Analytical Model for Voice oer IP traffic characterization A.E.GARCÍA 1, K. D. HACKBARTH 1, A. BRAD 2, R. LEHERT 2 1 Telematic Engineering Grou of Communication Engineering Det. 2 Institut für achrichtentechnik Uniersity of Cantabria A. los Castros s/n, 39005 Santander (Cantabria), Tel: +34 42-201549, Fax: +34 42-201488 SPAI agarcia@tlmat.unican.es htt://www.tlmat.unican.es Abstract: - The scoe of this aer is to derie a set of simle formulas to dimension irtual aths in IP/ATM acket networks that carry comressed oice traffic. The roject further gies an oeriew of oice oer acket technology with a secial focus on oice oer IP and its most rominent standard ITU-T H.323. After introducing a network model for oice oer acket networks, the dimensioning formulas for the communication alication are deried for two different leels: call and burst leel. The obtained formulas for acketized oice serices are alidated with the use of the simulation software OPET. Key-Words: - Voice oer IP, Internet telehony, Traffic modeling, network simulation. 1 Introduction Voice transmission has more than enough networks tyically based on ackets like for examle IP, ATM or Frame-Relay are winning ositions regarding traditional circuit switching networks as PST and ISD. Basically we can consider two reasons that they hae taken to the necessity of carrying out the integration of oice in acket networks. On one hand reduction of the costs comes gien by the best use in bandwidth that is made in these networks. This fact is translated in the case of oice in code outlines and efficient oice comression, silences comression, and the ossibility of carrying out statistical multilex. On the other hand new serices aears, secially based on IP, indeendent to the network technologies and user's latforms, see [1]. We are this way scenarios of such serices as multimedia data oer single line, ideoconference, multicasting, CCA's (Call Center A.), unification of messages, etc. Crucial oints so that comanies accet to use of IP oice serices it has more than enough they are fundamentally their readiness, qualities comarable to the ublic serice of oice, the reliability, and their manageability [2]. This way, client of business waits some concrete arameters of quality of serice [3], at least comarable to that of traditional serices. 2 Voice oer IP For technologies of such comressed oice as oice oer IP (VoIP), oice oer ATM (VoATM) and oice oer Frame-Relay (VoFR), different standard exist. 2.1 ITU-T H.323 Denominated "Systems for multimedia communications based on ackets", it is art of the family of standard H.32x that secify the serices of multimedia communication on different networks, as ISD (H.320) or BB-ISD (H.231 and H310). H.323 is not secific of IP, so that it can be used by IPX or AleTalk. Howeer, it makes use of IETF standards: RTP (Real Time Protocol) and RTCP (Real Time Control Protocol). It describes all the entities of a system H.323:!"Terminals: roide full-dulex connections in real time, oint to oint and oint-multioint, being able to be comuters or secial deices as ideohones.!"gateway: allows the interconnection with other terminal (H, PST or ISD).!"GateKeeer: roides the admission control and addresses translation serices on terminals, gateways and MCUs.!"Multioint Control Unit (MCU): gies suort for multioint conferences. 3 etwork and network layer model To carry out the modeling of the network we can leae of a scenario where a number of users of a cororate network can establish oice calls by means of the connection through a VoIP gateway and a sulier of VoIP serice. Gateway includes a IP router that guides the calls carried out in Internet toward a VoIP gateway of the PST network in which the destination telehone is located. Voice is comressed in client's art using G.729 recommendation with silences comression, what
