arXiv subjects

Fabien Mathieu

Publications and source records attributed to Fabien Mathieu.

30 records · Page 2Linked to original sources

arXiv2012

Spatial Interactions of Peers and Performance of File Sharing Systems

We propose a new model for peer-to-peer networking which takes the network bottlenecks into account beyond the access. This model allows one to cope with key features of P2P networking like degree or locality constraints or the fact that distant peers often have a smaller rate than nearby peers. We show that the spatial point process describing peers in their steady state then exhibits an interesting repulsion phenomenon. We analyze two asymptotic regimes of the peer-to-peer network: the fluid regime and the hard--core regime. We get closed form expressions for the mean (and in some cases the law) of the peer latency and the download rate obtained by a peer as well as for the spatial density of peers in the steady state of each regime, as well as an accurate approximation that holds for all regimes. The analytical results are based on a mix of mathematical analysis and dimensional analysis and have important design implications. The first of them is the existence of a setting where the equilibrium mean latency is a decreasing function of the load, a phenomenon that we call super-scalability.

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arXiv2012

On the Manipulability of Voting Systems: Application to Multi-Carrier Networks

Today, Internet involves many actors who are making revenues on it (operators, companies, service providers,...). It is therefore important to be able to make fair decisions in this large-scale and highly competitive economical ecosystem. One of the main issues is to prevent actors from manipulating the natural outcome of the decision process. For that purpose, game theory is a natural framework. In that context, voting systems represent an interesting alternative that, to our knowledge, has not yet been considered. They allow competing entities to decide among different options. Strong theoretical results showed that all voting systems are susceptible to be manipulated by one single voter, except for some "degenerated" and non-acceptable cases. However, very little is known about how much a voting system is manipulable in practical scenarios. In this paper, we investigate empirically the use of voting systems for choosing end-to-end paths in multi-carrier networks, analyzing their manipulability and their economical efficiency. We show that one particular system, called \Single Transferable Vote (STV), is largely more resistant to manipulability than the natural system which tries to get the economical optimum. Moreover, STV manages to select paths close to the economical optimum, whether the participants try to cheat or not.

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arXiv2011

On Using Seeders for P2P Live Streaming

Seeders (peers that do not request anything but contribute to the system) are a powerful concept in peer-to-peer (P2P). They allow to leverage the capacities of a P2P system. While seeding is a natural idea for filesharing or video-on-demand applications, it seems somehow counter-intuitive in the context of live streaming. This paper aims at describing the feasibility and performance of P2P live seeding. After a formal definition of "live seeding" and efficiency, we consider the theoretical performance of systems where the overhead is neglected. We then propose a linear overhead model and extend the results for this model, for a single seeder and for a set of seeders as well (it is not always possible to perfectly aggregate individual efficiencies in a given system).

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arXiv2009

Size Does Matter (in P2P Live Streaming)

Optimal dissemination schemes have previously been studied for peer-to-peer live streaming applications. Live streaming being a delay-sensitive application, fine tuning of dissemination parameters is crucial. In this report, we investigate optimal sizing of chunks, the units of data exchange, and probe sets, the number peers a given node probes before transmitting chunks. Chunk size can have significant impact on diffusion rate (chunk miss ratio), diffusion delay, and overhead. The size of the probe set can also affect these metrics, primarily through the choices available for chunk dissemination. We perform extensive simulations on the so-called random-peer, latest-useful dissemination scheme. Our results show that size does matter, with the optimal size being not too small in both cases.

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arXiv2009

On Resource Aware Algorithms in Epidemic Live Streaming

Epidemic-style diffusion schemes have been previously proposed for achieving peer-to-peer live streaming. Their performance trade-offs have been deeply analyzed for homogeneous systems, where all peers have the same upload capacity. However, epidemic schemes designed for heterogeneous systems have not been completely understood yet. In this report we focus on the peer selection process and propose a generic model that encompasses a large class of algorithms. The process is modeled as a combination of two functions, an aware one and an agnostic one. By means of simulations, we analyze the awareness-agnostism trade-offs on the peer selection process and the impact of the source distribution policy in non-homogeneous networks. We highlight that the early diffusion of a given chunk is crucial for its overall diffusion performance, and a fairness trade-off arises between the performance of heterogeneous peers, as a function of the level of awareness.

