Network Planning Aspects for 3G/4G Mobile Systems

Transcription

1 Julkaisu 545 Publiation 545 Andrey Krendzel Network Planning Aspets for 3G/4G Mobile Systems Tampere 2005

2 Tampereen teknillinen yliopisto. Julkaisu 545 Tampere University of Tehnology. Publiation 545 Andrey Krendzel Network Planning Aspets for 3G/4G Mobile Systems Thesis for the degree of Dotor of Tehnology to be presented with due permission for publi examination and ritiism in Tietotalo Building, Auditorium TB09, at Tampere University of Tehnology, on the 23rd of September 2005, at 2 noon. Tampereen teknillinen yliopisto - Tampere University of Tehnology Tampere 2005

3 ISBN (printed) ISBN (PDF) ISSN

4 ABSTRACT The thesis Network Planning Aspets for 3G/4G Mobile Systems is foused on two topis. The first part of the researh is mainly devoted to Core Network (CN) planning aspets for the third generation (3G) wireless systems. This is beause of the fat that a large diversity of 3G servies based on paket swithing leads to dramati hanges in the harateristis and nature of the data traffi. In partiular, there will be a onsiderable inrease in the rate of transations and in the total traffi intensity on Paket Swithed Core Network (PS CN) domain elements of the 3G networks, espeially, when the Internet Protool (IP) Multimedia CN Subsystem (IM-subsystem) is involved. Besides, it is neessary to take into aount the fat that the multiservie traffi in the 3G networks may have the self-similar nature due to the high variability of burstiness. It may lead to ongestion situations and paket-drops in the 3G networks. As a result of these fats, some 3G network planning problems arise and beome more omplex than ones relating to the urrent mobile systems. The following ones are onsidered in the first part of the thesis: the estimation problem of prospetive 3G users, the predition problem of 3G data traffi harateristis, the problem of performane evaluation of IMsubsystem elements. It should be emphasized that the CN evolution is quite onservative and it is supposed that the enhaned CN of the 3G systems will be able to support the funtionality of servies of the fourth generation (4G) mobile systems. It is expeted that the major hanges in 4G systems will our in the Radio Aess Network (RAN). For this reason, the seond part of the researh deals with RAN planning aspets for the 4G wireless systems. In partiular, the 4G systems should be designed to offer higher bit rate hannels (up to 00 Mb/s) and aommodate a signifiantly larger amount of traffi than the 3G systems. These requirements will make the 4G RAN different from urrent RANs and will innovate in its arhiteture. In the 4G systems, a new ring topology of a RAN physial links onfiguration may be applied in ontrast to RANs of urrent wireless systems. In the seond part of the study the RAN ring topology of physial links onfiguration is estimated from the viewpoint of ost and reliability parameters and the obtained parameters are ompared with those of other topologies. As a result, some reommendations on using different topologies of physial links depending on the number of Base Stations (BSs) in the 4G RAN are developed. Besides, the problem of the minimum-ost onfiguration of physial links between BSs in the 4G RAN ring topology is onsidered. 2

5 PREFACE The researh work for this thesis has been arried out during the years at the Institute of Communiations Engineering of Tampere University of Tehnology, Finland. This thesis was finanially supported by Tampere Graduate Shool of Information Siene and Engineering (TISE), NOKIA Foundation, and Finnish Cultural Foundation. Their support is appreiatively aknowledged. First I would like to express my sinere gratitude to my supervisor Professor Jarmo Harju for his enouragement, wise guidane, valuable advies, ontinuous support and infinite tolerane. I wish to express my sinere appreiation to the reviewers, Professor Heikki Hämmäinen from the Networking Laboratory, Helsinki University of Tehnology, Finland and Professor Timo Hämäläinen from the Department of Mathematial Information Tehnology, University of Jyväskylä, Finland for their extremely useful and detailed omments and suggestions on the final version of the manusript. I am also truly grateful to Professor Markku Renfors of TISE diretor and Dr. Pertti Koivisto of TISE oordinator for giving an opportunity for me to be involved in a major program to advane dotoral studies in the Tampere region. Speial thanks to Professor Sergey Lopatin and Dr. Vera Derzhavina from St. Petersburg Researh and Development Institute of Teleommuniations (LONIIS), Russia for fruitful, long-term o-operation and o-authoring of my publiations. I wish to thank my olleagues Roman Dunaitsev, Yevgeni Kouheryavy, Dmitri Molthanov in Finland for interesting sientifi and nonsientifi tea-table debates. I am most grateful to Tarja Erälaukko, Sari Kinnari, Elina Orava for taking the time and efforts to settle pratial matters. Finally I take this opportunity to express my deepest gratitude to my wife Marina, my son Andrey, my mother Lubov and my father Valery for their love, kindness, support, inspiration, tolerane and understanding during the preparation of this thesis. Tampere, August 2005 Andrey Krendzel 3

