A Recovery Algorithm for Reliable Multicasting in Reliable Networks

Transcription

1 A Recovery Algorithm for Reliable Mlticasting in Reliable Networks Danyang Zhang Sibabrata Ray Dept. of Compter Science University of Alabama Tscaloosa, AL {dzhang, Ragopal Kannan S. Sitharama Iyengar Dept. of Compter Science Loisiana State University Baton Roge, LA {rkannan, Abstract Any reliable mlticast protocol reqires some recovery mechanism. A generic description of a recovery mechanism consists of a prioritized list of recovery servers/receivers (clients), hierarchically and/or geographically and/or randomly organized. Recovery reqests are sent to the recovery clients on the list one-byone ntil the recovery effort is sccessfl. There are many recovery strategies available in literatre fitting the generic description. In this paper, we propose a polynomial time algorithm for choosing the recovery strategy with low recovery latency withot sacrificing mch bandwidth. We compared or method with two existing recovery methods, SRM (Scalable Reliable Mlticast) and RMA (Reliable Mlticast Architectre), by simlation and fond that or method performs better. Althogh or theoretical analyses are based on a reliable network, or simlation reslts show that or strategy performs as well with the per link loss probability in a network p to 20% or more.. Introdction and literatre srvey Best-effort IP mlticast transmission withot any garantee of reliability has led to a wide and deep discssion of how to provide efficient and scalable error recovery schemes for reliable mlticast. Nmeros sch schemes have been sggested by researchers. Althogh their naming conventions and techniqe details are different, these schemes can be classified into three main categories, i.e., sorce-based, server-based and peerbased recovery schemes, with respect to the responsibility of retransmission and the need for frther groping (for other taxonomies, please refer to [] and [2]). In sorce-based recovery schemes, the sorce exclsively retransmits all the lost packets to the reqesting receivers. This mechanism garantees that one recovery attempt is enogh for each reqest, and ths redces the overhead incrred by failed recovery attempts. However, it needs some techniqe to handle ACK/NACK implosion problem and exposre [3] problem. Or previos research [4] is an endeavor to resolve these problems. NP [5] and [6, 7] are also sorce-based recovery protocols. This paper does not focs on this category. Server-based recovery schemes sally partition grop members into sbgrops (or local grops) hierarchically and/or geographically and allocate one server for each sbgrop to detect recovery reqests and recover the lost packets. A common problem existing in this mechanism is how the server recovers the lost packet in the case that the server itself does not receive it. The sal soltion for this problem is to send reqest to a prioritized list of servers/proxies/sorce one-by-one till sccess. A nmber of server-based recovery protocols [9, 0,, 2, 3, 4, 5, 6] either simply send reqests to some pstream servers/sorce or constrct a tree-based hierarchy to organize these servers. The prioritized list for the treebased hierarchy contains those nodes along the path from the reqesting server to the sorce in sch order. Treebased strctre can not garantee the prioritized list have low recovery latency, while or strategy gives a polynomial time algorithm to compte the prioritized list of servers/proxies with low recovery latency. Note that or strategy does not belong to this category, bt it can be sed as part of any scheme in this class. In peer-based recovery schemes, it is p to the receivers to detect packet loss and send the reqest to other receivers [7, 8, 9] or third-party [20]. There is no sbgroping operation in this scheme. This mechanism also needs some recovery strategy, which shold satisfy two conditions, ) low latency; 2) low correlation of packet loss. Nearby receivers/proxies can be efficient, bt they are tightly correlated in terms of packet loss since they share many common links in the mlticast tree. Receivers/proxies closer to the sorce have a better chance of receiving the lost packet, bt the farther, the longer the latency is. SRM (Scalable Reliable Mlticast) [7] is an early peer-to-peer recovery scheme. In SRM, if a receiver R lost a packet P, R will set a reqest-sppression timer, once this timer expires and R has not received any reqest for packet P, R will mlticast its reqest. If receiver/sender S receives R s reqest and S has packet P, then S will set a repair-sppression timer, once this timer expires and S has not received any repair for packet P, then S will mlticast that repair. SRM is qite scalable and the reqestsppression and repair-sppression timers effectively

