Abstract. In this paper, we develop a rigorous, unified framework based on Ordinary Differential Equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study of Markovian models is quite complex and numerical solution impractical for large networks, the corresponding ODE models yield closed-form expressions for several performance metrics of interest, and a numerical solution complexity that does not increase with the number of nodes. Using this ODE approach, we investigate how resources such as buffer space and power can be traded for faster delivery, illustrating the differences among the various epidemic schemes considered. Finally we consider the effect of buffer management by complementing the forwarding models with Markovian and fluid buffer models.

Denial of service attacks on peer-to-peer (p2p) systems can arise from sources otherwise considered non-malicious. We focus on one such commonly prevalent source, called “churn”. Churn arises from continued and rapid arrival and failure (or departure) of a large number of participants in the system, and traces from deployments have shown that it can lead to extremely stressful networking conditions. It has the potential to increase host loads and block a large fraction of normal insert and lookup operations in the peer-topeer system. This paper studies a cooperative web caching system that is resistant to churn attacks. Based on the Kelips peer-to-peer routing substrate, it imposes a constant load on participants and is able to reorganize itself continuously under churn. Peer pointers are automatically established among more available participants, thus ensuring high cache hit rates even when the system is stressed under churn. In addition, the system improves on the network locality of cache accesses in previous web caching schemes. The paper presents experimental results from a real implementation running over a commodity PC cluster, as well as trace-based simulations that use real host availability traces obtained from another deployed p2p system. 1.

In social systems, meaning can be communicated in addition to underlying processes of the information exchange. Meaning processing incurs on information processing with hindsight, while information processing recursively follows the time axis. The sole assumption of social relatedness as a variable among groups of agents provides sufficient basis for deriving the logistic map as a first-order approximation of the social system. The anticipatory formulation of this equation can be derived for both anticipation in the interaction term and in the aggregation among subgroups. Using this formula in a cellular automaton, an observer is generated as a reflection of the system under observation. The social system of interactions among observations can improve on the representations entertained by each of the observing systems.

How we act, as well as how we are acted upon, are to a large extent influenced by our relatives, friends and acquaintances. This is true of which profession we decide to pursue, whether or not we adopt a new technology, as well as whether or not we catch the flu. In this chapter we provide an overview of research that examines how social structure impacts

Abstract This paper proposes a framework to translate certain subclasses of differential equation systems into practical protocols for distributed systems. The generated protocols are intended for large-scale distributed systems that contain several hundreds to thousands of processes. The synthesized protocols are state machines containing probabilistic transitions and actions, and they are proved to show equivalent stochastic behavior to the original equations. The protocols are probabilistically scalable and reliable, and have practical applications in large-scale distributed systems, e.g., peer to peer systems. In order to illustrate the usefulness of the framework, it is used to generate new solutions for the problems of (i) responsibility migration (giving rise to a novel model of dynamic replication), and (ii) majority selection. We present mathematical analysis of these two protocols, and experimental results from our implementations. These two protocols are derived from natural analogies that are represented as differential equations- endemics and the Lotka-Volterra model of competition respectively. We believe the design framework could be effectively used in transforming, in a very systematic manner, well-known natural phenomena into protocols for distributed systems.

How we act, as well as how we are acted upon, are to a large extent in‡uenced by our relatives, friends and acquaintances. This is true of which profession we decide to pursue, whether or not we adopt a new technology, as well as whether or not we catch the ‡u. In this chapter we provide an overview of research that examines how social structure impacts

this paper we consider a di#erent approach to the modelling of the dynamics of diseases based on the recognition that (i) populations are both finite and discrete and (ii) that it is necessary to include spatial degrees of freedom in a more realistic way. This is done in the context of a cellular automaton, where we focus on the two essential features in disease spreading, i.e. a transmittance mechanism and an availability of susceptible individuals. The justification of such a simple approach is primarily to investigate su#cient conditions for recurrent epidemic behaviour without any external forcing in terms of seasonal variations etc. (Anderson, 1982; Bailey, 1975). Thus, the focus of this study will be the spatial and temporal behaviour of the infectious population. + Present address

present in the group at a given point of time. The problem is related to aggregation, and several solutions have been proposed. In this paper, we present two new sampling-based algorithms for estimation in dynamic groups (i.e., where processes are constantly joining and crashing), and thoroughly evaluate them using real-life traces. One scheme spreads a gossip into the overlay first, and then samples the receipt times of this gossip at different processes. The second scheme measures the density of processes when their identifiers are hashed into a real interval. The schemes have low latency, per-process overheads, while providing high levels of probabilistic accuracy. We present simulation studies that measure and compare the performance of these approaches in static groups, and groups with significant turnaround (arrival and departure) of processes. The latter are done by using traces from deployed peer to peer overlays. The schemes are generic enough to be used by any distributed application.

We study the impact of topology and mobility on gossip based broadcast in a wireless network. We focus on the specific context of broadcast during route discovery procedures, and attempt to characterize the performance of probabilistic broadcast when deployed in networks exhibiting diverse mobility patterns. We also examine some heuristics for dynamic modulation of gossip probabilities, without making any special demands on the routing protocol, or the device, in terms of neighborhood or location information.

Abstract: Distributed replication forms a significant component in many distributed systems. We consider migratory solutions for replica location in a large-scale distributed system. Replica location strategies decide dynamically how many times an object is replicated and where it is placed, in order to ensure availability, attacker-resistance, and scalability. Most traditional replica location schemes are static and reactive to failures. This paper presents dynamic and migratory schemes for replica location. More specifically, we present a new class of probabilistic protocols called endemic protocols. By using analytical techniques borrowed from the study of non-linear systems, and through large-scale simulations, we show how an endemic protocol can be used in building a decentralized and persistent file storage service. The protocols continuously migrate a small number of replicas of each object through the host population. This means an attacker will not be able to predict the exact number and locations of all replicas of a object. Contrary to intuition, endemic protocols can provide good performance by generating only a constant amount of network traffic at each host. Endemic protocols are resistant to massive failures and host churn. Existence of even one residual replica of an object in the system causes the system to regenerate more replicas. Analytically, endemics have the potential to preserve an object for several human generations, much like the persistent survival of folklores and endemic diseases such as common cold. The protocols are also very simple to implement.