6 CONTENTS ABSTRACT... 2 PREFACE... 3 CONTENTS... 4 LIST OF PUBLICATIONS... 6 ABBREVIATIONS... 7 LIST OF TABLES... 9 LIST OF FIGURES... 0 INTRODUCTION.... SCOPE AND THE OBJECTIVE OF THE RESEARCH....2 OUTLINE OF THE THESIS RESEARCH METHODOLOGY ESTIMATING THE NUMBER OF PROSPECTIVE 3G USERS APPROACH FOR ESTIMATING THE NUMBER OF PROSPEROUS 2G USERS USING THE PARETO LAW THE APPROACH FOR ESTIMATING THE PARETO PARAMETER THE CHOICE OF THE EXCESS COEFFICIENT VALUES CASE STUDIES SUMMARY ESTIMATING PARAMETERS OF 3G DATA TRAFFIC THE DECOMPOSITION OF A SET OF 3G SERVICES INTO SOME SUBSETS THE DISTRIBUTION OF 3G USERS INTO SOME SUBGROUPS FORMING THE PROBABILISTIC MODEL OF EVENTS INITIATED BY 3G CALLS THE APPROACH FOR ESTIMATING THE SPECIFIC RATE OF TRANSACTIONS AND THE TRAFFIC INTENSITY CASE STUDY SUMMARY PERFORMANCE EVALUATION OF IM-SUBSYSTEM ELEMENTS UMTS REL 5 CORE NETWORK ARCHITECTURE ASPECTS THE TRAFFIC MODEL AND THE QUEUEING SYSTEM MODEL THE EVALUATION PROBLEM AND ITS SOLUTION CASE STUDY SUMMARY RELIABILITY AND COST PARAMETERS ESTIMATION FOR THE 4G RAN RING TOPOLOGY RING TOPOLOGY DEFINITION FOR 4G RAN RING TOPOLOGY RELIABILITY ESTIMATION RING TOPOLOGY COST ESTIMATION RECOMMENDATIONS ON USING DIFFERENT TOPOLOGIES IN THE 4G RAN SUMMARY THE MINIMUM COST RING CONFIGURATION OF PHYSICAL LINKS BETWEEN BASE STATIONS IN 4G RAN DEFINITION OF THE CONFIGURATION PROBLEM OF PHYSICAL LINKS APPROACH FOR THE PROBLEM SOLUTION CASE STUDY SUMMARY CONCLUSION

7 8 SUMMARY OF PUBLICATIONS OVERVIEW OF PUBLICATIONS AUTHOR S CONTRIBUTION TO THE PUBLICATIONS ANNEX REFERENCES

8 LIST OF PUBLICATIONS P. Krendzel A., Kouheryavy Y., Derzhavina V., Harju J. Method for Estimating the Number of Potential 3G Users, in proeedings of 0-th Open European Summer Shool on the Advanes in Fixed and Mobile Networks (EUNICE 2004), Tampere, Finland, June 4-6, P2. Krendzel A., Kouheryavy Y., Lopatin S., Harju J. Method for Estimating Parameters of 3G Data Traffi, in proeedings of the IEEE International Conferene on Communiations (ICC-2004), Paris, Frane, June 20 24, P3. Krendzel A., Derzhavina V., Lopatin S. Method for Estimating Parameters of NGN traffi, in proeedings of the International Conferene on Next Generation Teletraffi and Wired/Wireless Advaned Networking (NEW2AN), pp , St.-Petersburg, Russia, February 02-06, P4. Kouheryavy Y., Krendzel A., Lopatin S., Harju J. "Performane Estimation of UMTS Release 5 IM-Subsystem Elements", in proeedings of the 4-th IEEE Conferene on Mobile and Wireless Communiations Network (MWCN 2002), Stokholm, Sweden, September 9-, P5. Kouheryavy Y., Krendzel A. "Analysis of Web Traffi and Users Behavior Modeling During Busy Hour", in proeedings of the 6-th Open European Summer Shool (EUNICE 2000), University of Twente, Enshede, the Netherlands, September 3-5, P6. Krendzel A., Kouheryavy Y., Harju J. Cost and Reliability Estimation of Radio Aess Network Strutures for the 4G Systems, in proeedings of the IEEE 58-th Vehiular Tehnology Conferene (VTC 2003-Fall), the Symposium on Wireless Communiations: 3G and Beyond, Orlando, USA, Otober 6-9, P7. Krendzel A., Kouheryavy Y., Harju J. Radio Aess Network Topology Planning for the 4G Networks, in proeedings of the 5 th European Wireless Conferene Mobile and Wireless Systems beyond 3G (EW-2004), Barelona, Spain, February 24 27, P8. Krendzel A., Kouheryavy Y. "Remote Units Loation Problem in Multiservie Aess Network", in proeedings of International Conferene on Teleommuniations (ICT-2002), Beijing, China, pp , June 23-26,

9 ABBREVIATIONS 2G Seond Generation 3G - Third Generation 3GPP - Third Generation Partnership Projet 4G Fourth Generation ATM - Asynhronous Transfer Mode BH Busy Hour BS Base Station BSC Base Station Controller BSS - Base Station System BTS Base Transeiver Station CAMEL Customized Appliation for Mobile Network Enhaned Logi CDMA 2000 A CDMA System in North Ameria CN Core Network CS - Ciruit Swithed CS CN - Ciruit Swithed Core Network domain CSPDN Ciruit Swithed Publi Data Network EDGE Enhaned Data Rates for GSM Evolution ETSI - European Teleommuniation Standard Institute GGSN Gateway GPRS Support Node GDP Gross Domesti Produt GERAN GSM/EDGE Radio Aess Network GPRS General Paket Radio Servie GSM - Global System for Mobile ommuniations HSS Home Subsriber Server IM-subsystem (IM CN) IP Multimedia Core Network Subsystem IMT International Mobile Teleommuniations System 2000 IN - Intelligent Network IP Internet Protool IPv4 Internet Protool Version 4 IPv6 Internet Protool Version 6 IS-95 North Amerian Version of the CDMA Standard ISDN Integrated Servies Digital Network ITU - International Teleommuniation Union I u UMTS Interfae Between 3G-MSC/SGSN and RNC MAP Mobile Appliation Part MM Mobile Management MS Mobile Station MSC Mobile Swithed Center N-ISDN Narrowband ISDN NGN Next Generation Network NMS Network Management Subsystem NPV Net Present Value NSS Network Sub System PDC Paifi Digital Communiation PDSN Paket Data Serving Node PLMN - Publi Land Mobile Network PS - Paket Swithed PSCN - Paket Swithed Core Network domain PSTN - Publi Swithed Telephone Network 7

10 QoS Quality of Servie RAN Radio Aess Network RNC Radio Network Controller RNS Radio Network Subsystem SGSN Serving GPRS Support Node SIP Session Initiation Protool SS7 Signaling System No. 7 TDMA Time Division Multiple Aess UE User Equipment UMTS - Universal Mobile Teleommuniation System U m Radio Interfae for GSM BSS UTRAN Universal Terrestrial Radio Aess Network U u Radio Interfae for UTRA VAS Value Added Servie Platform VHE Virtual Home Environment VLR - Visit Loation Register VoIP Voie over IP WAP Wireless Appliation Protool WCDMA Wideband Code Division Multiple Aess 8

