Optimizing Resource Utilization in Wireless Multimedia Networks

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1 Optmzng Resource Utlzaton n Wreless Multmeda etworks Paramvr ahl Imrch Chlamtac András Faragó Dgtal Equpment Corporaton Unversty of Texas at Dallas Techncal Unversty of udapest Massachusetts, USA Texas, USA udapest, Hungary bahl@acm.org chlamtac@utdallas.edu farago@ttt-atm.bme.hu Abstract The task of supportng ntegrated mult-rate multmeda traffc n a bandwdth poor wreless envronment poses a unque and challengng problem for network managers. In ths paper we propose a novel bandwdth allocaton strategy whch parttons the avalable bandwdth amongst the dfferent traffc classes n a manner that ensures qualty of servce (QoS) guarantees for dgtal vdeo whle mnmzng the maxmum blockng probablty for voce and data connectons. At the connecton level, optmum utlzaton of the reserved bandwdth s acheved through ntra-frame statstcal multplexng, whle at the systemlevel, the delcate task of parttonng the bandwdth s accomplshed by developng an effcent algorthm whch uses traffc parameters consstng only of aggregate traffc load and the total avalable bandwdth. The algorthm bult on non-trval mathematcal results, s smple, robust, and well suted for practcal mplementatons.. Introducton Dfferent broadband servces requre dfferent amounts of bandwdth and have dfferent prortes. For example, a connecton for vsual communcatons wll n general requre more bandwdth than one for data communcatons, and a voce connecton wll n general be of hgher prorty than ether a data or a vdeo connecton. In response to these vared demands, the network desgner may choose to assgn dfferent amounts of bandwdth to dfferent types of traffc. The motvaton for such an approach stems from the desre to support dfferent knds of multmeda servces wth a reasonable level of performance and wthout lettng the demand from any one type shut-out other types of servces. The challenge for the desgner s to come up wth technques that are able to balance the needs of the varous applcatons wth the need of the system to accommodate as many connectons as possble. Ths task of provdng guaranteed qualty of servce wth hgh bandwdth utlzaton whle servcng the largest possble number of connectons can be acheved through a combnaton of ntellgent admsson control, bandwdth reservaton and statstcal multplexng. Supportng real-tme VR vdeo along wth voce and data over bandwdth-constrant networks contnues to be formdable problem. The dffculty arses because VR vdeo s unpredctably bursty and because t requres performance guarantees from the network. Whle resource reservaton schemes work best for CR traffc, there s no consensus on whch strategy should be used for VR traffc. On one hand, snce real-tme VR traffc s delay senstve, a resource reservaton scheme seems to be the rght choce, on the other hand, because VR vdeo s bursty, f resources are reserved accordng to peak rates, the network may be under-utlzed f the peak-to-average rate ratos are hgh. These two opposng characterstcs have resulted n a common belef that t s unlkely that performance guarantees can be provded to such bursty sources wth very hgh network utlzaton. Ths s the problem we address n ths paper, that s, can performance guarantees be provded to VR vdeo wthout sgnfcantly under-utlzng the bandwdth and can ths be done n conjuncton wth mnmzng the maxmum blockng probablty for voce and data connectons? Our soluton to ths problem conssts of three parts: () use a jont source-channel vdeo codec, (2) provde connecton lfetme reservaton for real-tme vdeo connectons wth optmum bandwdth utlzaton, and (3) partton the avalable bandwdth n a manner that ensures that the maxmum blockng probablty for voce and data traffc s mnmzed. From a connecton s perspectve, we advocate the use of a mult-resoluton jont source-channel vdeo codec Dependng upon the applcaton, ths codec may ether be a subband vdeo codec or a regon-based vdeo codec [], [2]. We then propose reservng the peak bandwdth for the prmary subband (or regon) whle lettng the secondary and tertary subbands (regons) compete for bandwdth dynamcally. A potental problem wth reservng accordng to the peak requrement s that most of the tme the actual amount used by the prmary subband s far below the amount reserved. To avod under-utlzng and wastng reserved bandwdth we have ntroduced the noton of ntra-frame statstcal multplexng n []. The bandwdth left over after the prmary subband (regon) has been transmtted s used for transmttng the remanng subbands (or regons). Also packets receved n error and whose retransmsson has been requested by the recever can be sent usng ths left-over bandwdth. In essence the dea combnes statstcal multplexng In the Proceedngs of the IEEE Internatonal Conference on Communcatons, Montréal, Québec, Canada (June 997)

