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Full-Text Articles in Physical Sciences and Mathematics
Unstructured P2p Link Lifetimes Redux, Zhongmei Yao, Daren B. H. Cline
Unstructured P2p Link Lifetimes Redux, Zhongmei Yao, Daren B. H. Cline
Computer Science Faculty Publications
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 nonexponential 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 Superposition Of Heterogeneous Edge Processes In Dynamic Random Graphs, Zhongmei Yao, Daren B. H. Cline, Dmitri Loguinov
On Superposition Of Heterogeneous Edge Processes In Dynamic Random Graphs, Zhongmei Yao, Daren B. H. Cline, Dmitri Loguinov
Computer Science Faculty Publications
This paper builds a generic modeling framework for analyzing the edge-creation process in dynamic random graphs in which nodes continuously alternate between active and inactive states, which represent churn behavior of modern distributed systems. We prove that despite heterogeneity of node lifetimes, different initial out-degree, non-Poisson arrival/failure dynamics, and complex spatial and temporal dependency among creation of both initial and replacement edges, a superposition of edge-arrival processes to a live node under uniform selection converges to a Poisson process when system size becomes sufficiently large. Due to the convoluted dependency and non-renewal nature of various point processes, this result significantly …
On Node Isolation Under Churn In Unstructured P2p Networks With Heavy-Tailed Lifetimes, Zhongmei Yao, Xiaoming Wang, Dmitri Loguinov
On Node Isolation Under Churn In Unstructured P2p Networks With Heavy-Tailed Lifetimes, Zhongmei Yao, Xiaoming Wang, Dmitri Loguinov
Computer Science Faculty Publications
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 …
On Static And Dynamic Partitioning Behavior Of Large-Scale Networks, Derek Leonard, Zhongmei Yao, Xiaoming Wang, Dmitri Loguinov
On Static And Dynamic Partitioning Behavior Of Large-Scale Networks, Derek Leonard, Zhongmei Yao, Xiaoming Wang, Dmitri Loguinov
Computer Science Faculty Publications
In this paper, we analyze the problem of network disconnection in the context of large-scale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1-o(1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closed-form the probability that a P2P network develops isolated nodes, and therefore partitions, …