Path Diversity for Overlay Multicast Streaming

Transcription

1 Path Diversity for Overlay Multiast Streaming Matulya Bansal and Avideh Zakhor Department of Eletrial Engineering and Computer Siene University of California, Berkeley Berkeley, CA 9472 {matulya, Abstrat In this paper, we propose a new path-diversity based sheme for appliation layer multiast streaming over the Internet. Rather than building simple trees as in traditional multiast, we onstrut multiast k-dags, haraterized by the property that eah reeiver has k parents. This multipliity of parents, not only allows for streaming from multiple soures at the same time, thereby deorrelating losses, but also reates an opportunity to dynamially adapt streaming rates from these senders depending on the existing error onditions in the network. To exploit these possibilities, we use a simple ratealloation algorithm and a paket-partitioning algorithm that allows a reeiver to o-ordinate the sending of data from amongst its parents. Our results show that our sheme is effetive in dealing with paket losses in the network, and inreases the goodput of FEC-oded video data by 5-3%. I. INTRODUCTION With the inreasing user demand for multimedia ontent, video multiast is beoming more important for both network servie providers and ontent distributors. The inability of IP multiast to provide the desired support for various multiast appliations inluding video multiast appliations has led to the evolution of several overlay based multiast solutions. These overlay or appliation-layer multiast solutions support the appliation requirements in several ways inluding network-adaptive routing, multipath routing, redundant routing et. In this paper, we propose an overlay multiast sheme for streaming multimedia based on a new ontent distribution mehanism, alled a k-dag. A k-dag is a Direted Ayli Graph in whih eah reeiver has k parents. This differs from the traditional multiast tree, where eah reeiver has a single parent. As observed in [4], [6], [7], this multipliity of parents improves multiast streaming performane in two ways. First, by streaming multimedia from multiple parents, it is possible to de-orrelate loss among various paths to the reeiver, redue loss-burstiness at the reeiver, and therefore improve the effetiveness of shemes suh as Forward Error Corretion (FEC) [7]. Seond, by adapting sending rates from eah parent based on loss harateristis of eah path, it is possible to minimize overall loss at the reeivers. This paper is organized in the following manner. In Setion II, we desribe the idea behind a k-dag and the various trade-offs involved in onstruting one. We then present a k- DAG onstrution mehanism in Setion III, and a k-dag maintenane algorithm in Setion IV. In Setion V, we present a simple rate-alloation algorithm that allows a reeiver to determine streaming rates from eah of its parents. This is Fig.. A simple k-dag with k = 2. Unlike a traditional multiast tree, every reeiver here is onneted to 2 parents. The dotted line shows how to handle a single soure situation. In this ase, the first k nodes that join this soure serve as the soure nodes for building the k-dag downstream from then on. followed by a reeiver-based paket-partitioning algorithm that ensures that all the required data is reeived while avoiding dupliation. Finally, we present simulations omparing our sheme with simple overlay multiast and a non-adaptive variant of our sheme in Setion VI. II. K-DAGS In this setion, we present the data-struture for onstruting multiast distribution networks suh that every reeiver has k senders. Sine there are multiple parents per node, our proposed distribution network is no longer a tree, but a Direted Ayli Graph (DAG). Figure shows an example of a simple 2-DAG. We now begin with some definitions and assumptions. Level of a node: We define the level of a node as the length in hops of the longest path from the soure to this node. The level of the soure nodes is assumed to be. Degree of a DAG (dag degree): We define a DAG to have a degree k if all its nodes have k parents. We denote dag degree by k. Clearly k = results in traditional multiast trees with one parent per reeiver. Fration of bitstream bandwidth reserved by a reeiver at eah parent (f ra bw per parent): For a given multimedia session, we define fra bw per parent as the ratio 8

