APPLICATION OF STRUCTURED QUEUING NETWORKS IN QOS ESTIMITION OF TELECOMMUNICATION SERVICE

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1 APPLICATION OF STRUCTURED QUEUING NETWORKS IN QOS ESTIMITION OF TELECOMMUNICATION SERVICE 1 YAROSLAVTSEV A.F., 2 Al-THUNEIBAT S.A., 3 AL TAWALBEH N.A 1 Depatment of Netwoking, SSUTI, Novosibisk, Russia 2,3 Depatment of Electical Engineeing, BAU, Ibid, Jodan ABSTRACT We pesent the stuctued queuing netwok as effective mathematical model of telecommunication system; this model is oiented on the analysis of delay in telecommunication netwoks. A set of special components ae identified fo poviding stuctuization of such models. QoS paametes: the aveage delivey time and the utilization coefficient ae calculated fo MPEG video LAN implementing stuctued queuing model. In this pape, we popose the use of stuctued queuing netwoks to model high speed communication netwoks, which is moe adequate than conventional analytical models, and expends less computational time than simulation models. Keywods: QoS; Modeling; Stuctued Queuing Netwoks; Closed Heteogeneous Queuing Netwoks 1. INTRODUCTION Duing analysis and design of asynchonous telecommunication netwoks using diffeent potocols of packet switching, the development of mathematical tool fo delay analysis of data tansmission ove such netwoks is actually. This task is especially actually fo communication netwoks, which had been inceased the poductivity fo poviding vaious multimedia sevices. Taffic of sevices in telecommunication netwok, by natue, has synchonous chaacte, but passed by asynchonous mode, and functioning of these sevices substantially sensitive to delay of taffic and, especially sensitive to Jitte. Real telecommunication netwok have lage dimension, iegula, dynamically change stuctue and povide a set of sevices with heteogeneous taffic. The evaluation of delay in such netwoks is vey seious task. Difficulty of thei estimation is caused by the fact, that infomation elements of taffic undego casual delay duing tansmission ove netwok. This delay is fomed by sum of delays poduced by each component of the netwok which contibute in the outing pocess of taffic elements. Routing, in geneal, consideed to be andom and depends on the cuent status of the netwok. Thus, the aveage delay and Jitte values of delivey time fo some infomation element of taffic is detemined by the distibution of delay pobabilities to all possible outes in the netwok. In ode to suppot multimedia taffic ove digital netwoks, it is impotant to assue sevice qualities; delay, jitte and bandwidth. In geneal, modeling of digital netwoks suppoting multimedia taffic is complex and thus QoS estimation is challenging. Fo the estimating of QoS in high speed telecommunication netwok, the simulation methods using queuing analysis, Makov models can be applied [1] [2]. Also, in pape [3], simulation study of the VoIP packet taffic on a netwok of outes has been used to investigate QoS of Intenet voice communication (VoIP). In woks [4] [7] Makov models and queuing analysis have been used to model the tansmission of multimedia data ove communication netwoks ove vaious achitectue (GSM and CDMA wieless netwoks, ATM -netwoks, and othes). Thee wee a lot of woks, which investigate tansmission of multimedia taffic ove IP netwoks [8] [13]. Usually simulation methods ae used to eseach such communication netwoks. But this appoach has a seies of limitations. These models eithe suppose fixed stuctue of modeled netwok, do not take account of tansfeing multimedia taffic, no do not conside tanspot and 19

2 netwok potocols. In addition simulation methods ae complicated. Thee ae geat difficulties in adequate epesentation of the tansmission of multimedia taffic by analytical models. In this pape, we popose the use of stuctued queuing netwoks to model such high speed communication netwoks, which is moe adequate than conventional analytical models, and expends less computational time than simulation models. The complexity of QoS estimation ove communication netwok aises fom seveal factos. Some of them ae listed below: Lage scale communication netwok and its complex topology; Lage numbe of clients; Complex distibuted opeating algoithms in communication equipments; Uneliability of communication