A Survey on Modeling Peer-to-peer Video Streaming Systems

Transcription

1 CSC 551 Course Project Report A Survey on Modeling Peer-to-peer Video Streaming Systems Le CHANG Uvic Number: V Department of Computer Science, University of Victoria, Victoria, BC, Canada V8W 3P6 lechang@uvic.ca

2 1 CONTENTS I Introduction 2 II Models and System Settings 3 II-A An overview of existing work II-B Modeling techniques II-B1 Tree, push-based models II-B2 Mesh-based Models III Measuring Metrics 9 III-A Streaming rate/ throughput III-B Transmission/ deffusion delay III-C Startup delay/ initial buffering delay III-D System scale III-E Continuity / goodput / sustainable streaming rate IV Fundamental Limits 10 IV-A Bandwidth availability IV-B Chunk Availability IV-C Chunk Diversity V Data Scheduling Algorithm 12 V-A Sequential/ greedy V-B Random V-C Rarest first V-D Anchor-based V-E Network coding VI Conclusion and Open Issues 15 References 15

3 2 Abstract Peer-to-peer(P2P) video streaming systems have become popular in recent years. This paper presents a most up-to-date survey of modeling work in the area of P2P video streaming. Different system models and settings, major measuring metrics, theoretical bounds concerning these metrics, approaches towards these bounds and some open issues are covered in this paper. Index Terms P2P video streaming, system modeling, survey I. INTRODUCTION Peer-to-peer(P2P) video streaming have become increasingly popular in recent years since Coolstreaming [1] appeared as the first P2P live video application. A common agreement in this area is that P2P video streaming data will dominate the internet in the near future. Traditionally, video stream on the Internet follow the client-server model, in which a bunch of servers with much larger capacity support many other capacity-limited clients. This model has several problems. First, the capacity and bandwidth of servers is not infinite, which results in scalability problem. Moreover, the extreme centralization of the system makes it vulnerable to single point of failure. According to different kinds of service provided, P2P video streaming systems can be broadly classified into two categories: live streaming and video-on-demand (VoD). In a live streaming system, the live video content is disseminated in real time while video-on-demand allows users watch whatever video clips whenever they want. In either of these systems, peers not only download data from the servers and other peers, but also upload what they have downloaded to those requesting it. This will significantly reduce the bandwidth burdens of the servers and also provide peers with improved quality of service. The major issue in P2P live streaming is to provide users with real time and fluent playback experience. This means the difference of playback point between peers must be minimized. To maintain the attribute of real time, sometimes peers are even forced to skip certain amount of content to avoid falling behind other peers. Some representative P2P live streaming systems are Coolstreaming [1], PPLive [2], PPstream [3], UUsee [4], Anysee [5], and Joost [6] etc. On August 2005, when PPLive was carrying Super Girl Finals in China, a number of concurrent

4 3 500,000 watchers online were recorded, setting a milestone of P2P live streaming systems. Very recently, P2P VoD (Video-on-demand) becomes the new interest of researchers. Different from P2P live streaming which provide live programs, this new kind of service allows users to watch different videos programs, or different parts of a certain video, or even allows VCR operations like fast forward, fast backward and etc. This brings much flexibility and convenience to users, while increasing scheduling complexity of the system on the other side, as peers no longer watch the same part of a video. Typical VoD systems are PPLive [2], Joost [6], GridCast [7], PFSVOD [2], PPStream [3], UUSee [4] etc. Although many applications have been proposed and successfully deployed, little work of theoretical analysis had been published before After that, the following three years have witnessed a graduate increasing of theoretical studies in this area [8] [20]. According to the existing work, researchers are mainly concerned about following natural questions. How can we model different kinds of overlay structure of P2P video streaming systems? What measuring metrics are suitable to characterize system performance? What are the fundamental limits bounding such system performance? How can we gain insights from the modeling work to make P2P video streaming systems closer to these theoretical bounds? These four issues above are our major concerns in this report. And we attempt to present a comprehensive literature review of existing work as well as open problems remaining unsolved. The remainder of this report is organized as follows: In Section II we give a brief introduction of different system models and settings at present. In section III we introduce common accepted measuring metrics in this area. We present and explain theoretical bounds derived from fundamental limits of the system in IV and discuss approaches towards that optimality in V. Finally we summarize our work with some open problems in section VI. II. MODELS AND SYSTEM SETTINGS In this section, we focus on how to build theoretical models for P2P video streaming systems. We first briefly summarize exsiting work in modeling P2P video streaming, and then move to modeling techniques in detail.