11 LIST OF TABLES TABLE I. CORE NETWORK DEVELOPMENT TABLE II. INITIAL DATA FOR ESTIMATING 3G DATA TRAFFIC PARAMETERS TABLE III. EXPRESSIONS FOR ESTIMATING 3G DATA TRAFFIC PARAMETERS TABLE IV. INITIAL VALUES FOR THE CASE STUDY TABLE V. ESTIMATED VALUES OF 3G DATA TRAFFIC PARAMETERS TABLE VI. 3G VARIANTS AND THEIR BUILDING BLOCKS 9

12 LIST OF FIGURES FIGURE. THE SET OF LORENZ CURVES FIGURE 2. THE LOGISTICAL FUNCTION FIGURE 3. THE RELATIONSHIP BETWEEN THE RELATIVE NUMBER OF POTENTIAL 3G USERS AND THE PENETRATION LEVEL OF 2G SERVICES FIGURE 4. VISION OF UMTS REL 5 FIGURE 5. SELF-SIMILARITY INFLUENCE ON THE SERVER UTILIZATION FACTOR FIGURE 6. GGSN SERVER CAPACITY ESTIMATINGFIGURE 7. THE UPPER BOUND FOR AVERAGE QUEUE LENGTH IN THE GGSN BUFFER FIGURE 8. THE UPPER BOUND FOR THE AVERAGE SERVICE TIME OF INFORMATION UNITS IN THE GGSN BUFFER FIGURE 9. THE MODELS OF RAN CONFIGURATION FIGURE 0. RELATIONSHIPS OF THE AVERAGE NUMBER OF KNOCKED OUT BSS FROM THE NUMBER OF RINGS AND THE NUMBER OF BSS IN EACH RING WHEN THE AVAILABILITY FACTOR IS FIGURE. RELATIONSHIPS OF THE NORMALIZED LENGTH OF LINKS FROM THE NUMBER OF RINGS AND THE NUMBER OF BSS IN THE RAN FIGURE 2. AN EXAMPLE OF THE 4G-RAN RING CONFIGURATION FIGURE 3. AN EXAMPLE OF THE DETERMINATION OF THE RING CONFIGURATION WITH THE MINIMUM COST FOR 7 BSS IN 4G RAN 0

13 INTRODUCTION. Sope and the objetive of the researh There has been an evolution in wireless ommuniations almost every ten years. The first generation (G) in 980s and the seond generation (2G) mobile systems in 990s have been oriented mainly for providing iruit-swithed (CS) servies to users. The 2G subsribers have used the rate for data transfer up to 4 kb/s as a maximum. In 996, European Teleommuniations Standards Institute (ETSI) deided to enhane 2G GSM standard in annual Phase 2+ releases that inorporate the third generation (3G) features suh as General Paket Radio Servie (GPRS) and Enhaned Data Rates for GSM Evolution (EDGE). The data rates for users of the systems are limited to 384 kb/s []. Universal Mobile Teleommuniations System (UMTS) as the 3G mobile system will be introdued during first deade of new entury. It is speified by ETSI and the world-wide 3G Partnership Projet (3GPP) within the framework defined by the International Teleommuniation Union (ITU) and known as International Mobile Teleommuniations (IMT-2000). The 3G systems should offer the data rates up to 2 Mb/s depending on mobility/veloity. ETSI and 3GPP are introduing UMTS in phases and annual releases. UMTS Rel 3 (sometimes alled as Rel 99) is a 3G GSM suessor standard using the GSM Phase 2+ enhaned ore network (CN). The most important evolutionary step toward UMTS is to introdue a paket swithed ore network (PS CN) domain. The main funtion of the PS CN domain is to support all servies (GPRS, WAP, et.) provided to both GSM subsribers and UMTS users []. The following phases after Rel 3 speify how voie and multimedia an be supported by IP tehnology. It is haraterized by reating of the Internet Protool (IP) Multimedia Core Network Subsystem (IM-subsystem), whih omprises all PS CN domain elements for providing teleommuniation servies within UMTS Rel 4,5,6. The IM-subsystem ontains a uniform way to maintain Voie over IP (VoIP) alls and offers a platform to multimedia servies. The examples of IM servies are voie telephony, real-time interative games, videotelephony, instant messaging, emergeny alls, multimedia onferening [2]. In the UMTS Rel 5,6 the traffi oming from Radio Aess Network (RAN) to the CN is supposed to be always paket swithed; and here the question is whether it is real-time or non-real-time []. The next step of wireless ommuniations evolution is the fourth generation (4G) of mobile ommuniation systems (the systems beyond IMT-2000). Now it is diffiult to predit when the 3G evolution ends and the 4G really starts []. The 4G systems should offer signifiantly higher bit rate than 2 Mb/s, have high apaity with a low bit ost and be able to support all types of teleommuniation servies from the viewpoint of multimedia ommuniations [3]. It is supposed that on the CN side of the 4G systems the main purpose is to minimize hanges and utilize the 3G CN elements and the 3G CN funtionality as muh as possible []. The CN development is summarized in the Table I.