2 at the system level wth statstcal multplexng at the connecton level to acheve optmum utlzaton. From the system s perspectve, we develop a smple algorthm that parttons the avalable bandwdth n a manner that mnmzes the maxmum blockng probablty for voce and data connectons whle guaranteeng bandwdth for VR vdeo connectons. It should be noted, that even when the dstrbuton of the dfferent traffc types s gven, fndng the optmal parttonng of bandwdth s a very dffcult task, and for the general case can be modeled by an Pcomplete graph colorng problem. The ntractablty of fndng the optmum s present already n the smplest stuaton when the traffc conssts of voce connectons only and the statstcs of the offered traffc are completely known. However the problem becomes even more dffcult when the wreless network s carryng ntegrated non-homogeneous traffc, a stuaton occurrng naturally n the case of wreless multmeda networks. In ths case estmatng the blockng probablty of connectons and ts applcaton n resource allocaton strateges s further complcated for two fundamental reasons: Although there are methods for computng blockng probabltes for ntegrated systems under specfc statstcal assumptons [8] (e.g. multrate Posson models), there are no smple closed formulas that can easly be appled to optmzng resource allocaton. It s realstc to expect that tradtonal statstcal assumptons wll not descrbe the traffc load precsely. Therefore, t s njudcous to make concrete assumptons based on any advance knowledge regardng the detaled statstcal propertes of traffc n a wreless multmeda network. Ths calls for a bandwdth management methodology that works under ncomplete nformaton and does not crtcally depend on specfc statstcal assumptons. In sectons 2 and 3, we propose a soluton for the allocaton of transmsson resources among dfferent traffc classes under ncompletely known condtons. When combned wth our ntra-frame statstcal multplexng proposal [], our soluton has the followng man propertes:. It provdes guaranteed QoS for on-gong real-tme vdeo sessons. Ths guarantee does not come at the expense of bandwdth, snce all of the reserved bandwdth s utlzed through ntellgent statstcal multplexng. 2. It s robust and nsenstve to statstcal assumptons, as t depends only on the average rates of the aggregated flow of traffc classes, but not on the detaled statstcs of the traffc mx and of the arrval process. From a practcal vewpont, ths nsenstvty s hghly advantageous, snce the detaled statstcal nformaton s typcally unavalable or uncertan. 3. The resultng allocaton s based on mnmzng a bound on the blockng probabltes that s proven to be asymptotcally optmal. The optmalty s also mportant as t sgnfes that for large systems t s suffcent to know aggregate flow rates, as the detaled knowledge of the traffc mx would not sgnfcantly contrbute to achevng smaller loss. 2. andwdth Parttonng Several bandwdth parttonng strateges that allocate bandwdth farly for dfferent traffc classes whle attemptng to acheve maxmum network throughput have been proposed n lterature [4], [5], [6]. Prevous studes of these technques n wreless networks have focused on the co-exstence of data and voce traffc, whle packet vdeo has generally been gnored. At the two extremes of such strateges s the Complete Sharng (CS) and Complete Parttonng (CP) (also called Mutually Restrcted Access) strateges, and n between are the rest, generally referred to as hybrd strateges. As the names suggest n CS, all traffc classes share the entre bandwdth. Although trval to enforce the man drawback of ths strategy s that a temporary overload of one traffc class results n degradng the connecton qualty of all other classes. In CP, bandwdth s dvded nto dstnct portons wth each porton correspondng to a partcular traffc class. CP s wasteful of bandwdth f the predcted bandwdth demand for a partcular traffc class s greater than the actual bandwdth demand. A compromse between CP and CS s a strategy n whch bandwdth s allocated dynamcally to match the varyng traffc load. Put another way an attempt s made to acheve statstcal multplexng at the burst level rather than at the connecton level. One such technque s called Prorty orrowng (P). A movng boundary exsts between the bandwdth allocated for the varous traffc classes and prorty users (usually voce traffc) are allowed to borrow bandwdth from non-prorty users (data traffc). It has been shown that ths hybrd scheme provdes better performance than both CS and CP, over a range of offered loads both n mcrocellular and macro-cellular envronments [5]. The reader s referred to [4] for a survey of such schemes. 