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PERSPECTIVE APPROACH TO DRAW UP ROUTING TABLES
OF SELF-SIMILAR TELECOMMUNICATION TRAFFIC IN IP NETWORKS BY SUPPLEMENTARY ROUTE WEIGHING
USING HURST EXPONENT
Anatoli N. Martianov,
Military Academy of Strategic Missile Forces of Peter the Great,
Moscow, Russia
Valeriy I. Volokhov,
Military Academy of Strategic Missile Forces of Peter the Great,
Moscow, Russia, [email protected] Keywords: frnctd, selfsimti^ty, Hurst,
telecommunications, connection, DTN
Pavel Yu. Belov, (data transmission network), resource reservation,
Moscow University named after Witte, Moscow, Russia pi-ovidmg of QoS (Quality of ^rvke^ i-outing,
engineering.
Modern principles of operation of routing protocols in IP networks are based on selection of the shortest route using topology and rarely on the information about the current congestion. Rather weak use of routing protocols which take the current traffic load into account is caused by the necessity of constant collection of data on channel occupancy using feedback. Due to the strong dynamics of change of conditions it requires allocation of supplementary capacity resources to timely update the data on the channel congestion. This approach doesn't allow routers to quickly update the routing tables, especially referring to those network segments, where congestion had already appeared, and the information about it comes with a delay as well. One more significant disadvantage of use of current congestion as metrics in determining the optimal route is the fact that in case of a strong bursty traffic methods of providing the Quality of Service (QoS) will be unable to maintain the level of delay, variations (of root-mean-square deviation) of delay and probability of refusal in service at a required level. Currently the existing models and methods do not fully take the heterogeneity of data (provided service), i.e. complexity and clustered structure of traffic into account.
Operation of modern information resources in conditions of strong variability can be compared with chaos. It is stated today that chaos is not only a stage of full disorganization and disintegration of a structure, process or phenomenon, but also a necessary condition of process genesis. In other words, chaos is a potential source of evolution of complex and more organized system. Chaos can bring the order under the influence of minor impact in bifurcation point. Transition to determined chaos in non-linear dynamic process is connected with bifurcation, and reverse transition to order - with strange attractors which represent fractals. Studying fractals, especially random ones allows to discover the patterns in random processes, inaccessible for traditional methods.
Information about authors:
Anatoli N. Martianov, Military Academy of Strategic Missile Forces of Peter the Great (VA Strategic Missile Forces of Peter the Great), Doctor
of Engineering, professor, Moscow, Russia
Valeriy I. Volokhov, Military Academy of Strategic Missile Forces of Peter the Great (VA Strategic Missile Forces of Peter the Great), senior
researcher, Ph.D, Moscow, Russia
Pavel Yu. Belov, Moscow University named after Witte, associate Professor of mathematics and computer science, Ph.D, Moscow, Russia
Для цитирования:
Мартьянов А.Н., Волохов В.И., Белов П.Ю. Перспективный подход к составлению таблиц маршрутизации самоподобного телекоммуникационного трафика в IP сетях путем дополнительного взвешивания маршрута по показателю Харста // T-Comm: Телекоммуникации и транспорт. 2017. Том 11. №5. С. 70-73.
For citation:
Martianov A.N., Volokhov V.I., Belov P.Yu. (2017). Perspective approach to draw up routing tables of self-similar telecommunication traffic in IP networks by supplementary route weighing using Hurst exponent. T-Comm, vol. 11, no.5, pр. 70-73.
L Setting the task
Operation of modem information resources in conditions of strong viiriability can be compared with chaos. It is stated today that chaos is not only a stage of full disorganization and disintegration of a structure, process or phenomenon, hut also a necessary condition of process genesis. In other words, chaos is a potential source of evolution of complex and more organized system. Chaos can bring the order under the influence of minor impact in bifurcation point.
Transition to determined chaos in non-linear dynamic process is connected with bifurcation, and reverse transition to order -with strange attractors which represent fractals.
Studying fractals, especially random ones allows to discover the patterns in random processes, inaccessible for traditional methods.
Network traffic fall into the category of self-similar stochastic fractals llj. In the data transmission networks most of measured traffic routes possess the properties of stochastic self-similarity (fractality). In that case a type of traffic with corresponding amplitude norming is taken as a measure of similarity.
The essence of self-similarity depends on the presence of a certain pattern in a time sequence, independently from degree of its resolution. Strong influence on behavior of succession, caused by the phenomenon of self-similarity in data transmission networks, brings an urgent necessity of studying methods of its use to optimize these systems. Self-similarity (scaling) represents invariance in relation to the change of scale or size. In the world around us the phenomenon of self-similarity can be encountered everywhere, and in fact is the main type of symmetry, on the basis of which the universe if formed.
The subject, containing the property of self-similarity, behaves similarly or looks similarly in case of its examination from different scales. A value subject to scaling can be time, a result of geometric measuring or a process. Telecommunication traffic represents an object displaying the property of self-similarity in relation to the scale of time.
Thus, the task of engineering the algorithms of routing, able to take the bursty structure of telecommunication traffic into account.
