In-degree dynamics of large-scale P2P systems

Abstract

This paper builds a complete modeling framework for understanding user churn and in-degree dynamics in unstructured P2P systems in which each user can be viewed as a stationary alternating renewal process. While the classical Poisson result on the superposition of n stationary renewal processes for n→∞ requires that each point process become sparser as n increases, it is often difficult to rigorously show this condition in practice. In this paper, we first prove that despite user heterogeneity and non-Poisson arrival dynamics, a superposition of edge-arrival processes to a live user under uniform selection converges to a Poisson process when system size becomes sufficiently large. Using this finding, we then obtain closed-form results on the transient behavior of in-degree, paving novel ways for a variety of additional analysis of decentralized P2P systems.

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Index Terms

• Computer systems organization

  • Dependable and fault-tolerant systems and networks

• General and reference

  • Cross-computing tools and techniques

    • Performance

• Networks

  • Network performance evaluation