SERVICE MODEL OF THE VOICE TRAFFIC IN MULTIPROTOCOL LABEL SWITCHING NETWORKS

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1 33 UDC SERICE MODEL OF THE OICE TRAFFIC IN MULTIPROTOCOL LABEL SWITCHING NETWORKS olodymyr B. Makovskiy, Oleksadr I. Romaov Natioal Techical Uiversity of Ukraie KPI, Kyiv, Ukraie This paper proposes ad ivestigates a service model of the voice traffic i multiprotocol label switchig etworks. The study of Multiprotocol label switchig etworks (MPLS) requires a formal descriptio of processes occurrig i them, developmet of mathematical models, reflectig mai properties of the ivestigated object ad allows calculatig the values i the required operatig mode. I this paper, we develop the model of fuctioig MPLS etwork i the form of a multi-phase, multi-chael, ope-loop system. We propose aalytical expressios describig the process of mutual ifluece whe servicig requests of various commuicatio directios. To determie parameters of quality of service quality ad badwidth chaels MPLS etwork, ecessary compare them with the values of ormed ad assess the compliace of the specified stadards. Itroductio The cocept of costructig ext-geeratio commuicatio etworks (NGN) defies the perspective for developmet ad costructio of etworks, which will be competitive i the telecommuicatios market i the ear future. May experts ote that techologies used i the etwork NGN should meet the followig basic requiremets [1, 2]: 1. IP based Protocol. 2. Esure collaboratio with etworks built earlier, ad especially with etworks ATM preset i large quatities i the telecommuicatios market of may developed coutries. 3. Maitai preset idicators of service quality i etworks usig a variety of techologies. 4. To esure the high peormace of equipmet, especially o highways etwork. 5. To guaratee required values of the delay ad jitter whe servicig the real-time load ad others. Problem statemet The purpose of this paper is to preset the MPLS etwork i a form of mathematical model reflectig itsservice operatio of voice load. I this case, the mai task of formal descriptio of the fuctioig etwork is to be a tool that eables practically to solve the problem determiig idicators of badwidth ad quality of service (QoS) o the etwork. Telecom33muicatios etwork MPLS belogs to the class of complex systems. Accordig to the existig defiitio i scietific ad techical literature of these systems [7,8] they have a set of properties. Mai properties amog them are the followig: heterogeeity of elemets, whose every elemet solves a particular task i the framework of a commo goal of the whole system operatio; relatioships complexity betwee elemets of the system ad parameters describig them; complexity of solvig the tasks; accidetal character i the system processes; multivariate descriptio of the system; the QoS depedece from may disparate of facts impact, etc. Whe buildig a model of the MPLS etwork, is advisable to adhere the followig priciples: 1. The fiiteess of the mathematical descriptio. This priciple implies that it should be processed iformatio o the fiite state variables i every poit of time. 2. The hierarchy of mathematical presetatio. This priciple is related to partitio of the studied MPLS etwork at several hierarchical levels with their iheret mathematical descriptio. 3. The modularity of the mathematical descriptio. The implemetatio of this priciple implies completeess of the mathematical descriptio o every level. 4. The equivalece of mathematical presetatio. This method reflects the fact that each of the followig o the level of descriptio cosideratio of processes should result i simplifyig all system properties. Proceedig from the above, MPLS etwork at the first stage of formalizatio is advisable to provide i the form of graph G ( N, M ), where N odes or switchig ceters, ad M brach etwork or budles of chaels, which they coect. To mathematically describe the telecommuicatios etwork, you should be able to aalyze aggregate braches i every way of iformatio trasmissio ISSN , Telecommuicatio Scieces, 2013, olume 4, Number , Natioal Techical Uiversity of Ukraie Kyiv Polytechic Istitute

