Designing communication architectures for interorganizational multimedia collaboration

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Designing communication architecturesfor interorganizational multimediacollaborationSrinivas Ramanathan a , P. Venkat Rangan a b & Harrick M. Vin aa University of California , San Diegob Department of Computer Science and Engineering , University ofCalifornia at San Diego , La Jolla, CA, 92093–0114Published online: 04 Nov 2009.

To cite this article: Srinivas Ramanathan , P. Venkat Rangan & Harrick M. Vin (1992) Designingcommunication architectures for interorganizational multimedia collaboration, Journal ofOrganizational Computing, 2:3-4, 277-302, DOI: 10.1080/10919399209540187

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JOURNAL OF ORGANIZATIONAL COMPUTING, 2(3&4), 277-302 (1992)

Designing Communication Architectures forInterorganizational Multimedia

Collaboration

Srinivas RamanathanP. Venkat Rangan

Harrick M. VinUniversity of California at San Diego

Advances in computer and communication technologies have stimulated the inte-gration of digital video and audio with computing, leading to the development ofvarious computer-assisted collaborations. In this article, we propose a multilevelconferencing paradigm called super conference for supporting collaborative interac-tions between geographically separated groups of users, with each group belong-ing to possibly a different organization. In a super conference, each participantmust receive and display the composite media stream obtained by mixing mediastreams transmitted by all the other participants. Hierarchical communication ar-chitectures are naturally suited for media mixing in super conferences. We presentalgorithms for designing hierarchical mixing architectures that optimize real-timeend-to-end delays of media. In order to improve their real-time performancefurther, we propose multistage mixing techniques by which mixers can carry outmixing concurrently with communication. Surprisingly, the optimal architecturesfor multistage mixing are widely different from those of monostage mixing (in which,mixing and media communication sequential as opposed to concurrent). Based onreal-time delay constraints of multimedia, we obtain interesting limits on the sizesof both super conferences and groups within super conferences in optimal hier-archical architectures, which go to show their high scalability in terms of both themaximum number of participants and the geographical separation between them.

At the Multimedia Laboratory at the University of California, San Diego, wehave implemented a conferencing system on an environment of Sun SPARCsta-tions equipped with digital multimedia hardware. As an interesting application ofthe conferencing system, we have developed a telepresenter by which users canremotely attend lectures in progress. We present initial experiences with the sys-tem.

interorganizational multimedia conferencing, hierarchical communicationarchitectures, monostage and multistage mixing

Correspondence and requests for reprints should be sent to P. Venkat Rangan, Department ofComputer Sdence and Engineering, University of California at San Diego, La Jolla, CA 92093-0114.

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278 S. RAMANATHAN, P.V. RANGAN, & H.M. VIN

1. INTRODUCTION

Whereas recent advances communication technology have made available largebandwidth at modest cost, advances in computer technology have led to thedevelopment of high-performance workstations with digital audio and videocapabilities (Cochrane & Brain, 1988). These advances have made it feasible tosupport many computer-supported collaborative applications. One such class ofapplications is multimedia conferencing between geographically separatedgroups of users, with each group possibly belonging to a different organization.The design of software paradigms and optimal communication architectures forsupporting intergroup multimedia conferencing on computer networks consti-tutes the subject matter of this article.

We propose a multilevel conferencing paradigm (called super conferences) forsupporting collaborative interactions among groups of users. Hierarchical archi-tectures are naturally suited for carrying out media communication in superconferences. We study the performance of hierarchical communication architec-tures, and present algorithms for designing hierarchies that minimize real-timeend-to-end delays. We derive limits on the maximum sizes of both superconferences and groups within super conferences so as not to violate bandwidthand delay requirements of multimedia.

We have implemented a multimedia conferencing system on a network ofpersonal computers equipped with digital video- and audio-processing hard-ware, connected by Ethernets. As an interesting application of the conferencingsystem, we have developed a telepresenter by which users can remotely attendlectures in progress. We present our initial experiences with the system.

The rest of this article is organized as follows: In Section 2, we introduce themultilevel conferencing paradigm. Architectures for media communication insuper conferences are presented in Section 3. Algorithms for designing hier-archies that optimize real-time communication delays are devised in Section 4,and a model for evaluating the limits of performance of such hierarchies isproposed in Section 5. Section 6 presents an implementation and performanceevaluation of the conferencing paradigm. Section 7 describes some of the relatedwork, and finally, Section 8 concludes the article.

2. PARADIGMS FOR MULTIMEDIA CONFERENCING

In our system, a conference is the basic paradigm for carrying out collaborativeinteractions among multiple participants. Participants in a conference can beeither individual users (called individual participants), or other conferences (calledgroup participants). A conference containing at least one group participant istermed as a super conference. A group participant may itself recursively be asuper conference containing other group participants. Although super confer-ences can always be flattened into simple conferences containing only individualparticipants, the super conference paradigm serves as a better (more natural andefficient) abstraction to model interorganizational collaborations among groups

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DESIGNING COMMUNICATION ARCHITECTURES 279

of users, with each group possibly belonging to a different organization. As anillustration, consider a meeting between two groups of managers (belonging totwo different organizations) being held to negotiate policies for technical cooper-ation between their respective organizations. The nature of the collaborationmay require that members of each group discuss policies among themselvesbefore proposing them to the other group. Such a collaboration can be modeledusing the super conference paradigm by creating a super conference C betweentwo group participants Gj and G2, with Gi and G2 themselves being conferencesinternal to the two organizations, with their respective managers forming theindividual participants of the corresponding groups, thereby permitting theseparation of intragroup and intergroup collaborations. Furthermore, additionof new individuals to groups Gi or G2 automatically enrolls those individuals asparticipants in C, which would not have been the case had C been flattened intoa simple conference consisting of individual participants only.

The establishment of a super conference involves the setting up of transmis-sion channels between its participants, after which media communication cantake place. Architectures for carrying out media communication in super confer-ences are outlined in the next section.

