Priority-Based Distribution Trees for Application-Level Multicast

Transcription

1 Priority-Baed Ditribution Tree for Application-Level Multicat Jürgen Vogel, Jörg Widmer, Dirk Farin, Martin Mauve, Wolfgang Effelberg Praktiche Informatik IV, Univerity of Mannheim, Germany vogel, widmer, farin, mauve, ABSTRACT In thi paper, we propoe a novel multicat routing algorithm that i baed on application-level prioritie and network characteritic: The application may pecify an individual priority for each packetreceiver pair. The multicat ditribution tree i then contructed uch that the higher the priority, the more direct the path from the ender to the packet detination and the lower the reulting endto-end delay. Thi algorithm can be ued to realize applicationlevel multicat for delay-enitive application uch a networked computer game. However, optimizing the multicat tree with repect to the end-to-end delay come at the cot of an increae in link tre the more direct a path, the le likely it i that it can be integrated efficiently into an overlay ditribution tree. Our algorithm take thi tradeoff into account and contruct efficient prioritybaed multicat tree. We demontrate the performance and characteritic of the algorithm through imulation. Keyword Application-Level Multicat, Multicat Routing, Ditribution Tree.. INTRODUCTION Group communication, or multicat, i needed by ditributed interactive application to deliver data from one ender to multiple receiver. Example are video conference, groupware ytem, and networked computer game. In many cae, realizing group communication by etting up a direct connection from a ender to each receiver i not a viable olution becaue of reource limitation. In the Internet, IP multicat provide efficient group communication by duplicating packet within the network router o that data travere phyical link only once. But due to variou technical and adminitrational reaon, IP multicat ha not been widely deployed. A promiing alternative i application-level multicat ALM) [-8]: The key idea i to ue the end-ytem a node in a multicat ditribution tree. The contruction and maintenance of the tree i done at the application level without any upport from the network. Router within the network do not have to keep tate information about group memberhip. Furthermore, ALM can be deployed immediately without any change to the network. Thi eliminate two key problem of IP multicat. Permiion to make digital or hard copie of all or part of thi work for peronal or claroom ue i granted without fee provided that copie are not made or ditributed for profit or commercial advantage and that copie bear thi notice and the full citation on the firt page. To copy otherwie, to republih, to pot on erver or to reditribute to lit, require prior pecific permiion and/or a fee. NetGame May -,, Redwood City, CA, USA Copyright ACM -8-7-//...$.. Exiting approache for ALM focu on network characteritic e.g., latency) to contruct the multicat ditribution tree. A long a thoe characteritic remain contant and no change in the et of eion member occur, all packet from a ender will take the ame path toward the detination. Thi approach i well uited when all packet hould be delivered to all receiver with the ame priority e.g., in a multi-detination file tranfer). However, a number of application exit where the priority of a packet may be different for the receiver. In a networked computer game, for example, the action of a player i very important to competing player that are cloe by. Thee player hould receive information about uch action with a very low delay. Other player may be able to tolerate a higher delay, depending on their location and orientation within the game. Furthermore, a packet priority may change over time for ome or all receiver. For example, if enor data i tranmitted by a ender, thi data may typically have a low priority for all receiver, unle an extreme enor reading occur which require the tranmiion of a packet with very low latency to ome receiver. Traditional tree routing algorithm are unable to handle thee ituation. In thi paper, we propoe to ue a combination of applicationlevel prioritie and network characteritic in order to build and maintain a multicat ditribution tree. Since multicat routing i handled at the application level, integrating application knowledge into the routing deciion come natural and introduce little overhead. The general idea of our approach i to allow the ending application to aign a priority to each pair of packet and receiver. The higher the priority, the more direct will be the path that the packet take toward it detination. The cot for reduced latency i a poible increae in link tre i.e., the number of copie of a packet that travere the ame link). Thu, the key challenge i to find an appropriate algorithm for the contruction of a multicat ditribution tree which take thi tradeoff into account. The remainder of thi paper i tructured a follow: in Section we briefly outline exiting approache for application-level multicat. The algorithm for the contruction of multicat ditribution tree which take application-level emantic into account i decribed in Section. In Section we dicu practical iue uch a the maintenance of a ditribution tree that may change on a perpacket bai and how to efficiently ditribute topology information to other node. Section contain an evaluation of the preented algorithm by mean of imulation. We conclude the paper and give an outlook on future work in Section.. RELATED WORK Typically, application-level multicat algorithm contruct their ditribution topologie baed on path characteritic uch a endto-end) latency, available bandwidth and packet lo rate. Their