2 34 TELECOMMUNICATION SCIENCES OLUME 4 NUMBER 1 JANUARY JUNE 2013 g ν µ ( i, j 1, N ) ad ways i every direct commuicatio g ( i, j 1, N). The mathematical apparatus of the graph theory allows peormig the procedure ad optimizig the solutio takig ito accout: possibilities of usig weighted coefficiets at the graph edges reflectig the essece of this process; the distribute load i ways of a miimum umber of edges (braches) or trasit odes i ways of trasmissio iformatio; possibilities to use a set of formalized algorithms, simplified simplex methods that allow determiig the most effective QoS; the trasitio from graph of matrix for the etwork descriptio ad, for example, usig the mathematical apparatus of theory of matrices to obtai the required cross-sectio i the etwork or to determie the totality of ways of iformatio trasmissio i direct commuicatio. Badwidth is oe of the most importat etwork characteristics. I the classic sese, badwidth is a etwork ability to serve a give load volume per time uit i all commuicatio directios to meet the requiremets of service quality. Estimatio of quality of service ad badwidth of telecommuicatio etworks Several works preset possible methods of problems solutio of estimatig the badwidth telecommuicatio etworks. We employ various assumptios to take the decisio sice problems of this class are quite complex. I the works [8, 9], the etwork is cosidered as a graph havig the braches, which represet paths with a certai speed trasmissio or a give umber of chaels. The developed mathematical apparatus eables to determie the miimum cross-sectios i directios of commuicatio determiig their limit o badwidth. I this case, we propose to assess the chael badwidth a total umber of chaels sectio without takig ito accout idicators of the service quality. I works [6] tesor models are used to estimate the badwidth of telecommuicatio etworks. The braches peormace i the etwork is described by relative weighted characteristics. The mutual ifluece of differet directios of commuicatio i the service process of load s is ot take ito accout o the braches of etworks. Ad i real etworks, each brach participates i the requests maiteace of 60% or more areas of commuicatio. I the work [7], i geeral, a etwork of direct commuicatios is cosidered ad the impact of usig alterative routes is ot take ito accout. I the work [10], we cosider the process of supplyig the same elemets etwork of load of differet directios of commuicatio ad use alterative routes i the process of service. However, some ucertaities arise causig errors i the calculatio process. Ad these errors are detected oly at the fial stage of calculatio leadig to icrease i time of the problem solvig. I additio, ew techologies (e.g. MPLS) have features that do ot take ito accout published methods. The aalysis shows that the methods of problems solvig of badwidth estimatio must take ito accout the followig factors: 1. Real operatig coditios of etworks, whe its elemets are iflueced ad should be take ito accout whe aalyzig the flows of various commuicatio areas, i.e. all threads operatig i the etwork. 2. Requests flows that go ito the service i telecommuicatios etwork have radom character. This irregularity of streams applicatios requires the service descriptio usig the mathematical apparatus of the probability theory. 3. Regardless of the type of the et flux, the decisio must be take i the form that allows users to obtai umerical values of required idicators. 4. Mathematical model of the badwidth evaluatio should take ito accout the idicator of quality of the service load. If this is ot the case, the this is ot the idicator of badwidth, ad fuctioig or service load. To solve problems of badwidth estimatio takig ito accout the above factors it is reasoable use the mathematical apparatus of queuig system (QS). Additioally, we should defie idicators of service quality, which allow estimatig the system suitability to peorm its fuctios. QS with obvious losses is used as a model for etworks servig the load real time (for example, voice load). I this case, q value, the service probability, ca be the idicator of the service quality. I practice, the iverse value: p = 1 q [9] is usually used at the load service i telephoe etworks. It is the probability of failure i maitaiig the logical chael with desired badwidth or trasmissio speed. Ofte the value p = 1 q is referred to as simply the probability of losses probability. Mathematical model of voice service i MPLS etwork We will costruct a mathematical model of voice load service i the MPLS etwork based o aalysis of the fuctioig etwork (twelve hosts) whose structure is show i Fig. 1.