3. COMMUNICATION ARCHITECTURES FOR SUPERCONFERENCES

In a super conference, each participant (individual or group) must receive anddisplay the composite media stream obtained by mixing media streams transmit-ted by all the other participants. In the case of audio, mixing multiple streamsinvolves digitally summing audio samples and then normalizing the result.Mixing in video domain may require some image processing: In the simplestcase, it may require reducing the individual video images to a fraction of theframe size, and combining the fractions to form a composite frame. For example,in a conference consisting of four participants, video frames from each of theparticipants may be reduced to the size of a quadrant, and the four quadrantscombined to form a composite image. In general, mixing of a given set of mediais carried out by combining their media units, which are the smallest quantagenerated or played back by their I/O devices, to yield composite media units.1 Theagent that performs mixing is called a mixer, and can be implemented in eitherhardware or software on any of the hosts on the network.

The simplest conference is a two-party conversation in which each partici-pant transmits media units to the other participant. A direct extension of thetwo-party architecture to multiparty conference would be for each participant toreceive media units from all the other participants and carry out mixing indepen-dently at its site, yielding a fully distributed mixing architecture (see Figure la).

At the other end of the spectrum is a centralized mixing architecture in which

•Media units may be further subdivided into packets during transmission on a packet-switchednetwork.

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(•)

(b)

Figure 1. Mixing architectures: (a) distributed, and (b) centralized

each participant, instead of duplicating mixing effort at its site, transmits itsmedia units to a central mixer that combines all the media units and transmitscomposite media units back to all the participants. Each participant, on receivinga composite media unit, may have to remove its own contribution before playingit back.

The distributed architecture incurs duplication of mixing computation andincreased bandwidth usage at each of the participants, and does not scale well(with either the number of participants or the geographical separation betweenparticipants) if a participant's network, network interface, or processing poweris a bottleneck. The centralized architecture, on the other hand, does not scalewell if the mixer's network, network interface, or processing power is a bot-tleneck. Therefore, both centralized and distributed architectures may not bepractical for large interorganizational conferences.

By clustering together closely situated participants, and using a hierarchicalconfiguration of mixers and participants (see Figure 2), the bandwidth andprocessing requirements at both mixers and participants can be bounded. Insuch a hierarchical architecture, participants constitute leaf nodes, and mixersconstitute nonleaf nodes. Each mixer combines media units received from itschildren and transmits the composite unit to its parent. The mixer that is at the

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Mixer] Height = 2

Height =1

Figure 2. A hierarchical architecture for mixing

root of the hierarchy, forwards the final composite unit to each of the leaf nodes.By bounding the maximum number of children of each node (which we call thedegree of a mixer), both the network usage (media transmission and receptionrates) and the mixing overhead can be bounded.2

In a super conference containing a large number of geographically separatedgroup participants, associating a mixer (or a set of mixers) with each group givesrise to a mixing hierarchy. Each mixer in the hierarchy can multicast the compo-site media unit to either all of its children (to carry out intragroup communica-tion) or its parent (to carry out intergroup communication), thereby enabling theseparation of intragroup and intergroup collaborations. Hence, hierarchical ar-chitectures are naturally suited for media communication in super conferences.

4. DESIGNING OPTIMAL HIERARCHICAL ARCHITECTURES

Real-time multimedia conferencing demands that end-to-end delays of mediaunits be bounded. In hierarchical architectures, media units generated by partic-ipants may have to pass through several levels of mixers between the time theyare generated and the time they are played back, and hence may suffer end-to-end delays that increase with number of levels in a hierarchy. The cumulativedelay of a media unit from a participant to the root, which represents thedifference between its instant of generation and the instant at which a compositemedia unit of which it is a constituent is available at the root, is dependent on

2A generalization of the hierarchical architecture yields a graph-structured mixing architecture.In a nonhierarchical graph, there may be multiple paths between a participant and a mixer. Hence, amixer may receive multiple mixed units containing the same unit of a participant. To eliminate theduplication, the participant's unit may have to be transmitted in addition to the mixed unit forpurposes of subtraction, leading to wastage of bandwidth. Because graph-structured architecturesdo not afford any special advantages over hierarchical ones, they are not very interesting for mixing.

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the transmission delays between mixers at successive levels of the hierarchy,and the mixing delays at each level. The end-to-end delay suffered by a mediaunit is the sum of the cumulative delay from a participant (i.e., a leaf) to the rootand the delay due to direct transmission from the root back to the participant. Ahierarchy is considered optimal if it minimizes the maximum cumulative delayfrom the leaves to the root.

The delays due to mixing at each mixer in a hierarchical architecture (of asuper conference) depend on whether the mixer has to wait for media units fromall of its children before it can start combining the media units, or whether themixer can start mixing as soon as it receives media units from at least two of itschildren. These techniques are referred to as monostage and multistage mixing,respectively, and are elaborated next.

• Monostage Mixing. In monostage mixing, a mixer waits until a media unithas been received (or is determined to be lost using a timeout) from each ofits children before beginning to combine them. This may be necessary incases where the set of media units that can be mixed together can bedetermined only after all the constituent media units are received. Forexample, in applications such as teleorchestra, composition of coherentmusic requires that differences between generation times of media unitsbeing mixed together be minimized. In the presence of variation in sam-pling rates of media devices and the network transmission delays, such aset can be determined only after receiving media units from all the sources.Another example is video mixing in which relative positions of each of theparticipants in their respective individual images may be necessary beforea composite image can be created. If TV T2, . . .,Tn are the arrival times ofmedia units at a mixer from its n children, respectively, and if the mixingcost is assumed to increase linearly with the number of sources (to a firstdegree of approximation), then the instant at which a composite mediaunit is created by a monostage mixer is Tn = maxfa, T2, . . .,Tn) + (n - 1) *tmixi where tmix represents the time taken by the mixer to mix a pair ofmedia units.