2 Sorce Backbone network of mlticast-capable roters Shared Roters in the grop Ghost Recipients Figre. A mlticast network tree redce the nmber of dplicate NACKs and repairs to be mlticasted, however, these timers also increase the recovery latency. Frthermore, mlticasting NACKs/repairs adds some nnecessary load on roters and significantly increases the nmber of bandwidth being sed. In RMA (Reliable Mlticast Architectre) [9], each receiver that lost some packet attempts to achieve the shortest delay from the nearest pstream (from this receiver toward the sorce) receiver that has received the packet. Once the reqest approaches an pstream receiver that has the packet, this receiver will mlticast the repair to the sbtree that contains all the receivers that have been reqested. This scheme is efficient in that when the reqest reaches a repairer, it garantees that all receivers that have been reqested also lost that packet. This scheme is not efficient in that one-by-one searching is st besteffort, not strategic. These two schemes did not deeply analyze the peerbased recovery problem, ths cold not provide a recovery strategy with low recovery latency and bandwidth sage, which is primary contribtion of this paper. Or simlation compared the performance of or recovery strategy with that of SRM and RMA. PGM [8] and STORM [20] are two other peer-based recovery schemes, bt they apply repair server placement mechanism, which is ot of the scope of this paper s discssion, therefore, or simlation did not take these two schemes into accont. The rest of this paper is organized as follows. In section 2, we describe the network topology and or recovery strategy. In section 3, we give or algorithmic framework for peer-based recovery, along with the obective fnction for compting the recovery latency. In section 4, we present a polynomial time algorithm to compte the recovery strategy with low delay and exploit a directed acyclic strategy graph to show how we get the shortest delay in the digraph from or algorithm. Section 5 depicts or simlation reslts. Or conclsion for this paper is given in section 6. Figre 2. Ghost nodes represent shared links 2. Problem description Refer to Table in [26] for the meaning of some of the symbols we are sing in this paper. We are interested in the reliable mlticast problem over a reliable network, for example, distribting a large file to a nmber of clients, etc. Sch applications need fll reliability. As discssed in introdction, the peer based and server-based schemes distribte the recovery load in different regions of the network and hence introdce little extra delay over the delay created by the ambient (or backgrond) traffic. 2.. Topology of the Network Withot loss of generality, we assme that the sorce and clients are individal compters connected to a backbone of roters. Algorithmically, this assmption pts the clients at the leaves and the sorce at the root of the mlticast tree. Strictly speaking, we really need to pt the sorce at the root of the mlticast tree otside roter backbone. The clients/proxies/servers may as well be internal nodes. Figre describes the network topology pictorially and demonstrates a convention followed over the rest of this paper. A straight line between two nodes means a direct link, while a wavy line implies a mlti-hop path withot any branching in the middle. This topology simplifies the description of or algorithm and may be relaxed with little extra effort. And or theoretical research is based on a reliable network, like ATM or optical network, i.e., the per-link loss probability p is so low that we can assme p 2 0. This is a reasonable assmption in a reliable network [24] and we make this assmption becase most of or theoretical analyses are based on low loss probability, however, in section 5, or simlation reslts show that or recovery strategy conclded from the theoretical research can still have qite low recovery latency and bandwidth sage even if the per-link loss probability is p to 20% or more. Therefore, we can claim that this assmption is reqired for or theoretical work, bt not necessary for the application of or strategy. 2

