Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least r active neighbors. Such process, originally studied on regular structures, has been recently investigated also in the context of random graphs, where it can serve as a simple model for a wide variety of cascades, such as the spreading of ideas, trends, viral contents, etc. over large social networks. In particular, it has been shown that in G(n,p) the final active set can exhibit a phase transition for a sub-linear number of seeds. In this paper, we propose a unique framework to study similar sub-linear phase transitions for a much broader class of graph models and epidemic processes. Specifically, we consider i) a generalized version of bootstrap percolation in G(n,p) with random activation thresholds and random node-to-node influences; ii) different random graph models, including graphs with given degree sequence and graphs with community structure (block model). The common thread of our work is to show the surprising sensitivity of the critical seed set size to extreme values of distributions, which makes some systems dramatically vulnerable to large-scale outbreaks. We validate our results running simulation on both synthetic and real graphs.

In this paper we develop an analytical framework, based on Che's approximation [2], for the analysis of Least Recently Used (LRU) caches operating under the Shot Noise requests Model (SNM). The SNM was recently proposed in [10] to better capture the main characteristics of today Video on Demand (Vod) traffic. In this context, Che's approximation is derived as the application of a mean field principle to the cache eviction time. We investigate the validity of this approximation through an asymptotic analysis of the cache eviction time. Particularly, we provide a large deviation principle and a central limit theorem for the cache eviction time, as the cache size grows large. Furthermore, we obtain a non-asymptotic analytical upper bound on the error entailed by Che's approximation of the hit probability.

We analyze a peer-assisted Video-on-Demand (VoD) system in which users contribute their upload bandwidth to the redistribution of a video that they are downloading or that they have cached locally. Our target is to characterize the additional bandwidth that servers must supply to immediately satisfy all requests to watch a given video. We develop an approximate fluid model to compute the required server bandwidth in the sequential delivery case, as well as in controlled nonsequential swarms. Our approach is able to capture several stochastic effects related to peer churn, upload bandwidth heterogeneity, and nonstationary traffic conditions, which have not been documented or analyzed before. Finally, we provide important hints for the design of efficient peer-assisted VoD systems under server capacity constraints.

We consider a communication system in which a given digital content has to be delivered sequentially at constant rate to a set of users who asynchronously request it according to a Poisson process. Users can retrieve data: 1) from one or more sources that statically store the entire content; and 2) from users who have previously requested the content, and contribute (for limited time) a random amount of upload bandwidth to the system. We propose a stochastic fluid framework that allows characterizing the aggregate streaming rate necessary at the sources to satisfy all active requests. In particular, we establish the conditions under which the system becomes asymptotically scalable as the number of users grows. Our theoretical results apply to increasingly popular video-on-demand systems exploiting users' cooperation.

Interference among simultaneous transmissions represents the main limitation factor for the capacity and connectivity of dense wireless networks. In this paper, we provide efficient simulation laws for the tail of the interference in a simple wireless ad hoc network model. Particularly, we consider node locations distributed according to a Poisson point process and various classes of light-tailed fading distributions.

We consider a peer-assisted Video-on-demand system, in which video distribution is supported both by peers caching the whole video and by peers concurrently downloading it. We propose a stochastic fluid framework that allows to characterize the additional bandwidth requested from the servers to satisfy all users watching a given video. We obtain analytical upper bounds to the server bandwidth needed in the case in which users download the video content sequentially. We also present a methodology to obtain exact solutions for special cases of peer upload bandwidth distribution. Our bounds permit to tightly characterize the performance of peer-assisted VoD systems as the number of users increases, for both sequential and non-sequential delivery schemes. In particular, we rigorously prove that the simple sequential scheme is asymptotically optimal both in the bandwidth surplus and in the bandwidth deficit mode, and that peer-assisted systems become totally self-sustaining in the surplus mode as the number of users grows large.

We analyze a peer-assisted Video-on-Demand system in which users contribute their upload bandwidth to the redistribution of a video that they are downloading or that they have cached locally. Our target is to characterize the additional bandwidth that servers must supply to immediately satisfy all requests to watch a given video. We develop an approximate fluid model to compute the required server bandwidth in the sequential delivery case. Our approach is able to capture several stochastic effects related to peer churn, upload bandwidth heterogeneity, non-stationary traffic conditions, which have not been documented or analyzed before. We provide an analytical methodology to design efficient peer-assisted VoD systems and optimal resource allocation strategies.

Interference from other users limits the capacity, and possibly the connectivity, of wireless networks. A simple model of a wireless ad hoc network, in which node locations are described by a homogeneous Poisson point process, and node transmission powers are random, is considered in this paper. A large deviation principle for the interference is presented under different assumptions on the distribution of transmission powers.