• Multistage Mixing. On the other hand, in multistage mixing a mixer canstart combining units as soon as the first two media units are received, andmixing of units that have already arrived can proceed concurrently withreception of media units that are yet to arrive. To compute the mixingdelay precisely, let us suppose that a multistage mixer receives n (n > 2)streams at times Ti, T2, . . ., Tn, and for definiteness, let TJ < T2 ̂ . . . ̂ Tn.The mixer can combine the first two units by T2 = T2 + tmix. The third unitcan be combined by T3 = max(j3, T2) + tmix, and so on. All the units canbe combined to form the composite media unit by Tn where Tn = max(jn,Tn-i) + tmix. If T, = T2 = . . . = Tn, we notice that Tn = Tj + (n - 1) * tmix,which is the same as the time to form a composite media unit when amonostage mixer is employed. However, if Tlr T2, . . .,Tn are all distinct anddiffer from one another by at least tmix, then Tn = Tn + tmix, which is anorder of magnitude better than the corresponding value when using

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monostage mixing. This is because, when a media unit arrives at a mixer,all the earlier media units would have already been mixed. The addition ofa new media source (as a child of a mixer) whose media units arrive earlierat the mixer than from an existing child may not increase the mixing delay.This is in contrast to monostage mixing in which the addition of a newchild to a mixer always increases the mixing delay at that mixer by tmix. Itshould, however, be noted that the order in which media units are mixedin multistage mixing is the order in which they arrive, which can bearbitrary. Hence, multistage mixing is feasible only if the mixing operationis commutative and associative. This is most applicable to audio mixing,which involves a simple addition of audio samples and subsequent nor-malization.3

We now devise algorithms for constructing optimal mixing hierarchiesamong a set of participants. Each mixer is guaranteed to have at least twochildren, and hence the number of mixers (all of which are assumed to be ofcomparable processing power), is implicitly guaranteed never to exceed thenumber of participants in a hierarchy. We assume that the network transmissiondelay between any two nodes (participants or mixers) is bounded by tnet, andthat all participants can begin generation of media units at the same instant andcarry on both generation and playback of media units at a uniform rate. Becausethe end-to-end delays are different in monostage and multistage mixing, theiroptimal hierarchies are also different. We first focus on optimizing monostagehierarchies, and then consider multistage hierarchies.

4.1 Optimal Monostage Mixing Hierarchies

Consider a monostage hierarchy of height H, as shown in Figure 3a, in whichM(i,j) denotes ;th mixer (numbered from left to right) at height i.

Let Tcum(h,i) denote the cumulative delay that a media unit will have sufferedfrom the time of its generation to the time of completion of mixing at a mixernumbered i at height h. Tcum(h,i) is the sum of the maximum cumulative delayat height h - 1 (h > 0), the transmission delay between heights h - 1 and h,and the mixing delay at height h, and is recursively formulated as follows (seeFigure 3b):

Tcum(h,i) = max [Tcum(h - l.j)] + t,,e, + [degree{h,i) - 1] * lnix.\fj:j is a child of i

For the leaf nodes, h = 0 and for all /, TCHm(0,/) = 0. The cumulative delay at theroot is given by:

3An inverse mixing operation is also necessary because each participant, when it receivescomposite media units back, may have to remove its own contribution so as not to hear its own voiceback. Together with the silence unit,which serves as an identity element and is used when a mediaunit transmitted by a participant is lost, multistage mixing can be viewed as an algebraic AbelianGroup.

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h-H/\M(H.l)

'Multicast to all participants

h - l f )M(1.1)

P(0,l) W3)

M(k.l)

(a)

TcunAO

Xumft-l.!) TixtoQx-1,2) tunC-LJ)

(b)

Figure 3. (a) A hierarchy of height H, and (b) Computation of cumulative delay Tcum

W H , 1 ) = max [Tcu

V;':;' is a child of the rootAH - l,y)] + hrt + [degree(H,l) - 1] . tmix. (1)

By Equation 1, the two components of cumulative delay of a hierarchy thatdepend on hierarchy's structure are the number of subtrees at the root (i.e., itsdegree) and the maximum cumulative delay of those subtrees. Hence, in anoptimal mixing hierarchy, given the number of subtrees at the root, each subtreeof the root should also be optimal, so that the maximum of cumulative delays ofall the subtrees is minimized. Furthermore, the cumulative delay of optimalhierarchies monotonically increases with the number of leaf nodes in the hier-archy. This can be proved by contradiction: Suppose a hierarchy with n + i,i > 0, leaf nodes has a lesser cumulative delay than one with n leaf nodes. Sinceremoval of leaf nodes from a hierarchy does not increase its cumulative delayany further, a hierarchy with n leaf nodes can be created using the optimalhierarchy with n + i leaf nodes, by removing i leaf nodes. The resultinghierarchy with n leaf nodes will have a lesser cumulative delay than that of thesupposed optimal hierarchy with n leaf nodes, which is a contradiction. There-

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Figure 4. Construction of an optimal hierarchy for two participants

fore, cumulative delay of a hierarchy is a monotonically increasing function ofthe number of leaf nodes, and hence, in order to minimize the cumulative delayof a hierarchy of a given number of subtrees at the root, the size of its largestsubtree must be minimized. It follows that, given a fixed number of participants,the participants must be divided equally among all the subtrees, that is, thehierarchy must be leaf balanced.4

We will now devise an inductive method for constructing optimal mono-stage hierarchies. The optimal hierarchy for two participants is trivial: a central-ized architecture in which both participants are connected to a mixer. Figure 4shows such a hierarchy with leaf nodes P1 and P2, connected to a mixer Mv Inthis case, the cumulative delay at the root is tmix + tnet.

Given such a hierarchy, consider the addition of a third participant P3 (i.e., aleaf node) to the hierarchy. Assigning P3 to M\ (Figure 5a) increases the cumula-tive delay to 2 * tmix + tnet. The only other alternative is to increase the height ofthe hierarchy to two, yielding the configuration shown in Figure 5b, which has acumulative delay of 2 * tmix+ 2 * tnd. Hence, the centralized architecture (Figure5a) is also optimal for three leaf nodes.

Now consider the addition of a fourth leaf node. Adding a fourth leaf to Mjin Figure 5a increases the cumulative delay to tnet + 3 * tmix, whereas increasingthe height to 2 and balancing the hierarchy yields a cumulative delay of 2 * tmix +2 * tnet. A hierarchy of height 3 with four leaf nodes cannot be balanced andyields a larger cumulative delay of 3 * tnet + 3 * tmix. Hence, the optimal configura-

4Optimal hierarchies that are not leaf balanced may exist, but for every such hierarchy anequivalent leaf-balanced hierarchy must exist.