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arXiv2009

Heterogeneity in Distributed Live Streaming: Blessing or Curse?

Distributed live streaming has brought a lot of interest in the past few years. In the homogeneous case (all nodes having the same capacity), many algorithms have been proposed, which have been proven almost optimal or optimal. On the other hand, the performance of heterogeneous systems is not completely understood yet. In this paper, we investigate the impact of heterogeneity on the achievable delay of chunk-based live streaming systems. We propose several models for taking the atomicity of a chunk into account. For all these models, when considering the transmission of a single chunk, heterogeneity is indeed a ``blessing'', in the sense that the achievable delay is always faster than an equivalent homogeneous system. But for a stream of chunks, we show that it can be a ``curse'': there is systems where the achievable delay can be arbitrary greater compared to equivalent homogeneous systems. However, if the system is slightly bandwidth-overprovisioned, optimal single chunk diffusion schemes can be adapted to a stream of chunks, leading to near-optimal, faster than homogeneous systems, heterogeneous live streaming systems.

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arXiv2008

The stable configuration in acyclic preference-based systems

Acyclic preferences recently appeared as an elegant way to model many distributed systems. An acyclic instance admits a unique stable configuration, which can reveal the performance of the system. In this paper, we give the statistical properties of the stable configuration for three classes of acyclic preferences: node-based preferences, distance-based preferences, and random acyclic systems. Using random overlay graphs, we prove using mean-field and fluid-limit techniques that these systems have an asymptotically continuous independent rank distribution for a proper scaling, and the analytical solution is compared to simulations. These results provide a theoretical ground for validating the performance of bandwidth-based or proximity-based unstructured systems.

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arXiv2008

Scalable Distributed Video-on-Demand: Theoretical Bounds and Practical Algorithms

We analyze a distributed system where n nodes called boxes store a large set of videos and collaborate to serve simultaneously n videos or less. We explore under which conditions such a system can be scalable while serving any sequence of demands. We model this problem through a combination of two algorithms: a video allocation algorithm and a connection scheduling algorithm. The latter plays against an adversary that incrementally proposes video requests.

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arXiv2008

From Random Graph to Small World by Wandering

Numerous studies show that most known real-world complex networks share similar properties in their connectivity and degree distribution. They are called small worlds. This article gives a method to turn random graphs into Small World graphs by the dint of random walks.

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arXiv2007

Acyclic Preference Systems in P2P Networks

In this work we study preference systems natural for the Peer-to-Peer paradigm. Most of them fall in three categories: global, symmetric and complementary. All these systems share an acyclicity property. As a consequence, they admit a stable (or Pareto efficient) configuration, where no participant can collaborate with better partners than their current ones. We analyze the representation of the such preference systems and show that any acyclic system can be represented with a symmetric mark matrix. This gives a method to merge acyclic preference systems and retain the acyclicity. We also consider such properties of the corresponding collaboration graph, as clustering coefficient and diameter. In particular, studying the example of preferences based on real latency measurements, we observe that its stable configuration is a small-world graph.

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arXiv2006

Stratification in P2P Networks - Application to BitTorrent

We introduce a model for decentralized networks with collaborating peers. The model is based on the stable matching theory which is applied to systems with a global ranking utility function. We consider the dynamics of peers searching for efficient collaborators and we prove that a unique stable solution exists. We prove that the system converges towards the stable solution and analyze its speed of convergence. We also study the stratification properties of the model, both when all collaborations are possible and for random possible collaborations. We present the corresponding fluid limit on the choice of collaborators in the random case. As a practical example, we study the BitTorrent Tit-for-Tat policy. For this system, our model provides an interesting insight on peer download rates and a possible way to optimize peer strategy.

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arXiv2006

On Using Matching Theory to Understand P2P Network Design

This paper aims to provide insight into stability of collaboration choices in P2P networks. We study networks where exchanges between nodes are driven by the desire to receive the best service available. This is the case for most existing P2P networks. We explore an evolution model derived from stable roommates theory that accounts for heterogeneity between nodes. We show that most P2P applications can be modeled using stable matching theory. This is the case whenever preference lists can be deduced from the exchange policy. In many cases, the preferences lists are characterized by an interesting acyclic property. We show that P2P networks with acyclic preferences possess a unique stable state with good convergence properties.

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