinate system is

obtained according to the rules of transformation unit vectors, called covariant. Index

denoting the number of coordinate axes, the relevant projections covariant vector is

placed below: . If the vector by transforming the coordinate system is

changed by the inverse transformation rule unit vectors, such vector called contrvariant.

Index in the projection vector is placed at the top: [13].

Model structure of the network can be represented as a directed weighted graph

G(N,V) and consist from N nodes, that are connected by V links, as it is shown

at fig 3.1.

25

N1

N2

N3

N4

N5

ν1

ν2

ν3 ν4

ν5

ν6

ν7

Figure 3.1 – Network structure example

Step 2. Invariant representation of the equations of system behavior, its basic

properties and characteristics. Determination of invariant covariant and contravariant

values.

The difference tensor of other geometric objects is that when you change the

coordinate system of its components converted from the old to the new coordinates

linearly [14]. Linearity is a very important property tensors which means that if we

know the projection tensor in one coordinate system, then we can get its projection in

any coordinate system, if known formula transformation from one coordinate system to

another - invariant equation. The very object tensor is not changed by coordinate

transformation, changing only its components [15, 16].

As an invariant equation that characterizes a given model will use, for example,

Little formula that defines the relationship between the length of the queue, the average

packet delay and signal intensity of the load.

The presence of such a formula transformation allows to know the projection of

only one coordinate system and without a new design to find the projection of the same

object in any other type of coordinate system - is the main property of the tensor

method, which is called invariance property relative to the coordinate system to be used

in constructing mathematical models communication systems [17].

Step 3. Substantiation and choice sets of coordinate systems within which allowed

to make the calculation of the unknown network parameters.

To describe the network we introduce a system of coordinates. As the coordinate

system will take a set of independent paths that pass through the branches of the

network. That is, each path through independence sets in the reporting structure of

space-coordinate axis. Convert the network structure while preserving the original

26

number of branches or the transition from one set of independent paths to another is

treated as a conversion of coordinate systems. The set of structures that correspond to

different variations compounds branches treated as a set of partial coordinate systems

introduced in the space [16].

The basic requirement which must be satisfied in the selection process is

informative of coordinate systems, i.e., in these coordinate systems to be desired or

known projection various components of the tensor [16].

3.5 Generalizing postulates of tensor analysis

The basis of the construction of functional tensor models telecommunication

networks first formulated G. Kron [17] generalized postulates. These postulates define

the principles of complex systems is the steps that allow you to develop a functional

tensor model.

Postulate of first generalization, according to [17] involves the replacement of the

algebraic equation, just for basic network with one degree of freedom, the matrix

equation in which each symbol algebra is replaced by the corresponding n-matrix,

extending the original equation on the network as a whole with n-degrees of freedom,

thus it is an algebraic equation or a system of algebraic equations generalized vector-

matrix equation.

Postulate of second generalization extends the use of the matrix equation registered

for one coordinate system, due to its transformation into invariant equations by

replacing each n-matrix corresponding geometric object. This change allows for

invariant equation for a large number of objects presented in the same space, but in

different coordinate systems. This is accomplished by the group transformation matrix

through which functional equations of any system of coordinates can be transformed

into the equation of any other coordinate system or projection coordinates of the same

geometric object in different coordinate systems interconnected a certain functional

dependence, using which it is possible to pass from one projection to another.

The third postulate of generalizations formulated by G. Kron [17] believes that the

functional equation is invariant descriptive network or system should be such that the

geometric objects that it includes gained tensor character. Then the network can be

modeled invariant described from different points of view, objects of different classes.

Thus, the use of the above postulates provides a holistic view of the simulated

telecommunications network in which the projection of the same tensor in different

27

coordinate systems linked tensor law, and the projection of various tensors in a

coordinate system associated matrix equation.

28

4 TENSOR METHOD OF MPLS NETWORK QUALITY

CHARACTERISTICS OBTAINING

4.1 Investigation of the quality characteristics of MPLS-TE/FRR network

Consider a network of MPLS/TE-FRR, which provides the basic methods and

mechanisms to achieve load balance resources through choice of ways of passing

traffic, load balancing, application procedures, redundancy and load distribution.

