Several peer-to-peer systems for live streaming have been recently deployed (e.g. CoolStreaming, PPLive, SopCast). These all rely on distributed, epidemic-style dissemination mechanisms. Despite their popularity, the fundamental performance trade-offs of such mechanisms are still poorly understood. In this paper we propose several results that contribute to the understanding of such trade-offs. Specifically, we prove that the so-called random peer, latest useful chunk mechanism can achieve dissemination at an optimal rate and within an optimal delay, up to an additive constant term. This qualitative result suggests that epidemic live streaming algorithms can achieve near-unbeatable rates and delays. Using mean-field approximations, we also derive recursive formulas for the diffusion function of two schemes referred to as latest blind chunk, random peer and latest blind chunk, random useful peer. Finally, we provide simulation results that validate the above theoretical results and allow us to compare the performance of various practically interesting diffusion schemes in terms of delay, rate, and control overhead. In particular, we identify several peer/chunk selection algorithms that achieve near-optimal performance trade-offs. Moreover, we show that the control overhead needed to implement these algorithms may be reduced by restricting the neighborhood of each peer without substantial performance degradation.

Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. However for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges as slowly as flooding (O(n 2) messages). A recently proposed algorithm called geographic gossip improves gossip efficiency by a √ n factor, by exploiting geographic information to enable multi-hop long distance communications. In this paper we prove that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional √ n factor and is order optimal (O(n) messages) for grids and random geometric graphs. We develop a general technique (travel agency method) based on Markov chain mixing time inequalities, which can give bounds on the performance of randomized message-passing algorithms operating over various graph topologies.

In this paper we consider the problem of sending data in real time from information sources to sets of receivers, using peer-to-peer communications. We consider several models of communication resources, and for each model we identify schemes that achieve successful diffusion of information at optimal rates. For edge-capacitated networks, we show optimality of the so-called “random-useful” packet forwarding algorithm. As a byproduct, we obtain a novel proof of a famous theorem of Edmonds, characterising the broadcast capacity of a capacitated graph. For node-capacitated networks, assuming a complete communication graph, we show optimality of the so-called “most-deprived ” neighbour selection scheme combined with random useful packet selection. We then show that optimality is preserved when each peer can exchange data with a limited number of neighbours, when neighbourhoods are dynamically adapted according to a particular scheme. Finally, we consider the case of multiple information sources, each creating distinct information to be disseminated to a specific set of receivers. In this context, we prove optimality of the so-called “bundled most-deprived neighbour random useful packet” selection.

Abstract—The growth of real-time content streaming over the Internet has resulted in the use of peer-to-peer (P2P) approaches for scalable content delivery. In such P2P streaming systems, each peer maintains a playout buffer of content chunks which it attempts to fill by contacting other peers in the network. The objective is to ensure that the chunk to be played out is available with high probability while keeping the buffer size small. Given that a particular peer has been selected, a policy is a rule that suggests which chunks should be requested by the peer from other peers.. We consider consider a number of recently suggested policies consistent with buffer minimization for a given target of skip free playout. We first study a rarest-first policy that attempts to obtain chunks farthest from playout, and a greedy policy that attempts to obtain chunks nearest to playout. We show that they both have similar buffer scalings (as a function of the number of peers of target probability of skip-free probability). We then study a hybrid policy which achieves order sense improvements over both policies and can achieve order optimal performance. We validate our results using simulations. I.

Abstract—The rapid growth of media content distribution on the Internet in the past few years has brought with it commensurate increases in the costs of distributing that content. Can the content distributor defray these costs through a more innovative approach to distribution? In this paper we evaluate the benefits of a hybrid system that combines peer-to-peer and a centralized client-server approach against each method acting alone. A key element of our approach is to explicitly model the temporal evolution of demand. In particular, we employ a wordof-mouth demand evolution model due to Bass [2] to represent the evolution of interest in a piece of content. Our analysis is carried out in an order scaling depending on the total potential mass of customers N in the market. Using this approach, we study the relative performance of peerto-peer and centralized client-server schemes, as well as a hybrid of the two—both from the point of view of consumers as well as the content distributor. We show how awareness of demand can be used to attain a given average delay target with lowest possible utilization of the central server by using the hybrid scheme. We also show how such awareness can used to take provisioning decisions. Our insights are obtained in a fluid model, and supported by stochastic simulations. Index Terms—Bass diffusion, Peer-to-peer, content distribution, delay guarantees. I.

Abstract—Peer-to-peer (P2P) file distribution is a scalable way to disseminate content to a wide audience. For a P2P network, one fundamental performance metric is the average time needed to deliver a certain file to all peers, which in general depends on the topology of the network and the scheduling of transmissions. Despite its apparent importance, how to minimize average finish time remains an open question even for a fullyconnected network. This is mainly due to the analytical challenges that come with the combinatorial structures of the problem. In this paper, by using the water-filling technique, we determine how each peer should use its capacity to sequentially minimize the file download times in an upload-constrained P2P network. Furthermore, it is argued that this scheduling also potentially minimizes average finish time for the network. This result not only provides fundamental insight to scheduling in such P2P systems, but also can serve as a benchmark to evaluate practical algorithms and illustrate the scalability of P2P networks. I.

Peer-to-peer (P2P) file distribution is a scalable way to disseminate content to a wide audience. This paper presents an algorithm by which download times are sequentially minimized; that is, the first peer’s download time is minimized, and subsequent peers’ times are minimized conditional on their predecessors’ times being minimized. This objective gives robustness to the file distribution in the case that the network may be partitioned. It is also an important step towards the natural objective of minimizing the average download time, which is made challenging by the combinatorial structure of the problem. This optimality result not only provides fundamental insight to scheduling in such P2P systems, but also can serve as a benchmark to evaluate practical algorithms and illustrate the scalability of P2P networks.

In unstructured P2P content distribution systems, the most important algorithms to ensure optimal flow of content along multiple dynamically created distribution trees are piece selection algorithms and load balancing algorithms. This paper models practical load balancing algorithms and derive a number of insights.

Abstract—In this paper we investigate the impact of peer bandwidth heterogeneity on the performance of a mesh based P2P system for live streaming. We show that bandwidth heterogeneity constitutes an important resource for P2P live streaming systems. Indeed, by effectively exploiting it, the overall performance of the system is significantly improved. This requires the adoption of smart schemes for both the overlay topology construction and chunk scheduling mechanisms that discriminate among peers based on their bandwidth. Index Terms—P2P streaming systems, diffusion algorithms, bandwidth-aware scheduling, fluid models 1

Abstract—Motivated by peer-to-peer content distribution and media streaming applications, we study the broadcasting problem in a time-discretized model, with integer valued upload and download capacity constraints at nodes. We analyze both deterministic centralized and randomized decentralized protocols that can achieve optimal packet receiving rates at the nodes. In particular, we consider a simple scheme that requires each node, in each time slot, to transmit to a random neighbor that is not yet chosen by any other nodes in that slot. We prove that such a surprisingly simple scheme can asymptotically achieve the optimal receiving rates in complete graphs with homogeneous node capacity. The proof involves applying randomized network coding and deriving the max-flow bounds achieved in the resulting transmission schedule. We extend the results to more general topologies, and bound the performance of randomized neighbor selection with randomized network coding. I.