The paper has two objectives. The first is to study rigorously the transient behavior of some peer-to-peer (P2P) networks whenever information is replicated and disseminated according to epidemic-like dynamics. The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against P2P networks. We first introduce a stochastic model that extends a classical epidemic model and characterize the P2P swarm behavior in presence of free-riding peers. We then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases, the network is shown to exhibit phase transitions: A small change in the parameters causes a large change in the behavior of the network. We show, in particular, how phase transitions affect measures of content providers against P2P networks that distribute nonauthorized music, books, or articles and what is the efficiency of countermeasures. In addition, our analytical framework can be generalized to characterize the heterogeneity of cooperative peers.

The paper has two objectives. The first is to study rigorously the transient behavior of some peer-to-peer (P2P) networks whenever information is replicated and disseminated according to epidemic-like dynamics. The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against P2P networks. We first introduce a stochastic model which extends a classical epidemic model, and characterize the P2P swarm behavior in presence of free riding peers. We then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases the network is shown to exhibit phase transitions: a small change in the parameters causes a large change in the behavior of the network. We show, in particular, how phase transitions affect measures of content providers against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.

An ALOHA-type communication system with many nodes accessing a common receiver through a time-slotted shared radio channel is considered. Due to topological and environmental conditions, the receiver is prone to fail to detect some or all of the packets transmitted in a slot; this phenomenon is called erasure. The receiver may also capture, that is, detect a single transmission out of many. In addition, noise errors may cause the receiver to detect nonexistent collisions. Using the feedback information regarding the detection of zero or one packet or a collision at the receiver, the nodes determine their transmission policy. A class of decentralized multiaccess algorithms that maintain system stability under the above phenomenon is presented, and the maximal throughput they can support is determined. The maximal throughput of these algorithms is insensitive to some noise errors and erasures.>

The basic adaptive filtering algorithmX_{n+1}^{\epsilon} = X_{n}^{\epsilon} - \epsilon Y_{n}(Y_{n}^{'}X_{n}^{\epsilon} - \psi_{n})is analyzed using the theory of weak convergence. Apart from some very special cases, the analysis is hard when done for each fixed\epsilon > 0. But the weak convergence techniques are set up to provide much information for small\epsilon. The relevant facts from the theory are given. Definex^{\epsilon}(\cdot)byx^{\epsilon}(t) = X_{n}^{\epsilon}on[n\epsilon, n\epsilon + \epsilon). Then weak (distributional) convergence of\{x^{\epsilon}(\cdot)\}and of\{x^{\epsilon}(\cdot + t_{\epsilon})\}is proved under very weak assumptions, wheret_{\epsilon} \rightarrow \inftyas\epsilon \rightarrow 0. The normalized errors\{(X_{n}^{\epsilon} - \theta ) / \sqrt{\epsilon} \}are analyzed, where\thetais a "stable" point for the "mean" algorithm. The asymptotic properties of a projection algorithm are developed, where theX_{n}^{\epsilon}are truncated at each iteration, if they fall outside of a given set.