2. Prorty Sharng wth Restrctons Good bandwdth allocaton schemes rely on dynamc allocaton of bandwdth to acheve hgh utlzaton. Whle dynamc allocaton at the burst level provdes good statstcal multplexng, t performs poorly for connectons that requre a certan qualty of servce. It wouldn t be too extreme to clam that the only practcal way to guarantee qualty of servce s by provdng bandwdth reservaton for entre lfetme of the connecton. In prevous studes, bandwdth allocaton for VR vdeo at connecton establshment tme was not seen as an nterestng and vable alternatve snce no real technque had been developed that would prevent wastage of reserved bandwdth. Snce t s very dffcult to accurately predct at connecton establshment tme the bandwdth requrement of a VR vdeo connecton, statc reservaton of bandwdth was generally gnored. However usng the technque from [] and [2] statc reservaton can be provded wthout wastng the precous bandwdth. Wth ths technque we can buld nto a medum access protocol provsons for both statc (lfetme) and dynamc bandwdth reservatons. Wth statc bandwdth reservaton we are able to guarantee a qualty of servce and wth In the Proceedngs of the IEEE Internatonal Conference on Communcatons, Montréal, Québec, Canada (June 997)

3 dynamc reservatons we are able to mprove the vsual qualty of the mages when addtonal bandwdth s avalable. A natural queston s to ask s, whch s the best scheme (CS, CP, or P) for bandwdth allocaton from the pont of vew of provdng guaranteeng qualty of servce for vsual communcatons. Clearly complete sharng s not sutable. Complete Parttonng, on the other hand can delver, but as noted earler s wasteful of bandwdth. Prorty orrowng s thus the most vable canddate. We have extended Prorty orrowng to nclude statc bandwdth reservaton wth a movng boundary. We call ths new scheme Prorty Sharng wth Restrctons (PSR). Fgure llustrates ths scheme. Packet Vdeo Data Packet Voce Contend Reserved Fgure : Prorty Sharng wth Restrctons refly, n ths scheme only real-tme vdeo connectons are allowed to make lfetme (or statc) reservatons; voce and data connectons make reservatons dynamcally. At connecton establshment tme bandwdth for vdeo connectons (for the man subband or regon) s allocated from the Reserved porton the avalable spectrum. Data Voce Vdeo- Dynamc Vdeo- Statc Data - P P P Voce - P Vdeo-Dynamc P - P Vdeo-Statc X X X - - orrowng allowed; P - orrowng allowed, preempton possble; X - orrowng not allowed; - - Don t care Table : Rules for Prorty Sharng wth Restrctons The amount of bandwdth reserved for such statc reservatons s determned by the network desgners (see secton 3). The remanng spectrum s dvded among voce, data and vdeo (for secondary, tertary subbands/regons) users and s used for dynamc burst level reservaton. In terms of prorty, voce users have a hghest prorty, followed by vdeo users, and data users n that order. Table provdes an example of who can borrow from whom.. Fgure 2 shows a sample of the performance data for the PSR scheme as compared to the P and CS schemes. Detals of the experment are provded next to the graph. The vdeo codec used for the experment was a regon-based ITU s H.263 vdeo codec. A segmentor preceded the H.263 codec dvdng the mage nto 5 dstnct regons before compresson. Ths s shown Fgure 3. The average voce and data traffc load was 30 Erlangs and 0 Erlangs respectvely. The traffc load for vdeo was ncreased by usng the same compressed vdeo stream multple and the average PSR was computed by calculatng the average PSR of each btstream at the output of the decoder and then takng the average of all these averages. Average PSR andwdth Parttonng and VR Vdeo Vdeo Traffc Compresson = Regon-based H.263 Avg. Frame Rate = 7.5 Hz Avg. Vdeo t rate = 24 kbps Image Dmensons = QCIF (76 x 44) # of Regons/Image = Offered Vdeo Traffc Load (Erlangs) Fgure 