Modeling gossip-based content dissemination and search in distributed networking

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Abstract

This paper presents a rigorous analytic study of gossip-based message dissemination schemes that can be employed for content/service dissemination or discovery in unstructured and distributed networks. When using random gossiping, communication with multiple peers in one gossiping round is allowed. The algorithms studied in this paper are considered under different network conditions, depending on the knowledge of the state of the neighboring nodes in the network. Different node behaviors, with respect to their degree of cooperation and compliance with the gossiping process, are also incorporated. From the exact analysis, several important performance metrics and design parameters are analytically determined. Based on the proposed metrics and parameters, the performance of the gossip-based dissemination or search schemes, as well as the impact of the design parameters, are evaluated.

Introduction

The problem of disseminating and searching for content1 in distributed and unstructured networks – such as typical peer-to-peer (P2P) and ad hoc networks – is challenging. Content dissemination can be realized in two ways: either the content itself is disseminated or, instead, an advertisement message indicating its availability and location is spread. Searching for content is typically achieved through the dissemination of a query looking for the content itself or for the information about its location. In both cases, a message needs to be disseminated. For content dissemination, this message contains either the content itself, or the advertisement information about the content. During content searching, the message to be disseminated is a search query looking for the content. Consequently, a scheme that effectively disseminates the message, would be applicable to all the aforementioned problems and such a scheme is the focus of this paper.

We consider gossip-based (or commonly referred to as epidemic-based) message dissemination schemes that emerge as an approach to maintain simple, scalable, and fast content dissemination and searching in today’s distributed networks. In this paper, two major contributions are achieved.

First of all, distributed systems nowadays are large-scale and highly dynamic. Therefore, peers may only communicate with a subset of peers in the network, and they have to update their views of the network periodically with others to ensure reliability2 during information dissemination. However, performing an exact analysis of the gossip-based information dissemination process with dynamic peer partial views is extremely difficult. As we will show in Appendix A.1, the major challenge of analyzing the aforementioned problem is to define the dissemination process rigorously. The total number of states that it requires to describe the entire system exactly is 2(N+1)2+N+1. Hence, an exact analysis of such a scenario requires a very large state space, which is computationally not feasible.

Secondly, to guarantee the reliability of gossip-based information dissemination, it is preferred to achieve uniformity3 during neighbor selection, as underlined in [6]. Consequently, we are motivated to perform an exact analytic modeling of gossip-based message dissemination schemes under the assumption of uniform selection of multiple neighbors over the entire distributed network. The self-concerned nature and social dimensions of the peers is also captured, by incorporating the notion of cooperation. Important performance metrics, that can reflect the performance of the gossip-based algorithms, are also determined analytically: e.g. the distribution of the gossiping rounds to achieve a certain network coverage, or to discover content located in one or more locations. In addition, the impact of key factors such as (a) the number of neighbors to forward the message to, (b) the level of cooperation of the nodes, and (c) the number of content replicas available when searching for it, etc., are evaluated. Our modeling, as well as the evaluated metrics, provide insights in selecting proper design parameters so as to achieve a targeted performance.

The rest of the paper is organized as follows. In Section 2, we review two major assumptions when employing gossip-based content dissemination schemes, and previous work performed with respect to the two assumptions. Section 3 presents preliminary definitions and the description of the gossip-based message dissemination algorithms under study. Section 4 describes the analytic models developed for the study of the algorithms, along with the metrics to be employed to assess the effectiveness of the considered schemes. Related work on spreading a rumor, that appears in [18], is also discussed in this section. In Section 5, we present the analytic results and a discussion about the impact of the key design parameters. In Section 6, we conclude the paper.

Section snippets

Gossip-based information dissemination models: background and related works

In recent years, gossip-based algorithms, which mimic the spread of disease or rumor, have been considered as efficient and robust means for database maintenance and replication [4], information dissemination [6], topology construction [11], peer membership management [16], data aggregation [12] and failure detection [22]. It has also been implemented in many real-world applications: e.g. in Tribler [19], gossip-based algorithms are used to update and maintain peer information; in CoolStreaming

Preliminary definitions and algorithm description

We focus on the gossip-based information dissemination problem under the fundamental assumption of uniform neighbor selection over the entire network. The exact analysis of modeling gossip-based information dissemination when peers have dynamic, partial views is not feasible, as illustrated in Appendix A.1. The assumption of complete uniformity during neighbor selection allows exact modeling and performance analysis, as discussed by Pittel [18] and Karp et al. [14] in the case of information

Analysis of the gossip-based message dissemination

In this section, a rigorous and exact analysis of the proposed gossip-based message dissemination schemes is presented. An early study of the information dissemination problem is found in [18]. In each round, every informed person passes on the information to k = 1 neighbors, selected randomly and independently of all its previous choices and of all the choices of the other N people. A person may choose itself as gossiping target. Pittel [18] has derived the exact expression for the transition

Results and discussions

In this section, we developed a simulation program to simulate message dissemination/search through gossiping by using C language. The results of the analysis are compared with the results derived from the simulated program. In [20, pp. 515], it is shown that the average error over the non-zero values returned from the simulations decreases as O1n, where n is the number of times that a simulation is performed. In this paper, 104 iterations are carried out for each simulated result. For both of

Conclusions

In this paper we have demonstrated the difficulty of performing an exact analysis of information dissemination in dynamic, large-scale distributed networks. Consequently, we focused on modeling the process of gossip-based message dissemination under the assumption of uniform neighbor selection over the entire nodes in the network. The level of cooperation by the nodes selected as the gossiping-targets was also incorporated in the model. The cases of the blind gossiping-target selection and of

Acknowledgements

This work has been supported by European Network of Excellence (NoE) CONTENT (FP6-IST-038423). The work of the National and Kapodistrian University of Athens has been supported in part by SOCIALNETS (FP7-IST-217141).

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