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(a)

(b)

Figure 5. Construction of an optimal hierarchy for three participants: (a) A one-levelhierarchy versus (b) A two-level hierarchy

tion has a height of 1 or 2, depending on whether tmt ̂ tmix or not. These resultsare summarized in the following claim:

Claim 1Whereas the centralized architecture is always optimal (irrespective of the relative valuesof tnet and tmix) for conferences with two or three participants, it is optimal for a conferencewith four participants if and only iftnel > tmix. A balanced, two-level hierarchy is optimalfor a conference with four participants, otherwise. a

Thus, in general, the choice of the optimal configuration depends on therelative values of tmix and tnet. We call the ratio R = tnetltmix as the mixing ratio.

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Intuitively, when R < 1, tnel < tmix, the transmission overhead does not exceedthe mixing overhead, and an increase in height of the hierarchy is preferred toan increment in the degree of a mixer. On the other hand, if the transmissionoverhead exceeds the mixing overhead, tnet > tmix (i.e., R > 1) and increasing thedegree of a mixer to at least [R] is preferred to an increment in the height. In thelimit, if tnet » tmix, it is preferable to use a one-level hierarchy (which is nothingbut a centralized architecture). The exact number of participants beyond which aone-level hierarchy ceases to be optimal and an increase in height becomesnecessary is called the critical conference size, Ncrit. As a first step in constructingoptimal hierarchies, we try to compute the value of Nm ( .

Observe that an optimal hierarchy for a conference of size NOT( + 1 must betwo-level (and not higher), because the root of an optimal hierarchy must havesubtrees of sizes Ncrit or less, each of which, therefore, must be one-level.Furthermore, for all conferences of size NOT, + i, i > 1, a two-level hierarchymust be better (i.e., yield smaller cumulative delays) than a one-level hierarchy.This can be proved by contradiction: Suppose that a two-level hierarchy is betterthan a one-level hierarchy for a conference with Ncrit + i participants but a one-level hierarchy is better for a conference with Ncrit + i + 1 participants. In theone-level hierarchy for N^,-, + i + 1, we could substitute the subtree consistingof the root and the leftmost N m , + i children by a two-level hierarchy that isgiven to be better (for NOT, + i participants), yielding an even better hierarchy forNcu + i + l participants, thereby contradicting our assumption that the one-level hierarchy was better. Hence, a one-level hierarchy cannot be better than atwo-level hierarchy for any size N^,, + i, i s 1. This implies that Ncrit is thelargest size for which a one-level hierarchy is better than a two-level hierarchy.

The cumulative delay in a one-level hierarchy with Nm-t participants is(NOT( — 1) * tmix + tnet. In order to compute the cumulative delay in the best two-level hierarchy with the same number (i.e., Ncrit) of participants, notice that, asobserved earlier, the participants must be divided as equally as possible amongall the subtrees of the root. Thus, if d is the number of subtrees of the root insuch a two-level hierarchy, each of those subtrees will contain at most | — j 2 - | par-ticipants. The cumulative delay of such a two-level hierarchy will be the sum ofthe mixing delays at both the levels of the hierarchy: (d - 1) * tmix + f —f- ] - 1) *tmix, plus the transmission delays on the two links between a leaf and the root: 2 *tnet- Ncrit represents the largest size for which the cumulative delay in a one-levelhierarchy does not exceed that of a two-level hierarchy. That is, N m , is thelargest integer such that, for all integers d, 2 < d < Ncril.

(AU - 1) . tmix + tnel < (d - 1) . tmix + (| ^f- I - 1) • tmix + 2 . („„,. (2)

The RHS of inequality (2) is smallest when [Ncrit/d] + d is minimum over allintegers d, 2 s d ^ Ncnf. Using the principles of maxima and minima offunctions, it can be shown that the preceding factor is minimum when d is thelargest integer dcri, that does not exceed VNcn-,. Substituting dcrit for d in Equation2 and solving for Ncrit we obtain:

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(Ncn. -

N m ( -

AUdaU

I d m , I

- dm 1 + 1) * fni l s fnf,

- dcril + 1 <Lix

dcril- d^, < R - 1

In order to find N ,̂-,, one may start by approximating dcrit by dapprox = VNOT-,, andsolving the resulting quadratic equation for dapprox. It can be shown that LdflpprMJ2

< Nm( < \dapprox].2 Hence, in order to find Ncril, one may start by testing theinequality (2) for values Napprox = [dapprox\,

2 Napprox + 1, . . ., until the inequality isreversed (the maximum value up to which this step has to be carried out is\dapprox\2)' a t which point Ncrit is reached.

The equality between the LHS and RHS [of Inequality (2)] occurs when themixing ratio R is the square of some integer. Upon solving the equation, weobtain that, dappmx = dait = 1 + VR, Napprox = dcrit = (1 + VR)2, and thecumulative delay is the same for both one-level and two-level hierarchies for aconference with Ncri, participants. Figure 6 illustrates the variation of Nm, with R.

I8^ 60

i

I"40

30

20

10.

0 10 20 30 40 SO

Mixing ratio (R)

Figure 6. Variation of the critical conference size NOT( with the mixing ratio R for mono-stage mixing

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When R < 1, it can be shown that Ncrit = 3 (corroborating the arguments used inthe derivation of Claim 1), and that Ncri, cannot decrease with increase in thevalue of R.

The fact that N^t represents the conference size beyond which a one-levelhierarchy ceases to be optimal leads to a surprising result that every mixer in anoptimal hierarchy of any size can have at most Ncrit children, which we prove inthe next theorem. The proof follows directly from the following Lemma:

Lemma 1

Given a mixing ratio R, the root mixer in an optimal hierarchy of any size will have adegree of at most Ncrit, where Ncri, is the largest integer satisfying inequality (2).