Develop tensor method for solving the problem of performance evaluation as

network configuration MPLS/TE-FRR to TE-tunnel, taking into account the structural

properties and functional characteristics of the network when organizing TE-tunnel fast

reroute FRR.

Let be set initial network structure MPLS-TE/FRR, as a graph consisting of n

nodes represented routers LSR, coupled m branches - paths.

Capacity in the branches of the network is specified and represented as a

coordinate of matrix . Directions of transmission are also set with the length of

income packet queue .

It is necessary to calculate the minimum packet delay from the queue for

incoming LSR, and queue load on all transit LSR to determine in the network

unidirected tunnel TE-tunnel of traffic passing MPLS-TE/FRR by selecting a sequence

of LSR, for which a delay will be the same for all possible routes of packets delivery.

Tensor modeling of MPLS-TE/FRR network provides its description in a metric

space [16-18]. As a metric can serve even traffic in channels that can be clearly

demonstrated by the tensor generalization of Little formula[5]:

, , (4.1)

where – queue length in which packets for i-th communication channel are

situated;

– average packet delay in i-th communication channel;

- traffic intensity in i-th communication channel;

- total quantity of trunks.

By analogy with the tensor approach, offered by G. Kron and developed in works

[18-20] structure describes MPLS-TE/FRR network as simplicial one-dimensional

complex, which determines the discrete m-dimensional space.

Network branches , modulated by trunks, and nodes of the network Nj ,

– LSR.

29

Under the given scheme of MPLS-TE/FRR node network, shown in Figure 4.1,

we choose the output node LSR-1 as a reference, thereby identifying the skeleton

network, in which will perform relatively basic sections choice that are represented by

node pair of a network.

Figure 4.1 – Scheme of MPLS-ТЕ/FRR network

Dependence between nodal pairs , and network branches , for

selected LSR-1:

(4.2)

In the selected m-dimensional space tensor perform a description of system

within nodal networks [10,17,21]. As informative coordinate system will introduce for

consideration two coordinate systems. The first system of coordinates is a network of

30

branches and the second coordinate system of node pairs. In the coordinates system of

branches is necessary to calculate unknown values - the load packets queue at LSR

buffers and time delays in each path.

In node pair coordinate system projections of tensor define outcome queue

length on LSR-sender. In nodal networks as a pop-up variable in equation (4.1) is the

value , and as a response variable - delay . Then equation (4.1) can be represented in

tensor form:

, (4.3)

where – double contravariant tensor of traffic intensity.

In the coordinate system of branches equations take the form

,

, (4.4)

where vector defines queue length in coordinate system of branches,

packet delay vector in coordinate system of branches,

– square matrix of traffic intensity in the branches of the network of m-th

order, which has a diagonal structure.

Equation (4.3) in coordinate system of node pairs is:

,

, (4.5)

where , и – projections of , и in nodal pair basis,

и – vectors of queues length and packet delays in node pairs respectively,

– square matrix of traffic intensity in the system of coordinates of node pairs ρ-

th order, which has a diagonal structure.

31

Tensor character of geometrical objects , и with respect to coordinate

systems is proved by linear dependence of their transformation at coordinate system

change [18, 21]. Projections of tensor in coordinates of nodal pairs are defined as:

, (5.5)

where - basis matrix of sections (node pairs) that formed on the basis of given

transmission directions [11]:

, (4.6)

- coordinates of income queue length,

- vector of queue length in node pair basis.

Double contravariant traffic intensity tensor in coordinate system of node pairs

defined by the expression:

. (4.7)

where - basis matrix,

– square matrix of traffic intensity in the nodal pairs basis,

– square matrix of traffic intensity in the branches basis,

- matrix transpone.

Tensor of packet delay calculation in the coordinate system of pairs is performed

using the following formula:

,

, (4.8)

where inverse matrix to ,

– vector of packet delays in nodal pair basis,

32

- vector of queue length in basis of nodal pairs.

