On the Efficiency of Shaping Live Video Streams

Transcription

1 On he Efficiency of Shaping Live Video Sreams György Dán and Vikoria Fodor KTH, Royal Insiue of Technology Elecrum 9, 6440 Kisa, Sweden Absrac In his work he efficiency of shaping live video sreams is considered. We propose low complexiy shaping algorihms adequae for real-ime operaion and supporing applicaions wih a wide range of delay olerance. The effec of shaping is invesigaed considering video sreams muliplexed a an oupu link wih a small buffer o absorb packe scale congesion. The advanage of using small buffers when ransmiing video sreams is he limied delay and delay variaion. Consequenly, we concenrae on he loss characerisics o evaluae he performance of he proposed soluions. We presen mahemaical analysis based on fluid flow modeling and he heory of large deviaions and confirm he resuls wih ulaion. Keywords: qualiy of service, live video ransmission, source shaping, packe scale buffering, large deviaion heory INTRODUCTION The ransmission of live video raffic over he Inerne is a fundamenal problem of nework design, since many video applicaions require limied end o end packe loss, delay and delay variaion. I is generally acceped ha raffic conrol funcions mus be employed o guaranee hese service requiremens a a reasonably high nework load. The inroducion of new conrol funcions in he Inerne, however, is a criical issue. Firs, a very high number of neworking devices has o be updaed or replaced, second, he complexiy of he conrol funcions may limi he span and he ransmission capaciy of he nework. Recenly research effors address his quesion by proposing probe based endpoin admission conrol (PBAC) soluions [6, 3] o provide qualiy of service guaranees in a way ha he funcionaliies of he rouers are kep ple and raffic conrol funcions are placed ino he hoss or edge gaeways only. In he PBAC schemes a hos, before ransmiing raffic wih QoS requiremens, probes he nework s ransmission capabiliy by sending a sequence of probe packes and decides abou he ransmission based on he saisical quaniies of he probing process. While he admission conrol ensures ha he load of he nework says reasonably bounded, addiional conrol funcions can be applied a he hoss o increase he accepable load, like raffic shaping o decrease he bursiness of he raffic sreams and hus decrease he packe loss a he muliplexing nodes and forward-error correcion o recover from packe losses. In his work we invesigae how source shaping can increase he efficiency of live video ransmission considering MPEG video sreams muliplexed a an oupu link wih small buffer. The advanage of using small buffers is ha he delay and delay variaion is sricly limied by he buffer size an hus only he packe loss has o be conrolled. Source shaping provides he following favorable properies: i) i does no require global decision or any modificaion in he nework, ii) can improve he service qualiy of sreams wih differen QoS requiremens and raffic characerisics and iii) can be inroduced in he nework gradually. We propose wo soluions o shape video sreams wihou packe loss and wih given delay bound. The firs scheme follows he ideas presened in [0], and deermines he shaper rae considering he delay bounds of all he frames waiing in he shaper buffer. The second scheme considers only he delay bound of he las frame in he buffer, hus provides a soluion wih very low compuaional complexiy. We evaluae he performance of he proposed schemes wih ulaion and wih analyical mehods based on fluid flow approximaion applying he heory of large deviaions []. As he delay and delay variaion is limied by he buffer size, he analysis focuses on he packe loss characerisics, as average loss, he loss of shaped and unshaped sreams and he disribuion of packe losses among he frame ypes of he MPEG sream. The paper is organized as follows. In he nex secion we discuss relaed works and resuls. Secion 3 describes he sysem model wih he sources, he shapers and he muliplexer. Secion 4 explains he wo shaper algorihms we propose, and Secion 5 presens he analyical model o evaluae he efficiency of source shaping. In Secion 6 we presen and discuss numerical resuls and in Secion 7 we conclude our work. PREVIOUS WORK In his secion we survey previous research resuls ha inspired our work on shaping and ransmission of on-line video