5 4 A. An overview of existing work For building a model for P2P video streaming systems, a first thing is to decide the overlay structure. In early days, tree-based systems such as Overcast [21] and ESM [22] were proposed using application level multicast. However, theoretical analysis of tree-based P2P video streaming model was proposed only after the year 2007 by Y. Liu [11] and S. Liu et al. [13], [20], deriving theoretical results for system performance with or without node degree bound. Due to its complexity and rigidity, tree-based approaches are then replaced by the mesh-based technique. Nowadays commercial P2P video streaming applications like Coolsteaming [1], PPLive [2] and PPstream [3] mainly adopt this approach for its robustness and simplicity to implement and maintain. Concerning modeling work in this area, Massoulie et al. [8] proposed a simple model and the optimal streaming rate for their push-based streaming protocol, which is further improved by Bonald and Massoulie et al. [15] with a refurbished modeling for several popular push-based scheduling algorithms. They also proved in theory several performance bounds these algorithms. Another work by Liu [11] focused on the metric of minimum delay and proposed a snowball algorithm to achieve the lower bound for their push-based model. With respect to pull-based algorithms, Zhou et al. [10] compared different scheduling strategies based on the continuity metric and startup delay. They also proposed a mixed strategy to balance the tradeoff between these two metrics. This is further refined by their latest paper [16], in which they tried to use Markov chain to find the optimal scheduling strategy using a highly unified model. With the global information, Kumar et al. [9] derived the maximum sustainable streaming rate. And Feng et al. [18] characterized the gap between the actual system performance and fundamental constraints. Specifically, concerning flash crowd scenario, Li et al. [23] gave an empirical study with the interest of user behaviors and system scales, and Liu et al. [19] later characterized these effects using a stochastic model. An comprehensive study of network coding in peer-topeer streaming under flash crowd scenarios was proposed by Feng et al. [14]. It is shown in the paper that if network coding is applied under certain principles, guaranteed desirable performance can be achieved. Different from the work aforementioned, Wu et al. [17] developed an infiniteserver queuing network model to characterize multi-channel P2P live streaming systems, and provided insightful rules for designing such kind of practical systems.

6 5 Fig. 1: A single tree-based P2P streaming system [12]. B. Modeling techniques Now we are ready to detail these modeling techniques. According to the overlay structure of a P2P streaming system, we have tree, push-based models and mesh-based models. The term push-based or pull-based is more suitable in the context of mesh-based systems, as data stream is no longer accurate in such systems. The minimum data unit in these systems is video chunk. If in a system, upstream peers decide which peer to select and forward chunks, we call it a pushbased system. If downstream peers decide which peer to select and send requests for chunks, it is a pull-based system. In this report, if not specified, these terms refer to the same concepts: peer and node; server, seed, and source; and chunk, block and file piece. 1) Tree, push-based models: In a tree-based system, peers are connected and organized into a streaming tree where the server (or seed) serves as the root. Each peer only download from its parent node and upload to its children. Therefore, the tree-based systems inherently require a push-based data driven method. Fig. 1 [12] shows the structure of a single tree-based P2P streaming system. There are two major drawbacks of the single-tree based approach. First, the maintenaince is complex and resource consuming. Moreover, it is difficult for leaf nodes to contribute their upload bandwidth. Therefore the multi-tree structure is introduced, in which a peer is enrolled in different streaming trees with different positions, as shown in Fig. 2 [12]. To model tree-based systems, graph theory is mainly applied.