2: Comparsons of andwdth Parttonng Schemes 3. Mnmzng Maxmum lockng Probablty PSR Let us consder a wreless multmeda network supportng traffc types (denoted by T, K,T ) and wth a total avalable bandwdth. Let us assume that users from an arbtrary fnte populaton ndependently generate connecton requests that may requre dfferent amounts of bandwdth. Also let us assume that the average aggregate load (or traffc demand) D for traffc class T, s known ahead of tme. CP P Image Segmentor C A A H.263 Vdeo Compressor D Secondary Regons E Prmary Regon Fgure 3: Regon based H.263 codec In the Proceedngs of the IEEE Internatonal Conference on Communcatons, Montréal, Québec, Canada (June 997)

4 ow, gven ths traffc demand, we wsh to determne a nomnal allocaton of the bandwdth to be gven to the dfferent traffc classes, that s, the values, K, such that T receves under the constrant = =. (ote: transmsson bandwdth s assumed to consst of a number of basc bandwdth unts (U s). If the access protocol s TDM-based then the bandwdth resource translates to S Us, where S s the number of bts n one U.) Let d (t) be a random varable descrbng the actual nstantaneous aggregated demand by traffc class T. Assumng statonarty, the average demand D s the expected value of d (t) ndependent of t, that s, D = E{ d(t) }. We measure the Grade of Servce (GoS) for traffc class T by the saturaton probablty Θ = P ( d ( t) ). Ths s the probablty of the event that the nstantaneous load for traffc class T exceeds the bandwdth allocated for ths traffc type. The system GoS s measured by the worst,.e. the maxmum, of these saturaton probabltes : Θ = max Θ = max P( d ( t) ) () Thus, our optmzaton task can be stated as follows: Gven the aggregate load D for each traffc class T and the total system bandwdth, determne the allocated transmsson capacty for each traffc type such that subject to Θ = max P( d ( t) ) s mnmzed, = = The Smart Allocate Algorthm At frst glance, t appears mpossble even to reasonably approxmate the optmum n the above task, snce the only quanttes avalable for computng or at least estmatng the probabltes P ( d ( t) ) for any gven T are the D values. It s therefore vald to ask how can one tghtly estmate the saturaton probabltes from knowng merely the expected value of the randomly fluctuatng traffc load from each traffc type, as the generally used estmatons of such tal probabltes, known from the theory of large devatons, typcally requre much more nformaton, such as e.g. the knowledge of the moment generatng functon. In what follows we show that despte the presence of the unknown saturaton probabltes n the problem t s possble to fnd a good practcal soluton whch s based on transformng the problem nto a well defned optmzaton task, based on an asymptotcally optmal estmaton. For example, Θ = 0. 0 represents at most a % probablty that a gven request wll be blocked due to unavalablty of suffcent bandwdth. (2) The key mathematcal tool n ths soluton s a robust and tght estmaton of the saturaton probabltes, whch s based on the followng theorem. Theorem : Let X, K, X be ndependent random varables takng ther values from the nterval [ 0,]. Ther probablty dstrbutons are otherwse arbtrary and not necessarly dentcal. Set X = X and D = E( X) then for any C D the followng estmaton holds: C D (3) C D ( X C) e P C Furthermore, ths estmaton s the best possble n the followng sense: For any fxed ε > 0 and for any fxed D and C wth C D there exst nfntely many counterexamples for whch C D holds (4) C D εn ( X C) > e P C The proof of Theorem s based on a bound due to Hoeffdng [7], whch s a powerful generalzaton of the well known Chernoff bound on the tal of the bnomal dstrbuton. ote that Chernoff's bound alone would not be enough for our purpose. For space lmtatons we omt the proof, t can be found n [3] Usng Theorem we can bound the saturaton probabltes P( d () t ) as follows. At any gven tme t let X j be a random varable that takes the value of the bandwdth b requred by user j. Wth b values beng normalzed to the nterval [ 0,], X j [ 0,] holds. Then accordng to our model, wth X = d(), t D = D and C = we obtan an asymptotcally optmal GoS estmaton: D D P( d() t ) e (5) The estmaton (5) makes t possble to transform our orgnal problem nto a well defned optmzaton task n whch the unknown exact saturaton probabltes are replaced by the optmal bound (5): Gven the aggregate load D for each traffc class T and the total system transmsson bandwdth, determne the allocated transmsson capacty for each traffc class, such that ~ D D Θ = max e s mnmum, (6) subject to = = The asymptotc tghtness of the estmaton (5) guarantees that, n the asymptotc sense,.e. for large user populatons, the soluton for (6) wll be a very good soluton to the orgnal In the Proceedngs of the IEEE Internatonal Conference on Communcatons, Montréal, Québec, Canada (June 997)