means that ackets will only be transmitted to the gateway and Internet when oice actiity is detected. During oice actiity a fixed number of audio samles is either acked in RTP, UDP or IP, taking a size of deterministic ackets. Protocols stack would be the corresonding to H323 standard: 5: Session H.323 4: Transort RTP/UDP RTCP/TCP /RSVP 3: etwork IP IP 2: Link (MLPPP/FR /ATM-AAL 1) (MLPPP/FR /ATM-AAL 1) 1: Physical (SET) (SET) Table 1 : Stack for H.323 oerip terminal 4. Analytic models for oice serices In general, analytic models can be diided in three different scale leels: call leel, burst leel and cell/acket leel. In this study call leel will be used to determine the number of irtual connections that they are necessary under a robability of gien loss. In the burst leel bandwidth will be calculated for each one of these connections, being obtained the width of uialent band for the oice transort through a irtual channel VBR. If this bandwidth was multilied by the number of established irtual channels at the call leel, it will be a good estimate of the width of global band. This estimation will be alidated ia the simulation in the next chater. 4.1. Call leel The VoIP gateway described in the reious chater can be characterized as a ure loss system because calls will only be acceted as long as there are free orts for the calls aailable. Thus a traffic model would look like the following: A R 1 2 S Fig. 1: Traffic model for call leel Origin of calls is characterized random when in a ery short time interal!t"0 three conditions are true:!"stationarity: robability for one call in this time interal tends to #!t indeendent of t with λ=const.!"single arrials: robability that more than one call arries in a ery small time interal tends to zero i.e. no batch arrials. Y!"Call indeendence: each call originates indeendent from other calls Assumtion of random call arrials is reasonable if the number of otential callers is large. With this assumtion call arrial rocess with the offered traffic A=λ t is oissonian. The number of serers (=orts) s is finite, therefore call losses can occur and offered traffic A is the sum of carried traffic Y and lost traffic R. The calls shall be sered first-in first-out (FIFO). If also call termination is considered as random, serice time can be assumed exonentially distributed, which agrees fairly well with actual telehone conersation times [1]. With that gien descrition of the call leel traffic system it can be classified using the Kendall notation as a M/M/s(0), that is Poissonian inut rocess, exonential serice (call holding) times, s serers and no waiting room. Traffic tye in this system is firstorder random traffic also known as Erlang-traffic. We are only interested in the steady state of the system, so we can derie formulas from global balances of the steady state transition diagram of the M/M/s(0) system: λ λ λ λ 0 1 r-1 r r+1 s-1 s µ rµ (r+1)µ sµ Fig. 2: M/M/s(0) steady state transition diagram Erlang formula will be used to determine the number of irtual channels under a gien loss robability. This loss robability P r is ual to the blocking robability P B = P(all connections are busy) = P(i=s) because of PASTA roerty (=Poisson Arrials See Time Aerage) of Poisson streams [4] which leads to the Erlang B formula. For the determination of the number of lines r needed for a gien loss robability recurrence formula is used iteratiely. 4.2. Burst leel 4.2.1. On-Off oice model Multimedia traffic is ery bursty in nature and simle models as the Poisson rocess do not cature the imortant characteristics of these sources. To model bursty traffic sources different aroaches are aailable many of them using Marko modulated rocesses (MMP). These are doubly stochastic rocesses in which each state of states of embedded marko chain originates another stochastic rocess. If this originated rocess is a Poisson rocess the MMP is called Marko modulated Poisson
rocess (MMPP), if it is deterministic it is a Marko modulated deterministic rocess (MMDP). One secial case that is ery suitable to model oice sources is the On-Off model. This is a MMDP with only 2 states as shown in the following figure: OFF Fig. 3: On-Off model According to the On-Off model signal stream of a single source is modeled through an alternating suence of burst and silence eriods. Duration times of burst and silent eriods are exonentially distributed with mean t =1/$ and t OFF =1/% resectiely. During the burst eriod ackets with fixed length are generated with constant interarrial time!t. Some studies hae roosed t =0.4 sec and t OFF =0.6 sec [5], setting the transition rates to $=1.6 and %=2.5. Steady state robabilities can easily be deried from balance uations of aboe grah: OFF =%/($+%)=0.6 and =$/($+%)=0.4. In the actie state ackets are generated with constant seed =L/!t (-eak rate) with L as the acket length and!t as the constant acket interarrial time. This is also deicted in the next figure: t =0.4 sec t=const t +t OFF = 1 sec t OFF =0.6 sec time Fig. 4: On-Off oice acketization Each generated oice acket with two G.729 