2 aim i to build ditribution tree that minimize the additional routing overhead compared to native IP multicat. Yoid [7] create a ingle multicat tree for all end-ytem that participate in a eion, independently of a pecific ender. Each node elect another node a parent, preferably a node with a low network delay to. Receiver gather a lit of poible parent on bai of periodic control meage and explicit querie. An initial lit can be obtained from a o-called rendezvou hot during the boottrap phae. Aide from the network delay, the maximum number of children that can be attached to a potential parent i.e., the fan-out) i conidered in the choice of a parent node. Becaue the lit of poible parent i uually incomplete and the fan-out i contrained, the reulting ditribution tree may be uboptimal. A a conequence, node periodically ping other eion member in order to find a better parent and optimize the tree tructure. An alternative method to elect a parent node in Yoid i provided for the tranfer of large data file: node connect to the parent that cache the larget amount of data. Other example for tree building ALM protocol are HMTP [], BTP [8], and Overcat [9]. They all form elf-organizing ditribution tree where node elect an appropriate parent, and they implement mechanim for integrating new member, detecting loop and partition, and for optimizing the tree by rearrangement. Unlike the other protocol, Overcat build ender-pecific tree intead of a ingle hared tree. With TMeh [], the author propoe to add additional link to the multicat tree. While thee hortcut reduce the number of hop on the way from a ender to the receiver, TMeh eek to optimize the average end-to-end delay for the whole group and build a rather table ALM tree. Thu, TMeh eem not to be flexible and fat enough to facilitate delay optimization for certain receiver in an environment where prioritie change dynamically. Intead of contructing a tree directly, Narada [] employ a twotep proce. Firt, a meh i built among the participating endytem. For the actual data tranport, Narada run a ditance vector protocol with latency and bandwidth [] a the routing metric on top of the meh. The reulting tree i a ender-pecific hortet path tree ) baed on the underlying meh. The crucial factor in thi approach i the quality of the meh that mut balance the number and the characteritic of the ued unicat link. If there are too many link in the meh, the reulting ditribution topology will reemble a tar of unicat connection from the ender to all receiver. A in Yoid, joining end-ytem obtain a lit of current eion member by a boottrap mechanim and connect to one or more lited node. Then, member periodically add link that improve the routing performance and remove link that are rarely utilized by a ditribution tree. Like Narada, Goamer [] alo employ the tree-over-meh approach where the meh i contructed in order to minimize latencie of the ditribution tree. The number of connection that a node can maintain at a certain point in time i explicitly retricted with Goamer in order to take bandwidth limitation into account. Approache where application-level emantic are ued for routing can be found in the area of content delivery network. The common idea of Bayeux [], Chord [], and Content Addreable Network [] i to realize a calable lookup ervice for object e.g., end-ytem) where the reponibility for managing the object pace i hared equally among a network of peer node. The multi-hop lookup path for a target object e.g., the receiver of a meage) i determined on bai of certain propertie of the hahgenerated) detination addre. For example, in Bayeux the current node ue the i-th digit of an object addre to reolve the next hop toward the detination. In contrat to the previouly dicued ap- A 7 B C Figure : Joint path to ditant receiver plication level multicat protocol, thee content delivery network bae their routing deciion almot) excluively on application emantic. Conequently, the reulting ditribution tree may be very inefficient with repect to end-to-end delay and link tre.. APPLICATION-LEVEL MULTICAST ROUTING An ALM routing algorithm build a data ditribution tree with the end-ytem a node connected by unicat link. The reulting tree hould ue the reource of the underlying network efficiently. Since on the application level there i no direct acce to network topology information, obervable parameter e.g., latency) may be ued to deduce a certain amount of knowledge about the actual topology: When node ha a high delay to both node and, and ha a low delay to, then it i likely that the route hare a ignificant portion of the phyical link with route ee Figure ). In the following, we will concentrate on unicat latencie a the network parameter that determine the ALM tree. Two well-known type of tree are the minimum panning tree ) and the hortet path tree ). The optimize the reource uage of the multicat tree but the path length i not conidered and can caue very large end-to-end delay. Hence, uing an i only reaonable when end-to-end delay are not an iue e.g., for non-interactive data diemination). When building an from the unicat delay, the ditribution tree will conit of eparate unicat connection from the ender to each receiver commonly, thi would be regarded a normal unicat rather than application-level multicat). With repect to end-to-end delay the i optimal but it caue a very high conumption of network reource. Furthermore, building a i not poible when the ender bandwidth i not ufficient to erve all receiver imultaneouly. Our aim i to contruct application-aware ditribution tree that balance the characteritic of and : For each packetreceiver pair the application may provide a priority. Depending on thi priority, the path along which the packet i forwarded hould gradually change from the path to the path. In order to find an algorithm with thi property, we firt invetigate well-known metric for the aement of ditribution tree. The optimization of reource uage lead to an, while the optimization of the cumulative end-to-end delay lead to an. We combine thoe two metric by uing one common application priority for the whole ditribution tree. The optimization of the combined metric allow the gradual tranition from path to path a the application priority increae. In a econd tep, we generalize the met- We will ignore that unicat routing protocol may give uboptimal route and aume that the underlying unicat routing algorithm caue direct path to a node to be horter than any indirect path over intermediate node.