7 6 Fig. 2: A multi-tree-based P2P streaming system [12]. Tree-based model [20]. A directed graph G = (V, E) is used to model a tree-based P2P network. A vertex v in V represents a source or a peer. An edge e = (v, u) in E means that peer v is allowed to forward data stream to peer u. The object of the system is to broadcast data stream from the source to all peers within the system. In a multi-tree based system, the number of all distinct parents of a node is defined as in-degree, that of distinct children as out-degree. The streaming capacity of the entire system is defined as the maximum possible value of the summation of streaming rate of all multi-trees. While it is simple to compute this streaming capacity without degree bound [9], under certain degree bound it turns out to be a nontrivial job. As proposed in [20], for total degree > 2, finding the streaming capacity is NP-complete. Other than streaming capacity, this model also seeks to find maximum streaming rate and transmission delay. We will introduce these metrics and their bounds under fundamental system limits in detail in section III and IV. 2) Mesh-based Models: Mesh-based approach has been adopted by recent P2P video streaming systems. In a mesh-based system, topology is highly dynamic. Each peer maintains a list of neighbors and all peers form almost a complete graph. Transmission occurs only among a peer and its neighbors. If one of a peer s neighbor leaves the system, the peer can choose other candidates immediately to maintain its download rate. This attribute makes such kind of systems extremly robust against peer churn. Early papers mainly consider the push-based approach [8], [15], while the pull-based approach is applied in practice, mainly due to its simplicity. Nevertheless, because peer s behaviors are highly dynamic and diverse, such model is very difficult to characterize, despite much work [9] [11], [14], [16] [19] published in this

8 7 area. Push-based models Single chunk model [11]. In such model, system runs in discrete rounds (or time slots). we focus on how to disseminate with the shortest delay (minimum number of rounds) one particular chunk that is originally on the server to the whole system. The key issue is to determine a proper scheduling strategy to keep every peer uploading. For instance, at the beginning, only the server has the chunk and transmit it to a peer. At next round, the server and one peer will have that chunk thus can support 2 other peers, and 4 peers at next next round. So the increase of number of peers receiving the chunk follows the exponential law, thus the transmission delay is minimized. We refer this to chunk availablity in section IV. Multi-chunk model [15]. The multi-chunk model applies random process to represent the distribution process. The system runs in discrete rounds (or time slots). Consider a source and N peers. The source creats a sequence of chunks (in its playback order) at rate λ. At each round, each node (including the source and all peers) forwards a chunk it has following certain rules to a destination peer. A random variable r(t) is built to represent the fraction of peers receiving a certain chunk in terms of rounds t. As a peer forward a certain chunk to another peer following certain rules, we are able to characterize the transition function as r(t + 1) = F (r(t)). Thus we can compute the transmission rate of the chunk. This doesn t provide us with any close-form bound, but by numerical method and simulation we can see clearly how chunks propagate within the system. Pull-based Models Capacity-oriented model [9], [14], [18], [19]. This model considers P2P streaming from the perspective of network capacity. The idea is that total upload bandwidth of the entire system should be larger than or equal to total download rate of all peers. Assuming that a server with capacity U s want to support N peers with average capacity of U p, and there is a proper scheduling algorithm to fully utilize this total upload capacity, it is simple to derive performance bounds concerning maximum streaming rate and startup delay. For convenience of our further discussion in section IV, we use Table I to summarize common notations in this model. This model may or may not run in discrete rounds, depending on different settings. Scheduling-oriented model [10], [16]. One problem of capacity-oriented model is that it