Covariant tensor projections in coordinate system of branches we can find

using the expression:

,

, (4.9)

where – vector of packet delays in nodal pairs of a network,

- basis matrix,

- matrix transpone,

vector of packet delays in branches of a network.

Thus demonstrated the use of tensor method for solving problems of performance

evaluation as a network MPLS-TE/FRR, allowing for obtaining results in analytical

form lengths packet queues in branches network (4.4), delays in packet transmission

paths network (4.9). These results allow you to choose the tunnel TE-tunnel bypass

towards rapid reroute FRR ensuring parameters of quality of service QoS.

In the specific example topology MPLS-TE/FRR and meanings carrying

capacities branches given in Table. 4.1, were calculated tunnel TE-tunnel, ensuring

minimum delay packet transmission queue on the source LSR congestion and queues at

each transit LSR network.

Table 4.1 - Bandwidth of communication lines of nodal network

Branch number v1 v2 v3 v4 v5 v6 v7 v8 v9

Throughput 0 400 200 100 200 600 200 300 200

Results of calculation delay packets and length of the packet queue in

transit LSR network are summarized in Table. 4.2, and the results of calculating the

average time delay packets and length of the packet queue in Table 4.3.

33

Table 4.2 - Results of calculating the time delay and packet length of packet

queue in transit LSR of a network

Node

number

Throughput ( ,thousand

packets/s) of transit LSR

Average time of packet delay (

,s) in transit LSR of a

network

Length of a packet

queue ( ,thousand

packets) in transit LSR

of a network

1300 0,255 100

500 0,219 0

1300 0,195 0

800 0,177 0

Table 4.3 - Results of calculation of the average time delays and packet length

packet queues in network links

Link numberThroughput ( ,thousand

packets/s) of links

Average time of packet

delay ( ,s) in links of a

network

Length of a packet

queue ( ,thousand

packets) in links of a

network

0 0,219 0

400 0,078 31,503

200 0,177 35,322

100 0,255 25,536

200 0,035 7,159

600 0,059 35,799

Continuation of Table 4.3

1 2 3 4

200 0,019 3,818

300 0,023 7,159

200 0,195 39,141

Analysis of the results of calculations show that to determine unidirectional TE-

tunnel of traffic passing and bypass in a case of emergency fast rerouting FRR for a

34

given network MPLS-TE/FRR, we can choose a defined sequence of LSR in the

direction of LSR-1 to LSR-3:

TE-tunnel-1 FRR LSR-1→LSR-3;

TE-tunnel-2 FRR LSR-1→LSR-4→LSR-3;

TE-tunnel-3 FRR LSR-1→LSR-5→LSR-4→LSR-3;

for which the value of the delay is the same for possible ways to deliver packages

and is 0,219 sec.

35

Fig

ure

4.2

– R

esul

ts o

f M

PL

S-Т

Е/F

RR

net

wor

k ca

lcul

atio

n

36

4.2 Investigation of the quality characteristics of MPLS/VPN network

Building VPN networks, ensuring the needs of users in a secure and high-speed

access to remote network resources based on MPLS technology provides opportunities

configuration, scalability and transfer traffic parameters of QoS. The study of such a

network requires a somewhat different approach, including the compound PE-CE, which

should be provided with guaranteed QoS parameters [22, 23].

For MPLS/VPN networks process of analyzing the characteristics of quality and

obtaining analytical solutions is extremely difficult because of the need to take into

account the complexity of the topology, large dimension and functional properties of

network objects. Using the solution obtained for networks MPLS-TE/FRR in Section 4.1,

apply the decomposition of the network to obtain the results of calculation of quality

characteristics for individual subnets, each object and network connections PE-CE.

Let the given initial network structure MPLS/VPN, represented as a graph in

Fig. 4.3, consisting of a core network MPLS, built on the basis of internal and border

routers and k geographically distributed virtual subnets VPN (k = 3), built on the border

routers CE and LSR routers. In Fig. 4.3 adopted notation routers of a kind PE-i/j-p, where i

- number of a router, j - subnet number, p - number of the router in this subnet. The same

numbering is used for the transmission channels [22, 23].