ProofThe proof is by induction on the size of the conference, that is, the number ofleaf nodes in a mixing hierarchy. Since the least value of Ncrit is 3 (which occurswhen R < 1), the lemma is trivially true for base cases of hierarchies with 1, 2, or3 participants. Furthermore, for any given value of R, the lemma is trivially truefor any size not exceeding Nmf (by the definition of Ncrit).

In the inductive step, assuming that the lemma is true for optimal hierarchies ofsize up to k s Nm, + 1, we show that it must hold for an optimal hierarchy ofsize k + 1. The number of children at the root of an optimal hierarchy of size k +1 can be 1, 2, . . ., k or k + 1. If the number of children is, at most kr then thesubtree consisting of the root and its k children can be replaced by an equivalentoptimal hierarchy, after which the root is guaranteed to have at most Ncrjj

children (by the induction hypothesis). On the other hand, if the number ofchildren is k + 1, each of the children must be a leaf, and we can replace thesubtree consisting of the root and the left most k children (leaves) by an optimalhierarchy of size k. The root of the resulting tree can have up to Ncrj, + 1children. Furthermore, if the root has Ncrit + 1 children, since the lemma is truefor all sizes up to k > Ncrit + 1, the subtree consisting of the root and the(Ncn( + 1) children can be further replaced by a more optimal hierarchy for (Ncrjt

+ 1) children, after which the root is guaranteed to have at most Ncrit children.Hence, in either case, a more optimal hierarchy with at most Ncrit children at theroot can be constructed, which goes to complete the inductive proof. n

Theorem 1

Given a mixing ratio R, every mixer (including the root) in an optimal hierarchy will haveat most N^i children, where Nm> is the largest integer satisfying Inequality 2.

ProofGiven a hierarchy of any size, starting from the top of the hierarchy, at everynode, the subtree rooted at that node can be replaced by an optimal hierarchy ofequal size. (The cumulative delay can only improve). Each such node becomes

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the root of an optimal subtree and by Lemma 1, it will have, at most, Ncnf

children.

Theorem 1 can be used to devise an efficient inductive algorithm for con-structing optimal hierarchies of any given size. The optimal hierarchy of a givensize N will consist of optimal subtrees of sizes smaller than N. Hence, thealgorithm starts with optimal subtrees of size 2 and 3, and inductively constructslarger subtrees of sizes 4, 5, . . .,N — 1, N and is presented in the following.

Algorithm 11. Compute the critical conference size, NOT(, using inequality 2. If N < N^,,,

the centralized architecture (in which all participants are connected to thesame mixer) is an optimal hierarchy, and the cumulative delay is given by

Topt(N) = (N - 1) • tmix + tnel.

2. If N > Ncril, repeat the following steps for size n = Ncrit + 1, Ncrit +2, . . .,N - 1, N(a) The optimal hierarchy for any size n can have a root with 2, 3, . . .,

or Ncrit subtrees of sizes at most \n/2], \n/3], . . ., or \n/Ncrit], respec-tively. Thus, we have to repeat the following computation for d = 2,3, . . ., Ncrit:

i. If there are d subtrees and n is divisible by d, then each subtreewill be of size nld. Otherwise, if n = p * d + q, where p is thequotient and 0 < q < d the remainder in dividing n by d, q of thesubtrees will have a size of p + 1 = | - j - ], and d - q subtreeswill each have a size of p. The cumulative delay for such aconfiguration is:

r « iT& (n) = (d - 1) » tmix + tml + T^d — \).

I a I(b) Compare T^,, (n) for various values of d, and choose the configuration

with the lowest one:

M«) = "tilK> («)]•

In Algorithm 1, the number of arithmetic operations and comparisons foreach n is of the order of N^,,, which is constant for a given mixing ratio R.Because the algorithm computes optimal hierarchies for all sizes upto N, it has alinear running time [i.e., O(N)]. However, because the maximum size of asubtree in an optimal hierarchy of size N is JN/21, the running time of thealgorithm can be further reduced by carrying out the iterations only for sizesn = 4, 5 , FN/21 - 1, JN/21.

Note that the optimal hierarchy for n participants may be different from thatfor n + 1 participants. As a result, if a new participant joins a conference, thecommunication topology may have to be reconfigured to attain the optimal

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configuration, necessitating interruption of the conference. Hence, this algo-rithm is most applicable to conferences in which the number of participantsremains constant for the most part.

There are a number of policies that can be adopted when admitting a newparticipant into a conference: the simplest policy is to permit participants to joinor leave at any instant and to reorganize the hierarchy every time a participantjoins or leaves the conference. This policy could result in frequent interruptionsin the conference and may be undesirable. Alternatively, participants may beallowed to join or leave only during the initial phase of the conference, the dur-ation of which could be decided by the conference initiator. At the end of theinitial phase, the conference may be interrupted in order to reconfigure the en-tire hierarchy optimally, after which, media communication between the partici-pants can resume. Likewise, it may be possible to restrict changes in the numberof participants in a conference to periods of inactivity. Yet another alternative isto avoid reconfiguring the entire hierarchy at the time when a new participantjoins the conference, but to choose the best available position at which a newparticipant can be introduced into the existing hierarchy so as to minimize theaccompanying increase in cumulative delay. Specifically, for a hierarchy ofheight H, when a new participant joins the conference, there are mixers at Hpossible levels to which the participant can be assigned. The increase in degreeof a mixer resulting from the assignment of the new participant to that mixercauses an increase in its mixing delay by tmix. As a consequence, all media unitsthat pass through the mixer on the way to the root experience an additionaldelay of tmix. New participants should be assigned to mixers that are on a pathfrom a leaf to the root in which the cumulative delay is minimum. Notice that anumber of such additions of participants to an optimal hierarchy may soon makethe resulting hierarchy suboptimal. The resulting increase in cumulative delaywill necessitate reconfiguration of the hierarchy after some time, because thecumulative delay experienced by media units in a conference is required to bebounded. At the time of reconfiguration, the transformation from the existinghierarchy to the new optimal hierarchy can be performed in stages, so as toeffect the reconfiguration in a transparent manner.