14 TABLE I. CORE NETWORK DEVELOPMENT WIRELESS SYSTEMS 2G 2G phase 2 + 3G (UMTS Rel 3) 3G (UMTS Rel 4) 3G (UMTS Rel 5,6) 4G CORE NETWORK DOMAINS CS CN CS CN and PS CN CS CN and PS CN (enhaned 2G phase 2+ CN) CS CN, PS CN, IM CN IM CN IM CN (enhaned 3G CN) There are some important features of the global evolution proess in wireless ommuniations. The 3G wireless systems should be designed to support for a high-speed transfer of a large amount of multimedia information between users. One of the main properties of the data traffi in the 3G systems is a large diversity depending on the profile of servies provided to 3G users. It is expeted that the traffi in the 3G systems will expand onsiderable [4]. The growing data/multimedia traffi leads to inreasing the total load on network subsystem elements. Moreover, traffi patterns generated by 3G servies may be quite different from traditional Poisson models used for iruit swithed voie traffi. When modeling paket-swithed multiservie networks it is neessary to take into aount the notion of self-similarity [5-8]. Due to the high variability of burstiness of the traffi, the use of the lassial teletraffi theory for performane evaluation of PS CN domain elements may give essential faults; in partiular, the network parameters an be underestimated. Suh faults are unaeptable when IMsubsystem planning as well, therefore, priniples of the teletraffi theory annot be applied in this ase. Due to above reasons, the following 3G network planning problems our: the predition problem of a demand for 3G servies; the estimation problem of 3G data traffi parameters; the problem of performane evaluation of IM-subsystem nodes taking into aount the self-similar nature of the multiservie traffi. It is worth mentioning that the effiient approahes to solve these problems taking into onsideration the above-mentioned aspets of 3G wireless systems have not been presented in the publiations onerning 3G CN network planning [9-2]. One more feature of the evolution in wireless ommuniations onerns hanges in the 4G wireless systems. It is seen from the Table I that the CN evolution is quite temperate. From the viewpoint of funtional apabilities the enhaned CN of the 3G systems will be able to support 4G servies []. So, it is expeted that the RAN will undergo the main hanges, in partiular, on a physial transmission layer. In the 4G systems, beause there will be a need to deal with the enormous amount of traffi, the Base Station (BS) ell size is supposed to be smaller than that of 3G systems [3]. Therefore, the 4G RAN will omprise more BSs and more frequent handover will our resulting in a heavy load on the links between suh elements of RAN as Remote Network Controller (RNC) and BSs, suggesting hanges to the RAN arhiteture [3,3,4]. 2

15 So, for the 4G RAN a new and innovative topology of physial links onfiguration has been proposed in addition to traditional topologies using in RANs of urrent wireless systems [3,3,4]. The topology is alled the luster-ellular or, in other words, it is known as the ring topology. In suh topology BSs are grouped in a luster and there is a luster-main BS onneted to the RNC. BSs in a luster may be onneted to eah other by optial fiber links that are preferred as the dominant links to onstrut the 4G RAN from the viewpoint of link apaity [5]. Note that the 4G RAN ring topology has been proposed and analytially argued with the viewpoint of a load and routing apabilities only [3,3,4]. It is obvious that it is very important to analyze the ring topology of the RAN physial links with respet to its reliability and ost as well, to ompare it with other topologies and give reommendations on applying of different ones in the 4G RAN. Besides, it is worthwhile to determine the optimal onfiguration of physial links between BSs in the ring topology to derease the 4G RAN deployment ost. Taking into aount the onsiderations above, the researh is onentrated on two subjets. The first part of the researh is foused mainly on the 3G CN planning problems. The seond part of the researh deals with the 4G RAN topologial planning problems. The main objetive of the researh is to develop solution methods for the above-mentioned problems. It will enable planning 3G/4G networks in suh a way that both tehnial and eonomial advantages an be ahieved when onstruting and exploiting the networks..2 Outline of the thesis We start the first part of the thesis devoted to 3G CN planning with the estimation problem of the number of prospetive 3G users. The problem may be onsidered as the initial one for network planning. The suessful solution of the problem gives a basis to solve other topial 3G network planning problems. After that, the predition problem of the main parameters of data traffi generated by 3G users is onsidered. In partiular, the method for estimating parameters of the 3G user traffi on a level of PS CN domain is developed. In aordane with the parameters obtained as a result of the problem solution it is possible to adjust performane measures of 3G network equipment in order to ensure Quality of Servie (QoS). In the end of the first part of the researh the evaluation problem of performane measures of 3G network equipment is onsidered. So, the method for performane evaluation of IMsubsystem nodes in UMTS Rel 5 is developed. The main purpose of seond part of researh devoted to 4G RAN planning is to work out the methods that allow reduing the 4G RAN deployment ost taking into aount the reliability requirements. The first problem deals with estimating reliability and ost parameters of different 4G RAN topologies of physial link onfiguration. In partiular, the parameters of one ring, multi-ring and radial topologies are onsidered and ompared with eah other. Then, the onfiguration problem of physial links between suh 4G RAN elements as BSs with a minimal onstrution ost for the ring topology is onsidered. The problem arises if the ring topology is seleted for 4G RAN planning as a result of the previous problem solution. Thus, there are the main five interdependent problems that are onsidered in the thesis. In next subsetion we disuss about researh methodology for solving these problems. 3

16 .3 Researh methodology The priniples of teletraffi theory, probability theory, mathematial analysis, graph theory, eonomis are used in the thesis to ahieve the appropriate results. So, the estimation problem of the number of potential 3G users requires the appliation of priniples from several disiplines suh as teleommuniations, mathematis and eonomis taking into aount that a demand for new teleommuniation servies depends on both Gross Domesti Produt (GDP) and its distribution within soiety. In partiular, the method for estimating the number of prospetive 3G users is based on the appliation of the Pareto law, the Lorenz urves, the Jipp urve and the Gini oeffiient [6-22]. Sine one of the main harateristi futures of 3G wireless systems is to provide a large diversity of servies to users it is reasonable for the predition of the main data traffi parameters to make deomposition of 3G servies into some subsets in aordane with average amount of transferred data per transation and distribution of 3G users into some subgroups in aordane with their demand for 3G servies from different subsets of servies. Inequality of the distribution of 3G users is taken into aount by different values of the Gini oeffiient for eah subset of 3G servies. Suh approah allows segregating several segments from the ommon flow of transations initiated in busy hour by support proedures of 3G servies. After that, the main parameters of data traffi are determined for eah segment of data traffi and the total traffi intensity on the PS CN domain is estimated. The method for performane evaluation of IM-subsystem nodes in 3G wireless systems should take into onsideration the influene of self-similar input. For this reason, it is proposed to analyze the performane measures of IM-subsystem nodes on a basis of FBM/D//W queueing system, where FBM is Frational Brownian Motion [23-25]. Topologial onfiguration of 4G RAN physial links is one of the most important problems of network planning beause it will determine the long-term performane and servie quality of 4G systems. Many fators influene on reliability and ost of RAN network topologies. It is proposed to make a quantitative estimation of reliability and ost parameters of different 4G RAN topologies inluding the new ring topology on a basis of probability theory priniples. The optimization problem of physial link onfiguration between BSs in 4G RAN presents an NP-omplete problem. The onfiguration problem for the new ring topology of 4G RAN is to find the shortest path (from the ost viewpoint) beginning and ending in the same node orresponding to the main BS loation. The dynami programming is used to provide an aeptable solution for the problem sine suh approah has some advantages in omparison with other algorithms for the shortest path searhing (see hapter 6). 4

