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6МЕТОД УПРАВЛЕНИЯ ЗАПРОСАМИ К УЗЛАМ БЕСПРОВОДНОЙ СЕТИ С ИСПОЛЬЗОВАНИЕМ МЕТОДА ПОЛЛИНГА
Височиненко М.
Государственное заведение «Киевский колледж связи», Преподаватель,кандидат технических наук
Харлай Л.
Государственное заведение «Киевский колледж связи», преподаватель, председатель комиссии «Информационные сети связи»
Федюнин C.
Государственный университет телекоммуникаций, г. Киев Директор учебно-научного института менеджмента и предпринимательства
Method of management by the hosts requests of wireless network with the use of polling method
Vysochinenko M., Kiev Colledg of Communication, Lecturer, Ph.D.
Kharlay L., Kiev Colledg of Communication Lecturer, Head of the Department «Information communication networks»
Fedyunin S., State University of Telecommunications, Kiev, Director of Training and Research Institute of Management and Entrepreneurship
АННОТАЦИЯ
При оптимизации параметров и структуры телекоммуникационных сетей в состав целевой функции входит большое количество основных и дополнительных параметров, от которых зависит качество сервиса QoS.
Для решения задач текущего управления сетями необходим системный подход. Критерии оптимизации ключевых параметров функционирования сети и текущего управления сетью неоднозначны и противоречивы. Учет этих противоречий и поиск компромиссных решений возможен при использовании статистических методов, согласования достоверности и детального анализа исходных данных с учетом физического смысла решаемых задач.
В этой статье предлагается рассмотреть математическую модель запросов к узлам беспроводной сети с использованием метода поллинга.
ABSTRACT
When optimizing parameters and structure of telecommunication networks of the objective function is a large number of basic and additional parameters that affect the quality of service QoS. To solve the current problems of network management required systematic approach. Criteria optimization of key parameters of the network and the current network management is ambiguous and contradictory. Taking into account these contradictions and the search for compromise solutions possible at the use of statistical methods, harmonization of authenticity and detailed analysis of the initial data, taking into account the physical meaning of tasks. In this article will propose the mathematical model of requests for items broadband wireless network using the method polling.
Ключевые слова: система поллинга, интенсивность потока, нестационарный поток запросов.
Keywords: polling system, the flow rate, the unsteady flow of requests.
Let's review the mathematical model of requesting broadband wireless network elements using polling [1]. Polling system consists of queues to M network elements. Every element receives a random request for data output of certain volume. Request receipt process is permanent and ergodic. Probability, that m element will receive more than one request at the same time, is considered to be the value of second order of smallness [2, 3].
In a servicing time [t,...t, + t] of m element ^ (l ) datasets can be sent. l stands for queue length in moment t.; ^ stands for servicing discipline (cyclic, periodic based on polling table, random law, with priorities). Let's designate the probability of servicing, which makes up k requests for interval t, as pTk.
Let's formulate the conditions, which servicing disciplines should follow.
If there is another request for m element, when queue to the same element already contains lm -1 requests, they should be served by discipline FIFO (first in, first out) or FIFO with priorities. Serviced requests leave the system. Then the request to the next segment moves forward. It is considered that conditions ym (1) = 1 with probability pTl = 1 and (lm )< lm with
probability pm < 1 are always executed.
May X stand for average request rate on the observation
interval, ^ stand for average request servicing rate, and pm stand for probability of request to hit the m element.
X 1
If
Т V
m m
< 1
the queue length decreases;
if
1
Pm,
X| —h max-Ц M TmV„
= 1
stationary value;
the queue length converges to the
X
if
1 pm
— + max m Ц M TmV„
> 1
the queue length in system increases to the infinite value so that queue will be filled.
In the last event the loss of requests may occur and then repeated request should be organized. v here stands for average amount of requests incoming to the m element on the observation interval.
Let's review the problem of queue length characteristic by non-stationary request rate. It is commonly known [4, 5], that
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in such case conditions of ordinariness and after-effect absence are applied to the wide range of conditions. At the same time assumption concerning stationary is doubtful and obviously wrong.
Typical example of such process in informational and telecommunication networks is Triple Play traffic (voice, video and data) and Quadro Play traffic (voice, video, data and mobile subscribers). Traffic becomes more self-similar [4]: by general low (in average) rate on separate short-time observation intervals bursts of momentary traffic rate occur, that can exceed continuous average rate by a huge ratio.