2 between the maximum bandwidth alloated by a parent to stream to a reeiver, and the total bit rate of the multimedia ontent being streamed by the soure. By definition, this quantity whih we denote by b, is always smaller than. For the reeiver to reeive the entire video-stream, we require that k b. Sine end-nodes are likely to be limited in outgoing apaity, we assume that reeivers proatively reserve the maximum bandwidth they might need, i.e. b * bitstream rate, from any parent for the entire duration of a session. When a reeiver reserves bandwidth at a parent, the upstream apaity of that parent dereases by that amount as the parent dediates that portion of its outgoing bandwidth for serviing a request from this reeiver, should the need arise in the future. Though onservative, this assumption ensures fairness to the ompeting simple overlay multiast sheme. Despite reserving more than the bitstream rate aross all parents, at any given point in time, data is streamed at preisely the bitstream rate. A. DAG-degree, Bandwidth reserved and Depth of the DAG The degree of the DAG is an important parameter of our proposed sheme. Intuitively, larger DAG-degrees will result in greater flexibility in adapting to losses. However, assuming that the upstream apaity for all nodes stays the same, distribution networks that use k-dags are likely to beome deeper as k b beomes large. This is beause the total bandwidth reserved aross all parents for a given piee of ontent exeeds its bitrate in order to allow for rate-adaptation. Sine the outgoing apaities of nodes are limited, more reserved bandwidth per reeiver results in deeper DAGs as nodes at any given level an support fewer reeivers. We now derive the relationship between dag degree k, fra bw per parent b, and the minimum depth of the DAG d for a given number of nodes N. We assume the outgoing apaity to be the same for all nodes and denote it by. Also, for simpliity, we assume that eah node has all its parents at the same level. Assume we have p nodes at the first level with the total outgoing apaity being p. Eah new node requires a apaity of b k. Therefore number of nodes that an be supported at the next level is (p )/(b k). Similarly, the number of nodes that an be supported at the next level is ((p )/(b k)) (/(b k)). This is a geometri progression. Therefore, the maximum number of nodes that an be supported for a k-dag of depth d, inluding the p nodes at the topmost level, is given by: p ( b k )d+ b k. () Alternately, to support N nodes, the minimum depth of the DAG would be log( N p ( b k ) + ) log( b k ). (2) The above relations show that for a given number of nodes and a fixed outgoing apaity, the depth of a k-dag Average Goodput for all nodes.8.6 Average Goodput versus Number of Nodes.4 *. 2*.5.2 3*.4 3*.5 4* Number of Nodes Fig. 2. This figure aptures the relationship between the overall expeted goodput or paket delivery ratio and b k. required to support these inreases with dag degree, k and fra bw per parent, b. B. DAG-degree, Bandwidth reserved and expeted loss For the same average loss rate per link in the network, deeper trees suffer from inreased average loss rates amortized over all the nodes. This is beause the longer the path the data is streamed along, the more the number of lossy links it has to enounter enroute to the reeivers, and hene greater the loss. We now derive the trade-off between the reserved bandwidth at the upstream nodes and the inreased loss rates due to inrease in depth of the tree. Assume that at eah level in the DAG, x perent of the pakets get lost. Then total loss for a stream of bandwidth say B, as it traverses l levels or hops beomes B(x + x( x) + x( x) x( x) l ) = B ( ( x) l ). Similarly, the amortized loss rate aross all nodes for a k- DAG of depth l, ontaining the maximum number of nodes that it an support, an be shown to be ) l ) b k ( ( b k )l ( x) ( ( ( x) b k ( x) b k ) (3) From Equation (3), we see that the total loss suffered inreases as the depth of the DAG inreases. Substituting the depth of the DAG onstruted for a given number of nodes from Equation (2), we an determine the relationship between loss, the dag degree k and the bandwidth reserved per parent b. Figure 2 shows average goodput as a funtion of the number of nodes for different k b values. As expeted, the amortized loss rate inreases with an inrease in k b. The urves for ases k =, b = and k = 2, b =.5 o-inide beause k b = in both the ases and the depth and the amortized loss rates are the same. III. K-DAG CONSTRUCTION In this setion, we present our k-dag onstrution algorithm. The DAG onstrution algorithm shown as Algorithm