3 . MANKOSKIY, O. ROMANO: SERISE MODEL OF THE OICE TRAFFIC IN MULTIPROTOCOL LABEL SWITCHING NETWORKS 35 Fig. 1. The structure of MPLS etwork The MPLS etwork is a set of odes ad braches, which are telecommuicatios resource. The iformatio is trasmitted the i etwork through commuicatio directios. Their idicators of the quality service ad badwidth ca be defied for every commuicatio directio. Therefore, the system should be, first ad foremost, obligatorily aalyzed for each directio of commuicatio. The we should register mutual ifluece all areas of commuicatio at each other. Ad oly the you ca make a coclusio o the accordace of mai idicators of the etwork required parameters. To reduce complexity ad dimesio of the problem, we propose to aalyze ad develop the model operatio of a MPLS etwork i several stages. A separate problem is solved at every stage such as: formalizig of the etwork descriptio with the specificity of the process operatio; decomposig the etwork o a set of directios coectio; ratig commuicatio directios o a level critical to fuctioig parameters; accoutig the mutual ifluece of lies commuicatio i uits ad braches of etwork; defiig the peormace idicators ad comparig them with regulatory parameters. The mai feature of telecommuicatio etworks is that the values of key idicators, such as quality of service, badwidth, reliability, are defied ad regulated by lies of commuicatio. Moreover, each lie ca have its ow differet from other ormative values. Therefore, whe solvig problems of aalysis ad sythesis of telecommuicatio etworks, it is ecessary to: 1. Cosider each commuicatio directio separately. 2. Take ito accout the mutual ifluece of commuicatio directios at each other i the process of load maiteace o the same etwork elemets. 3. To summarize fidigs ad draw a coclusio o coformity of required stadards of idicators for the etwork as a whole. The studies suggest that defiitio of required parameters of telecommuicatio etworks fuctioig should start with commuicatio lies with the most striget requiremets. As a rule, this is the commuicatio directio, from which the maximum umber of trasits i the shortest ways of iformatio trasmissio, the miimum umber of detours ad high demads to the service quality of icomig requests. We peorm the first stage of descriptio formalizatio of etwork operatio. To that ed, we fix the relatioship directio, havig a maximum umber of trasits i the shortest ways of iformatio trasmissio. We assume that it has the strictest requiremets to cotrolled parameters. Let it be the relatioship directio betwee the switchig ceter 1 ad 12 for this case. The braches of this commuicatio directio are preseted i the form of a set of queuig systems. Fig. 2 shows the etwork model. Fig. 2. The model of MPLS etwork Let us cosider this model behavior i terms that reflect real coditios of telecommuicatio etworks operatio. The quality idicator p = f (, ) [8] has oliear characteristics of chage depedig o parameters (the umber of physical or virtual chaels) ad (value of the load actig o the service) for a separate brach. For example, if the load is geerated by a ifiite umber of sources, otably by flows i the etwork

4 36 TELECOMMUNICATION SCIENCES OLUME 4 NUMBER 1 JANUARY JUNE 2013 of the simplest oes ad the etwork is calculated o the worst case p = f (, ), the depedece will have the form: p = i= i i 0 We will further use the mathematical apparatus for certaity. It describes the depedece p = f (, ) of the formula type (1). I additio, chage of ay parameter (p, or ) at least of oe brach etwork results i redistributio of the load flow, almost by 60 % of commuicatio lies. It meas that the model is very sesitive to chages of cosidered idicators ad parameters at ay etwork poit. The calculated expressio to determie the service quality ca be made for every commuicatio directio. If there is oly oe oly way of iformatio trasmissio i the directio, the probability of losses P i the directio of commuicatio ca be defied as follows: device, represetig a