equipments; Stochastic and heteogeneous taffic chaacteistic; Sevice of eal-time and multi-media applications. Cuently thee ae only a few models fo some communication netwoks with paticula topologies, in which distibution functions fo delays ae obtained analytically. Even analysis of mean values of these delays is vey complex and challenging fo geneal netwoks. This pape is oganized in 5 sections: paametes and chaacteistics of closed heteogeneous queuing netwoks, the stuctued queuing netwoks as model of telecommunication system; estimation method of telecommunication system quality paametes, an example netwok and simulation esults and conclusion. 2. PARAMETERS AND CHARACTERIS- TICS OF QUEUING NETWORKS Depending on the pesence of diffeent classes of jobs, queuing netwoks ae classified to homogeneous and heteogeneous netwoks [4]. In heteogeneous netwoks, unlike homogeneous, the jobs, which ciculate ove the netwok, have diffeent outes and spend diffeent sevice time in nodes of thei outes. The set of jobs which have identical outes and the same sevice time in nodes of thei outes foms class. Depending on the pesence of an extenal souce of jobs in netwok stuctue, the queuing netwoks ae sepaated to open, closed, and hybid types. In closed queuing netwok, unlike in open, a constant numbe of jobs always ciculate. In hybid sevice netwok, the numbe of jobs of one class is constant, and of othe classes is not. Recently the closed heteogeneous netwoks extensively have been implemented. The stationay distibution of closed heteogeneous netwoks statuses is invaiant with espect to distibution function within fist two moments of distibution. Futhemoe, it is always possible to appoximate an open netwok by closed, eplacing the souce of jobs by a node and inceasing the numbe of ciculating jobs in the netwok. The closed heteogeneous queuing netwoks ae geneally defined by the following set of paametes [15], [16]: Γ= LKW,,,, DA,, µ, Θ, π (1) Whee L epesents the numbe of queuing systems (nodes); K the numbe of job classes; N = { N k }, Nk the initial distibution K of N = Nk jobs of K classes; k = 1 = { i }, i > the victo of sevice devises numbe in a node; W = { W i }, the victo of distibution function (d.f) types fo andom values (.v), which detemine the sevice time peiod fo jobs in nodes; D= { D i }, the victo of sevice disciplines fo jobs in nodes; µ = { µ ( n) } the matix function of sevice intensity of jobs, whee µ ( n ) the sevice intensity of job within k -class in i - node, in conditions, that netwok is in some status n taken fom status space Ω, that is n Ω detemines some allowed distibution of N jobs by nodes and classes; Θ = ( θ ; jl,) the oute matix, whee an element θ ; jl, 1 detemines the tansition pobability of job within k -class, and which is completely seved by i -node, to a node with numbe j and to a class with numbe l ; 2

3 π = { π k }, k 1, K levels of job class. Hee we denote i, j 1, L and kl, = 1, K. =, the victo of pioity =, Depending on the value atio of paametes in Γ (expession 1) vaious methods of queuing netwoks analysis ae used, among which aise exact and appoximate methods [15]. These methods povide the calculation of the following basic chaacteistics of netwoks functioning in the stationay mode: u n mathematical expectation (m.e.) of job numbe within k -class, existing in i -node; n m.e. of job numbe within k -class, v seved in i -node; n m.e. of job numbe within k -class, w waiting in the queue of i -node; λ job steam intensity within k -class in i -node; v m.e. of sevice time of job within k - class in i -node; u m.e. of existence time of job within k - class in i -node; w m.e. of existence time of job within k - class in the queue of i -node; t m.e. of cyclic time of job within k -class that seved in i -node; τ m.e. of tansition time of job within ; jl, k -class that seved in i -node into l -class and j -node. 3. THE STRUCTURED QUEUING NET- WORKS AS MODEL In the technology of design and development of telecommunication netwoks an impotant place is allocated fo the use of the specialized softwae pogams in modeling. The effectiveness of the modeling scheme in a given application is defined by the set of basic mathematical models implemented and the epesentation methods of these models. Vaious types