3 below, onsists of three steps: Finding potential parents, probing these nodes for available network bandwidth and delay, and hoosing k nodes from these as parents. Before proeeding onto the details, we first present the idea of using speial overlay nodes, whih we simply refer to as Distributed Hash Table (DHT) nodes, for separating the data plane operations suh as data forwarding, from ontrol plane operations suh as hoosing new parents for a inoming node DHT Nodes Algorithm Steps in Node Join Algorithm request potential parents() probe potential parents() hoose k parents() 6 d 7 d 8 b a 9 A. Role of the DHT We use DHTs primarily to failitate node-joins and nodefailure reovery. This is useful from an administrative standpoint as well, sine it allows the sender or the owner of the ontent distribution network to selet the join loation of a new node in the tree, depending on the prie this new node is willing to way, its outgoing apaity, stability or a ombination of these. Another advantage of indiretion in the form of DHT nodes is that depending on the size of the multiast session, by hoosing a suitable hash funtion, the ontrol load an be distributed in a entralized or distributed manner. That is, for a small group, all key values may hash to a single node thus making the sheme effetively entralized, while for a large group, the workload might be distributed over a set of nodes, thereby ahieving salability. ) DHT Mapping: We manipulate information in the DHT by mapping level number of the nodes to DHT nodes. Thus, a given DHT node(s) will maintain information about all the nodes in the DAG at a partiular level. Even though this set grows exponentially with level number, it is possible to alleviate this problem by partitioning, either at the DHT or while assigning levels. 2) State maintained at the DHT: The DHT nodes merely maintain information about the level of eah node that is a member of the multiast session, and its available apaity. This information is made use of during Node Join and DAG Maintenane phases, as desribed in Setions III-B and IV respetively. 3) Inter DHT Nodes Communiation: We assume DHT nodes to ommuniate with eah other to find nodes at a given level with available apaity. This ommuniation an take plae either in the form of periodi proative or demand-driven reative message exhange. We do not assume the information reeived from the DHT nodes, suh as the available apaity at nodes, to be always onsistent with the atual values at the multiast nodes themselves, even though we expet it to be orret in most ases. Fig. 3. The proess by whih a node joins a k-dag. a) The node finds the address of the DHT nodes by a naming mehanism and requests a list of potential parents; b) The DHT responds by sending a list of nodes with available apaity; ) The node wishing to join the network then probes these parents for available bandwidth; d) The node hooses k of these to be its parents in the k-dag; B. Node Joins Sine our sheme is motivated by multimedia multiast and similar ontent distribution appliations, we hoose a DAG onstrution algorithm that allows nodes to join at any time during the lifetime of the multiast session. In the remainder of this setion, we desribe how a new node an join the multiast session. This is shown in Figure 3. Sine we onstrut a k-dag rather than a simple multiast tree, we assume that there exist at least h k soure nodes to begin with where h is the hoie fator signifying the flexibility a new node has in hoosing its k parents from the initial set of h k offered by the DHT. In ase there is only a single sender, the first h k nodes to join the session an serve as these h k nodes. Figure shows suh a senario where h =. ) Finding a list of Potential Parents: The first step for a new node to join the multiast session is to find a set of potential parents. In order to do this, the node first needs to know the address of a node maintaining the DHT or alternately that of a member node. This an be obtained via any of the ommonly used naming mehanisms suh as a publiized URL, DNS et. This node then requests the DHT for a list of prospetive parents. The DHT returns to it a set of nodes that have outgoing apaity available, based on some riterion suh as prie-willingness of this node, its stability, or outgoing apaity. 2) Probing Potential Parents: In order to ensure that our overlay links are IP-Network effiient, nodes evaluate the quality of their paths to prospetive parents before seleting them. We use a slightly modified paket-pair probing tehnique [] to estimate the available bandwidth and delay whereby a set of spaed paket-pairs is sent to potential parents to evaluate

4 path quality. 3) Parent Seletion: One a node has evaluated the quality of available paths, it hooses the parents it wants to stream from. Several riterion might be employed for this purpose inluding paths with maximum available bandwidth, or minimum delay, or paths that redue jitter or minimize buffer requirements, or a ombination of these. In our urrent implementation, nodes hoose the k widest paths. 