An Analytical Study of a Structured Overlay in the presence of Dynamic Membership

In this paper, we present a complete analytical study of dynamic membership (aka churn) in structured peer-to-peer networks. We use a master-equation-based approach, which is used traditionally in non-equilibrium statistical mechanics to describe steady-state or transient phenomena. We demonstrate that this methodology is in fact also well suited to describing structured overlay networks by an application to the Chord system. For any rate of churn and stabilization rates, and any system size, we accurately account for the functional form of: the distribution of inter-node distances, the probability of network disconnection, the fraction of failed or incorrect successor and finger pointers and show how we can use these quantities to predict both the performance and consistency of lookups under churn. Additionally, we also discuss how churn may actually be of different 'types' and the implications this will have for structured overlays in general. All theoretical predictions match simulation results to a high extent. The analysis includes details that are applicable to a generic structured overlay deploying a ring as well as Chord-specific details that can act as guidelines for analyzing other systems

Comparing Maintenance Strategies for Overlays

In this paper, we present an analytical tool for understanding the performance of structured overlay networks under churn based on the master-equation approach of physics. We motivate and derive an equation for the average number of hops taken by lookups during churn, for the Chord network. We analyse this equation in detail to understand the behaviour with and without churn. We then use this understanding to predict how lookups will scale for varying peer population as well as varying the sizes of the routing tables. We then consider a change in the maintenance algorithm of the overlay, from periodic stabilisation to a reactive one which corrects fingers only when a change is detected. We generalise our earlier analysis to underdstand how the reactive strategy compares with the periodic one.Comment: 10 pages, 8 figure

An analytical framework for the performance evaluation of proximity-aware structured overlays

In this paper, we present an analytical study of proximity-aware structured peer-to-peer networks under churn. We use a master-equation-based approach, which is used traditionally in non-equilibrium statistical mechanics to describe steady-state or transient phenomena. In earlier work we have demonstrated that this methodology is in fact also well suited to describing structured overlay networks under churn, by showing how we can accurately predict the average number of hops taken by a lookup, for any value of churn, for the Chord system. In this paper, we extend the analysis so as to also be able to predict lookup latency, given an average latency for the links in the network. Our results show that there exists a region in the parameter space of the model, depending on churn, the number of nodes, the maintenance rates and the delays in the network, when the network cannot function as a small world graph anymore, due to the farthest connections of a node always being wrong or dead. We also demonstrate how it is possible to analyse proximity neighbour selection or proximity route selection within this formalism

Physics-inspired Performace Evaluation of a Structured Peer-to-Peer Overlay Network

In the majority of structured peer-to-peer overlay networks a graph with a desirable topology is constructed. In most cases, the graph is maintained by a periodic activity performed by each node in the graph to preserve the desirable structure in face of the continuous change of the set of nodes. The interaction of the autonomous periodic activities of the nodes renders the performance analysis of such systems complex and simulation of scales of interest can be prohibitive. Physicists, however, are accustomed to dealing with scale by characterizing a system using intensive variables, i.e. variables that are size independent. The approach has proved its usefulness when applied to satisfiability theory. This work is the first attempt to apply it in the area of distributed systems. The contribution of this paper is two-fold. First, we describe a methodology to be used for analyzing the performance of large scale distributed systems. Second, we show how we applied the methodology to find an intensive variable that describe the characteristic behavior of the Chord overlay network, namely, the ratio of the magnitude of perturbation of the network (joins/failures) to the magnitude of periodic stabilization of the network

Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

The state of peer-to-peer network simulators

Networking research often relies on simulation in order to test and evaluate new ideas. An important requirement of this process is that results must be reproducible so that other researchers can replicate, validate and extend existing work. We look at the landscape of simulators for research in peer-to-peer (P2P) networks by conducting a survey of a combined total of over 280 papers from before and after 2007 (the year of the last survey in this area), and comment on the large quantity of research using bespoke, closed-source simulators. We propose a set of criteria that P2P simulators should meet, and poll the P2P research community for their agreement. We aim to drive the community towards performing their experiments on simulators that allow for others to validate their results

Designs and Analyses in Structured Peer-To-Peer Systems

Peer-to-Peer (P2P) computing is a recent hot topic in the areas of networking and distributed systems. Work on P2P computing was triggered by a number of ad-hoc systems that made the concept popular. Later, academic research efforts started to investigate P2P computing issues based on scientific principles. Some of that research produced a number of structured P2P systems that were collectively referred to by the term "Distributed Hash Tables" (DHTs). However, the research occurred in a diversified way leading to the appearance of similar concepts yet lacking a common perspective and not heavily analyzed. In this thesis we present a number of papers representing our research results in the area of structured P2P systems grouped as two sets labeled respectively "Designs" and "Analyses". The contribution of the first set of papers is as follows. First, we present the princi- ple of distributed k-ary search and argue that it serves as a framework for most of the recent P2P systems known as DHTs. That is, given this framework, understanding existing DHT systems is done simply by seeing how they are instances of that frame- work. We argue that by perceiving systems as instances of that framework, one can optimize some of them. We illustrate that by applying the framework to the Chord system, one of the most established DHT systems. Second, we show how the frame- work helps in the design of P2P algorithms by two examples: (a) The DKS(n; k; f) system which is a system designed from the beginning on the principles of distributed k-ary search. (b) Two broadcast algorithms that take advantage of the distributed k-ary search tree. The contribution of the second set of papers is as follows. We account for two approaches that we used to evaluate the performance of a particular class of DHTs, namely the one adopting periodic stabilization for topology maintenance. The first approach was of an intrinsic empirical nature. In this approach, we tried to perceive a DHT as a physical system and account for its properties in a size-independent manner. The second approach was of a more analytical nature. In this approach, we applied the technique of Master Equations, which is a widely used technique in the analysis of natural systems. The application of the technique lead to a highly accurate description of the behavior of structured overlays. Additionally, the thesis contains a primer on structured P2P systems that tries to capture the main ideas prevailing in the field