3 8 ) ric uch that one priority may be given for each detination. It optimization lead to a tree where each path from the ender to a detination change from the path to the path. Finally, we preent an efficient algorithm which provide a very good approximation for the optimal ditribution tree with repect to the lat metric.. Ditribution Tree Metric Let be a fully connected, directed graph, where denote the et of node and the et of edge, where connect the node and. We define the node a ource and the remaining node a receiver. Edge weight are aigned according to the delay of the correponding link. For %$ each ditribution '& tree!#", we can define two cot function and : Reource uage, defined a the product of link tre and link delay, ummed over all phyical link of the underlying network. Thi um i equivalent to the um of all edge delay in the overlay ditribution tree : $ *) +-,/. Cumulative end-to-end delay, meauring the total delay for the ditribution of a packet from the ource to all receiver. Let 798 :<;=>>>= -?@BA denote the route from the ource '& to the receiver on the current ditribution tree. Then i given by: '& ) C<DE $ ) +EGF-D When optimizing $ '&, the minimum cot tree i equal to the, when optimizing, it i equal to the.. Introducing Application-Level Semantic For many application, electing either of thee two metric a the optimization criterion doe not give the deired reult. While minimizing the total reource uage i deirable, overly large endto-end delay reduce the utility of the application. Hence, ome tradeoff between reource uage and end-to-end delay i required. Let HJI KL MON be the application priority with which it want to deliver data, where M mean that the end-to-end delay for the receiver hould be a low a poible, while K denote no pecial delay requirement. A balancing cot function can be defined a follow: ) P-M'QRHST) +-,U. WVXHY) C<D< $ ) +F D Figure viualize the effect of H when building the optimum ditribution tree according to ) for a ample ALM eion. The participant of the eion are numbered from M to Z, while intermediate router of the underlying network appear a unmarked node. The correponding table contain the pairwie end-to-end delay. Let node [ be the ender. The reulting ditribution tree that are optimal with repect to are depicted in Figure. When H i increaed, node farther away move up in the tree, reducing the end-to-end delay to the ender, ^]`_ until for H\#M K a tar-like _ba Given the ditribution tree = in Figure, the reource uage in the underlying network i MbcedeVf[gcgM`V\Mhch[ikj, which i equal to the um of edge weight in the overlay tree ZlVnm. The link tre i implicitly contained in the end-to-end delay. i reached. A can be een from the graph, the number of poible tree for a mall overlay network with only node i very limited. Following, we generalize the cot function for the cae of individual per-receiver prioritie, where information may be of high importance to ome receiver and hould therefore be delivered on a direct path) and of lower importance to other receiver. Let Hpo@ rqi K@ MON be the per-node prioritie for a ender. They can eaily be integrated into & t &, defining the cot function : & ) C<D< $ Hu e) +EGF D %$ Integrating the per-node prioritie into i more difficult ince the cot are calculated over the edge of the tree and not per receiver. However, in an, the relevant cot for a receiver i the weight of the edge over which it i connected to the ret of the tree. Conequently, the priority of a node can be aigned to thi edge. Thi lead to the following cot function $ : The total cot t $ *) -M'QRHu B +-,/. are defined a $ V & ) Note that pecialize to & if vwhulyxm, and to $ if vyhulz{k. Thi mean that the node prioritie determine the tructure of the minimum cot tree with the extreme and. Direct optimization of thi cot function i computationally complex. Thu, we approximate the cot term in a way that allow u to directly modify edge weight and compute an baed on thee modified weight. In order to calculate the modified weight, the cot function need to be baed olely on the weight of the edge of the tree, and not on complete path to individual receiver. The general idea i to plit the complete path to a receiver into the lat edge of the path and the path of all previou edge :<;= <;}-~=>>>>= -?@ A. We can approximate the cot of the path from to with the cot of the direct edge -, where - i a lower bound for the actual path cot. Thi lead to a implified approximate formulation for the global cot : *) -M'QRHu B +-,U. ) -M'QRHu >B +-,U. WV ) C<DE $ Hu e) +GF D V C<DE $uƒ HuB - `V\ C, G e +, D G ) VpHb B - +-,U. The lat equality follow from the property that a panning tree of a graph ha the ame number of edge a there are target node in the graph. Conequently, both um are calculated over the ame et of edge. In order to minimize, we can apply an algorithm on the graph with modified weight. The new weight are et to 7Š Œ `VpHuOB /--ˆ - ) With increaing HuO, indirect link to the target node > will become more expenive and eventually uch link will be removed from the ditribution tree. Note that a directed algorithm ha to be applied to obtain correct reult a it i not a priori known in which direction data i ditributed over the edge and the cot for