4) Updating state: One a node has hosen its list of parents, it requests them to join in as a hild. Depending upon the available apaity, this node may or may not hoose to aept this hild. This is beause the advertised apaity by the DHT may not neessarily be onsistent with the atual apaity at a given parent at all times. If aepted, the new node has ompleted finding one of its k parents. If rejeted, it may deide to hoose the next parent on its list of perspetive parents, or else it may hoose to request the DHT again. One a node is aepted by k parents, it has suessfully joined the k-dag multiast session. IV. DAG MAINTENANCE ALGORITHM Problems might arise when nodes fail in the network or abruptly terminate their multiast session. To mitigate the effet of suh ourrenes, we now present our DAG maintenane algorithm. While a parent node rash in a k-dag results in a large number of orphan nodes as ompared to a simple multiast tree, the effet of a parent loss on an individual hild is less pronouned sine eah hild has multiple parents. With an outgoing apaity of and fration of bitstream bandwidth requested from eah parent b, the rash of a fully-loaded node results in nodes being affeted in a simple multiast tree and /b nodes being affeted in a k-dag where b.. However, in the traditional multiast ase, any orphaned node suffers from a omplete blakout while in ase of a k-dag, orphaned nodes only lose a fration b of the total bitstream data. Moreover, orphaned reeiving nodes an potentially mitigate the effets of a parent loss by reserving spare upstream bandwidth ahead of time and adjusting the rate from surviving parents, until a new parent is found. Algorithm 2 Steps in Node Failure Reovery Algorithm rate adaptation() request potential parents() probe potential parents() hoose parent() inf orm vitim if required() rate realloation We now briefly disuss our node failure reovery algorithm as shown in Algorithm 2 above. When a node detets a parent loss, it immediately invokes a rate-realloation algorithm, disussed in Setion V, to minimize the impat of this loss. In ase of a k-dag where the upstream bandwidth reserved per sender is b, up to s node failures an be suessfully tolerated, where s = max(k r) b >.. (4) r In order to find a new parent, a node simply sends a request for a list of new potential parents to the DHT nodes. The DHT nodes need to ensure there are no loops formed as a result of new parent-hild relationships. This is where the notion of level omes in. By enforing that a DHT node only hoose a node whose level is less than or equal to the level of the requesting node as a potential parent, we guarantee no loops provided that the level values at all the atual nodes and that stored at the DHT are onsistent. To ensure the onsisteny of level values, we enfore that no node whose level has hanged within a ertain time-interval respond positively to a parent request or request a new parent. This time interval is hosen to be the time it takes for a level update to propagate through the network. If the DHT nodes, however, annot find apaity at any of the nodes with a level lower than that of the requestor beause they are already loaded to apaity, the DHT returns to the requestor a list of its siblings. The requestor then probes and hooses one or more of these nodes as its potential parents. If a node higher up the DAG is hosen and onsents, the requesting node has found a parent. If a sibling is hosen and has apaity, again the requesting node has found a new parent. However, sine a sibling is hosen, the requesting node needs to update its level and potentially of its desendents. If a sibling does not have the neessary apaity beause it is already fully loaded, it hooses one of its hildren as a vitim, aborts it by telling it to find a new parent, and after allowing it suffiient time to adjust its upstream rates, aepts the requestor as its hild. Intuitively, a hild of a sibling might need to be aborted in favour of the requesting node beause in order to avoid loops, an orphan node needs to be assigned a new parent whih is not its desendent. By definition of level, this hild has a greater level than the orphaned node and therefore the algorithm is guaranteed to terminate. Under extreme irumstanes, there might be asaded node failures with the number of orphaned nodes in the worst ase being max(outdegree) height of the failed node, where height of a node is defined as the maximum differene between the level of any node in the DAG and the level of this node; nonetheless, node failures and aborts ause the orphaned nodes to only lose a fration b of the bitstream. In addition, if the produt of degree of the DAG, k, and the fration of bitstream bandwidth requested from eah parent, b, is suffiiently high, as seen in Equation (4), a limited number of node failures may not result in any degradation of the FEC oded multimedia ontent at all. The above node-failure reovery algorithm ensures reovery from multiple node failures in a distributed fashion without the possibility of ourrene of loops. One a node has hosen and reeived aeptane from a new parent, it performs raterealloation and paket-partitioning, as desribed in the next setion, and updates the DHT with the new information.

