# Odessa National Academy of Telecommunications named after O.S. Popov, Odessa 2

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3 Системи обробки інформації, 015, випуск 1 (137) ISSN known from the classical teletraffic theory. However, for solving the LTE RAN and EPC network capacity design problems is necessary to find expressions which bind traffic parameters with probabilistic and temporal parameters of service requests. In modeling of traffic in the network is often used such laws as the Pareto distribution, Weibull, Gamma distribution or logo-normal. Among the most commonly used law is the Pareto distribution. This distribution is characterized by the parameter. If 1 < <, then this distribution has a "heavy tail" and has infinite variance. In this case, the dispersion index approaches infinity. However, in actual LTE EPC networks intervals between packets and the duration of processing on servers are limited. In this article we propose to use a limited distribution that allows not changing the shape of the "tail" (that adequately simulate the property of self-similarity) indicates the maximum interval between packets and duration of the processing request in the server. It provides limited value of dispersion index. The coefficient of dispersion in the case of restrictions of a Pareto distribution can be defined as 1 L k Lk L k Lk L k L k L k 1 L k, (1) where L and k respectively, the maximum and minimum possible value of the length of time intervals. If the packet arrival process is different from the Poisson and the distribution of service time - from the exponential (type system G/G/m), you can use the results of the theory of diffusion approximation [6]. The mean number of packets in the queue N q and the mean delay in the G/G/m can be defined as [7]: in out Nq P(,m) 1 w s, (), (3) s in out w P,m m(1 ) where s packet servicing mean time;, (4) w packet average waiting time in a queue; in, out squared dispersion coefficients, respectively, for the distribution of the interval between the packet arrival and time of servicing for G/G/m. In [7 10] for the calculation of packet loss probability in the G/G/1/l queuing systems with known distributions laws for input traffic and servicing time, proposed to use the following approximate formula obtained based on the diffusion theory P in out where buffer size; system utilisation. in out, (5) As you can see from (5), the magnitude of losses in the system depends on the coefficient of variation, seen as the main characteristics of the flow and service process. Let us consider some special cases. So for the system M/M/1, assuming that the interval between the packet arrival and packets servicing time is exponentially distributed, dispersion coefficients in 1 and out 1 and expression (5) degenerates to the known classical theory of teletraffic result 1 P 1 1. (6) Another possibility is when the server receives the flow of requests that can be described by a Poisson process, and the processing time is not distributed exponentially. This case can be viewed as a queuing system M/G/1. Accordingly, the formula Poliachek-Khinchin, the mean number of requests in the system can be determined [8] as N 1 out 1. (7) Using (7), with the use the formula Little obtain an expression to determine the mean residence time packet in the system, described by model M/G/1 s 1 out s 1. (8) Thus, the above expression () (8) allows the use of parameters that describe the parameters of individual sources to determine the basic quality of service parameters such as the probability of loss and average delay time. Analysis of the results of analytical modeling Let us analyze proposed models in the article and compare the values of the parameters of quality of service traffic in the network nodes. 14

4 Інфокомунікаційні системи At the beginning we investigate the packets delay in node for traffic which has interval between packets and processing time in the node described by Pareto distributions (model P/P/1). Results of research as a plot waiting time vs. node utilization for various values L, and for M/M/1 model shown in fig., a. Analysis of the results indicated that the traffic model described by P/P/1 has greater delay value than in the case of the M/M/1 traffic. In addition, when increasing the value of L, then increases waiting time in the node. Next, we make a comparative analysis of packet delay in the network node in the case of traffic that describes different distributions of service time in the node network. Results of research as a plot waiting time vs. node utilization for such processing time distribution as the lognormal, Pareto, Weibull, as well as the model M/M/1 shown in fig., b. Analysis of the results shows that the maximum delay is exposed traffic with logo-normal distribution of the service time. Traffic Weibull distribution is less important than the delay in the case of a Pareto distribution. The minimum delay for the case of traffic will be described by the model M/M/1. w , 0,4 0,6 0, a 0 0 0, 0,4 0,6 0,8 1 b Fig.. Mean waiting time for different traffic types Next, we make a comparative analysis of packet drop probability in the network node in the case of traffic that describes different distributions of service time in the node network. Results of research as a plot packet drop probability vs. node utilization for such processing time distribution as the lognormal, Pareto, Weibull, as well as the model M/M/1 shown in fig. 3. Fig. 3. Packet drop probability for different traffic types The experimental results are similar to the previous one case. So the maximum packet drop probability will be in case then traffic has logonormal distribution of processing time. Traffic with Weibull distribution has a lower packet drop probability than in the case of the Pareto distribution. The minimum packet drop probability in the case of traffic which described by M/M/1 model. Conclusion To maintain its competitive edge in the world of mobile networks in the future, 3GPP has initiated work on LTE. LTE is a packet optimized radio access technology with low latency and large bandwidths. Essential to ensure the effective functioning of EPS (including LTE RAN) is efficiency of network planning. Modern research effort traffic in telecommunication network show that its statistical characteristics are different from those adopted in the classical queuing theory. Recent studies of the properties of traffic in moderm networks have shown that the use of models of self-similar processes can more accurately describe the traffic transmitted in these networks. Network performance degrades gradually with increasing self-similarity. The more self-similar the traffic, the longer the queue size. 143