3 2.2. RP (Recovery strategy with Prioritized list) We model the network sing a graph G=(V, E) where V is the set of nodes (roters/clients/sorce) and E is the set of links. The word client is sed to mean recovery servers or grop members of the mlticast grop (except the sorce). We present the work sing only point-to-point links. However, a shared link may be expressed as mltiple point-to-point link sing ghost nodes (Figre 2). If the packet is lost over the shared link, depending on the natre of loss (partial or total), we may assign the loss to appropriate link(s) in the converted topology with ghost nodes. In fact, a shared link acts as a mlticast capable roter making copies of the packet sing broadcast capacity. Hence the ghost node may be viewed as the shared link itself. Frther, we assme that the mlticast is performed over a sbtree T of G where the vertex set of T = C T RT where C T is the set of clients and sorce (the leaves and root) and R T is the internal nodes (roters). We do not make any assmption abot the properties of T. T can be the mlticast tree generated by CBT or PIM or any other mlticast roting protocol [25] and its topology is therefore known. The roters do not save any data packet after forwarding. Hence, if a packet is lost, it needs to be recovered either from sorce or from another client (peer) which has received the packet. We define or recovery strategy as follows, For every node CT {} S, we have a prioritized list of peers (other clients) L = { v } and L CT {, S}. If detects a loss, it reqests v for the packet. If v does not send the packet (detected by timeot), reqests the packet from v 2 and so on. If the packet may not be recovered from v,,v, then will k recover it from S by defalt. We recognize the possibility that in some rare cases S may receive large nmber of recovery reqests. The recovery load on S may be redced by groping clients in a net neighborhood together. Whenever S receives a recovery reqest, it will mlticast the packet to all members of the sbgrop (sing the original mlticast tree) from where the recovery reqest came. Reference [4] discsses one sch sorce-based sbgroping strategy in detail. The size of the recovery strategy, k = may be different for different clients. L Since different recovery strategies have different delays, the performance of recovery algorithm depends on the choice of the recovery strategy. For the convenience of reference, we call or low-latency recovery strategy RP, meaning Recovery strategy based on Prioritized list. The rest of this paper is dedicated to developing an exact algorithm for compting RP. 3. Algorithmic framework for peer-based recovery 3.. Expected vale of rond trip time The primary appeal of peer-based recovery strategies lies in their potential to lower the recovery delay. Hence, we want to select the recovery strategy that will reslt in low recovery delay for each client. Let a recovery strategy for client be L = { v }. As described earlier, the recovery reqest will be sent to, only if the earlier recovery reqests (sent to v, ) fail. For notational convenience, let V i be the event that the recovery reqest to is sccessfl. The complimentary event V i is the reqest fails. Similarly, let U be the event that has received the packet and U be the event that has not received the packet. Let d ( ) be the time reqired to decide whether a recovery reqest to has been sccessfl. If the recovery reqest is sccessfl, then within d ( ) time (after sending recovery reqest), receives the packet. If the packet is not received by within d ( ) time, then assmes that the recovery effort has failed and sends a new recovery reqest to + or S. d may be estimated sing many different methods. For ( ) example, d ( ) may be estimated sing timeot. However, timeot is sally a gross overestimation of d ( ). Alternately,, if the roting algorithm sed in OSPF (Open Shortest Path First) and the network ses link-delay as link cost, then the roting Table will give an estimate of oneway delay between and [8], ths ( ) d may be estimated sing rond trip time (over twice the one-way delay) between and. However, this method nderestimates d ( ). We sggest the following method for estimation of d ( ). Let the timeot be t 0. This mch delay will incr if the recovery effort fails. Let the rond trip time between and be d i. d i is estimated from roting table and incldes all the qeing delays in intermediate roters. If the packet recovery effort from is sccessfl, the approximate delay is d i. Frther we assme that the packet recovery effort fails only if has not received the original packet. The probability that the reqest or the repair is lost is ignored. This is reasonable for a reliable network. Combining these two delays, we estimate d ( ) as d( v ) d P( V U V V ) t P( V U V V ) () is the conditional probability that has received the packet given have not received the packet. ) i = i i i + 0 i i P( Vi U V V i ), v,, P( V i U V V i is the 3