5 V. RATE ALLOCATION AND PACKET PARTITIONING ALGORITHM This setion desribes the rate adaptation algorithm used by the reeiver to optimally alloate the sending rates among its parents. Our rate-alloation algorithm is similar in spirit to that in [7] with some minor differenes. Synhronization issues are handled within the paket partitioning algorithm in a manner similar to the tehniques desribed in [7]. A. Initial Rate Assignment When a node initially joins the multiast session, it is unaware of the expeted loss rates from its parents. However, during the probing proess to hoose its parents, it has an estimate of the available bandwidth and delay. So, to begin with, a reeiver divides the stream bandwidth equally amongst its parents. That is, for a dag degree k, it streams /k of the bitstream from eah of its parent. B. Loss Estimator We use an exponential moving average loss estimator for estimating losses. We sample loss rates every five seonds by ounting the number of pakets lost in this period. However, sine we stream from senders at different rates, to make onsistent omparisons aross senders, we need to weigh the sample by the proportional rates at whih data is being reeived from the senders. Hene we alulate loss rates by loss rate[i+] = ( α) loss rate[i]+α β ur loss rate where α is the averaging parameter and β is the fration of the bitstream urrently being streamed from this parent. ur loss rate is the instantaneous loss rate and is obtained by dividing the differene between the number of expeted and reeived pakets by the number of expeted pakets over this five seond interval. C. Rate Realloation During the ourse of the multiast session, network onditions might hange resulting in bandwidth flutuations aross nodes. In our sheme, a reeiver performs rate-realloation whenever the loss-rate from a parent exeeds an experimentally determined threshold, or the quality of path between any two parents differs signifiantly. D. Rate Alloation Algorithm We use a rate alloation algorithm similar to the one used in [7]. As in [7], through the rate alloation algorithm, we minimize the overall paket loss experiened by a reeiver by sending as many pakets as possible along the path that experienes the lowest loss subjet to maximum bandwidth that the reeiver had reserved from this parent. This approah is appliable whenever b k > wherein it is possible to redue the overall loss rate experiened by a reeiver by requesting more of the video stream from the parent upstream the less error-prone path. This essentially orresponds to a water-filling algorithm. Slot # Fig. 4. Proposed Paket Partitioning Algorithm. To quantify this further, assume that we have a k-dag, and that there exists a node with k parents. Further assume that this node has measured the loss rates from eah of its parents, 2,..k to be l, l 2,..., l k, and that they are in an inreasing order. With the given rate realloation mehanism, the overall i loss rate experiened by this reeiver is bounded by l p b where i = min r r b p. p= E. Paket Partitioning p= One a node has deided the streaming rates for eah of its parents, a paket-partitioning algorithm is needed to determine whih paket is sent by whih parent. Unlike the proposed partitioning algorithm in [7] whih is sender-based and would have maintained a O(n 2 ) state in the number of reeivers in a multiast senario, the algorithm we use requires O(n) state in the number of reeivers at the expense of not minimizing paket delay. We believe that this trade-off is speially suitable for a multiast senario where exess load on the end-systems needs to be at a minimum. Figure 4 shows an example of our paket-partitioning algorithm. The slotsize in this example is. The reeiver node 4, has 3 parents, i.e. nodes, 2, and 3. After loss measurements, it has hosen to stream.4 of the bitstream from node,.3 from node 2 and.3 from node 3. The reeiver first disretizes the request rates and assigns a proportional number of slots from a slotsize to eah parent. With a slotsize of, 4 slots are assigned to node, and 3 eah to nodes 2 and 3. Requested slots are interleaved to minimize bursty losses. This information, along with the requested rate, is then sent in a rate request paket to the parents. As an example, node sends pakets, 4, 7,,, 4, 7..., node 2 sends 2, 5, 8, 2, 5... and node 3 sends pakets 3, 6, 9, 3, 6... to reeiver 4. F. Informing Parent Nodes When a reeiver node hooses to hange rates, it sends out a new rate request paket to its parents. The information in this rate request paket is similar to the information sent after