of queuing netwoks occupy one of the main places in modeling pocess. Futhemoe, the incease of compute poductivity and the development of effective methods of netwok analysis enable shaply incease the dimension of models, thus poviding thei adequacy. Fo this easons, the stuctuization mechanism of queuing netwoks appeas. The development of stuctuization mechanism of queuing netwoks pusues the following puposes: poviding adequacy in the desciption and pesentation of models fo eal telecommunication netwoks containing simila components; poviding the stuctuization of models with lage dimension, facilitates thei development and debugging; poviding the possibility of ceation of libaies fo standad models; poviding the ealization of hybid modeling methods fo the decomposition of models with lage dimension. Fo this pupose, we pesent the stuctued queuing netwok (figue 1), in the stuctue of which except the usual components (nodes ( nd ), we popose a set of sevice devices ( sv ) and job queues (buffes) (bf ), jobs ( d ) within classes ( cl ), job souces ( s ), also a set of specialised components defined: the distibution of job steams ( db ), which povide compounding and division of diffeent job steam types; modulus ( ), which compound in thei stuctue a goup of components with diffeent types, and epesenting subnetwok; couples (inputs (ic ) and outputs ( oc ), depending on the job steam diection), which detemine the location of subnetwok in the queuing netwok stuctue, and fomed by a pai of components (plugs and sockets); input plug (ip ), detemine the input job steam to the module; output plug ( op ), detemine the output job steam fom the module; input socket (is ), detemine the job steams diected into the module; output socket ( os ), detemine the job steams diected fom the module; plug and socket contacts, which detemine some homogeneous elementay steam in heteogeneous stuctue. The module of stuctued netwok defines the subnetwok, which descibed by all above mentioned types of components, including the modules. The netwok elated to the inside defined module as supe-module, but the module defined in the stuctue of this module consideed as submodule. When the module intes o exits the jobs 21

4 always change class to sub-module o supe - module class coespondingly. When the job seved in module and continue seving in supemodule it diected to the output plug, accodance to which an output socket is placed. Fo the beginning of job sevice in a sub-module the job diected into the input socket, accodance to which an input plug is placed in a sub-module. The numbe of contacts in coesponding plugs and sockets should coincide, and it is defined by the numbe of elementay job steams, which fom a homogeneous steam on socket. Thus, the module has a set of sockets by means of which it is included in the stuctued netwok. Modules ae the basic components of the stuctued queuing netwoks which povide stuctuization. Modules can be enclosed in othe modules and can contain sub-modules. The module can be emoved fom the stuctued netwok by the sepaation of the sockets placed on the contou of the given module, and can be eplaced with othe module accoding to the stipulated sockets. The components of stuctued queuing netwok ae defined by coesponding set of paametes. We supposed that the paametes of components depend on the status of the queuing netwok defined by a set of vaiables used fo the desciption of functioning pocess of the netwok. On the status of the netwok can depend: paametes of steams outing fom souces, nodes and jobs and distibutos; intevals of sevice duation in devices and intevals between adjacent jobs in steams fothcoming fom souces; sevice disciplines of jobs in node devices; a set of classification attibutes of jobs (class numbe, pioity level, task numbe). Fo the desciption of these dependences in the stuctued queuing netwok we intoduce an auxiliay component the status of model which defines some aggegated queuing netwok status, when defined paamete values of components. In the time of analysis and calculation of the stuctued netwok we tansfom it to non stuctued queuing netwok detemined by expession (1). Distibuto in the stuctued netwok is eflected as a node in non stuctued netwok which has infinite buffe size and the duation of