To ensure stationary (or similar) support mode of queue length by non-stationary request rate we have developed the modified polling method with feedback, which parameters are determined not only by consequences of analysing value of general buffer volume flow, as well as by flow speed. We reviewed comprehensive, gateway and l-restricted servicing disciplines (detailed determination and classification of servicing disciplines are provided in the work [6]). Model of polling system with periodical inquiry of station nodes is developed in the work [1]. Model structure is represented on fig 1.1.
Fig 1.1: model of polling system with periodical inquiry and restricted comprehensive servicing, and feedback by speed of
buffer flow.
Servicing system is asymmetrical. Signal and management information is received with delays, which in general are different for every serviced element. Such model is described using system of differential-difference equations (equations with rejected argument [7, 8]).
To simplify the problem and obtaining of asymptotic values let's suppose, that management system can be described using linear differential equations with constant coefficients on observation interval and accuracy acceptable for this object:
yL (t) = byasi (t - t,) + u (t -v,) + (t)
(1.1)
interval At equal to packages incoming period Tp to the management system. Incoming packages contain information about network parameters and status. In general the delay of control signals is not equal to the delay of informational signals.
The equation (1.2) for normalized elementary interval
At/Tp=1 will be of such form:
ysi (n)~ (n-1) + (n — k) + u (n— m), n = 0,1,2,3,... (13)
If we will execute z-transformation (1.3), we will get expression for system function of discipline parameters management system for servicing of station nodes:
It is considered [8], that method of approximation of differential equations using difference equation is especially efficient for equations with rejected argument.
Let's write difference equation with first-order differences for initial equation (1.1) without additive noise in observations:
^-At} ^(f-+ u,(t-mAt)
where At stands for elementary interval, kAt=x. stands for delay of information concerning object status, mAt=v, stands for delay of control signal.
In this problem it is reasonable to make the elementary
h ( z )
z
1 - z"1 - b
(1.4)
As a result if polling system with feedback by speed for organization of requests in network is used, stationary mode for support of queue length can be applied by non-stationary request rate as well.
In this work the mathematical model of requests for items broadband wireless network using the method polling. To ensure patient (or close to it) exposure mode queue length at unsteady flow of requests in Article polling proposed a
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modified method of feedback parameters are determined not only by the results of the analysis of the completed value of the total volume of buffer, but the rate of filling.
Considered comprehensive, gateway and l-limited discipline Service (detailed definition and classification of subjects in the maintenance data. Also work the model polling periodic survey of terminal nodes.
Literature
1. Vysochynenko M.S. / Vysochynenko M.S., Khalimon N.F. (April 22-25, 2014), Upravlenie zaprosami k stantsiyam besprovodnoy seti [Management of requesting wireless network stations], 8th International Scientific-Technical Conference "Problems of telecommunications", National Technical University of Ukraine "Kyiv Polytechnic Institute", p. 28.
2. Toroshanko Ya.I. / Toroshanko Ya.I., Hrushevska V.P., Shmatko V.S., Vysochynenko M.S. (2014), Klyuchovi parametry efektyvnosti bezprovodovykh telekomunikatsiynykh merezh ta metody yikh identifikatsiyi [Main efficiency parameters of wireless telecommunication networks and their identification methods], Scientific notes of Ukrainian research institute of communication, No. 4 (32)
3. Vysochynenko M.S. (2015), Upravlenie zaprosami s pereklyucheniyami k stantsiyam besprovodnoy seti [Request management with switch to wireless network stations], Telecommunication and informational technologies, No. 1, pp. 73-76.
4. Stallings W., High-speed networks and internets: performance and quality of service. - New York, NY. - Prentice Hall, 2002. - 715 pp.
5. Hnedenko B.V. / Hnedenko B.V., Kovalenko I.N. (1987), Vvedenie v teoriyu massovoho obsluzhivaniya [Fundamentals of mass service theory], Nauka, 336 pp.
6. Vyshnevskyi V.M. / Vyshnevskyi V.M., Lyakhov A.I., Portnoy S.L., Shakhnovych I.V. (2005), Shyrokopolosnye besprovodnye seti peredachi informatsii [Broadband networks for information transfer], Moscow, Tekhnosfera, 592 pp.
7. Elsholz L.Ye. / Elsholz L.Ye., Norkin S.B. (1971), Vvedenie v teoriyu differentsialnykh uravneniy s otklonyayushchim argumentom [Fundamentals of theory on differential equations with rejected argument], Moscow, Nauka, 296 pp.
8. Bellman R. / Bellman R., Kuk. K. (1967), Differentsialno-raznostnyye uravneniya [Differential-difference equations], Moscow, Mir, 548 pp.