An important consequence of the analysis presented in this section is thatthe optimal hierarchy for a given number of participants depends on the ratio oftnet and tmix. Hence, for different media, which could have different mixingratios, the optimal hierarchies may not be the same.

4.2 Optimal Multistage Mixing Hierarchies

In multistage mixing, mixing is performed in a pair-wise manner, and a mixercan start combining media units as soon as the first two media units arrive. Ateach mixer, mixing of media units that have already arrived proceeds concur-rently with reception of media units that have not yet arrived. The cumulativedelay is minimized if the overlap between mixing and reception of media units ateach mixer is maximized. A necessary condition for such an overlap to exist is

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that media units arrive at different times. To maximize this overlap, the arrival ofmedia units should be such that each media unit arrives exactly at the instant ofcompletion of mixing of all other media units that have arrived earlier. Assum-ing that media units are generated synchronously by all participants, if thesubtrees of a mixer have identical configuration and size, all the media unitsarrive at the same time, and there will be no overlap at all. Therefore, such aconfiguration should be avoided. This is in sharp contrast to monostage mixing,in which each of the subtrees of the root in an optimal hierarchy is almost of thesame size.

In order to devise an algorithm for constructing optimal multistage hier-archies, notice that the root mixes media units pair-wise, in the order in which itreceives the media units from its children. Consider the last such mixing opera-tion. It could consist of mixing either (1) the last arrived media unit from asubtree of nx participants (for some value of nx < N) to the partial composite unitof earlier arrived units from a total of n2 = N - nx participants, or (2) twosimultaneously arrived units from two subtrees (of sizes «j and n2). In anoptimal hierarchy, the cumulative time at which the last mixing operationcompletes is minimum. Hence, if we compute the optimal subtrees and theircumulative delays for all nj and n2 such that N = nx + n2, we can compute theoptimal hierarchy of size N by comparing the cumulative delays when either themedia unit from nx arrives at the root of n2 after the start of the last mixingoperation at the root of n2, or media units from both nx and n2 arrive at the rootsimultaneously. The exact algorithm is elaborated next.

In the algorithm, T^t(N) denotes the cumulative delay in a proposed hier-archy of size N, where N = Hj + n2, and T^N) denotes the cumulative delay inan optimal hierarchy of size N. The cumulative delay is a combination of mixingand transmission delays, and a cumulative delay of x * tmix + y * tnet will bedenoted by the tuple fa y). For any two tuples fa, yO and fa, y2) denotingcumulative delays, the following definitions are used:

net-• (*i. yi) 2 te, yJ if a n d only if xi * tmix + yx * f«, > x2 * tmix + y2 * t_• max[(xv yj), (x2, y2)] = (xlr yx) if and only if fa, yO > (x2, y2) and (x2, y2)

otherwise.• (Xi, yx) + {x2, y2) = fa + x2, y, + y2).

Algorithm 21. If N = 2 or N = 3, the centralized architecture is optimal, and the

cumulative delays are (1,1) and (2,1), respectively. Also, 7^,(1) = (0,0).2. For all n = 4, 5, . . ., N compute the optimal hierarchy:

(a) For all nx = 1, 2, . . ., [nil] do:Let n2 = n- nv T^wO = fa, y2) and Topt(n2) = fa, y2) (Both T^n^and T^(112) will be available from an earlier iteration). The optimalhierarchy for N depends on the relationship between fa, yx) and fa,Y2), and between tmix and tnet.i. If fa, yx) = fa, y2), then media units from roots of optimal

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hierarchies of « : and n2 may be transmitted to each other, or to anew root mixer (where they arrive simultaneously) (see Figure7a). The cumulative delay for either of the configurations is:

T&(n) = (*i + 1, yi + 1).

ii. If (xv t/i) < (x2, y2), nj's media unit will be available earlier thanthat of n2, and hence, it can be transmitted to n2's root so as tooverlap with the ongoing mixing at n2. The resulting configura-tion is shown in Figure 7b and the cumulative delay is given by:

T%t{n) = max[(xlr y, + 1), (x2, y2)] + (1,0)

iii. The case when (xv y{) > (x2, y2) is similar and the resultingconfiguration is shown in Figure 7c.

(b) Topt(n) = Ci TS&n).

In the preceding algorithm, the optimal hierarchy for a conference of Nparticipants is constructed after determining those for each of n = 4 ,5 , . . ., N —1 sizes. The optimal hierarchy for each size n considers [n/2] choices. Hence,the complexity of this algorithm is OfAT2). There are some optimizations that arepossible based on the relative values of tmix and tnet. For instance, for all N ^[tnet/tmix], a centralized architecture is optimal. Because the optimum delaycan only increase with the size n, if at any stage of the algorithm, T"^,t(N) =»̂p((W "" 1)' f° r some nx > 0, it can be immediately inferred that T^N) =

(c)

Figure 7. Construction of an optimal hierarchy of size n from optimal hierarchies of sizes«, and n2 when: (a) rop((«i) = Tovt(n2); (b) T^(«,) < Topl(n2); and (c) T^n,) > Topl{n2)

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Topt(N - 1). Furthermore, nx can start from [Nil], and be decremented in eachiteration until Topt{n^) £ Topt{n2) - tnet, and the computation for that particularvalue of n can immediately halt.

In all of the preceding algorithms, we have assumed synchronous genera-tion of media units and deterministic transmission delay for each media unit.Designing optimal hierarchies in a more dynamic environment is beyond thescope of this article. All of these algorithms minimize the cumulative delay of ahierarchy, assuming that there are no constraints for configuring a hierarchy ofmixers and participants. In general, in addition to the requirement for minimiz-ing the cumulative delay of a hierarchy, there may be additional constraintsimposed by the participation of individuals belonging to different organizationaldomains in a conference. In such a case, security considerations may not permita mixer belonging to an organization to service participants belonging to otherorganizations. In order to support intergroup collaborations, it may be requiredthat participants belonging to the same organization be clustered together,thereby constraining the configuration of a hierarchy. The algorithms presentedin this section, can be used not only for creating an optimal architecture for theentire conference but also for constructing optimal clusters within a conferenceso as to support intragroup collaboration.