2 raffic over he Inerne. Tradiional soluions o provide QoS guaranees in packe swiched neworks are based on per flow reservaion messages and capaciy reservaions (e.g., RSVP), and as a consequence, suffer from scalabiliy limiaions [7]. To circumven hese scalabiliy problems, several recen works have proposed some form of probe based endpoin admission conrol (PBAC). In hese soluions he hoss (endpoins) send a sequence of probe packes before user daa ransmission, o deec he level of congesion in he nework. The level of congesion and hus he possibiliy of user daa ransmission wih he required QoS parameers is deermined from he saisical quaniies of he probe ransmission process, like probe loss probabiliy [6], delay and delay variaion [] or packe marking probabiliy [5]. An excellen evaluaion of he various designs can be found in [3]. The PBAC schemes provide QoS guaranees wihou he need of conrol funcions inside he nework, suppor QoS requiremens depending on he users needs, and do no require he complex descripion of he raffic sreams. Our work follows he basic idea of hese soluions by invesigaing how addiional conrol funcions a he hos can increase nework efficiency. The ransmission of video sreams requires limied packe loss, end o end delay and delay variaion. Obviously, hese values depend on he size of he buffers a he rouers. Depending on he size of he buffer one can differeniae beween packe scale buffering and burs scale buffering. In he firs case only a small buffer is provided o absorb packes arriving ulaneously, hus he packe loss probabiliy migh be high while he delay is sricly limied. In he second case he buffer provides enough space o absorb larger burss and consequenly, limis he loss probabiliy while he conrol of delay and delay variaion becomes a complex issue [4]. The use of packe scale buffering for ransmiing delay and loss sensiive daa like coded video sreams have been proposed in [6, 5, 6], showing ha low packe loss probabiliy and high nework uilizaion can be achieved if he peak rae of he sreams is low compared o he link capaciies. In [5, 6] packe scale buffering is proposed ogeher wih source shaping. I is proved ha a single buffer leaky bucke is an opimal shaper in his scenario. The shaping of sored variable bi rae video sreams is widely analyzed in he lieraure. Recen soluions are based on nework calculus e.g., [4, ] or he bounding inerval dependen (BIND) characerizaion of he sreams [7, 8]. Only a few works address he shaping of live video sreams. The main quesions o face in his case are he radeoff beween he delay inroduced a he shaper and he available informaion on he raffic o be ransmied and he effeciveness and he complexiy of raffic predicion. A soluion for shaping wih limied packe loss is proposed in [9]. The shaping is based on he BIND characerizaion. The BIND parameers are coninuously updaed as he saisical properies of he sream change, which seems o be a raher complex process considering he real-ime operaion. In [] he auhors sudy saisically idenical, peak rae conrolled and leaky bucke shaped sources feeding a buffered muliplexer. The goal is o find he shaper rae ha minimizes nework resources like buffer and bandwidh, while keeping he delay limied. The soluion, however, can no handle muliplexed sources wih differen characerisics. Algorihms for lossless shaping of individual sreams are presened in [0] and [3]. In hese works he saisical quaniies of he shaped sreams are analyzed, bu nework scenarios are no considered. In [3] shaping wih delays in he range of -30 seconds is proposed, an adequae soluion for broadcasing applicaions. The algorihm shown in [0] works wih shaper delays less han a second. To avoid he flucuaion of he shaper rae, he algorihm uses pas frame sizes o predic fuure raffic inensiy, and needs o know he lengh of a GOP in advance. Our conribuion o his line of works is he definiion of shaping algorihms wih very low complexiy ha suppor he ransmission of live video sreams wih a wide range of accepable shaper delay and he analysis of he effec of shaping when he video sreams are muliplexed a an oupu link wih small buffer. To he bes of our knowledge, such resuls have no ye been presened in he lieraure. 3 MODEL DESCRIPTION MPEG source d r d n Shaper r n Muliplexer Figure : The considered sysem wih MPEG sources, source shapers and a muliplexer. The sysem model considered in his paper is shown in figure. The sysem includes raffic sources, source shapers and a muliplexing node wih a single oupu link. The sources generae MPEG coded sreams, he mos commonly used encoding scheme for he sorage and ransmission of video informaion. MPEG is a family of sandards used for coding visual informaion in a digial compressed forma. I has been designed o suppor a broad range of ransmission raes and hence a broad range of visual qualiy. In an MPEG sream informaion is sored as a sequence of frames, corresponding o a sequence of picures in a video, generaed wih fix ime inervals. Compression is achieved by eliminaing he spaial and emporal redundancy of he informaion in he C