5 Системи обробки інформації, 015, випуск 1 (137) ISSN An important task in parametric synthesis of telecommunications network such as EPS network is to determine QoS parameters when traffic processed on EPS network nodes. In this paper, presented mathematical models for the calculation of QoS parameters such as delay and loss probability taking into account properties of selfsimilar traffic. Estimates of the probability of losses and delays for systems G/G/1 derived from the diffusion approximation can be considered adequate process models to EPS. These studies are an important part of the planning method for LTE and EPS networks, which will be considered in our future research. Reference 1. Li Z. LTE Network Planning Based on Game Theory / Z. Li, S. Li // International Conference on Computer Science and Service System (CSSS) Р Aydin M. Multiuser Scheduling on the LTE Downlink with Simulated Annealing / M. Aydin, R. Kwan, J. Wu, J. Zhang // 73rd IEEE Vehicular Technology Conference, 011. P Gu J. A Novel Traffic Capacity Planning Methodology for LTE Radio Network Dimensioning / J. Gu, Y. Ruan, X. Chen, C. Wang // IET International Conference on Communication Technology and Application (ICCTA 011) Р Leland W.E. On the Self-Similar Nature of Ethernet Traffic (Extended Version) / W.E. Leland, M.S. Taqqu, W. Willinger, D.V. Wilson // IEEE/ACM Trans, on Networking Vol., Issue 1. P Paxson V. Wide-Area Traffic: The Failure of Poisson Modeling / V. Paxson, S. Floyd // Proc. ACM Sigcomm, London, UK С Зелигер Н. Проектирование сетей и систем передачи дискретных сообщений / Н. Зелигер, О. Чугреев, Г.Г. Яновский. М.: Радио и связь, с. 7. Нейман В. Новое направление в теории телетрафика / В. Нейман // Электросвязь С Bashforth B.N. Statistical Multiplexing of Self-Similar Video Streams: Simulation Study and Performance Results / B.N. Bashforth, C. Williamson // Proceedings of the 6th International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS'98) P Галкин А.М. Анализ характеристик сетей NGN с учетом свойств самоподобия трафика / А.М. Галкин, О.А. Симонина, Г.Г. Яновский // Электросвязь С Лосев Ю.И. Анализ моделей вероятности потери пакетов в буфере маршрутизатора с учетом фрактальности трафика / Ю.И. Лосев, К.М. Руккас // Вестник Харк. нац. ун-та, Сер. Математическое моделирование. Информационные технологии. Автоматизированные системы управления С Надійшла до редколегії Рецензент: д-р техн. наук, проф. О.О. Можаєв, Національний технічний університет «Харківський політехнічний інститут», Харків. МОДЕЛЮВАННЯ LTE EPS З САМОПОДІБНИМ ТРАФІКОМ ДЛЯ АНАЛІЗУ ПРОДУКТИВНОСТІ МЕРЕЖІ Намір Касім, Алі Аль-Ансарі, Моат Талат Рамадан Салах Важливим завданням під час параметричного синтезу телекомунікаційних мереж, таких як EPS мережі є визначення параметрів QoS, під час обробки трафіку мережними вузлами EPS. У даній статті, представлені математичні моделі для розрахунку параметрів QoS. таких як затримка і ймовірність втрат з урахуванням властивостей самоподібного трафіку. Це моделювання ґрунтується на застосуванні моделі Р/Р/1 з функцією розподілу Парето для інтервалів між пакетами і часу обробки, для випадку, коли інтервали між пакетами і тривалості обробки на серверах обмежені. Проведено зіставлення запропонованої моделі з іншими моделями систем масового обслуговування, яки описуються логнормальним і Вейбулла розподілами часу обробки пакетів і моделлю M/M/1. Ключові слова: LTE, EPS, модель, самоподібний трафік, затримка, ймовірність втрат, QoS. МОДЕЛИРОВАНИЕ LTE EPS С САМОПОДОБНЫМ ТРАФИКОМ ДЛЯ АНАЛИЗА ПРОИЗВОДИТЕЛЬНОСТИ СЕТИ Намир Касим, Али Аль-Ансари, Моат Талат Рамадан Салах Важной задачей при параметрическом синтезе телекоммуникационных сетей, таких как EPS сети является определение параметров QoS, во время обработки трафика сетевыми узлами EPS. В данной статье, представлены математические модели для расчета параметров QoS. такие как задержка и вероятность потерь с учетом свойств самоподобного трафика. Это моделирование основывается на применении модели Р/Р/1 с функцией распределения Парето для интервалов между пакетами и времени обработки, для случая, когда интервалы между пакетами и продолжительности обработки на серверах ограничены. Проведено сопоставление предложенной модели с другими моделями систем массового обслуживания, описываемыми лог-нормальным и Вейбулла распределениями времени обработки пакетов и моделью M/M/1. Ключевые слова: LTE, EPS, модель, самоподобный трафик, задержка, вероятность потерь, QoS. 144

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