5. LIMITS ON THE PERFORMANCE OF OPTIMAL HIERARCHIES

Optimal hierarchies, algorithms for designing which were presented in the lastsection, minimize the cumulative delays in a super conference. However, theinteractive and real-time nature of collaborations imposes absolute upperbounds on the tolerable cumulative delays of media units, leading to upperbounds on the number of participants in a super conference. If T£J£ denotesthe maximum tolerable cumulative delay, the maximum size N™* of a superconference is the largest integer such that Topt(N™*) < T££.

Each group participant within a super conference may also have a maximumtolerable size N^f associated with it, which generally arises due to limitationsin either the bandwidth or the media-unit-reception overheads at a mixer'snetwork interface. Given punit (the period of generation of media units), sunit (thesize of each media unit), and Bnet (the available network bandwidth, if all theparticipants within a group share bandwidth on the network, such as anEthernet), the maximum limit on the size of a group, N%£, which is imposedby bandwidth limitations is given by:

runil

±N»«* < Bnrt * Pun" msunit

Bounds o n N ^ due to media-reception overhead arise from the need tocomplete both the reception of all the media units on the network (which is a

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serial operation when the network is shared) and their mixing within a period ofgeneration of a media unit. Because the mixing time depends on whether themixer is monostage or multistage, the resulting bounds are different:

• Monostage Mixing. Consider a group consisting of N™™ participants con-nected to a monostage mixer. During each media-unit generation period,each mixer receives N^ units sequentially from the network, creates acomposite media unit, and then transmits it on the network. If trec and tim

define the times for receiving and transmitting one media unit, respec-tively, the sum of the total reception delay for media units from all theN™ participants, the total mixing time, and the transmission delay of thecomposite media unit should not exceed the generation period of mediaunit:

N™* * tm + (N™* - 1) » tmix + tlm < Vuni,

'mix T 'rec

• For a Multistage Mixer. The maximum size of a group supported by amultistage mixer depends on the relative values of reception and mixingdelays.

If trec S: tmix, before receiving each media unit, a multistage mixerwould have completed the mixing of all those media units that it hasalready received earlier. The total delay comprising of the receptiondelay of media units received from all the participants, N™^ * trec,the delay for mixing the final media unit, tmix, and the transmissiondelay, ttrn, should not exceed the period of generation of a media unit:

=»Ng? S *-» - ' - * - ' - . (5)lrec

If trec £ tmix, the mixing delay dominates over propagation delays. Thetotal delay comprising of the reception delays of the first two mediaunits, 2 * trec (after which the mixing operation can begin), the totalmixing delay, (N^f - 1) * tmix, and the transmission delay, ttrn,should not exceed the period of generation of a media unit:

2 * trec+ (N™* - 1) . tmix + tln s ?„„,.,

*N& * ^ " 2 ^ " t>m + 1 - (6)

Note that N^f also represents the maximum size of a conference that can besupported by a purely centralized or distributed architecture in comparison to

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the much larger (as will be experimentally shown in the next section) maximumsize N™* that can be supported by a hierarchical architecture, thereby revealingthe scalability of hierarchical architectures.

6. IMPLEMENTATION AND EXPERIENCE

Using our basic conferencing paradigm, we have built several multimedia collab-orative applications that are in daily use in our laboratory. One of the widelyused applications is a telepresenter that enables users at their workstations toremotely participate in lectures and discussions that are in progress (see Figure8). Each participant in a telepresentation receives snapshots of video (the snap-shots can be arranged to be captured whenever the speaker puts up a new slidefor presentation), as well as continuous audio. Users can also record on-line theproceedings of such lectures and discussions with or without themselves partici-pating in them.

6.1 Performance Evaluation

Using a network of a large number of SPARCstations (which encode audiosignals into 8-bit ix-law5 samples at a rate of 8000 samples/s) that was available tous, we carried out several experiments to evaluate the performance limits ofaudio communication and mixing in multimedia conferences. (Even though thesystem supports video conferencing, because the number of workstations withvideo hardware is four in our current setup, we had to restrict the experimentsto only audio.) Audio samples are packetized and transmitted on an Ethernet. Inorder to strike a balance between network transmission overhead (which favorslarge packet sizes), and packetization delay (which favors small packet sizes),the audio packet size was chosen to be 512 samples, yielding punit = 66.67 ms.The timing measurements for various operations of the audio conferencingsystem are given in Table 1.

Using the measurements observed in our conferencing environment, weevaluated the cumulative delays in optimal monostage and multistage mixinghierarchies. Figures 9 and 10 represent the variation of the optimal cumulativedelay for monostage and multistage mixing, respectively, with increase in superconference size for various mixing ratios (the mixing delay was kept constant at1.35 ms, and the geographical distances between participants were increased,leading to increases in transmission delays and consequent increases in mixingratios). It may be observed that cumulative delays increase in a step-wisemanner monotonically with R.

Clearly, since a multistage mixer overlaps media mixing with media trans-mission, optimal delays for multistage hierarchies are smaller than those formonostage hierarchies, and hence, multistage hierarchies can support much

5H-law is a CCITT standard for encoding audio.

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Figure 8. A telepresentation in progress

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Table 1Timing Measurements of the Mixing Parameters

Symbol Definition Time (in ms)

tmix Time to mix two media units 1.35t,rn Transmission delay of a media unit 2.21trcc Reception delay of a media unit 2.21Pmii Generation period of a media unit 66.67

larger super conferences. This fact is illustrated by Figure 11, which comparesthe optimal cumulative delays in our environment for which, tmin = 1.35ms andtnet = 2.21ms.