6 paket-partitioning, and onsists of the new rate requested by the reeiver from this sender, and the sequene numbers this sender is responsible for sending to this reeiver. The parents swith to this new request pattern after reeiving the request but ontinue to send aording to the old pattern for a short period of time in order to avoid losses during the transition. VI. PERFORMANCE EVALUATION We evaluate the performane of our sheme using NS-2 []. We ompare our proposed sheme with onventional overlay multiast, and a non-adaptive variant of our sheme. A. Simulation Parameters We generate the topologies for our simulations using the BRITE[8] topology generator. We use two different types of topologies for our simulations, based on Albert-Barabasi model and Two-Tier Hierarhial model. For ompatness though, we present results only for Albert-Barabasi model. We have found the results for the Hierarhial model to follow similar trends. We use 5 network nodes and 25 overlay nodes. All the overlay nodes are multiast reeivers. Only one DHT node is used. The overlay nodes and their order of joining are both randomly hosen for eah simulation. We use 7 soure nodes for all the simulations. The bitstream rate is 28Kbps and the paket size is 52 bytes. A (2,7) FEC ode is used for proteting the data. The outgoing apaity of all the nodes is fixed to be twie as large as the video bitstream rate and the slotsize is 2. Loss rates are updated, and the deision to realloate rates is evaluated every 5 seonds. All simulations are run for a duration of 3 minutes. Every point in a plot orresponds to an average of repetitions. The soure is started at the beginning of the simulation and all the overlay nodes join the multiast session within the first 4-5 minutes. Losses are introdued one all the nodes have joined the session. B. Metris We use the following metris for measuring the effetiveness of our sheme. Goodput or Paket Delivery Ratio This is the ratio of number of pakets reeived to the number of pakets expeted. FEC goodput We define FEC goodput as the ratio between the number of non-redundant FEC bloks suessfully reeived to the number of non-redundant FEC bloks expeted by the multiast reeivers. This metri evaluates and ompares the performane of different shemes from an appliation standpoint. Average delay experiened by the end-nodes Average delay is the average time it takes for a data paket sent by the soure to reah a reeiver. As seen later, there is a tradeoff between loss rate and average delay experiened by nodes. Average jitter experiened by the end-nodes We define jitter as the standard deviation in the delay experiened by a reeiver. Average jitter, alulated aross all the reeivers, indiates the buffer requirements at the reeivers. Having multiple senders is likely to result in inreased jitter. Even p g p q Fig. 5. This figure shows the two state Markov model we use for modelling losses in the network. State g represents the good state, while state b represents the bad state. No pakets are lost in the good state, while error rate perent of the pakets are lost in the bad state. error rate is a parameter of the simulation. We set p =.85 and q =.75 for our simulations. though with inreasing end-node apaities, buffer size is no longer an issue, we haraterize the tradeoff between required buffer size and path diversity. Average Control Overhead We define ontrol overhead as the ratio between the number of ontrol pakets sent and the data pakets reeived. C. Loss Model We use a two state Markov loss model shown in Figure 5 for generating losses. We vary the probability of losing pakets in the bad state as a parameter, while keeping the probability of losing pakets in the good state at. So an error rate of 3 perent orresponds to the probability of a loss in the bad state being.3. In all our error experiments, we randomly hoose and injet 2 perent of all the links with a speified error rate for a duration of 5 minutes after whih the error rate on these links is set to and a new set of links is hosen. We fix the probability of moving from good state to good state to be.85, while the probability of moving from bad state to bad state is fixed at.75. D. Legend We refer to all the shemes by a dag degree * fra bw per parent notation. So, a. sheme is simple overlay multiast, a 2.5 sheme uses a 2-DAG and splits the bitstream evenly between the two senders, and a 3.4 sheme builds a 3-DAG and in whih eah reeiver an stream upto 4% of the bitstream from eah parent. E. Link Losses and Path Diversity We examine the effet of using multiple upstream senders per multiast reeiver on burst lengths when losses prevail in the network. To evaluate this effet, we onstrut a simple multiast tree, a 2-DAG with b =.5, a 4-DAG with b =.25, and a 5-DAG with b =.2 and stream FEC oded data at 28kbps from the soures. The total bandwidth reserved at all the parents per reeiver in eah ase is also 28kbps, hene no rate-adaptation is possible. Figure 6 shows the perentage of lost pakets that our in a burst of size greater than s, as a funtion of s, when 2% of the links in the network suffer from a loss rate of 3%. While a simple multiast tree experienes more that 5% of its losses q b

