Most peer-to-peer content distribution sys- tems require the peers to privilege the welfare of the overall system over greedily maximizing their own utility. When downloading a file broken up into multiple pieces, peers are often asked to pass on some possible download opportunities of common pieces in order to favor rare pieces. This is to avoid the missing piece syndrome, which throttles the download rate of the peer-to-peer system to that of downloading the file straight from the server. In other situations, peers are asked to stay in the system even though they have collected all the file's pieces and have an incentive to leave right away. We propose a mechanism which allows peers to act greedily and yet stabilizes the peer-to-peer content shar- ing system. Our mechanism combines a fountain code at the server to generate innovative new pieces, and a prioritization for the server to deliver pieces only to new peers. While by itself, neither the fountain code nor the prioritization of new peers alone stabilizes the system, we demonstrate that their combination does, through both analytical and numerical evaluation. I. INTRODUCTION
@cite_4 models a BitTorrent P2P network and studies its scalability using a fluid model. It also models the peer selection mechanism and shows the convergence of the peer selection mechanism to a Nash equilibrium under some incentive structure. The paper only analyzes the BitTorrent protocol, and does not propose a novel mechanism. The fluid model was also studied in @cite_27 .
@cite_27 @cite_4
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In this paper, we develop simple models to study the performance of BitTorrent, a second generation peer-to-peer (P2P) application. We first present a simple fluid model and study the scalability, performance and efficiency of such a file-sharing mechanism. We then consider the built-in incentive mechanism of BitTorrent and study its effect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet. A number of analytical models exists that capture various properties of the BitTorrent protocol. However, until now virtually all of these models have been based on the assumption that the peers in the system have homogeneous bandwidths. As this is highly unrealistic in real swarms, these models have very limited applicability. Most of all, these models implicitly ignore BitTorrent's most important property: peer selection based on the highest rate of reciprocity. As a result, these models are not suitable for understanding or predicting the properties of real BitTorrent networks. Furthermore, they are hardly of use in the design of realistic BitTorrent simulators and new P2P protocols. In this paper, we extend existing work by presenting a model of a swarm in BitTorrent where peers have arbitrary upload and download bandwidths. In our model we group peers with (roughly) the same bandwidth in classes, and then analyze the allocation of upload slots from peers in one class to peers in another class. We show that our model accurately predicts the bandwidth clustering phenomenon observed experimentally in other work, and we analyze the resulting data distribution in swarms. We validate our model with experiments using real BitTorrent clients. Our model captures the effects of BitTorrent's well-known ‘tit-for-tat’ mechanism in bandwidth-inhomogeneous swarms and provides an accurate mathematical description of the resulting dynamics. One of the main reasons of the recent success of peer to peer (P2P)file sharing systems such as BitTorrent is their built-in tit-for-tat mechanism. In this paper, we model the bandwidth allocation in a P2P system as an exchange economy and study a tit-for-tat dynamics, namely the proportional response dynamics, in this economy. In aproportional response dynamics each player distributes its good to its neighbors proportional to the utility it received from them in thelast period. We show that this dynamics not only converges but converges to a market equilibrium, a standard economic characterization of efficient exchanges in a competitive market. In addition, for some classes of utility functions we consider, it converges much faster than the classical tat process and any existingalgorithms for computing market equilibria. As a part of our proof we study the double normalization of a matrix, an operation that linearly scales the rows of a matrix sothat each row sums to a prescribed positive number, followed by a similar scaling of the columns. We show that the iterative double normalization process of any non-negative matrix always converges. This complements the previous studies in matrix scaling that has focused on the convergence condition of the process when the row and column normalizations are considered as separate steps. In this paper, a simple mathematical model is presented for studying the performance of the BitTorrent (1) file sharing system. We are especially interested in the distribution of the peers with different states of the download job completedness. With the model we find that in the stable state the distribution of the download peers follows a U-shaped curve, and the parameters such as the departure rate of the seeds and the abort rate of the download peers will influence the peer distribution in different ways notably. We also analyze the file availability and the dying process of the BitTorrent file sharing system. We find that the system's stability deteriorates with the clustering of the peers, and BitTorrent's built-in "tit-for-tat" unchoking strategy could not help to preserve the integrity of the file among the download peers when the size of the community is small. An innovative peer selection strategy which enables more peers to finish the download job and prolongs the system's lifetime is proposed, in which the peers cooperate to improve the stability of the system by making a tradeoff between the current download rate and the future service availability. Finally, experimental results are presented to validate our analysis and findings.