Considered network consists of m nodes (m = 15), simulated routers interconnected

n branches - paths (n = 19).

To determine the characteristics of network quality MPLS/VPN must be defined:

• the minimum packet delay and length of packet queue for each of the routers (P

and PE) connections and paths in core networks MPLS;

• similar values for each of the routers (RE and LSR) and links of geographically

distributed virtual subnet VPN.

For network MPLS/VPN of high dimension and complex topological structure

appropriate to apply the method of decomposition of the network [5,6]. By decomposition

understand the division of network elements, each of which has the properties of the

system, and further independent research of each of these subsystems [5]. Using the

method of decomposition allows to calculate the original complex network, dividing it into

subnets and get solutions separately for each subnet and each object network, and then

maybe move these solutions to the original network.

37

Fig

ure

4.3

– F

unct

iona

l dia

gram

of

MP

LS/

VP

N n

etw

ork

38

To do this we provide next steps:

1) decompose the network MPLS/VPN to consider separately the supporting core

network and k isolated geographically distributed subnets VPN by removing the PE-CE

connections,

2) calculation of the required characteristics separately for each isolated subnet

VPN,

3) calculation characteristics of connections between subnets with the solutions

obtained for each isolated virtual subnet VPN [5].

To solve the problem using tensor analysis [10.17], which will allow both to

investigate the structural and functional characteristics of the network.

Tensor network simulation MPLS/VPN involves the description of a metric space

[16-18]. To calculate the length of the packet queue and packet transmission delay using

the formula (4.1). Expression (4.1) is invariant equation.

By analogy with the tensor approach proposed by G. Kron and developed in [19-

23], the structure of the network MPLS/VPN is a one-dimensional network consisting of m

nodes, which, in turn, defines a discrete-space. At the same time network branches ,

simulate links of a network and network nodes Nj , – routers.

In the input m-dimensional space, we make the tensor description of the system in

the node network. As informative coordinate system (CS), we introduce the two coordinate

systems. The first - coordinate system of branches, and the second - coordinate system of

node pairs of the network.

Then (4.1) can be written in tensor form in the coordinate systems of branches and

nodes of the network for MPLS/VPN as in (4.2), (4.3):

(4.2')

(4.3’)

where and – twice contravariant tensors of traffic intensity in the

branches and nodes respectively,

, - contravariant tensors of packet queues length in branches and

nodes respectively,

, - covariant tensors of packets delay in the branches and nodes

respectively.

39

The transformation formulas between the coordinate systems are defined according

to the tensor method proposed by G. Kron as in (4.5), (4.7), (4.8) [10,17,19]:

(4.5’)

(4.7’)

(4.9’)

where - packet query length in network nodes,

- basis matrix of a network,

- incoming packet query length,

- traffic intensity in network nodes,

- traffic intensity in network branches,

- packet delay time in branches of MPLS/VPN network,

- packet delay time in nodes of MPLS/VPN network,

t - denotes the transpose of the matrix.

Divide the network MPLS/VPN by removing branches that connect the core

network with virtual subnets VPN. Thus, we obtain an independent subnet - supporting

MPLS core network and geographically distributed subnet VPN. Then, for each of the

resulting isolated subnets may apply nodal tensor calculation method packet delay and the

length of a batch queue in the branches.

For the simultaneous solution of the problem of calculating the characteristics of

network quality MPLS/VPN all virtual subnets define the intensity of the traffic in the

branches in the form of a square matrix n-th order:

,

40

where - diagonal matrix of ji-th order , , on

the main diagonal of which are traffic load in the branches of VPN,

- diagonal matrix of of traffic intensity in the branches of core subnet MPLS,

k – quantity of isolated subnets.

To use nodal tensor method of consideration the original structure of the network

in each geographically distributed subnet VPN and MPLS core network by introducing an

imaginary branches shown in Fig. 4.3 by dashed lines [19].