7 Fration of pakets *..2 2*.5. 4*.25 5* Loss burst Distribution Node 5: *. Node 5: 2*.5 8 Node 5: 3*.4 Node 5: 3*.5 Node 5: 4* Sequene number of lost pakets Fig. 6. Loss burst distribution for a overlay node network when 2% of the links were injeted with an error rate of 3%. For eah lost burst size s, this plot shows the fration of pakets that were lost in a burst of size s or more Fig. 8. Sequene numbers of pakets lost between time=95 to 2 seonds for different shemes *. 2 5 (a) (b) () Rate Time (d) Fig. 7. Setup for observing mirosopi behaviour. Node 5 is hosen for observation in all the ases. Its upstream onnetivity in a -DAG is shown by (a), in a 2-DAG by (b), in a 3-DAG by () and in a 3-DAG by (d). Errors are introdued on the link between nodes and 5. The remaining part of the DAGs is not shown for simpliity. Fig Reeived rate at node 5 for. sheme 2*.5: Sender 2*.5: Sender 2 2*.5: Total in bursts of length 2 or more, the orresponding perentages for a 2-DAG is less 25%, and for 4-DAGs and 5-DAGs, it further redues to around 2%. Similar results were obtained for other values of loss rates. Thus path-diversity is suessful in reduing bursty losses in the network. Intuitively, this an be explained by onsidering that in a k-dag with k >, the senders split the bitstream and interleave the pakets. As suh, unless all the links to the parents are experiening loss at the same time, loss burst-lengths at the reeiver are redued. F. Mirosopi Behaviour To understand the mirosopi behaviour of the shemes, we perform a simple experiment in whih errors are introdued on a single link between a node and one of its parents in k- DAGs of different degrees. Figure 7 shows the hosen node 5 and its upstream onnetivity for different ases. The rest of the DAG is not shown for simpliity. None of the parents of node 5 share a link in the underlying network. An error rate of 4% is introdued on the link between node and node 5 for a period between to 5 seonds. Figure 8 shows the sequene number of pakets lost at node 5 for different shemes over a window of 25 seonds. We Rate Rate Time Fig.. Reeived rate at node 5 for 2.5 sheme 3*.4: Sender 2 3*.4: Sender 2 3*.4: Sender 3 3*.4: Total Time Fig.. Reeived rate at node 5 for 3.4 sheme

8 Rate Time 3*.5: Sender 3*.5: Sender 2 3*.5: Sender 3 3*.5: Total FEC Goodput FEC Goodput versus Error-Rate *..7 2*.5 3* *.5.6 4* Error-rate Fig. 2. Reeived rate at node 5 for 3.5 sheme Fig. 4. FEC Goodput with rate-adaptation. Rate *.4: Sender 4*.4: Sender 2 4*.4: Sender 3 4*.4: Sender 4 4*.4: Total Fration of Nodes *. 2*.5 3*.4 3*.5 4*.4 Fration of Nodes versus FEC Goodput Time FEC Goodput Fig. 3. Reeived rate at node 5 for 4.4 sheme Fig. 5. The umulative fration of nodes that reeive a FEC Goodput less than f, as a funtion of f. observe that an inrease in dag degree results in fewer and less bursty losses. We also observe that unlike shemes. and 2.5, shemes 3.5 and 4.4 suessfully adapt to the loss onditions in the network and thereby avoid losses later into the experiment, even though the error onditions still prevail on the lossy link. Sheme 3.4 also adapts, however it is limited by the apaity it has reserved and therefore has to stream from the parent upstream the lossy link at a redued rate. Figures 9,,, 2, and 3 show the reeived rate at node 5 as a funtion of time during the ourse of the experiment. Unlike. whih performs poorly, 3.5 and 4.4 are able to maintain a reeived bandwidth above 5kbps. Of these two, sheme 4.4 performs better sine even during the transition period, it streams only onefourth of the bitstream from the affeted node. Sheme 2.5 also performs poorly, even though it experienes fewer overall losses than. as it streams at only half the bitstream rate from the affeted link. Sheme 3.4 performs better than shemes. and 2.5 but worse than shemes 3.5 and 4.4 beause of its limited ability to adapt. G. Link Error Losses We examine the overall performane of our sheme by injeting losses with rates ranging between -5% on 2% of links in the network. Figure 4 shows FEC goodput ahieved by different shemes under varying loss onditions in the network. The results onfirm the observations made in the FEC Goodput Goodput FEC Goodput versus Error-Rate *. 2*.5.4 3*.4 3*.5.3 4* Error-rate Fig. 6. FEC goodput without rate-adaptation. Goodput versus Error-Rate *. 2* *.4 3*.5 4* Error-rate Fig. 7. Goodput without rate adaptation for different shemes.