multi-chael brach. If the service resource is eough i the first phase, it goes to the secod service phase ad passes through the secod ode o the brach adjacet to it. Ad so o. It meas that the etwork is a multi-chael ad multi-phase service system. I additio, if the resource is ot eough i the selected path, the the applicatio goes to service at the first roudabout way. If the resource at is ot eough at the first roudabout way, the applicatio goes to service at the secod roudabout way, etc. If there is o required resource i ay roudabout way, the request leaves the system ad is ot served. If the resource is eough, the request leaves the system after the service. It meas that the system is ope. Thus, the Telecom etwork is a multi-chael, multi-phase, multiple lie, ope (applicatios removed from the system after the service, or i the absece of a resource for the service) system. Fig. 12 presets further specificatio of the fuctioig etwork model takig ito the accout a multiphase, multi-lie ad breach system, which allows proceedig to the model preseted i figure 3. k k P = 1 (1 p ) 1 (1 ) = = 1 = 1 i i= 0 i where: k a umber of braches i the way of iformatio trasfer; load eterig the service of the -th brach i the way of iformatio trasfer; a umber of chaels i the -th brach ways of t iformatio trasmissio. If there is χ idepedet ways i the directio of cotext, the probability of losses P (meas the same as idicator of the service quality) is: P χ k = 1 (1 ) i l= 1 = 1 i= 0 i We peorm the secod stage of specificatio of formalized descriptio of the etwork model. The request received i the directio of SC1 SC12 etwork is set i the first shortest path. I the first phase of service request, through the first ode, falls o the service Fig. 3. Model fuctioig MPLS etwork i the directio of commuicatio It should be oted that each multiphase model reflects a oe-way iformatio directio of the coectio directio uder study for MPLS etwork (Fig. 4).

5 . MANKOSKIY, O. ROMANO: SERISE MODEL OF THE OICE TRAFFIC IN MULTIPROTOCOL LABEL SWITCHING NETWORKS 37 Fig 4. Tract model of MPLS etwork:1 Replace label L2 to L6; 2 Replace label L6 to L7; 3 Replace label L7 to L11; 4 Isert label L1; 5 Isert label L2 (L2 upper label); 6 Delete label L7 (upper); 7 Delete label L11 (last) To icrease the reliability ad peormace, we recommed usig a idepedet way. The ext step of the model formalizatio of a MPLS etwork requires further geeralizatio of operatio ad accoutig of the mutual ifluece of differet commuicatio directios at each other. To this ed, it is ecessary to specify the service processes i braches of a MPLS etwork. The coectio directio cosists of ways of iformatio trasmissio, which icludes from oe to к braches. The service quality i commuicatio directios is as a rule from the subscriber to the subscriber. Therefore, whe aalyzig ad sythesizig telecommuicatio etworks, it is ecessary to solve the problem of traatio of orms values of losses i areas of commuicatio to the amout of allowable losses i every brach. As far as each brach of the telecommuicatio etwork may participate i maiteace of applicatios i a umber of di commuicatio directios, the requiremets to the service quality i the etwork ca be described by the followig system of equatios: k P = [ 1 (1 p j = 1, N; i j ; s= 1 l = 1 k gd Pgd = [ 1 (1 p d = 1, N; g d ; r = 1 f = 1,...; khy Phy = [ 1 (1,, = 1, ; ; p h y N h y w= 1 z = 1 where: P, P... P requiremets for the valid gh hy values of ormalized values of losses i the directios of commuicatio; p, p... p permissible values of losses probability i braches of the telecommuicatios etwork providig set requiremets to the service quality i commuicatio directios. The aalysis of coditios of telecommuicatio etworks fuctioig, the system of equatios (4) will reflect real processes oly whe the umber of trasits i all ways of iformatio trasmissio is equal. To achieve equality of a umber of trasits i all ways of iformatio trasmissio is quite difficult, so i most cases the requiremets to the service quality i the etwork will be described as a system of iequalities i the form: k P [ 1 (1 p j = 1, N; i j ; s= 1 l = 1 k gd Pgd [ 1 (1 p d = 1, N; g d ; r = 1 f = 1...; khy Phy = [ 1 (1 p, h, y 1, N; h y ; w= 1 z = 1 The studies show the coditios of equality will be carried out oly for those lies of commuicatio,