audio frames has a fixed length of 20 bytes audio + 40 bytes oerhead = 60 bytes, generated eery 20 msec. So the eak bit rate of oice source in actie state is = 24000 bs or k = 50 ackets/sec. Aerage data rate is E() = = 9600 bs and the standard deiation. (1) σ () = (1- ) 11758 bs = 4.2.2. Aggregating On-Off sources The multilexing of indeendent On-Off sources is outlined in the figure 5. Each source generates bits/sec in it s actie state. Aggregated data rate would be in the CBR source case. source 1 2 E() = buffer serer C = ε > E() Fig. 5: Multilexing of On-Off sources Because of silence comression, one can rofit from statistical multilexing gain so that the needed serer caacity C will be C = ε with ε as the number of uialent CBR sources. If k indeendent oice sources are actie with robability, (-k) sources are inactie with OFF = (1- ). Further there are ( oer k) ossibilities for choosing k elements out of. Thus the robability of k actie sources follows a binomial distribution: (2) In the mean E(k) = sources are actie so the aerage data rate generated by sources is E() = E(k) =. Therefore ε should satisfy the condition ε > E(k) =. If serer caacity is less than otential maximum source data rate an oerload condition can aear. Under this condition serer buffer will be filled and if no more buffer sace is aailable acket loss occurs. This can also be deried from Marko chain of M()/M/ binomial source model. If the serer roides caacity for ε sources with S u < ε < S o all states from S o to cause oerload. (-1) (-s u) 0 1 2 s u s o -1 2 s o 2 s u s o (-1) Fig. 6: M()/M/ state transition diagram Oerload robability is calculated as the robability that they are more oice sources actie than caacity is aailable: P = P ( k > C) = i i ( 1 ) i ol (3) i= C + 1 with C as the serer (=backbone) caacity in number of sources, k as the number of actie sources and as the total number of sources. ote that for ure loss systems without buffers oerload robability becomes loss robability of the system. In the following we will assume a ure loss system. To take into account loss robability as a function of and the number of sources, serer caacity
must be augmented by a correction alue γ(p B,,). This γ can be interreted as a multilier of standard deiation of aggregated data stream. Corresonding formulas are deried below: (4) C = E( ) + γ ( PB,, ) σ ( ) = ( + γ ( PB,, ) (1 )) (5) C = = E ) + γ( P,, ) σ( ) = + γ( P,, ) (1 ) (6) (7) ( B B C C = = = = + γ ( PB,, ) CCBR const lim = lim( + ) = (1 Resectiely, total caacity of aggregated binomial sources in bs, total number of uialent circuits for sources in units, uialent caacity for one binomial source in units, and limiting behaiour of the uialent caacity. For a great number of sources uialent caacity of one source conerges against it s actie robability =40% esecially for great loss robabilities that go along with small γ alues. As an examle for 1000 sources under P B =0.1 needed number of uialent circuits is 420 which gies us a uialent caacity of 42%. Theoretically slowly conerges against with 1 /. 4.2.3.Poisson source with waiting system model M/M/1(m) In the first analytic model a ure loss system was resented which gae an exression to estimate the needed bandwidth of a acket oice backbone. ow we introduce a system buffer of size m to estimate further QoS arameters such as mean waiting time and mean queue length. This will allow a comarison with the alues obtained by simulation. To model the bursty traffic of On-Off sources in the waiting system, a simlification of the source behaiour will be done. The On-Off source in the reious chater was modeled with exonentially distributed actie and silence eriods with the mean alues t and t OFF resectiely. ow the burst length t and the burst interarrial time t +t OFF will be considered as exonentially distributed. This allows aroximating the system as M/M/1(m) and aoids comlicated models such as MMPP/E k /1(m), which are used in literature, see e.g. [4], [5]. The addition of two exonential distributions with mean t and t OFF and ariances t 2 and t OFF 2 leads to a hyoexonential distribution with the mean alue t +t OFF and the ariance t 2 +t OFF 2. Because we assume burst interarrial time as exonentially distributed with mean t +t OFF = 1 sec and not as hyoexonentially distributed, we oerestimate the ariance with (t +t OFF ) 2 = 1 sec 2 in comarison to the correct alue of the ) hyoexonential distribution with ariance t 2 +t OFF 2 = 0,52 sec 2. Therefore this model will also oerestimate the needed caacity and gies a essimistic scenario, which makes sure that results remain useful. 