sevice is constant and equals zeo. Plugs and sockets ae eflected in non stuctued netwok by distibutos with fixed outes fo jobs, and thei contacts by additional job classes detemined both in the module, and supe-module. Pobabilistic-time chaacteistics which elated to the stuctued components ae detemined depending on the type of these components. Let to some distibuto db fom the stuctued queuing netwok coesponds one node fom non-stuctued netwok with numbe i db, and to module coespond a set of nodes, distibutos, input and output plugs, modules and job classes, the numbes of which constitute the multitude nd, db, ip, op,, cl, coespondingly. Then the mean value of jobs with all classes in this system, in buffe of this system and in sevice devices equals zeo, u w v ni,,, db k = ni db k = ni db k =. The mean sojoun time fo job in this node, in buffe and in sevice device also equals zeo, ui,,, db k = wi db k = vi db k =. The intensity of job steam with k -class, entes coesponding distibuto, detemined by the following expession L K λi db, k = λi, k θi, l; idb, k. (2) i= 1 l= 1 The mean sojoun time u, k fo job with k -class, k cl in module detemined as the aveage of incoming and outgoing steams intensity of all tansition time fo job with k - class between input and output plugs of this module as follows u, k. 1 = λ λ il, jl, i ip l cl j op l cl λ τ λ ; jl, jl, i ip j op l cl. (3) The mean numbe n, k of jobs with k - class, k cl esiding in module defined as the sum of mean numbe of jobs with k -class in all components of this module n = n + n. (4), k i, k i, k i nd i Similaly, othe Pobabilistic-time chaacteistics may be constucted, elated to some module of the stuctued netwok, which ae defined 22

5 as some functional fom component chaacteistics, constitute this module. 4. ESTIMATION OF QUALITY PARAME- TERS The pimay goal of modeling and analysis of telecommunication systems is the estimation of quality paametes which this system can povide to subscibes. Two most impotant quality paametes ae the tansit delay of tanspot blocks of the data tansmitted ove established connection, and also the Jitte of this delay. The estimation of these paametes is especially impotant in analysis and planning of telecommunication systems which povide the sensitive to time delays- multimedia sevice. Most natually the tansit delay is defined as the aveage tansition time of jobs [17] between coesponding job classes and between coesponding nodes of the queuing netwok (coesponding element of the chaacteistic τ = { τ ; jl,} ). The job steam between these nodes and classes in the queuing netwok displays the steam of tanspot blocks between seve in telecommunication netwok and subscibe. Consequently, the estimation of Jitte is displayed as the dispesion of tansit delay. Conside an estimation of dispesion D τ ; jl, fo the andom value τ (.v.) ; jl,, which detemines the tansition time of some job with k -class, seviced in i - node into j -node and l -class. We assume that, this given.v. is detemined fo a multisevice netwok. Which means, that.v. u (existence time of job within k -class in i -node) ae independent. The.v. τ ; jl, itself is the sum of andom values u. Thus, with the assumption of thei independence, dispesion D τ ; jl, equals to the sum of dispesions of job existence time in all systems ove oute between coesponding nodes and classes D τ ; jl, = D u qp,, (5) whee [ ; jl, ] ( qp, ) R[ ikjl, ;, ] R is a set pai of nodes and classes, which detemines the job oute between these nodes and classes, ( ) [ ; jl, ] ( jl, ) [ ; jl, ] R, R. Dispesion D u of existence time fo job with k -class in i -node may be estimated by the appoximation of this job sevice pocess to equivalent sevice pocess of queuing system with M / M /1 type. Then, this dispesion is defined as follows vik, D uik, =. (6) 2 1 ρ ( ) 5. EXAMPLE NETWORK AND CALCULA- TION RESULTS The above pesented methodology is appoved by Example compute netwok (LAN) shown on figue 2, fo the tansmission of Figue 2. Conceptual LAN model MPEG pogam (film) on demand. Fo the calculation of the numbe of uses, which can eceive video films simultaneously, we design a calculation pogam using Math- CAD softwae and obtain the following esults figue 3-4. Figue 3 shows the aveage delivey time of diffeent I, P and B video fames, accoding to MPEG-4 standad, tansmitted fom seve to PC, depending on the numbe of simultaneously eceiving films uses. Figue 4 epesents the utilization coefficient of diffeent LAN components, namely seve, switch, Gigabit Ethenet, FastEhenet and PC, depending on the numbe of simultaneously eceiving films uses. The calculation pogam designed fo the stuctued queuing netwok model, which applied to the example communication LAN clealy and easily outputs the shown esults, fom which, it is seen that the aveage delivey time of I-fame (fo example) is geate than fo B- 23