4 R, R 2 Figre 3. Naming convention of the network x 0 R i- v v 2 Figre 4. A network scheme Assisting Proof conditional probability that has not received the packet given that, v have not received the packet. We did not cont the protocol stack exection cost in () explicitly. We assme that those costs are incorporated in d i and t Conditional probabilities R i In Lemma, we derive an expression for these conditional probabilities for a reliable network. And we compte the corresponding conditional probabilities assming p 2 0, which is necessary only for theoretical analyses as described and explained in sbsection 2.2. Here we introdce a naming convention for roters (refer to Figre 3). We call the first common roter of and v on the mlticast tree as R. Clearly we entertain the possibility that one roter may receive more than one name. Let DS be the length of the path (hop cont) from S to R on the mlticast tree. Withot loss of generality, let R i be nearer to S than R i-, i.e., DSi DS for all i (refer to Figre 4). i Lemma If the network is reliable, then DSi P( V i U V Vi ) =. DSi Proof Refer to proof for Lemma in [26]. - DS DS i- DS i R x v R i- R i x i- - S S x i The next lemma along with lemma allows s to compte all failre probabilities. Lemma 2 For a reliable network, P( V U V V V + Vi ) = if i. Proof Similar to the proof of lemma. Observation DSi P( Vi U V Vi ) = and DSi P( V U V V V + Vi ) = 0. Observation allows to compte expected delays in (). Lemma 3 For a reliable network, DSk P ( V V2 Vk U ) = DS Proof Similar to the proof of lemma. Observation 2 P( V V2 Vk U ) = P( Vk U ) for a reliable network. Lemma 3 and Observation 2 will be sefl to compte or obective fnction and to derive a polynomial time algorithm for optimizing the obective fnction. Example Compting conditional probability & delay () Refer to Example in [26] Obective fnction Given the lemmas and observations, we are ready to compte or obective fnction. As described earlier, or obective fnction is the expected delay for a recovery strategy. Let s assme that a recovery strategy for client is L = { v,, }. We assme earlier that a recovery reqest to may fail primarily if also has not received the packet, then the expected delay for the recovery reqest may be compted from the following formla, Delay( L ) = d( v) V U ){ d( v2) V2 U V )[ d( v3) + ] } = d( v) V U ) d( v2) V U ) P( V2 U V ) d( v3) + V U ) P( V2 U V ) P( Vk U V Vk ) d( S) This formla is obtained from the obective fnction that a recovery reqest to v will be sent only after all recovery reqests to v, v fail. Note that, from the definition of conditional probability, P( V U ) P( V U V ) P( V U V V ) 2 = P( V V U ) Therefore, the expected delay can be simplified as Delay( L ) = d( v) V U) d( v2) V2 V U ) d( v3) + (2) V Vk U) d( S) Eqation (2) gives s the expected delay for a recovery strategy. In next section, we give an algorithm that comptes the recovery strategy with low delay. Example 2 Comptation of the Obective Fnction Refer to Example 2 in [26]. 4

5 4. Compting low-latency recovery strategy We call two clients competitive clients with respect to if their nearest ancestor on the path from S to (in the mlticast tree) is the same. It is easy to see that two or more competitive clients may not belong to the lowlatency recovery strategy for. Lemma 4 Let, v be competitive clients. Let L = { v,, v } be a recovery strategy. Let L ' be another recovery strategy identical to L except that v is dropped, (i.e., L ' = { v,, v, v +, }), then L ' is at least as good as L. Proof Refer to the proof for Lemma 4 in [26]. Example 3 Competitive Clients Refer to Example 3 in [26] Clearly, the competitive relation is an eqivalence relation that partitions the clients into eqivalence classes. For each roter on the S to path in the mlticast tree, there may be one sch eqivalence class depending on whether that roter copies the packet or not. The recovery strategy with low delay may contain at most one client from each eqivalence class. In particlar, the member of an eqivalence class with shortest delay (as per ()) is the only possible entry from that class in the low-latency recovery strategy. To begin with, we identify the candidates from each class (tie broken at random) and call them candidate clients. The recovery strategy is a sbset of the set of candidate clients. Here we remember a notation introdced in sbsection 3.2. For the candidate client v, R is the first common roter of and v. The distance between S and R (in terms of hop cont) on the mlticast tree is DS. If a recovery reqest to v fails, then in all likelihood, v did not receive the packet. Both and v did not receive the packet implies (with a very high probability) that the packet was lost on the path from S to R. This in trn implies (with high probability) that the client downstream from R has not received the packet and any frther recovery reqest to them will fail almost certainly. This observation means that if, v appears in the optimal recovery strategy in the order and then v, then DS i > DS. The next lemma proves this reslt formally. Lemma 5 Let L = { v,, v } be a recovery strategy where DS i < DS. Let L ' be another recovery strategy