4 End-to-end delay 7 Figure : Example graph a) H I K@ KKyQ KL K@M^ b) H I KL K@MLQiKL [K c) H I K@ [KWQ K@ ZG[ d) H I KL Z[WQ KL j 8 e) H fi K@ j Q M KKG Figure : Optimal ditribution tree

5 oppoing direction may differ. We call the combination of modified edge weight and directed computation priority-baed directed minimum panning tree ) algorithm. Algorithm to contruct in directed graph have been decribed in [, ]. Peudo code for the implementation that wa ued for the imulation can be found in Appendix A.. DESIGN CONSIDERATIONS The preented algorithm improve the application influence on the data ditribution proce through the incluion of application emantic in the contruction of the ditribution tree. However, it i very cotly to recalculate the ditribution tree for each packet. Moreover, node in a pecific ditribution tree need to know which other node or node to forward a packet to and thu require ome information about the tree topology whenever the topology change. Thi information ha to be ditributed to the node in an efficient way. In thi ection, we will dicu how the algorithm can be integrated into application while avoiding exceive calculation in the end-ytem and meage overhead through the ditribution of topology information.. Maintenance of the Ditribution Tree Intead of rebuilding the ditribution tree whenever topology information or application prioritie change, an improved update mechanim can ignificantly reduce the number of neceary tree recomputation. The tree will not change under the following condition: the cot delay) of a link that i not in the directed increae, the cot of a link within the directed decreae, the priority for a receiver which i connected directly to the ender increae, and the priority for a receiver which i connected indirectly via another receiver decreae. In thee cae, it i only neceary to update the link weight. Furthermore, a change in receiver prioritie or link delay may be too mall to caue a tree change. An increae in link delay on a direct link between ender and receiver may caue the receiver to be connected through an indirect link correponding to a priority decreae). An increae in the delay of an indirect link may caue a node to be connected directly correponding to a priority increae). Similar conideration hold for a delay decreae on direct or indirect link. When computing a directed, it i poible to record for each tep of the algorithm by how much the cot of a link ha to increae before it i excluded from the ditribution tree, or by how much the cot of a link ha to decreae before it will be included in the tree. With thee conideration, rebuilding the tree can be limited to the cae where the tree tructure will change. If change to the tree tructure are neceary, it i deirable to keep the number of update mall. When a number of link delay or prioritie change imultaneouly, recomputing the whole tree i reaonable. For minor change, adjuting the exiting tree can be much le cotly. Note that ome of the improvement in the update mechanim are only poible becaue the overlay graph i fully connected and becaue the relative weight increae on the lat hop of an indirect path i baed on the weight of the link from the ender to the tart of the lat hop link and not on the complete path to the receiver. Let u aume that the cot of a ingle link increae ufficiently to caue a change in the ditribution tree. We have to ditinguih two cae: increae for p, : increae for ender. In the firt cae, Š i updated and > i connected to the ret of the tree via a le expenive link. However, the link cot for all node in the tree below > a well a the tree tructure remain unchanged. Becaue of the aymmetric link, it may be poible that it i now le expenive to connect via E, and o on. Hence, we have to revere the direction of link on the path from to a long a the cot Š in the direction toward the ender are le expenive than the link cot in the oppoite direction. In the econd cae when the cot of a link : from the ender increae, the change will alo increae the cot of Š v T. For all with!, it i neceary to check whether the node can be connected to the ret of the tree via