17 2 ESTIMATING THE NUMBER OF PROSPECTIVE 3G USERS The predition problem of a demand for 3G servies in a region before deployment of 3G network equipment may be onsidered as the first one for 3G network planning. Information about the demand for 3G servies is very useful for network operators, servie providers and network equipment manufaturers. Besides, the solution of the problem enables forming initial data for other 3G network planning problems. In this hapter the method for the preliminary estimation of the potential number of 3G users in a region is onsidered. It is based on relationships between the Pareto law, Gross Domesti Produt (GDP), inome distribution within population, and infoommuniation density. The method is presented in detail in [P]. 2. Approah for estimating the number of prosperous 2G users using the Pareto law The Pareto law was established on a basis of empirial data onerning inome distribution in different ountries [6,7]. This law has a mathematial formulation and shows a relationship between eah inome level and the number of people who reeive more than that inome. Note that the Pareto law is applied not only for eonomis. It is just for other fields of human ativity that are haraterized by statistial nature and have distributions, whih are nononvergent to the normal (Gaussian) law [26]. In partiular, the Pareto law may be extended for estimating a demand for various servies of infoommuniation infrastruture, inluding teleommuniation servies. This is beause of the fat that the demand for the servies depends on both GDP and its distribution within soiety and there is the relationship between a demand for teleommuniation servies, labour produtivity, distribution of inomes between individuals, and GDP [27]. It is proved in [27] that the relationship between a demand for teleommuniation servies and inome distribution is lose to the Pareto law. In [6] Pareto introdued inome distribution in the following view R ( x) = x α, < α <, (2.) where R(x) is the number of individuals who have inome more than x, α is the distribution parameter alled the Pareto parameter. The random variable x may be presented as the normalized inome that equals to the ratio G/G min, where G is one of inome values, G min is the minimum inome value. In aordane with (2.) the higher the individual inome level in a subgroup the less individuals are in the subgroup. In terms of integral distribution it is possible to define (see [P]) the integral funtion of probability distribution F(x) and the probability density w(x) with integral distribution F(x). Then, it is possible to get the n-th moment of distribution of the random variable given by the probability density w(x), M n = α / (α n). When α > the n-th moment of distribution does not exist and the average value of random variable distributed by the Pareto law is defined only. Therefore, the Pareto distribution belongs to the type of Cauhy distributions and is nononvergent to the normal one [26]. Using the normalization rule the minimum inome value may be expressed as G min (α) = G 0 /M(α), where G 0 is GDP per apita, M(α) =α /(α ) is the average value of the inome. Thus, the expression (2.) for estimating the number of individuals who have inome more than x = G/G min takes the following view 5

18 α Gα R ( G / G ) = α min, (2.2) G0 ( ) It is lear that teleommuniations as a part of soiety infrastruture influene on development of soiety and determine the eonomial level of soiety. At the same time, ountry eonomis determine the level of teleommuniation development. It is known that there is the relationship between infoommuniation density and a level of GDP per apita that may be desribed by the well-known Jipp urve [28]. For example, there is the linear dependene (in the first approximation) between the telephone density and GDP per apita. It is argued in [27] that the similar linear dependene takes plae between amount of produed information, generated by soiety, per an individual and GDP per head. Generally, it is possible to apply the dependene for other harateristis relating to teleommuniations and information servies. In our ase, it is assumed that there is the linear dependene between the penetration level of 2G servies and GDP per apita. Mathematially it may be presented as a A G 0 =, (2.3) where = N mt /00 is the penetration level of 2G servies, N mt is the average number of 2G mobile terminals per 00 individuals, A is the normalizing dimension fator, a is the power index. The index a is lose to, i.e. a = + a, a <<. So, in first approximation it may be rewritten as the linear dependene = AG 0. To analyze a demand for teleommuniation servies it is quite enough to have information about distribution of large inomes [27]. Besides, the area of small inomes has very small influene on statistial harateristis of inome distribution in aordane with the Pareto distribution. Note that the expression (2.) is true for large inome distribution and may be interpreted as probability that the inome is more than x. Sine parameters and G 0 are the average values obtained by averaging many initial and random data, in general ase, the following expression is fair T = AG, where T may be interpreted as the penetration level of 2G servies in the subgroup of the prosperous users. Thus, it is possible to get the follows T G k = =, k. (2.4) G 0 Here, the oeffiient k determines the exess of the penetration level of 2G servies in the subgroup of the prosperous users above the average value of the 2G penetration level relating to all individuals. It gives an opportunity to form the expression for determination of the relative number of individuals who have the penetration level of 2G servies more or equal than the parameter, or, in other words, we get the expression for estimating the relative number of the prosperous users of 2G servies α kα R ( k, α) =. (2.5) α As a rule, the penetration level of 2G servies in a region is known and may be found in statistial literature. Therefore, for estimation of the relative number of the prosperous 2G users (when given T) it is neessary to find the Pareto parameter α only. 6