obtained from L by dropping v, then L ' is at least as good as L. Proof Refer to the proof for Lemma 5 in [26]. At this point of time, we know that the clients in the low-latency recovery strategy are all candidate clients and sorted in descending order of DS s. Sch recovery strategies are called meaningfl strategies. Example 4 Descending-Ordered Strategy is Meaningfl Refer to Example 4 in [26] Now we rewrite or obective fnction as follows, if L = { v,, } is a meaningfl recovery strategy, then Delay( L ) d v [ DS d( v ) DSk d( vk ) DSkd( S) ] (3) = ( ) DS d(s) is the shortest delay from to S (not necessarily sing the path on the mlticast tree). DS is the hop cont from S to on the mlticast tree. Let { v,,v N } be the set of all candidate clients sorted in descending order of DS s. To choose the low-latency recovery strategy, we se a weighted directed acyclic graph called the strategy graph. Definition The strategy graph over the set of candidate nodes { v,,v N } is an edge-weighted directed acyclic graph with node set V = {, S, v,, v N }. There are directed edges from all nodes to S and from to all other nodes. In addition, there are directed edges vi v for all i<. Formally, the edge set is E = {( S )} {( vi ) i = N} {( vi S ) i = N} {( vi v ) i N} The edge weights are as follows, w ( S ) = d( S ) w( vi ) = d( vi ), i = N DSi w( vi v ) = d( v ), i N DS DSi w( vi S ) = d( S ), i = N DS Note that, any path from to S in the strategy graph is a recovery strategy for. The length of the path is the expected delay of that particlar strategy. More detail is given in the following example. Frther, the strategy graph may be modified to represent restricted strategies also. For example, if we do not want any client to go to sorce directly, we remove the ( S) edge from the strategy graph. Sch a strategy will alleviate congestion at sorce if there are many clients close to sorce. Many similar sefl restrictions of this graph are conceivable. Example 5 Strategy Graph Refer to Example 5 in [26] From the above example and discssion it is clear that the low-delay strategy is obtained by compting a shortest path from to S in the strategy graph. From definition, the strategy graph has O(N) vertices and each vertex has O(N) otgoing edges. Therefore the nmber of edges in the strategy graph is O(N 2 ). The shortest path algorithm (Dikstra s) rns in O( elog N ) time, where e is the nmber of edges in the graph. However, or strategy graph is a directed acyclic graph and hence the following algorithm will compte the shortest path in O(N 2 ) time, less than 2 O N log N. ( ) 5

6 Algorithm Searching_Minimal_Delay. For each node, have a distance field and a parent field. 2. Set the distance field of to 0 and parent field to nil. Set the distance field of other nodes to infinity and parent field to nil. 3. Process the vertices (step 4) in the following order,, v v, N S 4. If crrent vertex being processed is S, go to step 5. If the crrent vertex is x, do the following, If distan ce( x) dis tan ce( S ) then skip this node and go back to step 4 else for directed edge x y if dis tan ce( x) + w( x y) < dis tan ce( y) then dis tan ce( y) w( x y) + dis tan ce( x) ; parent( y) x 5. distance(s) is the shortest delay and the path Sparent(S)parent(parent(S)) gives the recovery strategy with the shortest delay in the digraph. Example 6 Searching the Exact Peer-based Recovery Strategy Refer to Example 6 in [26] Algorithm processes each edge exactly once, Hence the complexity of algorithm is O(N 2 ). Correctness of algorithm is trivial when compared with Dikstra s shortest path algorithm. N is the nmber of eqivalence classes obtained from the competitive node relation. 5. Simlation reslts and analysis The primary obectives of or simlation are to explore how short the recovery latency can be achieved from or recovery strategy RP and to verify that even if RP can make as low recovery latency as possible, no extra bandwidth needs to be sacrificed. Besides efficiency, or simlation also tests the scalability of or algorithm. And as mentioned before, althogh the whole theoretical research in this paper is based on a reliable networking environment, or simlation also examines the performance of or recovery strategy, conclded from or theoretical analyses, in an nreliable network environment with the per link loss probability p to 20% or more. We compared the performance of RP with that of SRM and RMA, as described in section. 