Resilience and reliability analysis of P2P network systems

Abstract

This paper conducts resilience and reliability analysis of P2P network by studying the isolation probability and the durable time of a single user. The network with user’s lifetime having stronger NWUE property is proved to be more resilient. Further, both graphical and nonparametric methods are developed to test the NWUE order between two data sets.

Introduction

A Peer-to-Peer (P2P) internet network allows a group of computer users equipped with the same networking program to connect with each other for the purpose of directly accessing files from one another’s hard drives, and it functions by connecting individual computers together to share files instead of going through a central server. P2P networks can be classified by what they can be used for, for instance, content delivery, file sharing, telephony, media streaming (audio, video) and discussion forums, etc. In the current studies of P2P networks, Kaashoek and Karger [1] and Stoica et al. [2] investigate the single-node isolation, Aspnes et al. [3], Ganesh and Massoulie [4], Gummadi et al. [5], and Massoulié [6] etc. discuss the disconnection of the entire graph. Bhagwan et al. [7] is among the first to pay attention to the more realistic P2P failure models, in which, other than those traditional binary metrics, the intrinsic behavior of internet users as well as the departures of users due to more complex factors such as attention span and browsing habit etc. are taken into consideration. In order to investigate the performance of such systems, Leonard et al. [8] recently introduce the node failure model based on users’ lifetimes and study the stochastic resilience of P2P networks. In their passive model, it is assumed that a broken link is never repaired and a user stays online for a random period of time till all neighbors of this user go off line or the user leaves the network on his own initiative. As a consequence, the random lifetime that an arriving user will stay on line reflects both the behavior of the user and the duration of the service to the entire P2P network community. This model is suitable for the scenario that the time to seek a new link or repair a broken link is prohibitively larger than the general lifetime of a new user or peers are not equipped with any neighbor-recovery strategy. For example, due to the rapid increase in size (number of peers), the central server of a Napster network usually cannot be updated and maintained in time. Consequently, it takes a longer time to repair/replace the broken link.

This paper proposes a more general passive model for P2P networks, in which a user is isolated only when a certain number of neighbors of the user leave the network and hence the passive model in [8] is included as a special case. Further, we investigate both the stochastic resilience and reliability properties of this new model, and it is proved that the network with the user’s lifetime having stronger NWUE property is more resilient. The rest of this paper is organized as follows: Section 2 introduces the new P2P network model. Section 3 studies the stochastic resilience by using the isolation probability of a single user, and Section 4 discusses some reliability properties of the durable time of a single user in the network. Finally, both graphical and nonparametric methods are developed in Section 5 to detect the NWUE order between two data sets. All main conclusions are consistent with those obtained through experiments in the literature.

Throughout this paper, the term increasing is used instead of monotone nondecreasing and the term decreasing is used instead of monotone non-increasing, and all random variables are assumed to be absolutely continuous and to have 0 as the common left end point of their supports.