Predicting the Impact of Measures Against P2P Networks: Transient Behavior and Phase Transition

Abstract

We analyze in this paper the transient behavior of a simplified model for torrents in P2P networks. We consider a large number of peers interested in a file which is initially available at a small fraction of the population. Our model has as parameters the number of interested peers, the rate of arrival of download request, the rate at which peers propose files for upload, the degree of the free riding phenomenon etc. Our goal is to predict the impact of measures against P2P networks on their performance. We provide a Markov model that describes the detailed dynamics of the system. We analyze the model first under the assumption of an infinite population-an approach based on a branching process. This process is shown to provide a bound for the behavior of the system with finite population. We obtain the extinction probabilities for this process as well as approximations to the expected time till extinction. We then study the case of a finite population for which we establish the mean field limit. We show that the limit simplifies to a well studied epidemic model in case of no free riders. The fluid limit allows us to evaluate the behavior of the expected duration of a torrent, the expected number of nodes that eventually receive the file and the maximal availability along with the time at which it is achieved. We finally use these results to evaluate the efficiency of measures against unauthorized file sharing and their impact on file bundling.

Lyapunov stability and performance of user-assisted Video-on-Demand services

“…Simulations confirm the resulting system is stable under different arrival rates and low uploading capacities. More recently, Altmann et al describe file-sharing as swarming under a trackerless system with seeders, leechers and free-riders, in an epidemic-like fashion [27]. The authors assume perfect transmission, where a peer connects to all the swarm before an exchange.…”

“…The exchange effectiveness is constant. It is known that the effectiveness varies with the evolution of the number of peers [36]. In our model we assume this value as a constant under the assumption that the system is working in an average situation.…”

A Novel Interest Detection-Based Video Dissemination Algorithm under Flash Crowd in Mobile Ad Hoc Networks

“…This paper used fluid limit ordinary differential equations to provide the selection of parameters for the control of content suppliers and address optimization problems for content delivery. Altman et al proposed an extensional epidemic model to characterize file sharing behavior in P2P networks including free-riding peers [25]. This paper modeled P2P network dynamics by a Markov chain, where the state of P2P system evolves from branching process to a supercritical P2P swarm with increasing network International Journal of Distributed Sensor Networks 3 size.…”

Exploring Coding Benefits in CDN-Based VoD Systems

“…However, owing to the complexity of the bandwidth allocation algorithm and significant overhead, the view-upload decoupling strategy has not been adopted by practical P2P live streaming so far. Reference [26] analyzed transient behavior of P2P networks whenever information is replicated and disseminated according to epidemic-like dynamics. Through stochastic model, they can predict how efficient are measures taken against P2P networks.…”