5 problem, as well. The bass for solvng (6) s provded by the followng property. egn l= 0, u= Intalze Theorem 2: An allocaton, K, wth = = s an optmal soluton for (6) f and only f: D D D D e = = e K holds. (7) σ = l+ u 2 Compute () σ Mdpont of [ lu, ] Usng eq. (8) For the proof of Theorem 2 see [3]. In vew of Theorem 2, all that remans to be done for solvng (6) s to fnd an allocaton, K, wth = = such that t makes the GoS bounds (5) equal. To derve an algorthm for ths we need an auxlary functon defned as follows. For any fxed D > 0 and 0 < σ, let ( σ) be the unque soluton for of the equaton: D D e = σ (8) The unque solvablty of equaton (8) follows from the facts that for = D the left-hand sde s and otherwse t s a strctly decreasng contnuous functon of that tends to 0 as grows. (For a proof see [3]). It follows from ths that the value of ( σ).e. the soluton of equaton (8), can be computed wth arbtrary accuracy by a smple teratve search (nterval halvng) that approaches the root at an exponentally decreasng error. Usng the auxlary functons ( σ) we solve (6) such that we successvely terate a value 0 < σ for whch = holds wthn a gven error bound ε > 0. Ths algorthm that we call Smart Allocate s shown n Fgure 4. The correctness of the algorthm and the rate of convergence are stated n the followng theorem (for the proof see [3]). Theorem 3 Algorthm Smart Allocate converges to an optmal soluton of equaton (8) at geometrc rate,.e. the error decreases exponentally. It should be noted that n our stuaton when the transmsson capactes have to be allocated knowng only the aggregated average load n each cell, one could easly argue on a common sense bass that wthout any other nformaton the only reasonable soluton s to allocate the capactes proportonally to the load values. The load-proportonal allocaton would mean that D = K = D holds. On the other hand, we know from Theorem 2 that the optmal soluton of eq. (7), whch s the asymptotcally optmal GoS estmaton, s obtaned f and only f D D D D e = K = e (9) holds, whch s dfferent n general. Strcter bound End u = σ Fgure 4: Algorthm Smart Allocate Calculatng D for Dgtal Vdeo, Voce and Data If we let p(, be the probablty that user j wth traffc class T demands bandwdth b at any gven tme and let h(, be the expected holdng tme of such a connecton. Then D can be expressed as: D = p(, h(, b (0) l = σ Ease up on bound Yes b ~ = = σ ~ > ~ < ε ( ) () ( = σ, K, = σ Soluton has been found In (0) t s assumed that there are fntely many possble b values and they are normalzed such that 0 b always holds, otherwse they are arbtrary. Furthermore, statonarty s also assumed so p(, and h(, are ndependent of tme. The problem n usng (0) for computng D s that p (,, h (, and b values and also the actual number of connectons are not assumed known fortunately we don t really need these to determne D For CR vdeo connectons, D s smply a multple of the constant bt rate. For VR vdeo connectons, demand can be estmated as the multple of the average peak value of the prmary subband (or regon) n mage frames from several vdeo sequences. Thus D s determned by examnng the densty functons of the prmary subbands (regon) of several smlar vdeo sequences and then dervng the dstrbuton for o o Compute Total Capacty Check f Capacty s overused Check f Capacty s underused In the Proceedngs of the IEEE Internatonal Conference on Communcatons, Montréal, Québec, Canada (June 997)