We also computed the maximum sizes of groups within a super conference.Given that the network bandwidth is 10 Mbits/s (Ethernet), bandwidth limita-tions (see Equation 3) yield a maximum group size, N™™ = 150. However,media reception overhead limitations (see Equation 4) yield a maximum groupsize, N%£ = 18 for monostage mixing. This is corroborated by the experimentalmeasurements shown in Figure 12, in which the fraction of media units reachinga monostage mixer goes below 98% leading to a rapid deterioration of voice

Monostage mixing

': 10.0

100 200 300 400 500

Conference size

Figure 9. Variation of cumulative delay with conference size in an optimal hierarchy withmonostage mixers for various values of the mixing ratio R

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Multistage mixing

t 70.0

100 200 300 400 300

Conference size

Figure 10. Variation of cumulative delay with conference size in an optimal hierarchywith multistage mixers for various values of the mixing ratio R

Monostage

Multistage

200 400 600 800 1000

Conference size

Figure 11. Comparison of maximum sizes of super conferences that can be supported bymonostage and multistage hierarchies in our multimedia network

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-*—*-»•k 100 « »-

I 90

"S 80

i70

60

OS? 50

40

30

10-

10-

O—O UulUttag* nixing* — * Uonostige mixing

10 IS 20 25 30 35

Group size

Figure 12. Performance of monostage and multistage mixing with increase in group sizein superconferences in our multimedia network

quality and a breakdown of the mixing hierarchy beyond a group size of 21.Similar computations (see Equation 5) carried out for multistage mixing yield amaximum group size of 28, whereas the experimentally observed value was 26.6

Hierarchical architectures have significantly higher scalability as comparedto centralized and distributed architectures. This is illustrated by Figure 13 formonostage mixing. The case when multistage mixers are employed is similar.The severe limitation of centralized and distributed architectures in their abilityto scale for real-time multimedia conferencing can be attributed to the linearincrease in end-to-end delays with conference size in those architectures.

'These slight differences between analytical and experimental values can be explained asfollows: Whereas the smaller value of 18 yielded by Equation 4 (in comparison with the value of 21yielded by experimental measurements) for monostage mixing is due to the pessimistic assumption(in Equation 4) that media reception and mixing are purely sequential, the larger value of 28 yieldedby Equation 5 (in comparison with the value of 26 yielded by experimental measurements) formultistage mixing is due to the optimistic assumption (in Equation 5) that media reception andmixing are completely concurrent, neither of which is absolutely valid in practice.

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j§ 100w

180

60

40

20-

Centralized

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Optimal end-to-end delay

Figure 13. Comparison of end-to-end delays for centralized, distributed, and optimalhierarchical architectures

7. RELATED WORK

In recent years, there have been many efforts towards integrating multimediaconferencing into computer systems. Ahuja, Ensor, and Horn (1988) at AT&TBell Laboratories, Ludwig and Dunn (1988), and Addeo, Gelman, and Daya(1988) at Bellcore, Casner, Seo, Edmond, and Topolcic (1990) at ISI, and Ranganand Swinehart (1991) at Xerox PARC have built conferencing systems thatinclude video. In these systems, there is a need for reception of multiple mediastreams by each participant to enable independent mixing of media streamsfrom all the other participants before displaying. These schemes involve duplica-tion of mixing effort at each of the participants, and may entail large bandwidthand computation overheads. Ziegler, Weiss, and Freidman (1989) presented adistributed voice-mixing mechanism for token ring-based networks. Thisscheme, which uses a circulating mixed-media token, is not scalable with thenumber of participants. Hierarchical architectures for supporting scalable con-ferences were first proposed in Vin, Rangan, and Ramanathan (1991), butalgorithms for designing optimal hierarchies have not received any attention.

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8. CONCLUSION

We have proposed a multilevel conferencing paradigm called super conference forsupporting interorganizational collaborations. Each participant in a super con-ference must receive and display the composite media stream obtained bymixing media streams transmitted by all the other participants. Hierarchicalarchitectures are naturally suited for carrying out media mixing in super confer-ences. We have presented algorithms for designing mixing hierarchies thatoptimize real-time, end-to-end delays. These algorithms reveal surprising differ-ences in optimal network topologies for tnonostage and multistage mixing. Basedon bandwidth and real-time delay constraints, we have obtained interestinglimits on the sizes of both super conferences and groups within super confer-ences when optimal mixing hierarchies are employed.

We have implemented a multimedia conferencing system on an environ-ment of Sun SPARCstations equipped with digital multimedia hardware. Perfor-mance analysis in this conferencing environment shows that hierarchical archi-tectures are two orders of magnitude more scalable than centralized anddistributed architectures, and multistage mixing outperforms monostage mixingby a factor of more than two. The conferencing system has been used to supportseveral collaborative applications, such as the telepresenter, that are in daily useat the UCSD Multimedia Laboratory.

REFERENCES

Addeo, E., Gelman, A., & Dayao, A. (1988). Personal multimedia multipoint communicationservices for broadband networks. In Proceedings of the IEEE Globecom '88 Conference (pp. 53-57).

Ahuja, S., Ensor, J., & Horn, D. (1988). The rapport multimedia conferencing system. In Proceedingsof COIS'88 Conference on Office Information Systems (pp. 1-8).

Casner, S., Seo, K., Edmond, W., & Topolcic, C. (1990). N-way conferencing with packet video.Proceedings of the Third International Workshop on Packet Video.

Cochrane, P., & Brain, M. (1988). Future optical fiber transmission tech. and networks. IEEECommunications Magazine, 45-60, November, 1988.

Ludwig, L., & Dunn, D. (1988). Laboratory for emulation and study of integrated and coordinatedmedia communication. Proceedings of SIGCOMM'88 Symposium on Communications Architecturesand Protocols, (pp. 283-291).

Rangan, P.V., & Swinehart, D.C. (1991). Software architecture for integration of video services in theetherphone environment. IEEE Journal on Selected Areas in Communication, 9(9), 1395-1404.

Vin, H.M., Rangan, P.V., & Ramanathan, S. (1991). Hierarchical conferencing architectures forintergroup multimedia collaboration. Proceedings of the Conference on Organizational ComputingSystems (COCS'91), SIGOIS Bulletin, 12, (2-3), 43-55.

Ziegler, C , Weiss, G., & Friedman, E. (1989). Implementation mechanisms for packet switchedvoice conferencing. IEEE Journal on Selected Areas Communications, 7(5), 698-706.

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Documents

Designing communication architectures for interorganizational multimedia collaboration