a le cotly link i.e., the ret of the tree may grow into the region with the increaed link cot). The tree part below the will not be affected. Thu, in both cae only very limited part of the tree will change. The ame calculation can be applied when link cot decreae. Moreover, priority change affect the cot of all incoming link of a node but ince only one of thee link can be in the current ditribution tree, the above tatement are even valid for priority change. Latly, even though a ditribution tree may no longer be optimal given the current edge weight, it may be ufficient for data ditribution a long a the change are mall i.e., ue a fuzzy update trategy where update are triggered by ignificant weight change only).. Efficient Topology Ditribution For the forwarding proce, a pecific tree topology need to be known by all node of the tree. Either, node may ditribute their priority table o that all other node can locally recalculate all ditribution tree, or node may ditribute the tree they already calculated. The econd alternative eem much better uited for the tak ince the communication overhead i imilar but much le calculation at the receiver are required. Furthermore, for the econd alternative inconitent delay information at the receiver will not reult in routing loop. In fact, node do not require the complete ditribution tree, but only need to know which node or node to forward the packet to. Thi information i updated by a ender whenever it ditribution tree change. It i either poible to include the information in the data packet header, or to end extra tree maintenance packet. The econd alternative i preferable if a ignificant number of packet are ent along the ame ditribution tree. If delay between node remain relatively contant and only ome application priority pattern are valid, the number of different ditribution tree i fairly limited. In thi cae it may be more efficient to precompute all poible tree or a limited ubet of uitable tree), ditribute thi information to all the other node, and then only include an identifier for a pecific ditribution tree in the header of a data packet.. SIMULATIONS We implemented a imple network imulator in order to evaluate the performance of our algorithm compared to the delay-baed and approache. The imulator i event-baed and allow

6 ƒ Table : Router Link End- Avg. # Avg. # of Sytem of Tree Edge Change ratio priority cla packet-level data ditribution on arbitrary network topologie. A network topology i characterized by a et of node connected via edge with a certain delay. We do not conider other factor uch a bandwidth, router load, and packet lo. All network topologie were generated with the Georgia Tech Internetwork Topology Model GT-ITM) [] toolkit. The topologie ue the tranit-tub method without extra tranit-tub or tub-tub edge. Edge between node are placed uing the random model. End-ytem were located on the network edge. Firt, we evaluate the propertie of for different network topologie when all receiver are aigned the ame applicationlevel priority. Following, we give imulation reult for realitic prioritie baed on a multi-player game.. Simulation for with a ingle priority In thi ection, we analyze how many ditinct ditribution tree are built by the algorithm and to what extent thee tree differ. We define the application-level priority H to be equal for all receiver according to Equation )) and calculate the et of tree! i.e., vghf I K@ MON ) for different network topologie. The reult are lited in Table. The firt three column decribe the topology ued in term of the number of router, the number of phyical link, and the number of end-ytem participating in the ALM eion. The average number of different ditribution tree i given in column four. A can be derived from the table, thi figure i correlated with the number of end-ytem. Next, we are intereted in the topological difference between two ucceive ditribution tree! and!, where! i the tree H with at leat one changed with the mallet priority H edge compared to!. The average number of edge change from one tree to the next i relatively mall ee column five). Thu, the optimization of tree maintenance a decribed in Section i able to achieve a ignificant reduction in tree calculation cot.. Simulation for a ample application In the following, we compare the characteritic of our algorithm to the delay-baed and approache on bai of a realitic application cenario... Simulation Setup Event pattern to determine application prioritie for the imulation were generated by tracing a imple multi-player game []. In thi game, each player control a pacehip which can accelerate, decelerate, turn, and hoot at one another with a laer beam of a certain