2. Solution of the task
In order to provide the Quality of Service of self-similar telecommunication traffic by the router with use of feedback it is necessary to transmit the control data, which take its fractality into account, across the network. Such modification of control and signal data allows to increase the quality of work of used algorithms of routing.
In order to estimate self-similarity of telecommunication traffic it is more convenient to use Hurst exponent. It characterizes the "degree" of self-similarity of telecommunication process.
The equation [2| works for enumerative characters of stochastic process with continuous time.
<7:[.V(0] =
,2«
x(t) = aH x{at), a> 0-
(1)
It follows from the equation (1) that the equations [3] work for mathematical expectation, dispersion and autocorrelation function of initial and scaled process with coefficient a:
M[x(t)] =
M[x{at)].
(3)
(4)
It is known that [2j value of Hurst exponent for self-similar process is within the limits of 0,5 <//<!■ At that value H <0,5 shows the absence of self-similarity of the process, and values of H (close to 1) show higher degree of self-similarity or long-range dependence (LRD) in the process. It means that if LRD process has a tendency to decrease (or increase) in the past, there is a great probability for it to tend to decrease (or increase) in the future.
The example of stochastic self-similar process is the process of standard Brownian motion. In that case self-similarity is characterized with value H =0,5-
in case of practical realization on electronic digital computer it is convenient to examine discrete in time stochastic processes {x„f = 0,1,2,3,...}. Let's examine the combined temporal series {X = A^"'), k =0,1,2,3,...} and divide them into non-overlapping blocks with size m
] k/n
(5)
xt ^ Xi m i=km-(m-\)
The received aggregation of the process x(t) on time intervals can be examined as a compression of time scale. If the statistical characteristics in different scales of compression remain, while performing averaging on each of the aggregated intervals, the process can be considered as self-similar. One of the signs of self-similarity of stochastic process with discrete time is a tendency of much slower dispersion to zero. Poisson distribution by-increasing the sample size.
Long-range dependence is the main cause of appearing of network traffic congestion. The presence of long-range dependence comes from the behavior of autocovariance function C(r)
for stationary process as a result of increasing time step-out r ■
A distinctive feature of a self-similar process in comparison with Poisson process is that during Poisson process function of autocovariance decreases with a speed close to the speed of exponent decay. As for self-similar process - function of autocovariance decrease much slower - hyperbolically. Long-range dependence shows inertia of self-similar process, instability of characteristics in all scales of time and presence of clustering.
Another notion which has a close connection with self-similarity is, so called, distributions with "heavy tails" or slowly lading distributions. The random value, which has a slowly fading dispersion possess unlimited value of dispersion, and sometimes unlimited mathematical expectation. Function of distribution of random variable X fades slowly if the condition [3, 4] is satisfied:
1
(6)
(2)
>*]- — • -v —> =o,0 < or,
where: P\_X > Jt] - probability of the event X>x~, F(x) ~
function of distribution.
The main idea of the offered approach is to transmit in addition to the data on congestion and current load the value of Hurst exponent for each type of traffic to a router via feedback chan-
T-Comm Vol.11. #5-2017
7T>
nels. In order to achieve this objective a method of determination of Hurst exponent value of combined sources of telecommunication traffic is used [4].
The developed approach to routing of self-similar telecommunication traffic using feedback includes the following sequence of steps:
Step 1. Determination of current traffic stationarity value in the examined node (data transmission channel).
Step 2. The comparison of current stationarity coefficient with the value, received during the last check.
Step 3. In case of change of stationarity coefficient - the determination of current Hurst exponent of each type of traffic for each source in the switching node. In order to determine the Hurst exponent in the given step, the collection of traffic data from each source and its subsequent analysis with splitting to the quality grade are performed [4, 5],
Step 4. Determination of resulting Hurst exponent for all types of traffic, including the switching node (transmission channel). In this step Hurst exponent general for all traffic for each type of priority separately is determined.
Step 5. Sending the data on the current Hurst exponent to the closest routers for them to form the routing tables.
Step 6. Forming the routing tables taking the Hurst exponent into account. Selection of the route not by criterion of less load, but by taking Hurst exponent into account.
In order to weigh the route it is offered to use analytic model of self-similar flow based on fractional Brownian motion [6]. While receiving the calculation the assumption of buffer infinity in constant time of service was used. According to this work, in case of satisfying certain assumptions, the dependence of the required buffer size q on the average coefficient of use of p is
described by the following law:
i-e^r- <7)
(1-pY "
When // =0,5 formula (7) takes the following form:
q=-£— (8)
1 ~P
Formula (8) describes classical system of mass service of M/M/1 type, and in case of constant time of service - M/D/l formula takes the form of:
___(9)
l-p 2(1 -p)
In Figure I the results of work of the mode! for H— 0,9 and H =0,75 and for models M/M/1, M/D/l (7,9).
it can be concludcd from the charts that in case of presence of long-range dependence in the law of receipt of data packet the
necessity in buffer ¡n comparison to M/M/1 and M/D/l rise sharply.
ca S
Fig. 1. Work of the router in different models of traffic service
Thus, the task of determining the optimal route of IP packets reduces to minimization of probable queue length.