9 8 Notation U s u s R N D p U p u p R i Definition Server uploading bandwidth Relative uploading bandwidth of the server, = (U s /R) Playback rate of the movie Scale peers in the system Average download bandwidth of peers Average uploading bandwidth of peers Relative average uploading bandwidth of peers, =(U p/r) Average streaming rate in time slot i (in blocks per slot) TABLE I: Main notations used in capacity-oriented models Fig. 3: Modeling the buffer shifting operation [16]. fails to characterize chunk distribution strategies. And there is no guarantee that upload bandwidth of every peer can be fully utilized. This is overcame by modeling the change of a peer s buffer. Assume there are n cells from B(1) (storing the newest chunk) to B(n) (oldest chunk) in the buffer, namely the buffer can store up to n chunks. And priority a W (i) is assigned to a corresponding cell B(i). At each round, a peer selects the empty cell with highest priority, and randomly select another peer to request for that chunk. This request may be rejected if there is no such chunk in that peer. After each round, the buffer cell makes a shift to feed B(n) to the local video player. The process can be demonstrated by Fig. 3 [16]. This model is especially efficient in charaterizing different scheduling strategies. For instance, if we want to model the random choosing algorithm, simply set W (i) = 1 for each i. For the greedy algorithm, assign W (n) the highest value. The probability that B(n) is filled up with a chunk is also a comfortable metric to characterize the playback continuity, which is hard to be quantified using other models. The problems of this model are 1) peers

10 9 are strictly synchronized, which is neither applicable nor necessary in practice; 2) the huge computational complexity; and 3) the optimal continuity of 70% (the latest result by [16]) is still not so meaningful as 3 seconds of skip (or pause) in 10 seconds is not satisfying. III. MEASURING METRICS In this section, we discuss common accepted measuring metrics in P2P video streaming. These metrics are useful in evaluating the system performance. A. Streaming rate/ throughput This metric means the data streaming rate in the system. Maximum average streaming rate and average streaming rate are often derived to demonstrate how efficient the system is. From the user s perspective, this refers to its download rate. Feng et al. [14] claims that this metric is not accurate in P2P streaming because there is no need to maximize such download rate. A download rate larger enough than the playback rate R will be enough to guarantee the fluency of watching experience. For theoretical results concerning this metric, see [8], [13], [14], [18]. B. Transmission/ deffusion delay This metric measures how long it takes for a chunk to be transmitted from the source to a end node. Users may see this as the difference of playback point between peers when they are watching the same live video. This is desired to be minimized in live streaming as such applications have real time requirement. For theoretical results concerning this metric, see [11], [15]. C. Startup delay/ initial buffering delay This metric is specific in P2P video streaming systems. To maintain the fluency of watching experience, end systems must download enough chunks before they can start playback. Some systems set a fixed value for the number of chunks. Other work consider enough buffering as the buffer being filled up with chunks. The time to transmit these chunks is called startup delay. For theoretical results concerning this metric, see [10], [14], [18].

11 10 Fig. 4: Definition of goodput in P2P VoD systems [24]. D. System scale Insead of maximize streaming rate, some modeling work claims that it is worth scaling the system to support more peers, as when average streaming rate exceeds the inheret playback rate of a movie, all the peers are probably able to playback fluently. Thus extra bandwidth of the system can be used to provide support to new peers to make the system scalable. The total number of all peers within the system is system scale. For theoretical results concerning this metric, see [14], [19]. E. Continuity / goodput / sustainable streaming rate This metric characterizes the key attribute of a P2P streaming system. This measures how likely the movie can be played without skips or pauses. It is also a proper measuring metric to evaluate how good a scheduling algorithm is. Different models may have different definition of this metric. Zhou et al and Zhao et al [10], [16] developed the probabilistic model to characterize continuity. In another paper [24], goodput is defined for VoD systems as the maximum slope of a line that does not exceed the y-coordinate at any time of the curve of consecutive arrived chunks (see Fig. 4 [24]). For theoretical results concerning this metric, see [9], [10], [15], [16]. IV. FUNDAMENTAL LIMITS In this section we discuss fundamental limits that bound system performance in terms of measuring metrics we mentioned in last section. These are general limits that can be applied on