range. The rectangular game field allow player who approach one edge of the field to reappear at the oppoite ide. Each pacehip ha a predefined amount of hit point: each time it i hit by a laer beam, one of the hit point i ubtracted. If no hit Figure : Ditribution of application prioritie point remain, the pacehip i removed from the game. Uer action together with timetamp and information about the current game tate were recorded for game with ix and eighteen player. In our network imulation, each recorded uer action led to one packet exchanged among end-ytem. The application prioritie Hu iki KL MON ued for the tree building algorithm are baed on the relative poition between the pacehip and their orientation. If the pacehip of a player i within hooting range of another player hip, the end-ytemg of et Hu JM. We define that i within hooting range of if the ditance between and i le than the maximum range of the laer beam and i oriented in uch a way that it can hit after conducting at mot one turn operation. For player outide the hooting range of, H i calculated depending on their ditance = to the ender: Hu rm'q, where i the maximum poible ditance. A typical ditribution of prioritie for a game eion with ix player i depicted in Figure. Prioritie cloe to M are common becaue the objective of the game i to core point by hooting other player and hence player will cluter together intead of preading out evenly on the game field... Simulation Reult for End-Sytem To evaluate the characteritic of our priority-baed tree-building algorithm ), we compare it to the and the, repectively. For the imulation, we ue two network topologie of different ize. The firt imulation cenario i baed on a game eion with ix player. The eion lated for econd and during that time pan a total of event were iued. The priority ditribution that reulted from the pacehip poition i depicted in Figure. Figure how the underlying network topology with end-to-end delay between and m and an average value of m. The delay propertie of a pecific ditribution tree can be meaured uing the cot & ee Section ). Figure a) depict the ditribution of & for the, the, and the, repectively. By definition, t the routing algorithm reult in the bet ditribution of, with 9% of all tree having a of le than & 7 & m. However, the difference between and i comparatively mall m at 9%), meaning that the end-to-end delay in the ditribution tree contructed with the algorithm are on average only marginally higher than the delay on the direct path. In comparion, ditribution tree created with the algorithm reult in a ignificantly higher difference for & 7 m at 9%).

7 & priority-baed 7 8 cumulative weighted end-to-end delay [m] a) Ditribution of relative delay penalty..... [.;.) [.;.) [.;.9) [.9;.] priority clae b) Average RDP reource uage [m] c) Ditribution of.. link tre d) Link tre ditribution Figure : Simulation reult for End-Sytem The receiver-pecific end-to-end delay, defined a +F-D, reulted in the following 99% confidence interval for thi imulation cenario: I j I M>KmL j@ M>KZL N. The relative delay penalty of the end-to-end delay: ^M>KLM [N, I MM <e UM M^[@M mn, and ) i a meaure for the optimality +EGF-D -B The compare the end-to-end delay of a receiver to the mallet poible delay i.e., the unicat delay fromg to ). By definition, for the ditribution tree <l#mzv Œ. Figure b) how the average value for different priority clae. In the cae of the algorithm, the decreae continuouly with increaing application-level prioritie from. for receiver with Hu XI KL KL K@/M to. for with Hu z I K@ j@ ^M KN. For application intance with a high priority, a delay cloe to the unicat latency can be achieved. The maximum range of the average i relatively mall.) ince only ix endytem participate in thi imulation cenario and the ditribution tree have path with at mot four hop. The load on the network caued by a certain ditribution tree can be meaured uing the reource uage metric $ a defined in Section. '$ take into account that more than one identical copy of a packet may be ent over the ame phyical link. The ditribution of $ i depicted in Figure c). The algorithm alway elect the ame et of edge for it tree, independently of the ource node. Thu, the '$ ha a contant value of 8 m which i at the ame time the lower bound for the reource uage of the other algorithm. 7% of all ditribution tree built by the algorithm have a $ between 8 m and 7 m which i cloe to the optimum and far better than the value obtained by. Hence, the optimization of end-to-end delay for certain application intance by the caue only a light increae in reource uage when compared to the. Link tre i another indicator for the network overhead caued by an ALM tree. reult in the lowet link tre with 77% of all ditribution tree having a link tre of and a maximum link tre of, a hown in Figure d). Ditribution tree contructed by the algorithm come cloe to thee value with the only difference being that.7% of the tree have a link tre of. The link tre for the tar-haped topologie lie between and and only % of the tree have a link tre of... Simulation Reult for 8 End-Sytem For the econd imulation cenario, we created a more complex network topology with router, 8 link, and 8 end-ytem participating in a virtual game eion. The delay among end-