5.. Simlation parameters and settings We se a discrete event packet level simlator. Network topology for se in the simlator is randomly generated and as described in section 2. The sorce or Average delay per packet recovered (milliseconds) SRM 450 RMA 400 RP Nmber of clients Figre 5. Average recovery latency per packet recovered (p=5%) Average bandwidth sage per packet recovered (hops) SRM RMA RP Nmber of clients Figre 6. Average bandwidth sage per packet recovered (p=5%) links are randomly generated to connect m backbone roters. The mlticast tree is st a spanning sbtree generated in the network topology. Mlticast packets are roted along the paths in mlticast tree while nicast packets are roted along paths that minimize expected vale of rond trip time in the network model, which match the descriptions of all the three strategies being compared in or simlation. Frther, the typical delay for each link i is d(i) and a niformly distribted nmber between d(i) and 2d(i) is generated as the expected delay being sed in or simlation. Let n be the total nmber of nodes in or network model and k be the total nmber of clients where n is an inpt to the program and k is decided by the randomly generated spanning sbtree. Frthermore, nlike a real network, the link delay and loss properties are independent of the nmber of packets traversing the link. The reslt is that simlations will favor protocols that generate more data. Since SRM that ses global mlticast and RMA that employs partial mlticast generate more data than RP, the simlator is likely to be optimistic abot 6

7 RMA s performance and more optimistic abot SRM s performance Simlation reslts and analyses In order to evalate the efficiency and scalability of RP, we ran simlations on topologies with 50, 00, 200, 300, 400, 500, 600 nodes in the network model which generates 4, 35, 77,, 57, 208, 246 clients respectively, as shown in Figre 5 and Figre 6. The per link loss probability in these simlations is 5%. According to Figre 5, average recovery latency of RP is 77.78% shorter than that of SRM and 7.3% shorter than that of RMA. From Figre 5, we can also see that the vales of recovery latency for RP and SRM are within a small range and not increased sharply, while the vales of recovery latency for RMA are not as steady as those of RP and SRM, which indicates RP and SRM are more scalable than RMA. According to Figre 6, RP does not sacrifice bandwidth compared to SRM and RMA. Actally, average bandwidth sage for RP is 38.53% smaller than that of SRM and 23.2% smaller than that of RMA. Figre 7 and Figre 8 show that when the nmber of nodes in the network model is 500, generating 208 clients, for per link loss probability is 2%, 4%, 6%, 8%, 0%, 2%, 4%, 6%, 8% and 20%, what the vales of average delay and bandwidth sage are. The prpose of these simlations is to examine the three schemes performance in the networks with varios reliabilities. The reslts show that the average vales of recovery latency for the three recovery schemes are almost constant when the per link loss probability changes from 2% to 20%, which means the three schemes can perform as well in nreliable network as in reliable network. Average bandwidth sage of SRM is decreased while that of RMA and RP is increased. This is becase with the per link loss probability increased, more clients lose the same packet, while SRM employs mlticast to the whole tree as retransmission method, i.e., the total bandwidth sage for SRM for recovering each packet is fixed, ths the average bandwidth sage drops with nmber of clients being recovered increased. While for RMA and RP, the cost of retransmission for a lost packet is not a fixed vale, it increases with the nmber of reqesters added. An anomaly happens when p is changed from 8% to 20%. This is becase the randomly generated mlticast tree strctre is more appropriate to RMA and RP than to SRM compared to mlticast trees previosly generated. And from Figre 7, average recovery latency of RP is 78.53% shorter than that of SRM and 56% shorter than that of RMA. From Figre 8, average bandwidth sage for RP is 5.83% smaller than that of SRM and 9.52% smaller than that of RMA. Average delay per packet recovered (milliseconds) SRM 450 RMA 400 RP Per link loss probability (%) Figre 7. Average delay per packet recovered (n=500 and k=208) Average bandwidth sage per packet recovered (hops) SRM RMA Per link loss probability (%) Figre 8. Average bandwidth sage per packet recovered (n=500 and k=208) 6. Conclsion In this paper we present a polynomial time algorithm for compting low-latency recovery strategy for reliable mlticast in a reliable network. The recovery strategies proposed in literatre either choose a locally random recovery strategy or prefers clients in the net neighborhood for recovery prpose. Random recovery strategies may increase the cost of recovery by choosing far-away clients or highly correlated clients. As the loss in a mlticast tree is correlated (if a link fails, all down stream clients lose the packet), choosing a nearby client for recovery prpose will increase the probability of failed recovery attempts. Or algorithm helps to choose the best recovery strategy, which may not be random or geography based. Or simlation shows that or RP scheme can achieve mch shorter recovery latency and cost low bandwidth, and it also performs well in nreliable network. RP 7