3. Conclusions
The use of the described approach to routing of telecommunication traffic, which possesses the property of self-similarity, allows to avoid unpredictable congestions due to underestimation of bursty stnicture.
The use of mechanism of updating of exponents of transmission channel self-similarity only as a result of change of telecommunication traffic stationarity allows to avoid the appearing of significant network congestion via feedback channels.
1. Shelukhin O.I. (2011 ). Multifractals. Infocommunicative applications. Moscow: Hoi line - Telecom, 576 p.
2. Shelukhin O.I. Tenyakshev A.M., Osin A.V. (2003). Fractal processes in telecommunications. Moscow: Radio technology, 480 p.
3. Shelukhin O.I., Tenyakshev A.V., Osin A.V, (2005). Information systems modeling. Moscow: Science-Press. 368 p.
4. Nazarov A.N., Sychev K.I. (2010). Models and methods of calculation of quality indices of operation of nodal equipment and structure-network parameters of next generation networks, Krasnoyarsk: Publisher LLC «Politcom». 231 p.
5. Polous A.!., Mikryukov A.A., Belov P,Y. (2014). Optimization of telecommunication traffic characteristics. Digest of 26th all-Russian science-practice conference in Krasnodar - Terskot. "Transmission, processing, display of information ".
6. Sychev K.I., Mikhalevich I.E. (2003). Models of moss service systems in practical tasks of mobile communication systems analysis. Orel: FAPSI. 211 p.
References
СВЯЗЬ
ПЕРСПЕКТИВНЫЙ ПОДХОД К СОСТАВЛЕНИЮ ТАБЛИЦ МАРШРУТИЗАЦИИ САМОПОДОБНОГО ТЕЛЕКОММУНИКАЦИОННОГО ТРАФИКА В № СЕТЯХ ПУТЕМ ДОПОЛНИТЕЛЬНОГО ВЗВЕШИВАНИЯ МАРШРУТА ПО ПОКАЗАТЕЛЮ ХАРСТА
Мартьянов Анатолий Николаевич, ВА РВСН им. Петра Великого, Московская область, Россия Волохов Валерий Иванович, ВА РВСН им. Петра Великого, Московская область, Россия,
[email protected] Белов Павел Юрьевич, Московский Университет имени С.Ю. Витте, Москва, Россия
Aннотация
В настоящее время существующие модели и методы не в полной мере учитывают разнородность передаваемой информации (предоставляемых услуг), т.е. многокомпонентность и пачечную структуру трафика. Функционирование современных информационных ресурсов в условиях сильной изменчивости можно сравнить с хаосом. Сегодня установлено, что хаос - это не только стадия полной дезорганизации и разрушения структуры, процесса, явления, но и необходимое условие для зарождения нового процесса. Иначе, хаос это потенциальный источник развития сложной и более организованной системы. Из хаоса может возникнуть порядок под влиянием малых воздействий в точке бифуркации.
Переход к детерминированному хаосу в нелинейных динамических процессах связан с бифуркацией, а обратный переход к порядку - со странными аттракторами которые представляют собой фракталы.
Изучение фракталов, особенно случайных позволяет выявить такие закономерности в случайных процессах, которые традиционным методам недоступны.
Ключевые слова: фрактал, самоподобность, Харст, телекоммуникации, связь, СПД (сети передачи данных), резервирование ресурсов, обеспечение качества обслуживания, маршрутизация, инжиниринг.
Литература
1. Шелухин О.И. Мультифракталы. Инфокоммуникационные приложения. М.: Горячая линия - Телеком, 2011. 576 с.
2. Шелухин О.И., Тенякшев А.М., Осин А.В. Фрактальные процессы в телекоммуникациях. Монография / Под ред. О.И. Шелухина. М.: Радиотехника, 2003. 480 с.
3. Шелухин О.И., Тенякшев А.В., Осин А.В. Моделирование информационных систем / Под ред. О.И. Шелухина. М.: Сайнс-Пресс, 2005. 368 с.
4. Назаров А.Н., Сычев К.И. Модели и методы расчета показателей качества функционирования узлового оборудования и структурно-сетевых параметров сетей связи следующего поколения. Красноярск: Изд-во ООО "Поликом", 2010. 231 с.
5. Полоус А.И., Микрюков А.А., Белов П.Ю. Оптимизация характеристик телекоммуникационного трафика. Сборник материалов 26-й всероссийской научно-практической конференции. Краснодар - пос. Терскол, "Передача, обработка, отображение информации", 2014.
6. Сычев К.И., Михалевич И.Ф. Модели систем массового обслуживания в практических задачах анализа систем мобильной связи. Орел: Академия ФАПСИ, 2003. 211 с.
Информация об авторах:
Мартьянов Анатолий Николаевич, ВА РВСН им. Петра Великого, профессор, д.т.н., Московская область, Россия Волохов Валерий Иванович, ВА РВСН им. Петра Великого, старший научный сотрудник, к.в.н., Московская область, Россия Белов Павел Юрьевич, Московский Университет имени С.Ю. Витте, доцент кафедры математики и информатики, к.т.н., Москва, Россия
T-Comm Vol.11. #5-2017