3 frames. Spaial redundancy is decreased by inraframe coding of he individual frames, while emporal redundancy is reduced by inerframe coding beween subsequen frames. Thus he sequence of frames consiss of inraframe coded frames (I frames), and inerframe coded prediced (P frames) and bidirecionally prediced frames (B frames). The subsequen frames beween wo consecuive I frames form a group of picure (GOP). The GOP srucure of he sreams can be differen, depending on he required qualiy. A ypical example for he sequence of frames is IBBPBBPBBPBB. As a consequence of he coding scheme, informaion loss in he hree frame ypes has differen effec on he perceped visual qualiy. The loss of daa in an I frame propagaes forward hrough he nex GOP and backward o he las P frame (affecing up o 4 frames if he number of frames in an open GOP is ). Meanwhile, he loss of daa in a B frame only affecs ha paricular frame. The inra- and ierframe coding resuls in he flucuaion of he frame sizes on wo imescales. The inraframe coding compresses complex scenes wih less efficiency, and consequenly, he frame sizes change on he long erm a he scene changes. The inerframe coding leads o shor erm frame size flucuaion, since I frames are usually significanly larger han P frames, and P frames are larger han B frames. The scale of he flucuaion is abou a facor of 3 on he long, and a facor of 0 on he shor erm. Shapers are used a he sources o decrease he frame o frame flucuaion of he coded video sream. The shaper we use in his work is a single buffer leaky bucke, as i is proved o be opimal for neworks wih small buffers [5]. Frames leaving he encoder are sored in he shaper buffer and are ransmied wih a given ransmission rae. The shaper is designed o inroduce limied delay and provide lossless ransmission, ha is, no daa can be los due o buffer overflow or delay limi violaion. To achieve his, he shaper ransmission rae has o be adjused depending on he size of he arriving frames and he buffer size has o be large enough o sore he frames waiing for ransmission. If he frames arrive a a regular basis, he maximum number of frames in he buffer can be bounded by he raio of he delay limi o he frame inerarrival ime. The shaped video sreams are muliplexed a a nework node wih a single oupu link. Since he arrival rae of he sreams can emporarily exceed he capaciy of he ougoing link, he node is equipped wih a buffer o sore arriving daa. In his work we consider packe scale buffering, he size of he buffer is in he order of he raio of he oupu link ransmission capaciy o he peak rae of he video sreams. 4 SOURCE SHAPING ALGORITHMS FOR LIVE VIDEO STREAMS In his secion wo algorihms are proposed o conrol he rae r of he source shaper when ransmiing live MPEG video sreams. Boh aim o minimize he maximum and he variance of he ransmission rae, and fulfill he following requiremens: i) The ransmission delay in he shaper does no exceed he predefined maximum shaper delay and he shaping is lossless. ii) The algorihms are ple in erms of he complexiy of he shaper rae calculaion and he amoun of informaion considered, a requiremen o assis real-ime operaion. iii) The algorihms provide efficien soluion for shaping wih a large range of shaper delays. iv) The algorihms do no require any apriori informaion on he encoding scheme of he video, i.e., he number and sequence of I, P and B frames in a GOP. Boh of he algorihms assume ha he shaper can deec he ype of he arriving frame. In general, he following rules apply o selec he shaper rae r:. The shaper rae can be changed a any ime when a new frame is generaed and placed ino he shaper buffer.. The shaper rae is increased if he new frame can no be ransmied wihin he delay limi d. 3. The shaper rae is decreased if he new frame is of ype I, and all he raffic in he shaper buffer can sill be ransmied wihin he delay limi. This rule is