19 2.2 The approah for estimating the Pareto parameter Generally the parameter value α depends on the inequality of inome distribution between individuals. With referene to our ase, this parameter depends on the inequality of distribution of the number of mobile phones between individuals. Usually the inequality of inome distribution in a subgroup of individuals is illustrated by the Lorenz urves [9,22,29,30]. If the Pareto law desribes the inome inequality in mathematial view then the Lorenz urves show the inome inequality in the integral form. The set of the Lorenz urves when α =.05;.6;.50; 3.00 is presented in Figure. If all individuals have the same inome, the Lorenz urve is a straight diagonal line, alled the line of equality. If there is any inequality in inome then the Lorenz urve falls below the line of equality. In Figure the Lorenz urves show relationships between the normalized (to the parameter value M) urrent average inome value in a subgroup of population Q and the normalized number of individuals in the subgroup F = R. The derivation of the analytial funtion Q(F) that allows assigning a set of the Lorenz urves is given in [P]. The funtion has the following view [26,3,32] α α Q ( α, x) = ( F( x)). (2.6) The set of the Lorenz urves shows that with inreasing the parameter value α inome in a subgroup is beoming more evenly distributed, i.e. the more α the loser a Lorenz urve to the line of equality. It is worth mentioning that the relationships Q(α, x) are the generalization of the well-known inequality of inome distribution between population that an be presented as ρ/ ( ρ), ρ < 0.5. The ratio means that in many aspets of human ativities the small part of population (ρ %) owns the most part of umulative inome ( ρ) %. The famous Pareto rule 20/80 (20 perent of the people owned 80 perent of the wealth) orresponds to the Pareto law given by the Lorenz urve Q(α,x) with α =.6 (ρ = 0.2, Μ = 7.25). The value α =.5 is usually assigned as the mean statistial estimation. It orresponds approximately to the parameter of the inequality ρ = 0.32 and the rule 30/70 [26]. As a rule the Gini oeffiient is onsidered in statistial literature as a measure of the inome inequality [26]. The Gini oeffiient is the integral parameter haraterizing deviation of a Lorenz urve from the equal inome distribution line. The oeffiient is numerially equal to the doubled area enlosed by the line of equality Q = F and the Lorenz urve Q(F) [26]. It should be emphasized that in eah stage of development of 2G systems a number of 2G subsribers is known only on a basis of statistial information. In other words, the number of individuals in a subgroup that has 00% even overage of 2G servies, i.e. has ompletely even distribution of 2G servies, is known. It is obvious that the Lorenz urve in this ase is transformed into the broken line (on the assumption that one subsriber has only one mobile terminal). It may be expressed as follows 0, 0 < F < Q (, F) = F +, (2.7), F The view of the distribution (2.7) when the penetration level = 0.3 is shown in Figure. 7

20 Q F "equality" line alfa=.05 alfa=.6 alfa=.50 alfa=2.00 Q(delta=0.3,F) Figure. The set of Lorenz urves Sine a mobile terminal of a subsriber may be used by some other people, for example, subsriber s family members, olleagues, friends, and so on, the distribution of 2G servies between individuals is more even than the distribution of 2G terminals. Note that in most ases this distribution orresponds to the Pareto law and in order to solve the problem of determination of a number of prosperous users it is neessary to find a transition from the distribution urve of subsribers Q(, F) to the distribution urve of users Q(α,F). In other words, in order to find the Pareto parameter α and for the expression (2.5) it is reasonable to approximate the distribution (2.7) depending on the parameter by the funtion (2.6) orresponding to the Pareto distribution with the parameter α where the parameter α satisfies the following requirement α opt = argmin d( Q(, F); Q( α, F)). (2.8) Here, d( Q(, F); Q( α, F)) is the distane between the approximated funtion and the approximating one. As a measure of the distane between these two funtions the differene module between the Gini oeffiients relating to the funtions Q(,F) and Q(α,F) respetively is onsidered in [P]. The desired solution has the following view 0.5(2 ) α opt =. (2.9) When α =α opt the funtion Q(α,F) has the same value of the Gini oeffiient as the funtion Q(,F). Thus, using the expressions (2.5) and (2.9) it is possible to find the relative number of the prosperous users of 2G servies. In the subgroup of prosperous users the penetration level of 2G servies T exeeds the average value of the 2G penetration level relating to all 2G users in k times. Let us all the oeffiient k as the exess oeffiient heneforth. Now it is neessary to determine the interval of values of the exess oeffiient k while the prosperous 2G users beome the potential users of 3G servies. 8

21 2.3 The hoie of the exess oeffiient values It was argued in [27] that the proess of the penetration of teleommuniation servies in time for a group of individuals orresponds to the logisti law. The logistial funtion is given as B y = [ ( t t0 )/ V ], (2.0) + e where B is the saturation level, t 0 is the infletion point of logistial funtion, V = /B. The view of the logistial funtion with parameters B =, V =, t 0 = 0 is shown in Figure y t Figure 2. The logistial funtion In aordane with the logisti law the proess of servie penetration in time may be divided into three parts, namely, the first part is exponential growth, the seond part is the linear growth, and the third part is saturation. From the viewpoint of eonomi priniples network operators should deploy the equipment that is able to support new servies at the time moment while the greatest demand for the urrent servie. It is so alled time for a new attak in marketing. It takes plae while the urrent servie development is getting to the seond part of linear phase (see Figure 2). In other words, the members of the subgroup of the prosperous users beome the potential users of 3G servies at the moment when the penetration level of 2G servies in the subgroup T ahieves 60-80%, i.e. when k = ( )/. This onlusion is onfirmed by the relationship between the relative number of potential 3G users and the penetration level of 2G servies presented in Figure 3. The relationship is arranged in aordane with (2.5) and (2.9) when T = 0.8. As it is seen from Figure 3 while the penetration level of 2G servies is the dramati growth of the relative number of potential 3G users is observed. Note that while the 2G penetration level relating to all 2G users is oming to the 2G penetration level in the subgroup of the prosperous users T then values of the exess oeffiient k is tending to. In this ase, there is a gradual growth of the relative number of potential 3G users depending on values of the Pareto parameter α only. For instane, if the 2G penetration level is more or equal to 0.8 (see Figure 3) then the exess oeffiient k is always equal to (oeffiient k an not be less than ) and the further growth of the relative number of potential 3G users beomes more slow. So, when k = the expression (2.5) transforms into R(α)=((α-)/α) α. It is seen from the formula that with inreasing α the 9