9 Delay/Jitter *. 2*.5 3*.4 3*.5 4*.4 Delay with jitter for different shemes Fig. 8. Delay and Jitter for Different Shemes. The bars show the delay while the vertial line between the bars and the small horizontal line at the top shows jitter. Control Overhead *. 2*.5 3*.4 3*.5 4*.4 Control Overhead for different shemes Fig. 9. Control Overhead for different shemes. earlier experiment. Sheme 4.4 has the highest FEC goodput, followed losely by 3.5 and manages to perform well for FEC goodput even with its limited ability to adapt beause FEC oding suessfully mitigates the effet of a limited number of paket losses. Also, the 2.5 sheme without rate-adaptation outperforms simple overlay multiast beause of the loss deorrelation property of path-diversity. Figure 5 shows the umulative FEC goodput distribution aross all nodes for a ase where 2% of the links are injeted with 5% loss rate. As seen, shemes that employ path diversity with rate adaptation outperform simple overlay multiast aross nodes. More importantly, even nodes that are deeper in the k-dag than they would have been in a simple multiast tree due to the fat that k b >, ahieve a gain in FEC goodput. Figures 6 and 7 show FEC goodput and goodput values without rate-adaptation respetively. As seen, without rateadaptation, losses due to inreased depth of the DAG offset the advantages of path diversity both for goodput and FEC goodput metris. Figure 8 ompares the delay and jitter values for different shemes. As expeted, average delay inreases with b k while jitter inreases with k. Figure 9 shows the ontrol overhead for the different shemes. As expeted, the ontrol overhead is proportional to dag degree and is quite low, i.e. less than 7%. VII. RELATED WORK Multiast Streaming has reently been an ative area of researh and as suh, several interesting overlay multiast shemes have been proposed. In this setion, we present a brief overview of existing related work and ompare our sheme to them. Narada [3] builds a dynami DVRMP style overlay multiast tree for video onferening. Even though it adapts the overlay topology to hanging network onditions, every reeiver is essentially onneted to a single parent. Splitstream [] addresses the issue of handling node failures by building multiple multiast trees suh that any node is an interior node in at most one of the trees. Eah tree orresponds to a layer in MDC oded multimedia stream. Our sheme is different in that it handles FEC oded streaming multimedia. In addition, Splitstream does not expliitly distinguish between node failures and network losses. Co-Op Net [2] is similar in spirit to Splitstream. It too builds multiple multiast trees eah for streaming a single MDC layer. However, Co-Op Net is entralized with tree management operations based at the soure rather than being peer-to-peer. In terms of motivation, distributed video streaming (DVS) [4], [6], [7], [8], [9] omes the losest to our work. DVS uses both path diversity and rate-adaptation for streaming video ontent from multiple soures to a reeiver. In this paper, we have extended this idea to multiast by introduing k-dags. Informed Content Delivery [5] addresses the problem of enabling large file transfers over overlay networks. It uses ollaborative transfers between reeivers to exploit potentially rih onnetivity between the reeivers. However, the main fous is primarily on traditional data transfer appliations rather than multimedia streams limiting the appliability of their oding and reoniliation mehanisms. VIII. CONCLUSION In this paper, we have proposed a new mehanism for appliation layer multiast streaming of multimedia data over the Internet. The proposed ontent distribution struture, k-dags, allows reeivers in the multiast session to have multiple parents. This differs from traditional multiast approah, where eah node has only one parent. This multipliity of parents enabled by k-dags enables two possibilities. First, by streaming data from multiple senders, we are able to deorrelate losses experiened by the end-nodes, thereby improving the performane of FEC oded streams. Seond, by dynamially adapting the requested video streaming rates between its various parents, a reeiver an mitigate the effet of outages in the network. We use a simple rate-alloation algorithm and a paket-partitioning algorithm to enable these possibilities. Our results indiate that our sheme improves FEC goodput of streaming multimedia by 5-3%. This performane gain omes at the ost of inreased delays as well as higher jitter values. While with inreasing end system apabilities, we do not expet jitter to be a major issue, the small additional

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