According to the structural model of the network MPLS/VPN, which includes core

and all geographically distributed virtual subnet, and given directions of transfer form the

basis matrix network profiles :

,

where basis matrix of subnet VPN, , ,

matrix of core network MPLS,

k – quantity of isolated subnets.

To determine the tensor of traffic intensity in the CS of nodal pairs will

use formula (4.7’). It is easy to determine that will take the form of a square matrix

of m-th order.

41

Using (4.5 '), we define the length of packet queues all nodes of the

network MPLS/VPN, represented as a vector:

,

where basis matrix of subnet VPN, , ,

basis matrix of core network MPLS,

- tensor of incoming packet queue length in subnet VPN,

- tensor of incoming packet queue length in core network MPLS,

- tensor of packet queue length in virtual subnetworks VPN,

- tensor of packet queue length in core network MPLS,

k – quantity of isolated subnets.

To calculate the time of packets delay in the nodes of geographically distributed

subnets VPN and MPLS core network, we use the following formula, which comes from

(4.8) and (4.3):

. (4.8’)

As we see from (4.3’) is a vector of order

.

42

,

where - diagonal matrix of traffic intensities in the branches of isolated subnet

VPN,

- diagonal matrix of traffic intensities in the branches of core network

MPLS,

- vector of packets delay time in the nodes of isolated subnets VPN,

,

- vector of packets delay time in the nodes of core network MPLS,

k – quantity of subnets.

According to (4.9'), we define the tensor packet delays in the branches

geographically distributed subnets VPN and core MPLS:

,

where basis matrix of isolated subnet VPN, , ,

basis matrix of core network MPLS,

- vector of packets delay time in the nodes of isolated subnets VPN,

,

- vector of packets delay time in the nodes of core network MPLS,

k – quantity of subnets.

For the calculation of the vector of the packet queue length

in links of the

network, we use formula (4.2 '):

43

,

where

, - vectors of the packets queue length in branches of isolated

networks VPN and MPLS respectively, ,

k – quantity of subnets,

- diagonal matrix of traffic intensities in the branches of isolated subnets

VPN,

- diagonal matrix of traffic intensities in the branches of core network

MPLS,

- vector of packets delay time in the nodes of isolated subnets VPN,

,

- vector of packets delay time in the nodes of core network MPLS.

Determine the value of the minimum of delay and packet length in a batch queue

MPLS core network and for each virtual subnet VPN, get characteristics of all network

elements required for establishing a connection between the VPN, except for connections

PE-CE. For their calculation, consider a network model, in which all geographically

distributed VPN subnet represented as nodes connected to the backbone network

supporting MPLS, also represented as a node, and the connections PE-CE are branches of

the network model. Construct a matrix of basic network cuts, according to Fig. 4.3, the

objects are the connection matrix of all subnets:

,

where basis matrix of network MPLS/VPN, , k – quantity of subnets

VPN .

44

Packet delay values at the nodes are defined as the sum of packet delay on each

subnet. According to (4.8) define the packet delay in subnets:

, (4.10)

where - packet delays in i-th network,

- packet delays in j-th ( ) router of i-th network ( , k –

quantity of subnets VPN),

p – quantity of routers in i-th network.

Similarly to (4.9 ') are calculated values packet delay in connections PE-CE

:

, (4.11)

proceeding to

,

where - packet delays in i-th network VPN,

- packet delays in connection PE-CE of i-th subnet, , k – quantity of

subnets VPN.

Queue length packets in a connection PE-CE in the coordinate system of branches

is defined similarly to (4.2 '):

, (4.12)

proceeding to

45

,

where - traffic load in connections PE-CE,

- packet queue length in connections PE-CE of i-th subnetwork, ,

k – quantity of subnets VPN.

Thus demonstrates the application of a tensor decomposition-based method for

solving problems of performance evaluation of network quality MPLS/VPN. Using the

decomposition method yielded analytically length packet queues (4.2’),

(4.11) and packet delay time (4.9’), (4.12) all subnets of considered

network, the whole network and the most important area in terms of the parameters of the

guaranteed QoS, connections PE-CE.