4.2.4. Aggregating the modified On-Off sources Multilexing of modified On-Off sources leads to an aggregated arrial rate of λ= bursts/sec. Serice rate µ of the system is a function of the mean burst length E(L) and the serer caacity C as shown in the traffic system model for M/M/1(m): λ E(L) P B m Fig. 7: M/M/1(m) traffic model Formulas for the QoS arameters of M/M/s(m) and their deriation can be found in any traffic theory book, e.g. [4]. System behaes like a M/M/1 system with infinite buffer when the buffer size is ual or greater than 100. 4.3. Cell/Packet leel In IP/ATM networks signal stream of a MMM or an On-Off source is normally not encasulated in only one acket but a suence of ackets or cells. Therefore cell leel ruires more sohisticated models such as semi-marko models, fluid models or Marko modulated oisson models. These models are mainly ruired for the design of router and switching uiment. They normally need much rocessing time and therefore are not well suited for dimensioning of large networks with many nodes. For reasons stated the cell leel will not be considered exlicitly. If oice ackets in On-Off model or the bursts in M/M/1(m) model are further diided into smaller transmission units such as ATM cells this can be taken into account by incrementing the source data rate in the burst model. 5. Validation of the VoIP models To carry out the erification of the reious models it is necessary to deelo the behaior of the oice sources comletely. Most of the rograms for alone network simulation hae defaulted traffic generators based on tyical distributions (exonential, Erlang, etc). This makes necessary to design a model on-off based on generic modules of this tye, emulating the behaior of the same one by means of the corresonding machine of finite states. C
5.1. on-off source model As it was indicated reiously, on-off source consists of two basic states, actiity and silence. It should gie the ossibility to establish such arameters as the distribution of time among arrials, silences distribution and distribution of calls duration. Resulting machine of states is directed by three tyes of eents, one to create the ackets, and two for the transition among states: Fig. 8: On-off source rocess model. 5.2. Gateway model For the interconnection of oice nodes, it is necessary to define a deice that format the oice ackets and route toward the address of corresonding destination. Gateway model roides transmission / recetion orts for 100 oice nodes, and an interconnection ort with other sub-networks, so that its direct connection is facilitated to the dorsal connection, which will be used for the study of statistical multilex of all the sources. Gateway has a finite queue of size m oice ackets that can be used to adjust the extreme retard to end. Also the routing caacities are ery simle, so that different ackets are addressed toward the destination node that should be modeled as a drain located in the sub-network. This tye of nodes allows to obtain ery interesting statistical figures, e.g. acket loss rate and total receied ackets. Additionally, by means of an additional arameter, gateway caacity in bits and/or in ackets, it is ossible to model the global queue of incoming oice ackets. 5.3. etwork model Once designed the different nodes, it is necessary to establish the network toology that allows to interconnect them. Selected network model consists on the interconnection of two subnetworks through a dorsal connection. First subnetwork contains the gateway node with access to 100 oice nodes in star. Second subnetwork consists on a single oice node that takes charge of icking u the traffic of the dorsal connection, writes statistics of receied ackets, and finally it destroys all them. Fig. 9: Full etwork model and delay comonents 6. Validation of the analytic models by means of simulation For the obtaining of corresonding results we will treat network model described before as a block in which inut arameters will be the number of users, the size of gateway queue m, and the caacity of dorsal connection C. Howeer, the behaior of the sources will be fixed for all the simulations (it is fixed the rate of burst for examle). Probabilities corresonding to each one of the states and OFF is also fixed resectiely at 0.4 and 0.6, and the time among arrials is of 0.02 sec. (for ackets of fixed size of 480 bits). The most interesting results are mainly the robability of loss P B and the mean and ariance of delay in the gateway queue. By means of these alues it is ossible to obtain the minimum of caacity low gien conditions of P B and delay. 