8 & cumulative weighted end-to-end delay [] a) Ditribution of relative delay penalty.8... [.;.) [.;.) [.;.9) [.9;.] priority clae b) Average RDP reource uage [m] c) Ditribution of link tre d) Link tre ditribution Figure : Simulation reult for 8 End-Sytem ytem lie between m and 8 m with an average value of. m. During the eion duration of econd, a total of event were iued by all player. The reulting application prioritie are imilar to the ditribution hown in Figure. The ditribution for the cumulative weighted end-to-end delay & are depicted in Figure a). Becaue of the increaed complexity of the ALM tree with up to hop on path of the ), the difference in & between and i larger 7 m to 9 m at 9%). However, the doe achieve a good optimization of the latency from the ource node to receiver with a high priority when compared to the value of & for the algorithm 9 m at 9%). The receiver-pecific end-to-end delay reulted in the following 99% confidence interval: I M L M GjL [N, I [ M d O[ m@ N, and I M d [@ M Z@ d^n. The optimization of end-to-end delay become alo viible in the average value for application intance within different priority clae ee Figure b)). For the algorithm, the decreae from. to. for receiver with Hu WkI K@ j@ M KN which i cloe to the optimum value. Thi i a ignificant improvement over multicat tree contructed uing the, even for the receiver within the lowet priority cla. At the ame time, priority-baed minimum panning tree caue a higher network load a can be een from Figure c). It how the reource uage ditribution for the three tree building algorithm: 9% of all have a reource uage that i up to % higher than $ of the. Shortet path tree have a reource uage that i by far larger. A in the firt imulation cenario, the algorithm generate the lowet link tre with 9% of all ditribution tree having a link tre of at mot and a maximum tre of ee Figure d)). The value for the algorithm are only lightly larger with 9% of all multicat tree having a link tre of at mot and a maximum link tre of. In comparion, the link tre of the tree ha a value of 9 at 9% and maximum link tre i 7... Introducing Uncertainty All imulation reult dicued above were calculated under the condition that the application alway had full knowledge about the actual end-to-end delay. In a real network, delay fluctuate depending on router load) and meaurement give approximation only. Thu, we alo conducted imulation for the algorithm when meaured delay differ t from the real value up to a certain &, degrade only by 8 m at 9% percentage. For P[K when compared to the value given in Figure a), and by 7 m for dk. In the highet priority cla, increae only lightly to. for [K, and to. for dk. The reource uage ditribution for [K i almot identical to the

9 one depicted in Figure c). For dk, 9% of all tree have a '$ between m and 88 m. Thee reult indicate that the algorithm i fairly robut againt inaccurate knowledge of delay. Summing up, the imulation reult how that the algorithm optimize the end-to-end delay for receiver for which the ender ha a high application priority. Even delay for end-ytem with a lower priority are in mot cae better than thoe that can be achieved with multicat tree built by the algorithm. At the ame time, the increae in network load i kept at a tolerable level.. CONCLUSIONS AND OUTLOOK We have preented a novel priority-baed routing algorithm for application-level multicat. It allow an application to influence the path that a packet take from the ender to a receiver by pecifying a priority for each packet-receiver pair. A the priority i increaed from K to M, the path change gradually from to. Thu, our can be conidered a a generalization of the and the. We have decribed an efficient algorithm for the contruction of the ditribution tree and dicued how tree maintenance operation can be minimized. Our imulation reult indicate that the algorithm build multicat tree with end-to-end delay that are cloe to the optimum for receiver with a high priority while the total network load increae only lightly. In the future, we plan to invetigate how to bet elect prioritie on the bai of application-layer emantic for performance-critical multicat application. Another important iue i to further reduce the computational complexity and to improve calability. One olution might be to cluter adjacent in repect to latencie and prioritie) end-ytem and to contruct local. Alo, we want to take capacity contraint on the link into account, and we intend to perform imulation for more complex topologie. Our final goal i to integrate the algorithm into a real-world multicat application, uch a an Internet game, and to perform meaurement over the Internet. 