based on he assumpion ha small P or B frames do no indicae inensiy change in he video sream. To decrease flucuaion, he new shaper rae is calculaed as he average of he curren rae and he minimum rae allowed by he delay limi. 4. P and B frames enering he shaper when he buffer is empy are ransmied wih a rae such ha he frame leaves he buffer before he new frame arrives, i.e., in one frame ime, in order o preven he shaper from keeping daa before larger I and P frames arrive. The wo proposed algorihms described in he following differ in applying rule 3. The firs algorihm is opimal in he sense, ha he residual accepable delay is considered for all he frames sored in he shaper buffer o deermine he minimum shaper rae. The second, plified algorihm does no follow he delays of he individual frames in he buffer, and calculaes he shaper rae based on he buffer conen only. Shaper rae conrol based on residual ransmission delays The algorihm based on residual ransmission delays (RTD) works as follows. For every frame enering he shaper, he size of he frame f i and is laes deparure ime i d is recorded. The minimum shaper rae r min, allowed by he delay limi is calculaed as r min max n N f 0 n j f i N j i N j ()

4 where N is he number of frames in he shaper a ime and f 0 is he residual size of he firs frame in he buffer a ime. The residual size is less han he original frame size if he ransmission of he frame has already sared. The complexiy of he shaper rae calculaion is O N addiions and O N divisions, where he value of N is bounded by d T f rame. In addiion o he acual shaper rae, he shaper has o remember he size and he arrival ime of he frames waiing for ransmission. A sysem clock has o be mainained and read a each frame arrival. Shaper rae conrol based on he buffer conen This soluion does no record he residual accepable ransmission delay for he frames waiing in he shaper buffer, he shaper rae calculaion is based on he buffer conen (BC). When frame i arrives o he shaper, is size is added o he amoun of daa in he shaper b b f i, denoing he buffer occupancy before he frame arrival as b. The minimum shaper rae is calculaed considering he buffer occupancy a he ime of he new frame arrival: r min b d To avoid delay bound violaion for frames sored in he buffer, he shaper rae can be decreased only if he buffer is empy before he new frame arrival (i.e., b ()=0), a significan consrain on rule 3 above. As a consequence, his plified BC algorihm follows he decreasing inensiy of he sream wih some delay compared o he RTD soluion. The complexiy of he BC algorihm, however, is very low (one addiion and one division a each frame arrival), here is no need for sysem clock informaion and only he number of byes waiing in he shaper buffer has o be sored. 5 ANALYTICAL MODEL In his secion we presen an analyical mehod o calculae he overall packe loss probabiliy and he disribuion of he packe losses among sources a a muliplexer performing packe scale buffering. The analysis is based on he fluid flow modeling of he raffic sreams and uses resuls of he heory of large deviaions o approximae probabiliies of rare evens. A shor summary of he basic ideas behind he large deviaion heory is presened in [], Chaper 4.3. The long erm overall packe loss probabiliy P loss is he raio of he average packe loss rae o he average packe arrival rae: P loss m E λ c () m λ c λ c dp (3) where m is he mean rae of he muliplexed flows, λ is he insananeous arrival rae, P is he probabiliy disribuion of he insananeous arrival rae and c denoes he link capaciy. We can express P loss wih he insananeous loss probabiliy p as P loss E p λ where p λ c λ Large deviaion heory provides a way o approximae ail probabiliies like P λ c and hus he loss probabiliy. Firs we inroduce P β, he shifed probabiliy measure of λ, such ha dp β e βλ dp where ψ β ψ β E e βλ and µ β, he cumulan generaing funcion as µ β lnψ β From his, he original probabiliy can be expressed as dp e βλ ψ β dp β (4) (5) (6) (7) This shifed disribuion can be accuraely approximaed around is mean m β E β λ by a normal disribuion wih he same mean. Since β is a free parameer m β can be moved o he value of ineres for he ail probabiliy, in our case o c. The corresponding value of β, denoed by β is given by m β c (8) From he definiion in Eq. 6 m β µ β E β λ, and σ β m β µ β are he expeced value and variance of he shifed disribuion P β. Consequenly, if λ is no consan (is variance, σ β is posiive), hen m β is sricly increasing where µ λ is finie and equaion 8 has a unique soluion. The evaluaion of he inegral in Eq. 3 leads o [] P loss πmβ e β c µ β σ β The above calculaed overall loss probabiliy gives also he loss probabiliy of he individual sreams if hey have he same characerisics. However, he loss disribuion among sreams wih differen characerisics will be uneven. Assume, ha packes arriving in overload periods have he same loss probabiliy independenly of he source of he packes. Sill, sources send a differen proporion of packes during hese periods. For bursy sreams he burss are correlaed o overload periods as hey are causing he overload hemself. As a resul, bursy sreams experience higher loss probabiliy han smooh ones. The loss disribuion among sources in he case of burs scale overflow can be esimaed as described in []. Similarly o Eq. 3, he loss probabiliy of he individual sream i is equal o P i loss E p λ i m i (9) (0)

5 is he insananeous rae, and p is he loss probabiliy a ime. The probabiliy shif mehod can be applied in his case as well. Assuming, ha he probabiliy ha λ significanly where m i is he mean rae of he sream, λ i exceeds c is very small, P i loss can be approximaed as P i loss P loss m m i β c m i () To calculae he overall loss probabiliy using Eq. 9 and he loss disribuion among he sources using Eq. he value of β, m i β, σ i β and m β has o be derived. These values can be expressed in closed form if λ i and λ have some sandard disribuion (e.g., for normal disribuion). In he case of real sources,however, hey have o be calculaed numerically. Assuming, ha he disribuions of he individual sreams are known from measuremens, and he muliplexed sreams are independen, he following sysem of equaions has o be solved m i β E λ i m β c () m β m i β (3) i σ β d dβ lne eβλ i e βλ i σ i β E e βλ i E e βλ i σ i β (4) i d E eβλ i dβ E e βλ i d dβ lne eβλ i E λ i e βλ i E λ i e βλ i E e βλ i 6 PERFORMANCE EVALUATION (5) (6) In order o assess he effeciveness of he proposed source shaping soluions we consider he saisical quaniies of he shaped video races and packe loss saisics in case of muliplexing video sreams a a single node wih packe scale buffering. The presened resuls are based on he analyical mehod described in secion 5 and on ulaions using ns-. The considered scenario is shown in figure. I consiss of n independen sources generaing MPEG video sreams, single buffer leaky buckes as source shapers and a muliplexing node. Each sream is shaped wih some delay consrain and hen muliplexed a he node wih a small buffer o resolve packe scale congesion. We presen resuls for wo MPEG-4 video races, a soccer game wih an average bi rae of. Mbps and a alk show wih an average rae of 540 kbps. The races are approximaely 3600 seconds, hus frames, and 700 seconds, hus frames long. The frames of he MPEG races are packeized o 88 byes, as given for he ranspor sream in he MPEG- sandard [IEC6883]. Throughou he ulaions we consider a single ougoing link a he muliplexing node wih a capaciy of 45 Mbps in he case of he soccer game and of.5 Mbps in he case of he alk show. We choose he link capaciies proporionally o he average rae of he sreams. This soluion allows us o compare resuls a he same link uilizaion and level of saisical muliplexing. The muliplexing buffer can sore up o 5 packes. Trace saisics Firs we consider he saisical properies of a single video sream before and afer shaping for differen values of maximum shaper delay d. Figures and 3 show he number of ransmied bis in a frame ime for he original and shaped race of he soccer game and he alk show respecively. The maximum shaper delays are 40 ms and 0 ms, he shaping is performed using he BC shaper algorihm. Even he relaively small shaper delay of 40 ms allows a significan reducion of he rae flucuaion. The maximum ransmission rae is decreased from 3.6Mbps o 3Mbps for he soccer game race and from 3.Mbps o Mbps for he alk show race. ϕ(ι) Bis/frame ime x Original Shaped 40ms Shaped 0ms Frame number (i) Figure : Number of bis ransmied in a frame ime for he soccer game race wihou shaping and wih shaping for d=40 ms and d=0 ms, using he BC shaper algorihm. ϕ(ι) Bis/frame ime 7 x Original Shaped 40ms Shaped 0ms Frame number (i) Figure 3: Number of bis ransmied in a frame ime for he alk show race wihou shaping and wih shaping for d=40 ms and d=0 ms, using he BC shaper algorihm.