6 fame. This esult is intuitively, acceptable due to the diffeence in size. Also, figue 4 impesses the bottleneck of the modeled LAN, which is the FastEthenet channel. With inceasing the numbe of simultaneously eceiving films up to appoximately 195 clients the utilization coefficient appoaches CONCLUSION Pactical expeience in modeling of eal telecommunication systems shows, that adequate model with lage dimension, detemined by numbe of nodes L and numbe of job classes K, exceeds the possibility of moden computing means. Consequently, the implementation of decomposition methods in telecommunication system modeling is pactically the unique way fo the solution of this poblem. This modeling appoach is validated and appoved by eal LAN and the obtained esults ae clealy demonstating the applicability of the stuctued queuing netwoks fo the modeling of communication netwoks. REFERENCES [1]. D.Ciullo, M.Mellia, and M. Meo, Taditional IP measuements: What changes in a today multimedia IP netwok. In Telecommunication Netwoking Wokshop on QoS in Multisevice IP Netwoks, pages IT- NEWS 28, 28. [2]. D.A. Rolls, G. Michailidis and F. Henández-Campos, Queuing analysis of netwok taffic: Methodology and visualization tools. Compute Netwoks, 48(3): , 25. [3]. T. Babu, J. Hayes. Modeling and Analysis of Telecommunications Netwoks. John Wiley & Sons, 24. ISBN [4]. R. Cohen and H. Radha, Steaming finegained scalable video ove packet-based netwoks Global Telecommunications Confeence, GLOBECOM., IEEE, vol.1, pp , 2. [5]. W.K. Wong, Y. Qian and V.C.M. Leung, Scheduling fo heteogeneous taffic in next geneation wieless netwok, GLO- BECOM, IEEE Global Telecommunications Confeence, IEEE, pp , 2. [6]. R.M. Guiguis and S. Mahmoud, Tansmission of eal-time multi-layeed MPEG-4 video ove ATM/ABR sevice, 2 IEEE Intenational Confeence on Communications, ICC 2., v.1, pp , 2. [7]. T. Inich and P. Stuckmann, Analytical pefomance evaluation of Intenet access ove GPRS and its compaison with simulation esults The 13th IEEE Intenational Symposium on Pesonal, Indoo and Mobile Radio Communications, v.5, pp , 22. [8]. Li Zheng and Lien Zhang, Modeling and pefomance analysis fo IP taffic with multi-class QoS in VPN MILCOM 2. 21st Centuy Militay Communications Confeence Poceedings, v.1, pp vol.1 [9]. Tao Tian, A.H. Li, Jiangtao Wen and J.D. Villaseno, Pioity dopping in netwok tansmission of scalable video, 2 Intenational Confeence on Image Pocessing, Poceedings., v.3, pp. 4-43, 2. [1]. D. Wu, Y.T. Hou, Y.-Q. Zhang and H.J. Chao, Optimal mode selection in Intenet video communication: an end-to-end appoach, 2 IEEE Intenational Confeence on Communications, ICC 2, v.1, pp , 2. [11]. F. Beitelli, G. Ruggei and G. Schemba, TCP-fiendly tansmission of voice ove IP IEEE Intenational Confeence on Communications, ICC 22, v.2, pp , 22. [12]. A.L. de Cavalho Klingelfus and W. Godoy J., Mathematical modeling, pefomance analysis and simulation of cuent Ethenet compute netwoks, 5th IEEE Intenational Confeence on High Speed Netwoks and Multimedia Communications, pp , 22. [13]. H. Shinbo, A. Idoue, T. Hasegawa and M. Ohashi, Evaluation of tcp pefomance on cdma2 1x system using compute simulation, 1th Intenational Confeence on 24

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8 Jounal of Theoetical and Applied Infomation Technology Figue1. Stuctued queuing netwok model 24 I-fame P-fame B-fame 21 Aveage delivey time, µsec Numbe of uses Figue.3.Tthe aveage delivey time of diffeent video fames, depending on the numbe of uses 26 5

9 Utilization Coefficien Sev Switch TansGEthe TansFEthe pc Numbe of Uses Figue 4. Utilization coefficient of diffeent LAN components, depending on the numbe of uses 27