6 38 TELECOMMUNICATION SCIENCES OLUME 4 NUMBER 1 JANUARY JUNE 2013 which have the most striget requiremets to the service quality. Takig ito accout the fact that the first Erlag formula describes idices of the service quality p, p... p i braches for the accepted system of restrictios ad use of a simple flow of applicatio i the etwork, a system of equatios (4) takes the followig form: k P = { 1 [1 j = 1, N ; s = 1 l = 1 a = 0 k gd Pgd = { 1 [1 = d 1, N ; r = 1 f = 1 a = ; k hy Phy = { 1 [1, h, y = 1, N ; w = 1 z = 1 a = 0 Ad a system of equalities iequalities (5) takes the form (7): k P { 1 [1 j = 1, N; s= 1 l = 1 a= 0 k gd Pgd { 1 [1 = d 1, N; r = 1 f = 1 a = 0...; k hy Phy { 1 [1, h, y = 1, N; w= 1 z = 1 a = 0 Havig determied a system of equatios (6) or iequality (7), you ca first idetify idicators of service quality i the braches of telecommuicatio etwork, ad the the real value of the service quality i the commuicatio directios. It is worthy of ote that by usig expressios (6) ad (7) we solve the problem of aalysis of the etworks fuctioig, which is already operatig. This is usually calculatio of idicators of the quality of service ad badwidth lies of commuicatio ad their compariso with ormative values. Coclusio 1. The study of such complex systems as a MPLS etwork requires formally describig processes occurrig i them, developig mathematical models describig mai properties, peormace of etwork ad calculatig values i required operatio modes. 2. The model of MPLS etwork fuctioig is developed i the form of a multi-phase, multi-chael, the ope-loop system. We show that a geeral coclusio o coformity of etwork parameters fuctioig to specified requiremets ca be made oly after determiig key parameters of fuctioig of every commuicatio directio ad evaluatio of mutual ifluece of commuicatio directios at each other. 3. The expressio (6) ad (7) allows us describig the process of mutual ifluece i the applicatios service of various directios of commuicatio directios at the same elemets of a etwork. By solvig the system equatios (6) or the system iequalities (7), we defie idicators of quality of service ad badwidth chaels MPLS etwork, compare them with orms values ad determie the coformity with specified stadards. Refereces 1. Baklaov I.G. NGN: Priciples of costructio ad orgaizatio / edited Yu.. Cheryshova. М.: Eko-Tredz, p. 2. Gulevich D.S. Next Geeratio Network. М: Uiversity of Iformatio techologies BINOMIAL. Laboratory of kowledges, 2007, 183p. 3. RFC 3031: Multiprotocol Label Switchig Architecture. E. Rose, A. iswaatha, R. Callo. Jauary 2001, 61p. 4. RFC 3032: MPLS Label Stack Ecodig. E. Rose, D. Tappa, G. Fedorkow, Y. Rekhter, D. Fariacci, T. Li, A. Cota. Jauary 2001, 23p. Опубликовано: Зв'язок. 2006, 5. C RFC 3270: Multi-Protocol Label Switchig (MPLS) Support of Differetiated Services. F. Le Faucheur, L. Wu, B. Davie, S. Davari, P. aaae, R. Krisha, P. Cheval, J. Heiae. May 2002, 64p. 6. Lemeshko A.. Tesor model decisio task of the multigroud routig traffic volume with the required time leadig i bipolar telecommuicatio etwork // Applied radio electroics ol.2, p. 7. Scherbia L. P. Theory of military commuicatio etworks. L.: AS, p. 8. Lazarev.G., Savvi G.G. Сommuicatio Networks maagemet ad commutatio. M.: Coectio, p. 9. Davydov G.B. Rogiskiy.N. Tolcha A.Y. Networks of commuicatio M.: Coectio, p. 10. Romaov O.I., Nestereko M.M. Modified method estimatio quality of service i TCNS with establishmet coectio // Collectio of scietific labours of ITI NTUU KPI. 3. K.: ITI NTUU KPI p. Received i fial form March 20, 2013

Importance Analysis of Urban Rail Transit Network Station Based on Passenger

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