7. REFERENCES [] K. Calvert, M. Doar, and E. Zegura. Modeling Internet Topology. IEEE Communication Magazine, ):, 997. [] Y. Chawathe. Scattercat: An Architecture for Internet Broadcat Ditribution a an Infratructure Service. PhD thei, Univerity of California, Berkeley, USA, Dec.. [] Y. Chu and T. Liu. On the Shortet Arborecence of a Directed Graph. Science Sinica, :9, 9. [] Y. Chu, S. Rao, S. Sehan, and H. Zhang. Enabling Conferencing Application on the Internet uing an Overlay Multicat Architecture. In Proc. ACM SIGCOMM, San Diego, CA, USA, Aug.. [] Y. Chu, S. Rao, and H. Zhang. A Cae For End-Sytem Multicat. In Proc. ACM SIGMETRICS, Santa Clara, CA, USA, June. [] J. Edmond. Optimum Branching. J. Reearch of the National Bureau of Standard, 7B:, 97. [7] P. Franci. Yoid: Extending the Internet Multicat Architecture. unrefereed report, available at Apr.. [8] D. Helder and S. Jamin. End-hot Multicat Communication Uing Switch-tree Protocol. In Proc. GPPC, Berlin, Germany, May. [9] J. Jannotti, D. Gifford, K. Johnon, M. Kaahoek, and J. J.W. O Toole. Overcat: Reliable Multicating with an Overlay Network. In th Sympoium on Operating Sytem Deign and Implementation OSDI), San Diego, CA, USA, Oct.. [] M. Mauve, J. Vogel, V. Hilt, and W. Effelberg. Local-lag and Timewarp: Providing Conitency for Replicated Continuou Application. To appear in: IEEE Tranaction on Multimedia. [] S. Ratnaamy, P. Franci, M. Handley, R. Karp, and S. Shenker. A Scalable and Content-Adreable Network. In Proc. ACM SIGCOMM, San Diego, CA, USA, Aug.. [] I. Stoica, R. Morri, D. Karger, M. Kahoek, and H. Balakrihnan. Chord: A Scalable Peer-to-peer Lookup Service for Internet Application. In Proc. ACM SIGCOMM, San Diego, CA, USA, Aug.. [] W. Wang, D. Helder, S. Jamin, and L. Zhang. Overlay Optimization for End-hot Multicat. In Proc. NGC, Boton, MA, USA, Oct.. [] B. Zhang, S. Jamin, and L. Zhang. Hot Multicat: A Framework for Delivering Multicat to End Uer. In Proc. IEEE INFOCOM, New York, NJ, USA, June. [] S. Zhuang, B. Zhao, A. Joeph, R. Katz, and J. Kubiatowicz. Bayeux: An Architecture for Scalable and Fault-tolerant Wide-area Data Diemination. In th International Workhop on Network and Operating Sytem Support for Digital Audio and Video NOSSDAV), Port Jefferon, NY, USA, June. APPENDIX A. PSEUDO CODE Figure 7 give the peudo code to compute the on a graph z < for a ender with priority function H. Firt, the weight Š of the directed graph are calculated a decribed in Section. Second, the directed minimum panning tree i determined according to the algorithm publihed by Edmond []. Thi algorithm i deigned to contruct a branching! with maximum total cot +-,/. on bai of. Thu, to build a minimum panning tree, we define all weight Š to be negative and enure that the branching contain QnM edge maximizing with negative weight i equal to minimizing with poitive weight). The baic idea of Edmond algorithm i to calculate an initial graph! by electing for each node except ) the incoming edge with maximum cot. While! contain any cycle, thee are broken up by exchanging appropriate edge. A branching i a directed graph without cycle where each node ha at mot one incoming edge, i.e., a branching i not necearily connected.

10 ) Compute weight Š for all edge in E: v = =< n o Š e Qy: VpHu/B ) Compute the directed minimum panning tree with ourceg on : Dicard all edge 7 entering the ource node. v node n = : elect the edge Y with maximum weight Š edge. While! o P E Š contain a cycle o r y= "Œ e= P" Š do -. Let Š be the et of elected Find the edge with minimum weight Š. Modify the weight Š of each edge T = : Š Ro 9 Š gvk Š 'Q Š, with b/r being the predeceor node with edge. ^ Select the edge J = with maximum weight Š, and et Š o ^ Š '. Build a new graph! by contracting all node into a peudo-node : *o. Modify and Š by replacing all edge with tail node or head node by or ^, and delete edge =. Create new weight Š accordingly. Replace all peudo-node p and the correponding edge in Š by the original node and edge.! repreent the directed with root. Figure 7: Peudo code for the computation of the optimum ditribution tree