12 11 many system models with slight difference. A. Bandwidth availability Rule 1 [9]. The maximum streaming rate of a system can not exceed download bandwidth or upload bandwidth. No matter what scheduling algorithms are applied, upload bandwidth or download bandwidth of the entire system is not infinite. If we use our notations in section II, we can write an inequality as ND min((u s + NU p ), ND p ), where D is the average download rate or streaming rate of peers. This provides an upper bound for D. We can use this inequality to derive a bunch of useful performance bounds [9], [11], [13], [14], [18]. If we let the buffer size divided by D, we gain the minimum startup delay. If we set D = R, which means peers download at its playback rate. Then given a server with capacity U s, we can derive the maximum number N of peers that can be supported in the system. Or if we set N to be a fixed value, we are able to derive the minimum server capacity required for such system scale. For tree-based systems, there is another limit on bandwidth, the server capacity and the degree bound. If there is no limit on node degree, as the server sum up all the streams, the maximum streaming rate is D = min(u s, U p ) [9], [20]. The streaming capacity under node degree bound, as we mentioned in section II, is an NP-complete problem if this degree bound is larger that 2. B. Chunk Availability Rule 2 [11], [18]. The upload bandwidth of a peer can not be fully utilized until it has downloaded some chunks already. Liu [11] discusses this constraint and proves that the snow-ball dissemination achieves the minimum average transmission delay. Feng et al. [18] further this work to develop the lower bound of the startup delay under a flash crowd scenairo. For a single chunk dissemination, according to the exponential law we discussed in section II, the average streaming rate at time i is also bounded by R i = U s2 i 1 N instead of bandwidth only. This improves previous theoretical bound and also help derive the bound for startup delay as SD min log m (N/u s ) + 1, where m = 1 + u p by lemma 3 in [18].

13 12 C. Chunk Diversity Rule 3. The distribution of chunks among the system should have certain diversity to facilitate exchange between peers. For instance, if peers all have the same chunk, or if all chunks sit in the same peer, then there will be no chance for peers to exchange. In this case, even if there is extra bandwidth within the system, we are not able to utilize it. This requires chunks to be uniformly distributed among peers. However, how to characterize this attribute is again a nontrivial work, despite some insightful work on modeling and evaluating scheduling algorithms by Zhao and Zhou [10], [16]. We summarize this section as follows. Among these three fundamental constraints, the first two are hard limits bounding the system performance, while the third one is that scheduling algorithms try to maximize to achieve those performance bounds. V. DATA SCHEDULING ALGORITHM The most important issue in designing a P2P video streaming system is chunk scheduling which should be able to provide high-quality service while maintain a high utilization of system resources. In this section we discuss data scheduling algorithms that play a very important role in achieving performance bounds derived in last section. These algorithms are most common ones with some of them deployed in practical systems. A. Sequential/ greedy Select pieces according to the closest order. This is also called greedy algorithm as peers attend to download chunks most close to its playback point. This follows users s immediate interests, while is actually the worst strategy in terms of chunk diversity, thus is only combined with other algorithms together. B. Random Select chunks randomly. This method, although is quite contra- intuitive, actually brings certain diversity of chunks among the system. The reason is, if every peer selects chunks randomly, then the expectation of the number of each chunk tends to equal each other in the long run. This conforms to the fact that the uniform distribution of chunks is the best distribution, as we mentioned in last section.

14 13 C. Rarest first Select the piece that is the rarest in the system (newest). Selecting the rarest piece helps increase the diversity of pieces, therefore enhances the quality of service of the system and helps it scale, which is clearly explained in [25]. Compared with random approach, we no longer depend on probability but attempt intentionally to balance the distribution of chunks among the system. Depending on with or without global knowledge, we have global rarest first or local rarest first algorithm. D. Anchor-based In VOD systems, users may jump forward or backward from its original playback point,which is called VCR operations. To facilitate such operations, some video anchor points are predistributed among a movie with a higher priority assigned for downloading. when users attempt to jump to another playback point, they are always redirected to an anchor nearest to the new playback point. In practical systems a mixture of strategies are usually applied, giving the first priority to sequential, then rarest-first, as in PPLive [2]. Anchor-based approach is still under study and not deployed yet. E. Network coding A promosing technique that may facilitate P2P video streaming is network coding. Network coding was initially proposed to improve the throughput by making the optimal use of bandwidth resources in a network for content distribution [26] [28]. Its effects have been studied in [29] and [24], which demonstrate that random linear network coding is easy and feasible for both P2P live streaming and VoD (video-on-demand) systems. In random linear network coding, a movie is divided into multiple segments, where each segment is further divided into blocks. Assume that for a movie we have N s segments and N b blocks within a segment. Let b i be a number selected from the Galois field of a fixed size q and represents a block, so for each segment, we have blocks as b 1, b 2,, b Nb. When sending a coded block E, the sender checks all the blocks (from b 1 to b t ) it already has within the corresponding segment and selects t coefficients randomly as C 1, C 2,, C t from the same Galois field, and generates the new coded block E = t i=1 C i b i. Note that the value of