6 BC RTD BC RTD Moving average CoV Moving average CoV Max delay[ms] Max delay[ms] Figure 4: CoV of he shaped soccer race versus maximum shaper delay d, considering he BC and RTD shaping algorihms. 0 0 Figure 5: CoV of he shaped alk show race versus maximum shaper delay d, considering he BC and RTD shaping algorihms. 0 0 Loss probabiliy Unshaped num 40ms Unshaped num 0ms Loss probabiliy Unshaped num 40ms Unshaped num 0ms Figure 6: Loss probabiliy of shaped and unshaped sreams for shaped sream. The alk show race and he BC shaping algorihm is considered. Simulaion validaes he analyical resuls. Relaive loss probabiliy Unshaped num 40ms Unshaped num 0ms Figure 7: Loss probabiliy of shaped and unshaped sreams for half of he sreams shaped. The alk show race and he BC shaping algorihm is considered. Simulaion validaes he analyical resuls. Relaive loss probabiliy Unshaped num 40ms Unshaped num 0ms Figure 8: Relaive loss probabiliy of shaped and unshaped sreams for shaped sream. The alk show race and he BC shaping algorihm is considered. Simulaion validaes he analyical resuls. Figure 9: Relaive loss probabiliy of shaped and unshaped sreams for and half of he sreams shaped. The alk show race and he BC shaping algorihm is considered. Simulaion validaes he analyical resuls.

7 Figures 4 and 5 show he coefficien of variaion (CoV) of he races, defined as CoV N r N r i ϕ i i j i N GOP ϕ j N GOP E ϕ (7) where N r is he number of frames in he race, ϕ i is he number of bis ransmied in he ih frame ime and E ϕ E f is he average number of bis ransmied in one frame ime. The CoV is calculaed using he moving average over one GOP ime as mean value. This way he CoV reflecs he frame o frame rae flucuaions wihou he rae variaion due o he scene changes in he race. The wo curves in he figure show he CoV values for he wo proposed shaping soluions. The graphs show ha for small values of shaper delay d he CoV decreases very rapidly, reflecing ha a delay of a couple of frame imes (0-80 ms) allows he smoohing of he ransmission raes of consecuive I, P and B frames. A larger delays he marginal gain decreases significanly. The wo shaping mehods resul in ilar changes in he CoV values. As expeced, he RTD mehod decreases he rae flucuaions beer. For large values of d he difference is around 0% in he erms of CoV reducion, since he RTD mehod can adjus he shaper rae more precisely based on he informaion mainained in he buffer, while he BC mehod over- and underesimaes he shaper rae and has o make correcions laer. As he difference is no significan, due o is pliciy we focus on he BC mehod in he followings. Packe loss probabiliies In his par we invesigae he average packe loss probabiliy of muliplexed video sreams as a funcion of he average load, defined by he raio of he sum of he mean raes of he sreams o he link ransmission capaciy. The presened resuls are based on mahemaical analysis, ulaion resuls are shown o demonsrae he accuracy of he mehod. Simulaions were run 0000 o seconds o have enough loss evens even in he case of loss probabiliies in he order 0 5. We show resuls for shaping he alk show race wih he BC mehod. To see he effec of inroducing shaping gradually a he sources wo scenarios are considered. In he firs one only one sream is shaped, while all he oher muliplexed sreams are ransmied unshaped. In he second scenario half of he sreams are shaped a he source. Figure 6 shows he loss probabiliy of he shaped and unshaped sources for shaper delays of 40 ms and 0 ms in he case of shaped source. Figure 7 shows he resuls for he scenario where half of he sources are shaped. Figures 8 and 9 show he relaive loss probabiliies of he shaped and unshaped sources compared o he average