# UTILIZATION OF 1st ERLANG FORMULA IN ASYNCHRONOUS NETWORKS

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1 Journal of ELECTRICAL ENGINEERING, VOL. 58, NO. 6, 2007, COMMUNICATIONS UTILIZATION OF 1st ERLANG FORMULA IN ASYNCHRONOUS NETWORKS Erik Chromý Ivan aroňák This paper emphasizes a possibility for the utilization the 1st Erlang formula in asynchronous networks. This statement is possible on the basis of research of statistical features of traffic source input flow. We consider ATM network type where in the case of VP important parameters are as follows: loss -, link utilization - ρ and bandwidth - c. The evidence for utilization the 1st Erlang formula in asynchronous networks is achieved through the model of video source traffic. To design the video source traffic discreet Markov chain has been used. K e y w o r d s: ATM, 1st Erlang formula, Markov model, video source model 1 INTRODUCTION It is obvious that with help of the 1st Erlang formula, where such parameters as loss -, link utilization - ρ and bandwidth - c are used, we are able to describe the traffic in synchronous networks. On the other hand, to describe the traffic in asynchronous networks of ATM network type the Markov chains [1, 2, 9, 11] are often used. Their disadvantage is that they are very complicated and at the same time demand complicated estimations. Papers [3, 4] deal with the idea of utilization ot the 1st Erlang formula. As in the case of ATM networks, the optical fibre is used as a transmission medium, it is possible to consider ATM networks to be networks with low losses. The networks with low losses are characterized by the 1st Erlang formula which expresses the connection loss probability in virtual path VP [5, 6]. The question if the utilization of the 1st Erlang formula is possible in asynchronous networks. In this paper we give some evidence while utilizing this formula in asynchronous networks c ρ c c! k=0 ρ k k! =, (1) where ρ represents the percentage utilization of a link, c - is the bandwidth and - is the link loss. 2 SEARCH FOR, ρ, C RELATIONS The aim is to estimate the relations between, ρ, c parameters on the basis of (1) formula in such a manner that always one parameter is kept constant and the dependence between remaining two parameters is observed. 2.1 Link utilization and bandwidth at constant loss Dependence of the link utilization ρ on bandwidth c at a given loss is shown Fig. 1 and Tab. 1. From the figure it can be seen that with the increasing bandwidth it is possible to increase the link utilization while that loss can be preserved. The narrower the loss requirement (ie parameter gets smaller value), the less link utilization is possible. Fig. 1. Dependence of link utilization on bandwidth at given loss Table 1. Data for Fig. 1 = 10% = 5% c ρ c ρ (Mbit/s) (%) (Mbit/s) (%) Slovak University of Technology, Faculty of Electrical Engineering and Information Technology, Department of Telecommunications, Ilkovičova 3, ratislava, Slovakia; ISSN c 2007 FEI STU

5 346 E. Chromý I. aroňák: UTILIZATION OF 1st ERLANG FORMULA IN ASYNCHRONOUS NETWORKS [3] FERNANDEZ, J. MUTKA, M.: A urst-oriented Traffic Control Framework for ATM Networks, Proceedings of the 4th International Conference on Computer Communications and Networks (1994), [4] CROCETTI, P. : Free andwidth for the Transport of Connectionless Traffic Generated by Web Interactive Multimedia Applications and Services, ITALTEL Central Research Labs, Milan, April, [5] CHMELÍKOVÁ, Z.: Methods for Sizing ATM Networks (Metódy dimenzovania ATM sietí), Presented at 2-nd Seminar of EaTT in Ostrava, Czech Republic, November, (in Slovak) [6] CHMELÍKOVÁ, Z. : Analysis of Present Sizing Methods (Analý za súčasných metód dimenzovania), Presented at 2-nd Seminar of EaTT in Ostrava, Czech Republic, November, (in Slovak) [7] Video Traces for Network Performance Evaluation, Arizona State University, [8] ROSE, O.: Traffic Modeling of Variable it Rate MPEG Video and its Impacts on ATM Networks, ayerische Julius-MaximiliansUnversitat Wurzburg, [9] SCOTT, S. SMYTH, P.: The Markov Modulated Poisson Process and Markov Poisson Cascade with Applications to Web Traffic Modeling. ayesian statistics 7, Oxford University Press, [10] CSELÉNYI, I. MOLNÁR, S.: VR Video Source Characterization and a Practical Hierarchical Model. Telecommunication Systems, [11] LIU, H. ANSARI, N.: Modeling MPEG Coded Video Traffic by Markov-Modulated Self-Similar Processes, Journal of VLSI Signal Processing Systems 29 No. August-September (2001), [12] SIMPSON, W. : Video Over IP: A Practical Guide to Technology and Applications. Focal Press, Received 15 January 2007 Erik Chromý (Ing) was born in Vel ký Krtíš, Slovakia, in He received the engineering degree in telecommunications in 2005 from the Faculty of Electrical Engineering and Information Technology of Slovak University of Technology (FEI STU) ratislava. In 2007 he submitted PhD work from on observation of statistical properties of the input flow of traffic sources on virtual paths dimensioning, his scientific research is focused on optimizing of the processes in convergent networks. Ivan aroňák (Prof, Ing, PhD) was born in Žilina, Slovakia, on July He received the electronic engineering degree from the Slovak Technical University ratislava in Since 1981 he has been a lecturer at Department of Telecommunications STU ratislava. In 1992 he submitted PhD work from the field of Terminal telephone equipment. In 1995 he became an Associate Professor for the subject applied information. Nowadays he works as a full Professor in the Department of Telecommunications of FEI STU in ratislava. Scientifically, professionally and pedagogically he focuses on problems of digital switching systems, ATM, telecommunication management (TMN), next generation networks, problems of optimal modelling of private telecommunication networks and services. of periodicals and of non-periodically printed matters, book s and CD - ROM s SLOVART G.T.G. s.r.o. GmbH Krupinská 4 PO OX 152, ratislava 5,Slovakia tel.: , fax.: SLOVART G.T.G. s.r.o. GmbH

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