8 References [] Marin S. Lacher, Jörg Nonnenmacher, and Ernst W. Biersack, Performance comparison of centralized verss distribted error recovery for reliable mlticast, IEEE/ACM Transactions on Networking, vol. 8, no. 2, pp , April [2] Sneha K. Kasera, Jim Krose, and Don Towsley, A comparison of server-based and receiver-based local recovery approaches for scalable reliable mlticast, in Proceedings of IEEE INFOCOM 98, San Francisco, CA, USA, March 998. [3] Christos Papadopolos, Gr Parlkar, and George Varghese, An error control scheme for large-scale mlticast applications, in Proceedings of IEEE INFOCOM 98, pp [4] Danyang Zhang, Sibabrata Ray and Ragopal Kannan, Static Sbgrop-based Sorce Recovery for Reliable Mlticast in Reliable Networks, in Proceedings of IEEE Globecom 2002, Nov. 2002, Taiwan. [5] J. Nonnenmacher, E. W. Biersack, and Don Towsley, Parity-Based Loss Recovery for Reliable Mlticast Transmission, IEEE/ACM Transactions on Networking, vol. 6, no. 4, pp , Ag [6] Sneha K. Kasera, Gisli Halmtysson, Don Towsley and Jim Krose, Scalable reliable mlticast sing mltiple mlticast channels, IEEE/ACM Transactions on Networking, vol. 8, no. 3, Jne [7] Sneha K. Kasera, J. Krose, and D. Towsley, Scalable reliable mlticast sing mltiple mlticast grops, Proceedings of ACM Sigmetrics Conference, Jne 997. [8] James F. Krose and Keith W. Ross, Compter Network: A Top-Down Approach Featring the Internet, 2 nd ed., Addison Wesley, 2002, pp. 350 [9] John C. Lin and Sanoy Pal, RMTP: A reliable mlticast transport protocol, IEEE INFOCOM '96, March 996, pp [0] Roger Kermode, Scoped Hybrid Atomatic Repeat reqest with Forward Error Correction (SHARQFEC), in Proceedings of ACM SIGCOMM 98, Vancover, BC, Canada, October 998. [] Kang-Won Lee, Sngwon Ha, and Vadvr Bharghavan, IRMA: A reliable mlticast architectre for the Internet, IEEE INFOCOM, 999, pp [2] Matthew T. Lcas, Bert J. Dempsey, and Alfred C. Weaver, MESH: Distribted error recovery for mltimedia streams in wide-area mlticast networks, in International Conference on Commnication, ICC 97, Montreal, Canada, Jne 997, pp [3] M. Lcas, B. Dempsey, and A. Weaver, MESH-R: Large-scale, reliable mlticast transport, IEEE International Conference on Commnication (ICC '99), Vancover, BC, Jne 999, pp [4] M. Hofmann, Enabling grop commnication in global networks, Proceedings of Global Networking 97, Calgary, Alberta, Canada, November 996. [5] Inong Rhee, Nallathambi Balagr, and George N. Roskas, MTCP: Scalable TCP-like congestion control for reliable mlticast, IEEE INFOCOM, 999, pp [6] R. Yavatkar, J. Griffioen and M. Sdan, A reliable dissemination protocol for interactive collaborative applications, Proceeding of ACM Mltimedia, November 995. [7] S. Floyd, V. Jacobson, C. Li, S. McCanne, and L. Zhang, A reliable mlticast framework for light-weight sessions and application level framing, IEEE/ACM Transactions on Networking, vol. 5, no. 6, pp , Dec [8] Speakerman, Tony, Farinacci, Dino, Lin, Steven, Tweedly and Alex, PGM Reliable Transport Protocol Specification, Internet Draft, [9] B.N. Levine and J.J. Garcia-Lna-Aceves, Improving internet mlticast with roting labels, IEEE International Conference on Network Protocols (ICNP- 97), October 28-3, 997. p [20] Knwadee Sripanidklchai, Andy Myers, and Hi Zhang, A third-party vale-added network service approach to reliable mlticast, SIGMETRICS '99. [2] D. Towsley, J. Krose, and S. Pingali, A comparison of sender-initiated and receiver-initiated reliable mlticast protocols, IEEE Jornal on Selected Areas in Commnications, vol. 5, no. 3, pp , 997. [22] Lin Y, Ma W, Long Keping, and Cheng Shidan, Analyzing the delay performance of server-based and receiver-based local recovery approaches for reliable mlticast, Info-tech and Info-net, 200. Proceedings. ICII Beiing. 200 International Conferences on, vol. 2, 200, pp [23] Athina P. Markopolo and Foad A. Tobagi, Hierarchical reliable mlticast: performance analysis and placement of proxies, Proceedings of NGC 2000 on Networked grop commnication, November [24] T. Chanoy, J. Fingerbt, M. Flcke, and J. S. Trner, Design of a gigabit ATM switch, Proc. Infocom 997, Kobe, Japan, pp.2-. [25] Sanoy Pal, Mlticasting on the Internet and Its Applications, Klwer Academic Pblishers: Massachsetts, 998. [26] Danyang Zhang, Sibabrata Ray, Ragopal Kannan and S. Sitharama Iyengar, An Optimal Recovery for Reliable Mlticasting with Sparse Clients, Technical Report, Department of Compter Science, University of Alabama, TR