loss probabiliy. The numerical resuls are validaed by ulaion. The resuls reflec, ha he mahemaical analysis works well for losses up o 0, hen slighly overesimaes he loss probabiliy as a consequence of he large deviaion approximaion. Comparing figures 6 and 7 i can be seen ha shaping half of he sources decreases he overall loss probabiliy by roughly one order of magniude. The resuls wih differen shaper delays show ha in he case of he considered alk show race, shaping wih a delay of 40 ms is almos as efficien as shaping wih a delay of 0 ms in he erms of reducing he loss probabiliy. For he soccer race shaping wih a delay of 0 ms has a slighly bigger effec. This is due o he lower raio of emporal redundacy which induces lower peak o mean raio. The resuls show in Figures 8 and 9 ha he decrease in he loss probabliy achieved by shaping he sources increases as he average load, and hus he loss rae decreases. Since he desired loss probabiliy of video sreams is in he order 0 5, he difference can be up o 35%, even if only one sream is shaped. The gain achieved depends on he sream characerisics, for he soccer race he experienced gain was less, around 0% a a loss probabiliy around 0 5. Packe loss probabiliies in I, P and B frames In addiion o he average packe loss probabiliy of he sreams i is worhwhile o evaluae he packe loss probabiliy in individual frame ypes, since i affecs he perceped visual qualiy. Relaive frame loss probabiliy Unshaped I P B Shaped I P B Figure 0: Relaive packe loss probabiliy in I,P,B frames of he shaped and unshaped sreams for d = 0 ms, half of he sreams shaped. The alk show race and he RTD shaping algorihm is considered. Simulaion resuls. Figure 0 shows he packe loss probabiliy in I, P and B frames relaive o he average loss probabiliy for he shaped and unshaped sources for he scenario when half of he sources is shaped wih a maximum shaper delay of 0 ms. The figure shows ha while in he case of unshaped sources he loss probabiliy in he I frames is he highes, up o 00% above he average loss probabiliy and ha in he B frames is he lowes, in he case of shaped sources he loss probabiliies in he individual frame ypes are roughly he same. In he I frames he decrease of loss probabiliy is around 60%. Consequenly, as losses in he I frame have a significan effec on he visual qualiy, he posiive effecs of he shaping include no only lower loss probabiliy bu also he improved disribuion of hese losses among he frame ypes.

8 The presened resuls show he following effecs of source shaping. Considering he race saisics, shaper delays in he 0-40 ms range decrease he CoV of he sream significanly, higher delays inroduce decreasing marginal gains. Comparing he wo proposed shaping algorihms, he ple BC algorihm works raher well, especially a small shaper delays. Resuls on muliplexing he video sreams a a muliplexer wih small buffer show ha he shaped sreams experience lower loss probabiliies han he unshaped ones, he difference is abou 30%. The gradual inroducion of he source shaping in he nework has a significan effec, he loss probabiliies decrease wih one order of magniude if half of he sources adop shaping. The posiive effec of shaping is refleced by he disribuion of losses among he differen frame ypes in he video sream. Muliplexing unshaped sreams resuls high loss probabiliy for he I frames, his loss probabiliy decreases significanly if he sream is shaped. 