22 relative number of potential 3G users R(α) is raised, in partiular, when α then R(α) that orresponds to the absolutely equal distribution of servies between population. Finally, the absolute value of the number of 3G potential users is obtained as N3 G = R( k, α )N, (2.) where N is the number of population in a region. 0.3 Relative number of potential 3G users Penetration of 2G servies when T=0.8 Figure 3. The relationship between the relative number of potential 3G users and the penetration level of 2G servies So, it is quite easy to approximately estimate with help of the expressions (2.5), (2.9), and (2.) the initial number of prospetive 3G users before deployment of 3G wireless systems in a region if the penetration level of 2G servies in the region is known. 2.4 Case studies In this setion two simple examples illustrating the proposed approah are onsidered. The first example is follows. Aording to statistial information (soure: Russian Federal State Statistis Servie) there was 8.5 million of population (N = ) in Mosow (Russia) and its suburbs in The penetration level of 2G servies in the region was not very high = Using the expressions (2.5), (2.9), (2.) it is possible to estimate both the relative number of potential 3G users in the ity as R(.;.6) = 0.8 and the absolute number of potential 3G users as N 3G = Let us onsider a region with high level penetration of 2G servies, for example, Finland where the 2G penetration level in 2002 was = 0.80 (soure: Statistis Finland). The population of Finland in 2002 was 5.2 million. In this ase the exess oeffiient k is oming to and the relative number of prospetive users depends on the Pareto parameter only (see explanation above). Thus, R(;3) = 0.3 and the absolute number of prospetive 3G users is N 3G = As it is seen from these two examples in these regions there are enough potential users in order to deploy 3G equipment and develop 3G servies. It is worthwhile to make the onluding remark in the end of the hapter that some foreasts of a demand for teleommuniation servies on a basis of the Pareto law were made in [26,27] in 994 and 997. In partiular, the telephone density and the number of Integrated Servies Digital Network (ISDN) users in some ountries were predited. Today the results of the 20

23 foreasts seem quite plausible. The predition error is not more than a few perent. So, for example, the very low demand for ISDN was predited, in partiular it was estimated that the number of ISDN users even in developed ountries annot exeed 5-6% from the number of Publi Swithed Telephone Network (PSTN) users that orresponds with the real situation. 2.5 Summary In this hapter the predition problem of a demand for 3G servies in a region has been onsidered. In partiular, the solution method of the problem using the Pareto law, the Lorenz urves, the Gini oeffiient and some eonomi harateristis was proposed. Besides, a novel approah for estimating the Pareto parameter was onsidered. If the number of population in a region and the penetration level of 2G servies in the region are known then the method enables estimating the initial number of prospetive 3G users before 3G equipment deployment. 2

24 3 ESTIMATING PARAMETERS OF 3G DATA TRAFFIC The seond problem of the 3G network planning is the predition of traffi parameters. The solution of the problem allows estimating a load on the 3G network equipment. The predition of data traffi harateristis beomes more ompliated when planning the 3G wireless systems beause of the following fators. The 3G wireless systems are haraterized by a large diversity of paket swithed servies that lead to essential quantitative and qualitative hanges of data traffi. In partiular, a dramati rise is expeted in the rate of transations and in the amount of data transferred during the transations. Furthermore, it is important to take into onsideration self-similarity that may our in the 3G wireless networks due to the high inonstany of burstiness of multiservie traffi [5-8] (see explanation in the beginning of the next hapter). In this hapter the estimation method for the main parameters of the data traffi, generated by users of 3G servies on a level of the PS CN domain, taking into aount the abovementioned 3G features is onsidered. The method is based on the probabilisti model of events initiated by 3G alls that is formed in aordane with both deomposition of a set of 3G servies into some subsets and distribution of potential 3G users into some subgroups. The method is desribed in detail in [P2]. Both the resulting table of the initial data and the resulting table of the expressions for estimating 3G data traffi parameters are presented in the end of the hapter before the ase study. 3. The deomposition of a set of 3G servies into some subsets The first step of forming the probabilisti model is to make deomposition of a set of 3G servies into some subsets. It is supposed that servies belonging to one subset generate approximately equal traffi intensity. As riteria for the deomposition an amount of transations in busy hour and an amount of data transferred during a transation are used. The deomposition of a set of 3G servies is fulfilled into three subsets. The first subset of servies (i = ) deals with transfer of a short amount of information ( s, Web-pages, hats, and so on). These servies are haraterized by integrity of information bloks. The subset inluding suh servies is named pages. An average volume of transferred data per transation for this type of servies is quite low, from tens to hundreds of kb. The seond subset (i = 2) inludes a transfer of text, olor pitures, graphis and so on, for instane, transfer of jpeg, gif, do, pdf, zip files. The subset is named pitures. A demand for the servies and an average amount of transferred information per transation are haraterized as the mean level, hundreds of kb. The third subset (i = 3) omprises multimedia servies, whih deal with a huge amount of information, for instane, a transfer of mp3, mpeg, avi files. The subset is alled multimedia and an amount of transferred information for the subset may ahieve several tens and hundreds of MB. The initial information onerning a speifi (per eah subset of servies) distribution of the total amount of transations in busy hour (γ i, i =,2,3) is used as the numerial riterion for the deomposition of a set of 3G servies into some subsets, γ + γ 2 + γ 3 =. 22