6 the maxmum (peak) values. From ths derved dstrbuton the desre mean can be computed [0]. In [0] t s shown that the dstrbuton for the peak values of vdeo frame szes s determned to be: α ( y u) FY ( y) = exp[ e ], < y < where u and α ( > 0) are the locaton and the scale parameters of the dstrbuton, and Y s the random varable representng the peak values of the prmary regon n varous vdeo sequences. Then t s trval to show that the mean of Y s gven as: η y = u + α fnally, Dvdeo = M η y, where M s the estmated number of vdeo connectons to be supported; Assumng CR for voce connectons wth a nomnal rate of R, D voce = R, where s the estmated number of voce connectons; Knowng Dvdeo and Dvoce, we get Ddata = Dvdeo Dvoce. 3.. Illustratve Example To demonstrate the effectveness of the Smart Allocate algorthm, let us consder a smple example n whch the wreless multmeda network carres two types of traffc voce (T ) and vdeo (T 2 ). Lets consder a TDM-based system (smlar to GSM, IS-36, PACs etc.) and quantfy the bandwdth by the number of basc bandwdth unts (Us). Let us assume that we have altogether 99 Us whch we want to dstrbute among the two traffc types such that the maxmum blockng probablty for the connectons s mnmzed. Furthermore, let the arrval process for connectons be Posson and the blockng probablty for the two traffc types be computed by Erlang's classcal formula wth the average demands beng D = 20 Erlangs for voce and D 2 = 40 Erlangs for vdeo. In what follows, we show that our soluton gves better results than the ntutve load-proportonal allocaton approach. The load proportonal allocaton would assgn = 33 and 2 = 66 Us to the respectve traffc types. Then the largest blockng probablty, computed from Erlang s formula, s %. In contrast, usng our Smart Allocate algorthm for ths smple example we obtan = 37 and 2 = 66 Us. Then our upper bound on the largest blockng probablty gves the value 0.57%. An mprovement of 43% over the load proportonal approach. Implct n the calculatons above s the assumpton that one type of users do not borrow Us from other type of users. Thus, for the case of Partal Sharng wth Restrctons, the largest blockng probablty calculated by the Smart Allocate algorthm s a conservatve estmate. If we take nto account the rules outlned n Table and ncorporate borrowng of Us, then wth the assumpton of ndependence, the maxmum blockng probablty calculated wll be smaller than the one computed above. 4. Concluson We have presented a bandwdth reservaton, utlzaton, and parttonng strategy for supportng multrate multmeda traffc n resource constraned wreless networks. Through adept combnaton of connecton -level mprovements usng a low-bt rate mult-resoluton VR vdeo codec wth ntellgent bandwdth reservaton, and system-level mprovements parttonng avalable bandwdth, a wreless network can smultaneously support dgtal vdeo (wth QoS guarantees), voce, and data communcatons. Our method for parttonng and allocatng transmsson capactes to dfferent traffc classes s useful as t does not requre detaled pror knowledge of the underlyng traffc. The parttonng algorthm (the Smart Allocate algorthm) s smple, easy to mplement, and the geometrc rate of convergence ensures that the result s found quckly. These propertes make t well suted for practcal applcaton, even n the case when the aggregate load values change and the bandwdth allocaton has to be re-computed from tme to tme. References [] P. ahl and I. Chlamtac, andwdth Allocaton n Wreless etworks for Multresoluton VR Vdeo traffc, Proceedngs of the IEEE Computer Communcatons Workshop, Reston, Vrgna (Sept. 996) [2] P. ahl and I. Chlamtac, Strateges for Transmsson of Compressed Vdeo Over Error Prone Rado Channels, Proceedngs of Workshop on Moble Multmeda Communcatons, Prnceton, ew Jersey (Sept. 996) [3] P. ahl, I. Chlamtac, and A. Faragó, A ovel Approach to andwdth Parttonng n Wreless ATM etworks, Unversty of Massachusetts, ECE Dept. TR-96-CSE-0 [4] Y. H. Km, and C. K. Un, Analyss of andwdth Allocaton Strateges wth Access Restrctons n roadband ISD, IEEE Transactons on Communcatons, Vol. 4, o. 5 (May 993): [5] M. Schwartz, etwork Management and Control Issues n Multmeda Wreless etworks, IEEE Persoanl Communcatons, Vol. 2, o. 5, (June 995): 8-6 [6]. Krameche and M. Schwartz, andwdth Allocaton Strateges n Wdeband Integrated etworks, IEEE Selected Areas n Communcatons, Vol. SAC-4 (Sept. 986): [7] W. Hoeffdng, Probablty Inequaltes for Sums of ounded Random Varables, Journal of Amercan Statstcs Assocaton, Vol. 58 (9963): 3-30 [8] K. W. Ross, Multservce Loss Models for roadband Telecommuncaton etworks, Sprnger, 995 [9] E. J. Gumber, Statstcs of Extremes, Columba Unversty Press, ew York, 988 [0] P. ahl and I. Chlamtac, Influence of Avalable andwdth on the Statstcal Characterzaton of Compressed Vdeo, Unversty of Massachusetts, ECE Dept. techncal Report TR- 96-CSE-7 In the Proceedngs of the IEEE Internatonal Conference on Communcatons, Montréal, Québec, Canada (June 997)

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