Having considered the above methodology the solution on a specific example. For

this, consider a network of MPLS/VPN, shown in Fig. 4.3

According to the proposed method we define the input data, namely the intensity

of the traffic in the links in the network (see Table 4.4) and the length of the packet

queues (Table 4.5).

Table 4.4 –Traffic intensity in the network branches

Branch number 1 2 3 4 5 6 7 8 9 10 11

Traffic intensity,

thousands packets/s200 800 0 500 800 400 800 900 400 300 0

Branch number 12 13 14 15 16 17 18 19 20 21 22

Traffic intensity,

thousands packets/s500 600 900 300 0 900 0 600 1200 1300 1400

Table 4.5 – Length of the packet queues

46

Branch number 1 2 3 4 5 6 7 8 9 10

Traffic intensity,

thousands

packets/s

0 0 100 0 0 0 0 0 0 0

Branch number 11 12 13 14 15 16 17 18 19

Traffic intensity,

thousands

packets/s

100 0 0 0 0 100 0 100 0

According to the topology of the network form the basic matrix of nodal pairs,

We aggregate the obtained results in Table 4.6 and Table 4.7.

Table 4.6 – The results of the calculation of packet delay and packet queue lengths

in subnets VPN and core MPLS network

Branch number Packets delays time

, s

Length of packet queue

, thousands packets.

1 0,181 36,364

2 0,068 54,545

Continuation of Table 4.612 2 3

3 0,251 100

4 0,091 45,454

5 0,022 18,181

6 0,159 63,636

7 0,088 71,186

8 0,079 71,186

9 0,072 28,813

10 0,096 28,813

11 0,168 100

12 0,109 54,794

13 0,091 54,794

47

14 0,050 45,205

15 0,150 45,205

16 0,200 1000

17 0,111 100

18 0,277 1000

19 0,166 100

Table 4.7 - Results of calculation of packet delay and packet queue lengths in the

connections PE-CENumber of

PE-CE

Packets delays time

, с

Length of packet queue ,

thousands packets.

0-1 0.166 182.952

0-2 0.045 55.056

0-3 0.068 88.686

The results of the calculation shown in Fig. 4.4.

48

Fig

ure

4.4

–Res

ults

of

MP

LS/

VP

N n

etw

ork

calc

ulat

ion

49

CONCLUSION

In the master's project we have investigated the possibilities of using tensor

methods and decomposition method for solving the problem of determining the

characteristics of the network quality MPLS/VPN with TE/FRR technology.

Demonstrated the practical implementation of the tensor method of traffic

managing in the MPLS-TE/FRR network, the possibility of simultaneous mathematical

modeling of structural properties and functional characteristics with a special way to set

the coordinate system and the invariance of the tensor, which is an invariant value of

traffic at any given time.

The use of tensor models for solving network routing in MPLS-TE/FRR enable

provision of the analytical results of the efficient use of network resources by

organizing TE-tunnel of fast reroute FRR with guaranteed minimum time of packet

delivery. It is shown that in the MPLS-TE/FRR network can be performed optimization

procedures for the most rational use of resources.

Solved the problem of traffic control in MPLS-TE/FRR networks, allowing for

selection of TE-tunnel bypass direction reroute FRR to ensure quality of service

parameters of QoS. Results are obtained values of packet delay and packet lengths of

the queues in the network paths that allow you to perform the selection of reroute TE-

tunnel.

On the basis of the solutions discussed the possibility of assessing the

MPLS/VPN network quality characteristics for which proposed to combine the

mathematical apparatus of tensor analysis and decomposition method.

The use of tensor methods for solving problems of finding quality characteristics

in the MPLS/VPN network will enable provision of the analytical results of the

evaluation packet delays and packet queue lengths for all subnets in the network and in

general.

Application of the decomposition method for MPLS/VPN networks with large-

scale and complex topological structure allows to calculate the results of quality

characteristics separately for each subnet, and then transfer them to the original

network.

On a specific example of the MPLS/VPN network topology and traffic intensity

in the network paths, obtained the values of packet delays and packet queue lengths in

the network links.

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