6.1. comarison with the binomial model Grahic results shown next reresent the caacities of the dorsal connection for robabilities of inferior losses at 10-4, 10-3 and 10-2, obtained by means of simulation and making use of binomial attern. It is obsered that binomial attern carries out an oerestimation of necessary caacity in the connection for all cases, such and like it was assumed in its theoretical analysis. Backbone caacity 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Loss robability PB<0.001 10 25 50 75 100 umber of sources Binomial model Simulation Fig. 10: Theoretical and simulated backbone caacity (loss rob. < 0.001)
The reason rests in that the size buffer m used by the simulated model disaear in the theoretical attern. This buffer diminishes the robability of loss substantially, imeding that it leaes of ackets that found the busy connection they can be lost. This is translated in a better use of connection. Howeer, an unexected effect aears, en-to-end delay then is increased. Backbone caacity 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Loss robability PB<0.01 10 25 50 75 100 umber of sources Binomial model Simulation Fig. 11: Theoretical and simulated backbone caacity (loss rob. < 0.01) fruency 0.5 0.4 0.3 0.2 0.1 0 Distribution of burst loss lengths simulation set: 100C1200000m80S128 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 burstlength in ackets Fig. 12: Distribution of burst loss length. 6.2. comarison with the M/M/1(m) system While for the comarison of indiidual alues it is not reresentatie, it was obsered that binomial model gae better results in comarison with M/M/1(M) attern. Howeer, it is ruired of more intensie studies that suort this statement. Another interesting fact when comaring both models was the one that stos relatiely big sizes of buffer (79 ositions) and caacities of connection dros (50%) Probability of loss in the M/M/1(m) model it is inferior to the one obtained by simulation. This way, theoretical model underestimates the caacities of the according connection it increases the size of the buffer and the load of the connection. A ossible exlanation is that due to the nature of the bursts generated by on-off sources, a buffer near to congestion is much easier that it is surassed its caacity that in the case of Posisson sources. A detailed analysis of this henomenon will be reason of future studies. 7. Conclusion Simulations and deeloed analytic models are relatiely simle leaing aside certain asects that aear in the reality. For examle, suosition used by M/M/1(m) system of a FIFO queue, suoses that sources with long eriods of burst can reent that other sources can be enqueued, when it would be ossibly more aroriate to use more ual oliticians of haing enqueued, as for examle Round Robin. Binomial model can be used for the estimation of the caacities of the connections and the control of admission of calls. Howeer, as ure system of losses that is, it cannot be used for the estimation of the buffer, in site of being fundamental arameter in the oice gateway. For the calculation of this alue, it is ossible to make use of M/M/1(m) model like comlement to binomial model. Bursty model that it neither follows the loss of ackets can be dear by means of theoretical models. Only by means of simulations it can be carried out, what takes to think of new studies that allow to define those arameters that affect to this behaior, taking like base the simulations for the obtaining of aroriate theoretical models. References: [1] Kulenkamff, G.: Der Markt fuer Internet Telefonie - Rahmenbedingungen, Unternehmensstrategien und Marktentwicklung. Diskussionsbeitrag r. 206. Wissenschaftliches Institut fuer Kommunikationsdienste GmbH, Juni 2000.. [2] White Paer: Market oortunities in Internet rotocol telehony. Killen & Associates, Inc 1997. htt://www.okint.com/01_05.html. [3] Rinde, J.: The future direction of Internet Telehony and its effect on business. V conference aer, 1997, htt://www.uler.com. [4] Akimaru, Haruo: Teletraffic: theory and alications. 2nd ed. Sringer-Verlag London 1999. [5] Schwartz, Mischa: Broadband Integrated etworks. Prentice Hall, 1996.