25 Note that 3G servies within eah subset generate the urrent traffi intensity that has a variane of parameter values of substantially smaller than one relating to the traffi intensity of the total set of 3G servies. 3.2 The distribution of 3G users into some subgroups The seond step of forming the probabilisti model is to fulfill the distribution of 3G users into some subgroups sine the inequality of a demand for 3G servies from different subsets will take plae between 3G users. This is beause of the fat that a demand for 3G servies depends on both a solveny of users and servie tariffs, and tariffs on servies from the different subsets will be unequal. All 3G users are divided into three subgroups in aordane with their demand for 3G servies from the different subsets defined earlier. The inequality of a demand for eah subset of servies is approximated by the Pareto law with the parameters (α i, i =,2,3). As a measure of the inequality of the servie distribution for eah subset the Gini oeffiients (K G,i, i =,2,3) are given and onsidered as the input data [20,2]. Note that α i = 0.5(K G,i + )/K G,i, i =,2,3 [24]. Values of the Gini oeffiients may be defined on a basis of statistial information and marketing researh regarding a demand for 3G servies. If there is no information about values of the Gini oeffiient then it is possible to extend and develop the approah for estimating the Pareto parameters proposed in the previous hapter. It is obvious that the least inequality of the distribution takes plae for the pages subset and the largest one takes plae for the multimedia subset. As a rule for the distribution of users into three subgroups (J = 3) the following one desribed below may be applied. Users from the third (j = 3) subgroup produe 90% of a demand for 3G servies from the multimedia subset. The subgroup is named rih. Users from both the third subgroup and the seond subgroup reate 90% of a demand for 3G servies from the pitures subset. The seond (j = 2) subgroup is named middle. All the rest of users belong to the first (j = ) subgroup named poor. Using the Lorenz urves (2.6) it is possible to get the relative number of users in eah of the subgroups (F 3, F 2, F ) in aordane with their demand for 3G servies from the subsets of 3G servies defined in the previous setion. It should be emphasized that that there are not speial restritions for both a hoie of the number of subsets of 3G servies (I) and a hoie of a number of subgroups of users (J). So, for example, in [P3] the present method is developed to estimate the main parameters for symmetrial and asymmetrial traffi separately. In the method, other priniples of deomposition of servies are proposed. In the first step of the deomposition, a set of servies is divided into two subsets. The first subset inludes servies onerning the realtime establishment of onnetivity between endpoints. It is haraterized by the transfer of the symmetrial traffi and the strit ontrol of QoS. The seond subset omprises of suh servies that generate the asymmetrial traffi. After that, eah of the above-mentioned subsets of servies is divided into three lasses in aordane with features of the generated traffi intensity. The division of the first subset of servies reating symmetrial traffi into three lasses is fulfilled taking into aount the flow rate initiated by users. The division of the seond subset of servies initiating the asymmetrial traffi into three lasses is fulfilled taking into aount an amount of information (on average) initiated by users. Suh kind of deomposition enables estimating separately the symmetrial and the symmetrial load on network equipment. 23

26 3.3 Forming the probabilisti model of events initiated by 3G alls In aordane with the rules of the deomposition of 3G servies and the distribution of users of these servies the probabilisti model of the initiation of transations based on an intersetion of events from two statistially independent exhaustive lasses is formed. The events inluded in the first lass orrespond with demands for servies from the pages, pitures, multimedia subsets respetively and denoted by index i=,2,3. The events inluded in the seond lass orrespond with demands initiated by users from the poor, middle and rih subgroups respetively and denoted by index j =,2,3. It is possible to arrange nine intersetions of events from these two lasses (i,j: i =,2,3; j =,2,3). The first event (i =, j = ) is that user from the first subgroup (j=) initiates a demand for a servie from the first subset (i = ). At the seond event (i = 2, j = ) user from the first subgroup initiates a demand for a servie from the seond subset. At the third event (i = 3, j = ) user from the first subgroup makes a demand for a servie from the third subset. The fourth event (i =, j = 2) is that user from the seond subgroup makes a request for a servie from the first subset and so on. Thus, the probabilisti model of the events allows segregating nine segments from the ommon flow of transations initiated in busy hour by support proedures of suh servies. The variane of parameter values of eah random flow is less than the one relating to the ommon flow. 3.4 The approah for estimating the speifi rate of transations and the traffi intensity After the probabilisti model has been omposed the problem is to determine the speifi (per user) rate of transations (λ ij ) in busy hour for nine (i,j =,2,3) intersetions of events from the two above-mentioned lasses. The approah for estimating values of the parameter is presented in detail in [P2]. It is based on solving system of three equations that are formed for eah subset of 3G servies. Eah system of the equations is assigned on a basis of the share of transations (β ij ) in busy hour relating to users of the j-th subgroup when servies from the i-th subset are initiated, i,j=,2,3. The parameters β ij may be expressed by two different ways that give a possibility to form the required equations. The first way is to define the parameter β ij on a basis of the inequality of a demand for 3G servies. Values of the share of transations β ij are alulated for eah of nine events using values α i, i =,2,3 and F j, j =,2,3 obtained earlier. So, the parameter values β ij are known. The seond way is to express the parameter β ij over the speifi (per user) rate of transations in busy hour λ ij (i,j =,2,3). It gives a possibility to formulate the above-mentioned system of the equations for eah subset of 3G servies with unknown parameters λ ij (i,j =,2,3). The system may be presented in the matrix-vetor form as follows ( βi ) F βi 2F βi 3F β F ( β ) F i2 i i3 2 β F 2 2 βi F3 λi 0 βi 2F3 λ i2 = 0. (3.) ( β ) i3 F3 λ i3 0 The system (3.) has three one-parameter families of solutions that are given in [P2]. In aordane with solutions the rate of transations in busy hour for 8 segments of data traffi is determined λ ij (i=2,3; j =,2,3). Usually, the parameter value λ is known on a basis of 24