15 14 Fig. 5: Traditional P2P streaming protocol VS. network coding [29]. t can be up to N b and all operations done in a Galois field of size q. The sender then forwards these coefficients C 1, C 2,, C t and the coded block E to its downstream peers. From the perspective of a receiver, it is receiving linear equations with N b unknown variables, so it needs to wait for N b equations if they are linear independent to each other to start extracting b 1 to b n. Any coded block (i.e., equation) within the same segment can be useful (i.e., linear independent with other received equations) with a high probability if the size of the finite field is large enough, according to [30]. Fig. 5 [29] demonstrates the difference between traditional P2P streaming approach and network coding. An intuitive benefit of network coding for P2P video streaming is that it does not need explicit block selection or scheduling algorithms. Any received block can be useful with a high probability if these blocks are coded properly by senders. A receiver only needs to wait for enough blocks, instead of specific blocks, to start decoding. An unavoidable issue in network coding is block redundancy α. As the Galois field is finite, there is a possibility that same coded blocks may be generated in many times of coding operations. If the same coded block has been received by a peer twice, then one redundant block is generated. Lemma 2.1 in [31] proves that if the space spanned by the coded blocks on the upstream peer is not covered by that of the download peer (denoted by S u S d ), after transmission, the probability that this block is useful to the download peer is P r = 1/q, where q is the size of the Galois field. Therefore, P r = 1/q serves as the lower bound of α. However, 1/q is still a loose bound for α. Feng et al. [14] proposes a proposition to improve bound for α, but their proposition is based on an assumtion not theoretically proved. If this problem remains unsolved, we are not able to characterize the effiency of network coding compared with other

16 15 scheduling strategies. VI. CONCLUSION AND OPEN ISSUES In this report we complete a survey concerning P2P video streaming systems. We present different system models such as tree-push-based, mesh-pull and push-based models, and explain their essential characteristics. Important measuring metrics are also discussed. In terms of these metrics, we explain fundamental system limits that bound the performance, and useful scheduling algorithms to approach these theoretical bounds. Finally, we present some open problems in this area. Which scheduling algorithm is the best? A major problem in this area is how to model scheduling algorithms. Only a small number of papers address this issue [10], [16], limited in live streaming. Most of other work is still capacity-oriented approach, which overlooks detailed algorithms to achieve those performance bounds. In P2P VoD systems, scheduling becomes even more complicated, requiring more efforts engaged in the modeling area. How to characterize the redundancy rate α in network coding? Current result is mainly based on capacity-oriented approach, taking the advantage of that network coding does not require complex scheduling algorithms. Therefore, there is still a gap between current theoretical results and the inherent characteristics of network coding that make it different from other scheduling algorithms. Unless we figure out α, we are not able to tell how good is network coding. How to model VoD system and VCR operations? The modeling work of VoD systems is just at its beginning. User patterns related to VCR operations remain unverified. And currently we are not able to characterize those algorithms supporting VCR operations. REFERENCES [1] Coolstreaming. [2] Pplive. [3] Ppstream. [4] Uusee. [5] Anysee. [6] Joost. [7] Gridnet. [8] L. Massoulie, A. Twigg, C. Gkantsidis, and P. Rodriguez. Randomized decentralized broadcasting algorithms. trees, 1:5.

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