7 CONCLUSION In his paper we proposed and evaluaed soluions ha assis live video ransmission over he Inerne. Specifically, we considered he scenario, when he MPEG coded video sreams are shaped a he source hos and nework rouers provide small buffers o resolve packe scale congesion, moivaed by he curren rends of designing raffic conrol soluions, where he main idea is o add funcions o he hoss and keep he operaion of he nework rouers ple. We proposed compuaionally ple shaping algorihms ha are adequae o shape live video sreams wih a wide range of delay olerance a he shaper and provided analyical mehod o evaluae he efficiency of he proposed soluions. The analyical and ulaion-based performance evaluaion proved ha i) a ple shaper algorihm based on buffer occupancy and delay limi resuls in efficien shaping in many cases; ii) even shaping wih very low delay bound, adequae for real-ime applicaions, improves he performance in erms of packe loss probabiliy and he packe loss disribuion among he differen frame ypes; and iii) shaping provides a means o improve he qualiy of individual video ransmissions even if no all he hoss shape heir raffic. Finally, as ongoing work we furher invesigae he mehods o assis video ransmission over he Inerne. Specifically, we are ineresed in he efficiency of source shaping versus buffering a he rouers and buffering versus forward error correcion. References [] Broadband nework eleraffic, Final repor of acion COST 4, Springer, 996. [] G. Bianchi, A. Capone, Ch. Perioli, Throughpu Analysis of End o End Measuremen-Based Admission Conrol in IP, in Proc. of IEEE INFOCOM 000,, March 6 30, 000, pp [3] L. Breslau, E. W. Knighly, S. Shenker, I. Soica and H. Zhang, Endpoin Admission Conrol: Archiecural Issues and Performance, in Proc. of ACM SIGCOMM 000, 8 Aug.. Sep., 000, pp [4] R. Cruz, A Calculus for Nework Delay, Par I: Nework Elemens in Isolaion, IEEE Transacions on Informaion Theory, vol. 37, no., Jan. 99, pp [5] R. B. Gibbens and F. P. Kelly, Disribued Connecion Accepance Conrol for a Connecionless Nework, in Proc. of he 6h Inernaional Teleraffic Congress, June 7, 999, pp [6] V. Elek, G. Karlsson, R. Ronngren, Admission Conrol Based on End-o-end Measuremens, in Proc. of IEEE INFOCOM 000,, March 6 30, 000, pp [7] E. W. Knighly, H-BIND: a New Approach o Providing Saisical Performance Guaranees o VBR Traffic, IEEE Infocom 96, March 996. [8] E. W. Knighly and H. Zhang, D-BIND: an Accurae Traffic Model for Providing QoS Guaranees o VBR Traffic, IEEE/ACM Transacions on Neworking, vol.5, no., April 997, pp.9-3. [9] H. Zhang and E. W. Knighly, RED-VBR: A Renegoiaionbased Approach o Suppor Delay-Sensiive VBR Video, ACM Mulimedia sysem Journal, May 997. [0] Simon S. Lam, Simon Chow, David K. Y. Yau, An Algorihm for Lossless Smoohing of MPEG video, ACM SIGCOMM Compuer Communicaion Review, vol. 4, no. 4, Oc. 994, pp [] J-Y. Le Boudec and O. Verscheure, Opimal Smoohing for Guaraneed Service, IEEE Transacions on Neworking, vol.8, no.0, Dec [] N. Modani, P. Dube and A. Kumar, Measuremen Based Opimal Source Shaping wih a Shaping+Muliplexing Delay Consrain Proc. of IEEE Infocom 000, March 6 30, 000,pp [3] J. Rexford, S. Sen, J Dey, W. Feng, J. Kurose, J. Sankovic and D. Towsley, Online Smoohing of Live, Variable-bi-rae Video Proc. of Inernaional Workshop on Nework and Operaing Sysems Suppor for Digial Audio and Video, May 997, pp [4] J. W. Robers, Traffic Theory and he Inerne, IEEE Communicaions Magazine, Jan. 00., pp [5] M. Reisslein, K. W. Ross, S. Rajagopal, Guaraneeing Saisical QoS o Regulaed Traffic: The Muliple Node Case, in Proc. IEEE Decision & Conrol 98, pp , 998. [6] M. Reisslein, K. W. Ross, S. Rajagopal, Guaraneeing Saisical QoS o Regulaed Traffic: The Single Node Case, in Proc. IEEE Infocom 99, pp , 999. [7] A. Mankin, F. Baker, B. Braden, S. Bradner, M. O dell, A. Romanow, A. Weiurib, and L. Zhang, Resource ReSerVaion Proocol - Version Applicabiliy Saemen Some Guidelines on Deploymen. RFC 08, Sepember 997.