Residual-Based Estimation of Peer and Link Lifetimes in P2P Networks

Existing methods of measuring lifetimes in P2P systems usually rely on the so-called Create-BasedMethod (CBM), which divides a given observation window into two halves and samples users ldquocreatedrdquo in the first half every Delta time units until they die or the observation period ends. Despite its frequent use, this approach has no rigorous accuracy or overhead analysis in the literature. To shed more light on its performance, we first derive a model for CBM and show that small window size or large Delta may lead to highly inaccurate lifetime distributions. We then show that create-based sampling exhibits an inherent tradeoff between overhead and accuracy, which does not allow any fundamental improvement to the method. Instead, we propose a completely different approach for sampling user dynamics that keeps track of only residual lifetimes of peers and uses a simple renewal-process model to recover the actual lifetimes from the observed residuals. Our analysis indicates that for reasonably large systems, the proposed method can reduce bandwidth consumption by several orders of magnitude compared to prior approaches while simultaneously achieving higher accuracy. We finish the paper by implementing a two-tier Gnutella network crawler equipped with the proposed sampling method and obtain the distribution of ultrapeer lifetimes in a network of 6.4 million users and 60 million links. Our experimental results show that ultrapeer lifetimes are Pareto with shape alpha ap 1.1; however, link lifetimes exhibit much lighter tails with alpha ap 1.8

Residual-Based Measurement of Peer and Link Lifetimes in Gnutella Networks

Existing methods of measuring lifetimes in P2P systems usually rely on the so-called create-based method (CBM), which divides a given observation window into two halves and samples users created in the first half every Delta time units until they die or the observation period ends. Despite its frequent use, this approach has no rigorous accuracy or overhead analysis in the literature. To shed more light on its performance, we flrst derive a model for CBM and show that small window size or large Delta may lead to highly inaccurate lifetime distributions. We then show that create-based sampling exhibits an inherent tradeoff between overhead and accuracy, which does not allow any fundamental improvement to the method. Instead, we propose a completely different approach for sampling user dynamics that keeps track of only residual lifetimes of peers and uses a simple renewal-process model to recover the actual lifetimes from the observed residuals. Our analysis indicates that for reasonably large systems, the proposed method can reduce bandwidth consumption by several orders of magnitude compared to prior approaches while simultaneously achieving higher accuracy. We finish the paper by implementing a two-tier Gnutella network crawler equipped with the proposed sampling method and obtain the distribution of ultrapeer lifetimes in a network of 6.4 million users and 60 million links. Our experimental results show that ultrapeer lifetimes are Pareto with shape a alpha ap 1.1; however, link lifetimes exhibit much lighter tails with alpha ap 1.9

On Node Isolation under Churn in Unstructured P2P Networks with Heavy-Tailed Lifetimes

Previous analytical studies [12], [18] of unstructured P2P resilience have assumed exponential user lifetimes and only considered age-independent neighbor replacement. In this paper, we overcome these limitations by introducing a general node-isolation model for heavy-tailed user lifetimes and arbitrary neighbor-selection algorithms. Using this model, we analyze two age-biased neighbor-selection strategies and show that they significantly improve the residual lifetimes of chosen users, which dramatically reduces the probability of user isolation and graph partitioning compared to uniform selection of neighbors. In fact, the second strategy based on random walks on age-weighted graphs demonstrates that for lifetimes with infinite variance, the system monotonically increases its resilience as its age and size grow. Specifically, we show that the probability of isolation converges to zero as these two metrics tend to infinity. We finish the paper with simulations in finite-size graphs that demonstrate the effect of this result in practice

Node Isolation Model and Age-Based Neighbor Selection in Unstructured P2P Networks

Previous analytical studies of unstructured P2P resilience have assumed exponential user lifetimes and only considered age-independent neighbor replacement. In this paper, we overcome these limitations by introducing a general node-isolation model for heavy-tailed user lifetimes and arbitrary neighbor-selection algorithms. Using this model, we analyze two age-biased neighbor-selection strategies and show that they significantly improve the residual lifetimes of chosen users, which dramatically reduces the probability of user isolation and graph partitioning compared with uniform selection of neighbors. In fact, the second strategy based on random walks on age-proportional graphs demonstrates that, for lifetimes with infinite variance, the system monotonically increases its resilience as its age and size grow. Specifically, we show that the probability of isolation converges to zero as these two metrics tend to infinity. We finish the paper with simulations in finite-size graphs that demonstrate the effect of this result in practice

Modeling randomized data streams in caching, data processing, and crawling applications

caching, search in large graphs) process streams of random key-value records that follow highly skewed frequency distributions. In this work, we first develop stochastic models for the probability to encounter unique keys during exploration of such streams and their growth rate over time. We then apply these models to the analysis of LRU caching, MapReduce overhead, and various crawl properties (e.g., node-degree bias, frontier size) in random graphs. I

Temporal update dynamics under blind sampling

Abstract—Network applications commonly maintain local copies of remote data sources in order to provide caching, indexing, and data-mining services to their clients. Modeling performance of these systems and predicting future updates usually requires knowledge of the inter-update distribution at the source, which can only be estimated through blind sampling – periodic downloads and comparison against previous copies. In this paper, we first introduce a stochastic modeling framework for this problem, where the update and sampling processes are both renewal. We then show that all previous approaches are biased unless the observation rate tends to infinity or the update process is Poisson. To overcome these issues, we propose four new algorithms that achieve various levels of consistency, which depend on the amount of temporal information revealed by the source and capabilities of the download process. I

Unstructured P2P link lifetimes redux

We revisit link lifetimes in random P2P graphs under dynamic node failure and create a unifying stochastic model that generalizes the majority of previous efforts in this direction. We not only allow non-exponential user lifetimes and age-dependent neighbor selection, but also cover both active and passive neighbor-management strategies, model the lifetimes of incoming and outgoing links, derive churn-related message volume of the system, and obtain the distribution of transient in/out degree at each user. We then discuss the impact of design parameters on overhead and resilience of the network

On sample-path staleness in lazy data replication

We analyze synchronization issues arising between two stochastic point processes, one of which models data churn at an information source and the other periodic downloads from its replica (e.g., search engine, web cache, distributed database). Due to lazy (pull-based) synchronization, the replica experiences recurrent staleness, which translates into some form of penalty stemming from its reduced ability to perform consistent compu-tation and/or provide up-to-date responses to customer requests. We model this system under non-Poisson update/refresh processes and obtain sample-path averages of various metrics of staleness cost, generalizing previous results and exposing novel problems in this field